Make a Game Out of Learning But don’t gamify it.

By Chris Berdik

Teachers predominantly use games as rewards or reinforcement, rather than starting points for learning.

Photo illustration by Slate. Photo by Brad Flickinger/Flickr.

In MIT’s Education Arcade, classic game consoles line the office corridor; rafters are strung with holiday lights; and inflatable, stuffed, and papier-mâché creatures lurk around every corner. When I stopped by recently, the arcade’s director, Eric Klopfer, and creative director, Scot Osterweil, talked enthusiastically about the surging interest in educational video games, now used by nearly three-quarters of America’s grade-school teachers, according to one survey.

But these optimistic, play-loving game gurus have come to despise the biggest buzzword in their field: gamification. According to Osterweil and Klopfer, both MIT professors, gamification too often means “making a game out of learning,” in which players win points, magical powers, or some other reward for practicing math, spelling, or another school subject. Klopfer and Osterweil argue that the best educational games capture what’s already fun about learning and make that central to the game. Gamification undermines what they see as the real opportunity for games to radically, albeit playfully, transform education.

The arcade, part of MIT’s Scheller Teacher Education Program, partners with schools, gaming companies, and nonprofits to make educational video games. The staff also trains teachers to make their own games and to weave them into lesson plans, via on-campus courses and a new massive open online course, “Design and Development of Games for Learning,” that launches Wednesday.

“If somebody comes to me and says, ‘I want to make math fun,’ I don’t want to work with that person,” said Osterweil, “because they don’t think math is already fun.”

In gamified math, equations are often wedged into high-energy video worlds with wacky characters, points and player rankings, and maybe some explosions. It’s a model used by many popular educational games, such as Math Blaster, which has sold millions of copies and been reissued several times since it was introduced in 1983.

In Math Blaster, players fly space ships while math problems appear on the ships’ consoles and numbered asteroids hurtle toward them. If a console reads “15 – 7 = ?” and the ship’s laser guns fire at asteroid 5, nothing happens, except a red cabin light flashes to indicate a mistake. When correctly aimed at asteroid 8, the guns blast it out of the sky. Osterweil and Klopfer call games like this “drill and practice,” or “shooting flashcards.”

“This game isn’t telling you why you got a problem right or wrong or asking you to think about what arithmetic is,” Osterweil said in a video in their new MOOC. “If you’re good at arithmetic, Math Blaster’s fun, because it reinforces that you’re good at math. If you’re not understanding arithmetic, you’re getting nowhere with this.”

Back in the arcade offices, Klopfer said games that “make math fun” typically don’t require players to use math in any real sense. Instead, he said, “it’s ‘do some math so you get to shoot some asteroids.’ ”

Whenever the arcade team brainstorms a game, by contrast, it starts by finding people who are passionate about math, history, science, or any other subject and asks what drives and engages them.

“Maybe they love solving puzzles with math or experimenting with science,” said Klopfer. “Maybe they like how understanding math and science make the world seem different, or more comprehensible. Tap into that thing people already find interesting, and enhance it in the game.”

Games that “make math fun” typically don’t require players to use math in any real sense.

For instance, Education Arcade is now piloting The Radix Endeavor, a free, multiplayer online game designed to supplement high school math and science lessons. Based on conversations with working scientists and engineers, the game has players explore a fictional world called Ysola that’s ruled by evil, science-hoarding overlords called the Obfuscati. Players encounter Ysola’s beleaguered citizenry and embark on various quests while evading the Obfuscati, such as finding a cure for a deadly disease or using math to reinforce dangerously weak buildings.

“It’s not about solving this math problem, so you get a magic wand that can make this building stronger,” said Klopfer. “It’s figuring out how to learn the math, so you can use that understanding to keep the building from collapsing.”

A few years ago, Osterweil distilled what he calls the “four freedoms of play,” including freedom to experiment, freedom to fail, freedom to assume different identities, and freedom of effort (meaning the ability to mix full-throttle effort with periods of relaxation and disengagement). For Osterweil, these freedoms are about more than good game design.

“I argue that real learning happens in moments of playful exploration,” he said, “and all those freedoms should be present.”

Schools overemphasize the learning of facts and formulas, as well as the right answers for standardized tests, he said. Rather than changing that educational model, “bad ideas like gamification replicate it.”

The problem isn’t just the drill-and-practice design of many games, according to Klopfer. It’s also that teachers predominantly use games as rewards or reinforcement, rather than starting points for learning.

“The game should be an experience, where kids get to explore and problem-solve,” Klopfer said. “Then a teacher or a peer can help them make the connection between the game experience and concepts that can be generally applied.”

Along with games, the Education Arcade creates optional lesson plans, online forums, blogs, and one-day teacher training sessions, all to help bridge game learning with other classroom instruction.

Mark Knapp was teaching biology in the Boston public schools in 2012 when he heard about the Education Arcade’s plans for Radix and volunteered to be one of the teachers who helped with the game’s development. Knapp said Radix isn’t a substitute for the science curriculum he covers. What the game does do, he said, “is get kids interested in how scientist think and solve problems.” Since 2014, Knapp has been teaching kids with special needs in grades six through 12, and continues to useRadix in class.

“There are so many little skills, like dealing with frustration, that these kids are also getting from this game,” he said. “I can see kids becoming less frustrated with stuff they don’t understand. That’s really important for any student.”

Klopfer doesn’t think games should be the only way kids learn in school. “There are lots of other things to do in school: dialogues with peers, solving problems, building things. Sometimes, even lectures are helpful,” he said. “But there are aspects of good games that work well in school, even if they’re not part of a game.”

“I agree,” said Osterweil. “There should still be rigor, and kids should be guided to explore topics they may not have known they were interested in. But, learning should still be damn near all play, all the time.”

This story was produced by The Hechinger Report, a nonprofit, independent news organization focused on inequality and innovation in education. Read more about Blended Learning.

Chris Berdik is a freelance science journalist and author of Mind Over Mind: The Surprising Power of Expectations.

Top 50 Chess Quotes of All Time

Written by Yury Markushin

Wednesday, 25 March 2015 00:00

Great quotes store big and important ideas in just a few words. They transport wisdom that great chess players have accumulated throughout decades of experience.This list of quotes is for those who is aiming for big success. These quotes will both motivate and educate you for becoming a better chess player. 1. “By the time a player becomes a Grandmaster, almost all of his training time is dedicated to work on this first phase. The opening is the only phase that holds out the potential for true creativity and doing something entirely new.” – Garry Kasparov 2. “When your house is on fire, you can’t be bothered with the neighbors. Or, as we say in chess, if your King is under attack, don’t worry about losing a pawn on the queenside.” – Garry Kasparov 3. “By strictly observing Botvinnik’s rule regarding the thorough analysis of one’s own games, with the years I have come to realize that this provides the foundation for the continuos development of chess mastery.” – Garry Kasparov 4. “Chess continues to advance over time, so the players of the future will inevitably surpass me in the quality of their play, assuming the rules and regulations allow them to play serious chess. But it will likely be a long time before anyone spends 20 consecutive years as number, one as I did.” – Garry Kasparov 5. “You can’t overestimate the importance of psychology in chess, and as much as some players try to downplay it, I believe that winning requires a constant and strong psychology not just at the board but in every aspect of your life.” – Garry Kasparov 6. “I … have two vocations: chess and engineering. If I played chess only, I believe that my success would not have been significantly greater. I can play chess well only when I have fully convalesced from chess and when the ‘hunger for chess’ once more awakens within me.”  – Mikhail Botvinnik 7. “If you are going to make your mark among masters, you have to work far harder and more intensively, or, to put it more exactly, the work is far more complex than that needed to gain the title of Master.” – Mikhail Botvinnik 8. “Above all else, before playing in competitions a player must have regard to his health, for if he is suffering from ill-health he cannot hope for success. In this connection the best of all tonics is 15 to 20 days in the fresh air, in the country.”  – Mikhail Botvinnik Note: If you want to dramatically improve your chess simply studying Grandmaster’s games or solving tactics it not enough. In order to take your chess to the whole new level you need to work on all aspects of the game. That’s what we call a “combined approach”. We will combine 5 most important elements of chess into a single training session to build a good training habits and to make sure you can get out maximum results in minimum amount of time. You will get a access to 3 weeks of trainingwhere you will learn: Tactics Positional play Attack on the king Endgame technique Classical games analysis Training secrets, self-evaluation, blunder avoidance and much more 9. “If you are weak in the endgame, you must spend more time analysing studies; in your training games you must aim at transposing to endgames, which will help you to acquire the requisite experience.” – Mikhail Botvinnik 10. “My forte was the middlegame. I had a good feeling for the critical moments of the play. This undoubtedly compensated for my lack of opening preparation and, possibly, not altogether perfect play in the endgame. In my games things often did not reach the endgame!” – Boris Spassky 11. “The shortcoming of hanging pawns is that they present a convenient target for attack. As the exchange of men proceeds, their potential strength lessens and during the endgame they turn out, as a rule, to be weak.” – Boris Spassky 12. “Of course, analysis can sometimes give more accurate results than intuition but usually it’s just a lot of work. I normally do what my intuition tells me to do. Most of the time spent thinking is just to double-check.” – Magnus Carlsen 13. “I started by just sitting by the chessboard exploring things. I didn’t even have books at first, and I just played by myself. I learnt a lot from that, and I feel that it is a big reason why I now have a good intuitive understanding of chess.” – Magnus Carlsen 14. “Self-confidence is very important. If you don’t think you can win, you will take cowardly decisions in the crucial moments, out of sheer respect for your opponent. You see the opportunity but also greater limitations than you should. I have always believed in what I do on the chessboard, even when I had no objective reason to. It is better to overestimate your prospects than underestimate them.” – Magnus Carlsen 15. “I didn’t picture myself as even a grandmaster, to say nothing of aspiring to the chess crown. This was not because I was timid – I wasn’t – but because I simply lived in one world, and the grandmasters existed in a completely different one. People like that were not really even people, but like gods or mythical heroes.” – Anatoly Karpov 16. “By all means examine the games of the great chess players, but don’t swallow them whole. Their games are valuable not for their separate moves, but for their vision of chess, their way of thinking.” – Anatoly Karpov 17. “The great mobility of the King forms one of the chief characteristics of all endgame strategy. In the middlegame the King is a mere “super”, in the endgame on the other hand – on of the “principals”. We must therefore develop him, bring him nearer to the fighting line.” – Aron Nimzowitsch 18. “If in a battle, I seize a bit of debatable land with a handful of soldiers, without having done anything to prevent an enemy bombardment of the position, would it ever occur to me to speak of a conquest of the terrain in question? Obviously not. Then why should I do so in chess?” – Aron Nimzowitsch 19. “When I today ask myself whence I got the moral courage, for it takes moral courage to make a move (or form a plan) running counter to all tradition, I think I may say in answer, that it was only my intense preoccupation with the problem of the blockade which helped me to do so.” – Aron Nimzowitsch 20. “It is a well known phenomenon that the same amateur who can conduct the middle game quite creditably, is usually perfectly helpless in the end game. One of the principal requisites of good chess is the ability to treat both the middle and end game equally well.” – Aron Nimzowitsch 21. “In mathematics, if I find a new approach to a problem, another mathematician might claim that he has a better, more elegant solution. In chess, if anybody claims he is better than I, I can checkmate him.” – Emanuel Lasker 22. “By positional play a master tries to prove and exploit true values, whereas by combinations he seeks to refute false values … A combination produces an unexpected re-assessment of values.” – Emanuel Lasker 23. “He who has a slight disadvantage plays more attentively, inventively and more boldly than his antagonist who either takes it easy or aspires after too much. Thus a slight disadvantage is very frequently seen to convert into a good, solid advantage.” – Emanuel Lasker 24. “A player, as the world believed he was, he was not, his studious temperament made that impossible; and thus he was conquered by a player and in the end little valued by the world, he died.” – Emanuel Lasker 25. “It is no secret that any talented player must in his soul be an artist, and what could be dearer to his heart and soul than the victory of the subtle forces of reason over crude material strength! Probably everyone has his own reason for liking the King`s Gambit, but my love for it can be seen in precisely those terms.” – David Bronstein 26. “It is annoying that the rules of chess do not allow a pawn to take either horizontally or backwards, but only forwards … This psychological tuning is ideal for attacking purposes, but what about for defence?”  – David Bronstein 27. “If you have made a mistake or committed an inaccuracy there is no need to become annoyed and to think that everything is lost. You have to reorientate yourself quickly and find a new plan in the new situation.” – David Bronstein 28. “When you play against an experienced opponent who exploits all the defensive resources at his command you sometimes have to walk time and again, along the narrow path of ‘the only move’.” – David Bronstein 29. “Chess is not for the faint-hearted; it absorbs a person entirely. To get to the bottom of this game, he has to give himself up into slavery. Chess is difficult, it demands work, serious reflection and zealous research.” – Wilhelm Steinitz 30. “The task of the positional player is systematically to accumulate slight advantages and try to convert temporary advantages into permanent ones, otherwise the player with the better position runs the risk of losing it.” – Wilhelm Steinitz 31. “Whenever Black succeeds in assuming the initiative and maintaining it to a successful conclusion, the sporting spirit of the chess lover feels gratified, because it shows that the resources of the game are far from being exhausted.” – Savielly Tartakower 32. “No one ever won a game by resigning.” – Savielly Tartakower 33. “It is always better to sacrifice your opponents’ men.” – Savielly Tartakower 34. “The blunders are all there on the board, waiting to be made.” – Savielly Tartakower 35. “A thorough understanding of the typical mating continuations makes the most complicated sacrificial combinations leading up to them not only difficult, but almost a matter of course.” – Savielly Tartakower 36. “All that matters on the chessboard is good moves.” – Bobby Fischer 37. “A strong memory, concentration, imagination, and a strong will is required to become a great chess player.”  – Bobby Fischer 38. “Tactics flow from a superior position.”  – Bobby Fischer 39. “To play for a draw, at any rate with white, is to some degree a crime against chess.” – Mikhail Tal 40. “I have always thought it a matter of honour for every chess player to deserve the smile of fortune.” – Mikhail Tal 41. “Naturally, the psychological susceptibility of a match participant is significantly higher than a participant in a tournament, since each game substantially changes the over-all position.” – Mikhail Tal 42. “I go over many games collections and pick up something from the style of each player.” – Mikhail Tal 43. “Strategy requires thought, tactics require observation.” – Max Euwe 44. “If it is true that a player’s style is his person, then everyone plays as he is intended to by nature. I am naturally cautious, and I altogether dislike situations which involve risk.” – Tigran Petrosian 45. “In almost any position the boundless possibilities of chess enable a new or at least a little-studied continuation to be found.” – Tigran Petrosian 46. “They knock me for my draws, for my style, they knock me for everything I do.” – Tigran Petrosian 47. “Even the most distinguished players have in their careers experienced severe disappointments due to ignorance of the best lines or suspension of their own common sense.” – Tigran Petrosian 48. “In some places words have been replaced by symbols which, like amulets from a witch’s bag, have the power to consume the living spirit of chess.” – Tigran Petrosian 49. “It is easy to play against the young players, for me they are like an open book.” – Tigran Petrosian 50. “They knock me for my draws, for my style, they knock me for everything I do.” – Tigran Petrosian

Instill a Love of Math

By Laura Lewis Brown

Parents are bombarded with messages to read with their children, but it’s rare to hear about the importance of doing math with them. Here are some helpful tips on why and how to instill a love of math in your children.

Early Math Matters
We may take for granted that our children will inevitably learn how to add, subtract, multiply and divide, but early math lessons establish the base for the rest of their thinking lives. “Mathematics that kids are doing in kindergarten, first, second and third grades lays the foundation for the work they are going to do beyond that,” says Linda Gojak, president of the National Council of Teachers of Mathematics (NCTM). “They are learning beyond just counting and numbers.” That’s why it’s so important to help children love math while they are still young. Parents can build on those first preschool lessons by counting with their children, asking them to look for patterns and recognize shapes, then moving on to numbers, Gojak says.

The goal should be to make math “real” and meaningful by pointing it out in the world around you. That could include checking and comparing prices at the grocery store, driving down the street counting mailboxes, reading recipes, calculating coupons, or even measuring food or drink at the dinner table. Kevin Mahoney, math curriculum coordinator at Pennacre Country Day School in Wellesley, Mass., says when his children were little, his wife kept a small measuring tape in her pocketbook. While they were waiting for their order at a restaurant, the children would measure different items on the table.

Just as you encourage your early reader to look for familiar letters, ask your child to watch for math, regarding math as highly as you do reading. “Every parent knows that it’s a good idea to read to your child every night, but they should also realize the importance of talking about mathematical situations with children every day,” says Mahoney.

So What If It’s Hard?
What if you hated math as a child? Parents should try to set aside their distaste for math and encourage their children as much as possible. Young children are eager to learn. “It’s hard to learn to talk or walk. But they don’t care,” says Sue VanHattum, a community college math teacher in Richmond, Ca., who blogs about math learning on http://www.mathmamawrites.blogspot.com. “They just push themselves over their limits. They are going to come at math with that same attitude.”

Avoid talking negatively about math, even if you have no need for trigonometry in your daily life. “A lot of people will only joke that they cannot do math or announce publicly, ‘I’m not a math person.’ When a parent does that in front of a child, it suggests that math’s not important,” says Char Forsten, education consultant and writer, who urges parents to create that desire to learn by constantly screening the environment for math. “Have you seen any good math lately?” she likes to ask students.

If your child believes that math doesn’t really matter, he’s not going to be as open to learn. “Attitude has everything to do with learning. You can’t make anyone learn. If a child has learned not to love math, if they don’t love math, and aren’t willing to learn, you have to deal with that first,” Forsten says.

If you are stuck on how to foster math enthusiasm, talk to your child’s teacher about some ways to support math learning at home. There may be a new game that you have never heard of, which both you and your child will love.

Play Games
With so many facts and figures to memorize and apply to math problems, children learn early that math is something that requires work. That doesn’t mean that it can’t be fun; keep the pleasure in math by playing games with your children. Many games, even the ones adults play, rely on math. With countless websites, computer games and phone apps, parents have endless options, but don’t forget about the nondigital games you loved as a child. The classics that require manipulating cards and game pieces, calculating along the way, may have the same appeal for your kids as they did for you. One game worth considering is Chutes and Ladders. A 2009 study conducted by Carnegie Mellon and the University of Maryland found that preschoolers who played the game improved math skills significantly compared to those in the study who played a different board game or did nonmath tasks.

As you play with your kids, try to tap into your own love for math. When you play Trivial Pursuit, you are using math to determine how many spaces you need to get to the next wedge or predict which category you can answer best. The game doesn’t have to be about math, but should involve it. If you have a good game store in your area, stop by and ask the salespeople for help. Some of VanHattum’s favorite games really push logic, which is the basis of math, and get children thinking visually. Check out Link, SET, Rush Hour, Blokus and Spot It, to name a few.

“Playing games is a great family activity,” VanHattum says. “The more you have a tradition of playing games, the easier it is to bring in other games you like.” So while you may not be passionate about your child’s latest board game, you can work up to another game you like. Try to make the game personal to your family by playing it in your own special way. “Mathematicians make up their own rules,” VanHattum says. “It’s really important to be open to making up your own games. Change the rules. ‘In our family, we play the game this way.’”

Flexing Math Muscles
Riding a bike, swimming in the deep end, and playing an instrument are just examples of our favorite childhood activities that require practice to master. So does math.

“Math is an intellectual muscle building; it’s crucial for fully developing a child’s potential,” Mahoney says. “Those muscles can atrophy. If school is the only place you do math, then it becomes something you only do at school. Then you don’t even think about using it in real life.” So brush off those negative feelings about math and instill enthusiasm. Math will play a role in your child’s life forever.

“It’s important to remember that those basics are essential for later learning. A lot of the stuff we learn in math we apply in different ways later,” says Gojak, who emphasizes the thinking skills that math provides. “I might not have to worry about what an isosceles triangle is, but it’s still an important part of education.”

As they grow, kids will learn that they are willing to work hard at something they love. It may just be math. Either way, remember that your child does not have to excel at math to enjoy it. “It doesn’t matter if they’re good, it matters whether they like it,” VanHattum says.

Add Math to Everyday Fun with these Activities:

• Adventures in Learning Math Activities
• Math Activities for Babies & Toddlers
• Math Activities for Preschool & Kindergarten
• Math Activities for First & Second Grades

The real reason why the US is falling behind in math

By Tara Holm FEBRUARY 12, 2015

If my seatmate on an airplane asks me what I do for a living, I tell the truth: I’m a mathematician. This generally triggers one of two responses. Either I’m told that I must be brilliant. . . or I hear about the person’s inability to balance a checkbook. The truth is, I’m not brilliant, just persistent, and I hate balancing my checkbook. Both responses, however, point to a fundamental misunderstanding about what mathematics is supposed to do and its current — and unfortunate — trajectory in American education.

Calculators have long since overthrown the need to perform addition, subtraction, multiplication, or division by hand. We still teach this basic arithmetic, though, because we want students to grasp the contours of numbers and look for patterns, to have a sense of what the right answer might be. But what happens next in most schools is the road ­to ­math­ Hades: the single ­file death march that leads towards calculus.  We are pretty much the only country on the planet that teaches math this way, where students are forced to memorize formulas and procedures. And so kids miss the more organic experience of playing with mathematical puzzles, experimenting and searching for patterns, finding delight in their own discoveries. Most students learn to detest — or at best, endure — math, and this is why our students are falling behind their international peers.

When students memorize the Pythagorean theorem or the quadratic formula and apply it with slightly different numbers, they actually get worse at the bigger picture. Our brains are slow to recognize information when it is out of context. This is why realworld math problems are so much harder — and more fascinating — than the contrived textbook exercises. What I’ve found instead is that a student who has developed the ability to turn a realworld scenario into a mathematical problem, who is alert to false reasoning, and who can manipulate numbers and equations is likely far better prepared for college math than a student who has experienced a year of rote calculus.

What can we do as parents? At my house, we sometimes talk through simple logic puzzles over dinner. There are lots of good examples on the Internet, even pirate puzzles to please my son. Sudoku, despite claims to the contrary, is all about logical problem solving. Or how about family board games night once a week? I’m not talking Candyland­style games, all luck and no skill. Some favorites in my household include logic puzzles like Rush Hour and board games like TransAmerica, Clue, and Carcassonne. Of course,there’s also always checkers and chess. These games teach kids to think logically several steps ahead, all while having fun. And they are far more effective than the SAT prep booklets which litter the homes of high school juniors each year. I’m not down on mathematical training. I’m just down on the persistent memorization approach, which works your intellectual muscles about as effectively as lifting loaves of Wonder Bread helps build your biceps. We are failing our children if all we teach them are dry formulas. The benefits just don’t add up.

Tara Holm is an associate professor of math at Cornell University and a 2015 public voices fellow of the OpEd Project.

5 Math Games Every Classroom Needs to Play

Guest post by Leigh Langton

Hey guys! It’s Leigh from The Applicious Teacher! I am super excited to be blogging at Corkboard Connections today. I’m sharing a practice that I use to help increase my students’ engagement and number sense during my math block.

Do you play games in your classroom? Wait… what?! No time? Well… you should make time! Especially during your math time. To me, math and games go together like Nutella and pretzels. Delicious separate, but amazing together.

As a third grade teacher, I know how limited our time can be, so I am here to share with you 5 math games you should take the time to play this year!  All of these games are fun, easy, and require little to no prep. They are math games that I’ve played for years with my second graders. When I moved up to third, I was able to easily modify these games for my new “big kids”.

First up… 100’s Game

This game can be played in a k-5 classroom. It is perfect for building number sense and it’s only prerequisite is that students can count. There’s no supplies needed to play and my kids loved playing this as a “brain-break” before math.

Here’s how to play… Have your class stand in a circle. Moving in a clockwise direction, have the students count out loud until they get to a hundred. The person who says, “100” sits down. The last person standing, WINS!

The idea is simple, but can be modified for your students. In second grade we’d count by 5’s,10’s, and 25’s (to help with money later on in the year). For third, we count the multiples of numbers. For numbers that don’t have a multiple of 100, I choose the last number in the sequence of 12 as the “end number.”

Other Variations 

Students sit down on a certain multiples (like the multiples of 7) Students don’t say the multiple. Students can count by ones to a hundred, but all the multiples of say, 4, are “off limits.” If a student says them, they sit down. You could also change it to student don’t say the divisors (perfect for those 4th/5th graders who need more practice with their facts!)

101 and Out…

 

 

This paper and pencil game works well in second to fifth grade classrooms and can be played by teams of students (like boys against girls) or in pairs. To play you will need a sheet of paper, a pencil, and one dice. The object of the game is to score as close to 101 without going over or “out.”

To play, students take turns rolling the dice. As they roll, they can either take the number as a one or a ten. For example, if a student rolls a 5, they could take it as a 5 or a 50.  Students keep a running record of their total as they play.

I love how the kids start to form a strategy for what numbers they want to roll next. It’s a great way to build mental math strategies. To introduce this game, I usually play it as, “The Teacher vs. The Class”. This allows time for modeling while keeping the kids in on the action. What class doesn’t love beating the teacher? They always want to play again if I win the round.

This game works best in longer stretches, so multiple rounds can be played. I usually like to use it at the beginning of the year as a class game before math centers. It then becomes an easy and fun game for the kiddos to play during math centers.

Back 2 Back

 

 

Seriously, hands down, my class’ favorite game to play! This game is perfect for inside recess as the whole class can play at once and everyone is excited for the game. This game requires some “brain sweat”, so it works well for grades 2-5. There are two different versions of this game. Supplies needed are minimal:  a writing surface, writing utensils, and someone who is quick with their math facts for a “caller.”

The object of the game is to guess the other player’s number before they guess yours. To play, two students come up to the board and stand back to back (hence the name). This allows for the students to write on the board, but blocks their view of the other person’s number.

The “Caller” states, “Numbers Up”. This signals the two students write a number of their choice on the board. I usually play with numbers 2-9 to keep kiddos from dwelling in the 0’s and 1’s easy train, but you can play with numbers as high or as low as needed for your group of kids.

The caller then states the sum (for younger students) or product (3rd-5th) of the two numbers.  The students use their understanding of math facts to figure out what they other person’s number is when added or multiplied by their number. The player to say the other person’s number first wins the round. The “loser” gets to choose the next person to come to the board. Please be warned… this game can get a little rowdy as students win and lose rounds and somehow the teacher always gets pulled up to “clear out” a player who’s been up a little too long… But it’s a lot of fun and well worth the 10-20 minutes! Beats the repetitious practice drills of flashcards!

Guess My Number

This next game is very versatile and can be modified in so many ways! It can be played in kindergarten all the way through 5th grade classrooms. To play, you need a number chart and a dry erase marker. This game can be played whole group, in pairs or in small groups of 3-4.

To begin, one student chooses a number. The other players try to guess the number by asking a series of questions. The student crosses off numbers it can’t be and circles numbers it could. The person who guesses the right number, wins and gets to choose the next number.

The best part of this game is that it can be played with laminated personal hundreds charts in small groups.

It can also be played as a whole group game using  a large chart.

For third grade, I encourage the use of question clues like “Is it a multiple of 5? Or greater than 70?” To introduce the game, I usually model crossing out numbers as students ask questions about the numbers and help link the clues to finding the right number.

For a kindergarten or first grade classroom, you may want to play with a number line with numbers 1-20.  Then, students could ask if the number is bigger or smaller than numbers within that range.  A 4th or 5th grade classroom can beef up the game with question clues like, “Is it divisible by 3?” or “Is it a multiple of 5?” The possibilities are endless! Time range to play can be from 5 minutes to 20 minutes and can be used as an inside recess game or a quick brain break before or after a lesson.

Math Fact Top It!

 

 

This last game works well in 1st through 5th grade classrooms and is best played in groups of 2-4 students. All that is needed to play are math fact flash cards. You can use addition, subtraction, multiplication or division cards. It just depends on where your students are in their math skills. I like to think of this game as “War for the Classroom,” as the rules for the traditional card game apply to this math fact version.

To play, students divide the flash cards evenly among all players. Then, on the count of three, all students throw down a card. The card with the highest sum or product wins all the cards in play. This can be modified to lowest difference or quotient. If students have the same answer, then they play each other again, with the winner capturing all the cards in play. Students play until all the cards are won. The student depending on the flashcards you are using. with the most cards at the end wins. I find this game works best in math centers and is an easy way for students to practice their math facts in a new and unique way!

Download Freebie with Game Directions 
So go forth and play! Get your students engaged and learning in the new year! If you’re not sure you’ll remember all these games I shared today, I’ve compiled all the directions in one file for you. It’s available here at my TpT store!

Leigh is a wife, mother, and a second-grade- turned-third-grade teacher. She currently resides in Central Florida where she has been teaching for 7 years. When Leigh isn’t teaching or writing for her teacher blog, The Applicious Teacher, she enjoys snuggling up with a good book, running a few miles, or spending time with her family.

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7 Surprising Health Benefits of Playing Chess

7 Surprising Health Benefits of Playing Chess

Written by Jenna Savage

Thursday, 25 October 2012 20:11

Grandmaster and world chess champion Bobby Fischer is famously quoted as saying, “Chess is life.”But can this two-player game, consisting of a square checkered board and playing pieces that are moved in different ways depending on their royal or military designation, benefit your mental and physical health? Absolutely! Check out these seven surprising health benefits of playing chess and then consider your next move. 1. Grows dendrites: Dendrites conduct signals from the neuron cells in your brain to the neuron they happen to be attached to. Learning and playing a game like chess actually stimulates the growth of dendrites, which in turn increases the speed and improves the quality of neural communication throughout your brain. Increased processing power improves the performance of your body’s computer, the brain. 2. Exercises both sides of the brain: To get the most benefit from a physical workout, you need to exercise both the left and right sides of your body. Studies show that in order to play chess well, a player must develop and utilize his or her brain’s left hemisphere, which deals with object recognition, as well as right hemisphere, which deals with pattern recognition. Over time, thanks to the rules and technique involved in the game, playing chess will effectively exercise and develop not one but both sides of your brain. 3. Prevents Alzheimer’s disease: A medical study involving 488 seniors by the Albert Einstein College of Medicine shows that playing chess, which stimulates brain function, measurably decreases the risk of dementia and combats its symptoms. Instead of letting the brain deteriorate, keeping the brain functioning at a normal rate, especially with a mind exercising activity like chess, will reduce your risk for Alzheimer’s disease as well as depression and anxiety. 4. Helps treat schizophrenia: Doctors at the Center for Cognitive Neuroscience in Bron, France, found that schizophrenic patients who were directed to play chess on a daily basis showed improvement in their condition when compared to patients who did not play. The chess-playing patients exhibited increased attention, planning, and reasoning abilities and interestingly, elected to continue playing chess as part of their daily routine, even after the study had concluded. 5. Improves children’s thinking and problem-solving skills: A child who is introduced to chess at a young age is likely to do better in school for years to come. Research shows that playing chess improves a child’s thinking, problem-solving, reading, and math scores. Educators and chess experts generally agree the second grade is the ideal time to introduce children to chess, although some as young as four or five may be ready to learn and play. 6. Builds self-confidence: With role models that include the young Norwegian grandmaster Mangus Carlsen as well as hip-hop producer RZA, the game of chess only seems to get cooler with every generation. But no matter what your age, playing chess will build up your self-esteem. When you play, you’re on your own, and if you lose, you have to take stock and analyze just where you went wrong. Playing and analyzing why you lost or won a game increases the level of mental strength and self-confidence that you bring to the world beyond the chessboard. 7. Helps with rehabilitation and therapy: Chess can be used to help rehabilitate patients recovering from stroke or a physically debilitating accident and as a form of therapy for those with autism or other developmental disabilities. Moving chess pieces across the board can help develop and fine tune a patient’s motor sills, while the mental effort required to play the game can improve cognitive and communication skills. Playing can also stimulate deep concentration and calm, helping to center and relax patients who are experiencing different degrees of anxiety. Reprinted on TheChessWorld.com with a permission from the publisher. Original can be found here.

Questions Before Answers: What Drives a Great Lesson?

 

By DR. RICHARD CURWIN’S 

DECEMBER 18, 2014

Photo credit: Scott McLeod via flickr (CC BY 2.0)

Recently, I was looking through my bookshelves and discovered an entire shelf of instruction books that came with software I had previously purchased. Yes, there was a time when software was bought in stores, not downloaded. Upon closer examination of these instruction books, I noticed that many of them were for computers and software that I no longer use or even own. More importantly, most were still in shrink-wrap, never opened. I recalled that when I bought software, I just put the disk into the computer and never looked at the book.

I realized that I did the same when I bought a new car — with one exception. I never read the instruction book in the glove compartment. I just turned on the engine and drove off. I already knew how to drive, so I didn’t need a book. The exception occurred when I tried to set the clock. I couldn’t figure it out, so I finally opened the glove compartment and checked the book.

This pattern was and is true for every device I buy. I never read the book that comes with a toaster, an iPod, or a juicer unless I have a question. There are some people who do read instruction books before using a device, but with no disrespect intended, those people are a small minority. Our minds are set up to not care about answers unless we have a question. The greater the question, the more compelling it is, the more we want the answer. We learn best when questions come before answers.

The Need to Know

Too many classrooms ignore this basic learning model. They spend most of class time providing information and then ask questions in the form of a quiz, test, or discussion. This is backward. Too many students never learn this way. It is simply too hard to understand, organize, interpret, or make sense out of information — or even to care about it — unless it answers a question that students care about.

Lessons, units, and topics are more motivating when they begin with a question whose answer students want to know. Not only do great questions generate interest, they also answer the question that so many students wonder about: “Why do I have to learn this?” Finally, great questions increase cognitive organization of the content by framing it into a meaningful answer to the opening question.

There is a catch, though, in using questions to begin your lesson. The question must be connected to the content, so that the following learning activities actually answer the question. The question must fit your students’ age, ability, and experiences. In addition, the question needs to provoke both thought and curiosity. In fact, it must be compelling enough to generate so much motivation so that students can’t help but want to know the answer.

Have you ever forgotten the name of a song and spent hours trying to remember it? It gets under your skin until you no longer want the answer — you need it. That’s what a great opening question does for students. Compulsion more than simple curiosity drives them to learn the information that follows. It’s what I felt when I finally wanted to read my car manual so that I could set the clock.

10 Questions That Motivate Learning

Questions this powerful are hard to find. I suggest collecting as many as you can (5-10 per year, for example), and after weeding out the ones that didn’t work, eventually you’ll be able to fill a notebook or computer file with them. I have been collecting these kinds of questions from teachers for years. Here’s a sample of some great ones that worked with students in creating enough motivation to drive an entire lesson.

• Middle school math: What does Martin Luther King have in common with algebra? (Answer: Both are concerned with equality.)
• First grade science class studying particles: What is the smallest thing you’ve ever held in your hand? (Warning: Do not use this question in high school.)
• Upper-level history class studying the Pilgrims: Is there anything your parents could ever do to you that would make you run away from home?
• Elementary art: If humans could be a color other than any of the colors that they already are, what color would they be? Why do you think this? Draw some people of this color.
• High school English: If Hamlet were a television sitcom, what would be a better name for it?
• Elementary English: What is the best name for a book about your life?
• Geography: Why does Israel have more fertile soil than other Middle East countries that share the same desert? (Answer: It has more trees to hold in moisture.)
• Second grade reading: We are going to redesign the alphabet. What three letters can be eliminated? (Answer: C, Q, X)
• Eighth grade physical education: Why is a soccer ball harder to control inside the gym than on the field? (Answer: Friction)
• Middle school English: Why don’t good and food rhyme? Given the definition of best, can you have more than one best friend?

Each of these questions was used by teachers to begin lessons that really motivated their students. Can you add any more to the list?

DR. RICHARD CURWIN’S PROFILE

Dipsticks: Efficient Ways to Check for Understanding by Todd Finley

JULY 30, 2014

 

What strategy can double student learning gains? According to 250 empirical studies, the answer is formative assessment, defined by Bill Younglove as “the frequent, interactive checking of student progress and understanding in order to identify learning needs and adjust teaching appropriately.”

Unlike summative assessment, which evaluates student learning according to a benchmark, formative assessment monitors student understanding so that kids are always aware of their academic strengths and learning gaps. Meanwhile, teachers can improve the effectiveness of their instruction, re-teaching if necessary. “When the cook tastes the soup,” writes Robert E. Stake, “that’s formative; when the guests taste the soup, that’s summative.” Formative assessment can be administered as an exam. But if the assessment is not a traditional quiz, it falls within the category of alternative assessment.

Alternative formative assessment (AFA) strategies can be as simple (and important) as checking the oil in your car — hence the name “dipsticks.” They’re especially effective when students are given tactical feedback, immediately followed by time to practice the skill. My favorite techniques are those with simple directions, like The 60 Second Paper, which asks students to describe the most important thing they learned and identify any areas of confusion in under a minute. You can find another 53 ways to check for understanding toward the end of this post, also available as a downloadable document.

In the sections below, we’ll discuss things to consider when implementing AFAs.

Observation: A Key Practice in Alternative Formative Assessment

A fundamental element of most AFAs is observation. In her Edutopia post, Rebecca Alber says there is much to learn by taking observational notes as students work in groups. “However,” she clarifies, “if it is quiet during this talk time, and they are watching you watch them, they are most likely lost.” Another Edutopia blogger, Elena Aguilar witnessed “a fantastic first grade Sheltered English teacher” who directed his students to respond to a story by making hand gestures and holding up picture cards. “In this way, the teacher was able to immediately see who was struggling with the concepts and provide corrective feedback.”

By methodically watching and recording student performance with a focused observation form, you can learn a lot about students’ levels of understanding in just a few moments. For example, on the Teach Like a Champion blog, watch how math teacher Taryn Pritchard uses an observation sheet, and note her description of how she pre-plans to assess students’ mastery levels in only ten seconds. Pre-planning methodical observations allow instructors to efficiently and effectively intervene when it counts most — the instant students start down the wrong path.

New to Alternative Formative Assessment? Start Slow

The National Capital Language Resource Center recommends the following when introducing alternative assessment for the first time:

• Integrate alternative assessments gradually, while still using the traditional assessments.
• Walk students through the rubrics and discuss expectations when you introduce assignments.
• Learn to score alternative assessments yourself, and then gradually introduce students to self-evaluation.
• Teach students how to thoughtfully give each other feedback as you introduce them to peer-response.

A Simple Way to Gain Information from Your Students: Ask Them

When preservice teachers are confused as to why their students performed poorly on an assignment, I gently say, “Did you ask them why?” After all, having learners use their own vernacular to articulate why they are stuck can be profoundly useful for identifying where to target support.

According to the American Institute of Nondestructive Testing, the simplest tool to encourage student self-assessment is evaluative prompts:

• How much time and effort did you put into this?
• What do you think your strengths and weaknesses were in this assignment?
• How could you improve your assignment?
• What are the most valuable things you learned from this assignment?

Learners can respond to those prompts using Padlet, a virtual corkboard where many computer users can simultaneously post their responses, followed by a focused whole-class discussion of students’ answers. The instructor doesn’t always have to develop prompts — students can invent and submit one or more potential exam questions and answers on relevant content. Tell them that you’ll include the best contributions on a forthcoming quiz.

Portfolios are a more complex form of ongoing self-assessment that can be featured during student-led conferences. James Mule, principal of St. Amelia Elementary School in New York, describes how children benefit from the student-led conferences that occur at his institution: “With the student in charge and the teacher acting as a facilitator, the authentic assessment gives students practice in self-evaluation and boosts accountability, self-confidence, and self-esteem.” Pernille Ripp’s Blogging Through the Fourth Dimension provides all the handouts needed.

The biggest benefit of integrating AFAs into your practice is that students will internalize the habit of monitoring their understanding and adjusting accordingly.

We created the following list as a downloadable reminder to post by your computer. In the comments section of this post, tell us which of these 53 ways you’ve used for checking on students’ understanding — or recommend other AFAs we should know about.

Click to download a PDF of these 53 AFA strategies (435 KB).

 53 Ways to Check for Understanding

1. Summary Poem Activity
   • List ten key words from an assigned text.
   • Do a free verse poem with the words you highlighted.
   • Write a summary of the reading based on these words.
2. Invent the Quiz
   • Write ten higher-order text questions related to the content. Pick two and answer one of them in half a page.
3. The 411
   • Describe the author’s objective.
4. Opinion Chart
   • List opinions about the content in the left column of a T-chart, and support your opinions in the right column.
5. So What? Journal
   • Identify the main idea of the lesson. Why is it important?
6. Rate Understanding
7. Clickers (Response System)
8. Teacher Observation Checklist
9. Explaining
   • Explain the main idea using an analogy.
10. Evaluate
    • What is the author’s main point? What are the arguments for and against this idea?
11. Describe
    • What are the important characteristics or features of the main concept or idea of the reading?
12. Define
    • Pick out an important word or phrase that the author of a text introduces. What does it mean?
13. Compare and Contrast
    • Identify the theory or idea the author is advancing. Then identify an opposite theory. What are the similarities and differences between these ideas?
14. Question Stems
    • I believe that ________ because _______.
    • I was most confused by _______.
15. Mind Map
    • Create a mind map that represents a concept using a diagram-making tool (like Gliffy). Provide your teacher/classmates with the link to your mind map.
16. Intrigue Journal
    • List the five most interesting, controversial, or resonant ideas you found in the readings. Include page numbers and a short rationale (100 words) for your selection.
17. Advertisement
    • Create an ad, with visuals and text, for the newly learned concept.
18. 5 Words
    • What five words would you use to describe ______? Explain and justify your choices.
19. Muddy Moment
    • What frustrates and confuses you about the text? Why?
20. Collage
    • Create a collage around the lesson’s themes. Explain your choices in one paragraph.
21. Letter
    • Explain _______ in a letter to your best friend.
22. Talk Show Panel
    • Have a cast of experts debate the finer points of _______.
23. Study Guide
    • What are the main topics, supporting details, important person’s contributions, terms, and definitions?
24. Illustration
    • Draw a picture that illustrates a relationship between terms in the text. Explain in one paragraph your visual representation.
25. KWL Chart
    • What do you know, what do you want to know, and what have you learned?
26. Sticky Notes Annotation
    • Use sticky notes to describe key passages that are notable or that you have questions about.
27. 3-2-1
    • Three things you found out.
    • Two interesting things.
    • One question you still have.
28. Outline
    • Represent the organization of _______ by outlining it.
29. Anticipation Guide
    • Establish a purpose for reading and create post-reading reflections and discussion.
30. Simile
    • What we learned today is like _______.
31. The Minute Paper
    • In one minute, describe the most meaningful thing you’ve learned.
32. Interview You
    • You’re the guest expert on 60 Minutes. Answer:
      1. What are component parts of _______?
      2. Why does this topic matter?
33. Double Entry Notebook
    • Create a two-column table. Use the left column to write down 5-8 important quotations. Use the right column to record reactions to the quotations.
34. Comic Book
    • Use a comic book creation tool like Bitstrips to represent understanding.
35. Tagxedo
    • What are key words that express the main ideas? Be ready to discuss and explain.
36. Classroom TED Talk
37. Podcast
    • Play the part of a content expert and discuss content-related issues on a podcast, using the free Easypodcast.
38. Create a Multimedia Poster with Glogster
39. Twitter Post
    • Define _______ in under 140 characters.
40. Explain Your Solution
    • Describe how you solved an academic problem, step by step.
41. Dramatic Interpretation
    • Dramatize a critical scene from a complex narrative.
42. Ballad
    • Summarize a narrative that employs a poem or song structure using short stanzas.
43. Pamphlet
    • Describe the key features of _______ in a visually and textually compelling pamphlet.
44. Study Guide
    • Create a study guide that outlines main ideas.
45. Bio Poem
    • To describe a character or person, write a poem that includes:
      • (Line 1) First name
      • (Line 2) 3-4 adjectives that describe the person
      • (Line 3) Important relationship
      • (Line 4) 2-3 things, people, or ideas the person loved
      • (Line 5) Three feelings the person experienced
      • (Line 6) Three fears the person experienced
      • (Line 7) Accomplishments
      • (Line 8) 2-3 things the person wanted to see happen or wanted to experience
      • (Line 9) His or her residence
      • (Line 10) Last name
46. Sketch
    • Visually represent new knowledge.
47. Top Ten List
    • What are the most important takeaways, written with humor?
48. Color Cards
    • Red = “Stop, I need help.”
    • Green = “Keep going, I understand.”
    • Yellow = “I’m a little confused.”
49. Quickwrite
    • Without stopping, write what most confuses you.
50. Conference
    • A short, focused discussion between the teacher and student.
51. Debrief
    • Reflect immediately after an activity.
52. Exit Slip
    • Have students reflect on lessons learned during class.
53. Misconception Check
    • Given a common misconception about a topic, students explain why they agree or disagree with it.

http://www.edutopia.org/blog/dipsticks-to-check-for-understanding-todd-finley?utm_source=facebook&utm_medium=post&utm_campaign=blog-dipsticks-to-check-for-understanding-image-repost

Other Assessment Resources

In Edutopia’s The Power of Comprehensive Assessment, Bob Lenz describes how to create a balanced assessment system.

The American Federation of Teachers (AFT) describes dozens of Formative Assessment Strategies.

The Assessment and Rubrics page of Kathy Schrock’s Guide to Everything website hosts many excellent assessment rubrics.

More Rubrics for Assessment are provided by the University of Wisconsin-Stout.

Jon Mueller’s Authentic Tasks and Rubrics is a must see-resource in his Authentic Assessment Toolbox website.

Debunking the Genius Myth

Holly Korbey | August 30, 2013 |

Picture a “genius” — you’ll probably conjure an image of an Einstein-like character, an older man in a rumpled suit, disorganized and distracted even as he, almost accidentally, stumbles upon his next “big idea.” In truth, the acclaimed scientist actually said, “It’s not that I’m so smart, it’s just that I stay with problems longer.” But the narrative around Einstein and a lot of accomplished geniuses — think Ben Franklin, the key and the bolt of lightning — tends to focus more on mind-blowing talent and less on the hard work behind the rise to success. A downside of the genius mythology results in many kids trudging through school believing that a great student is born, not made — lucky or unlucky, Einstein or Everyman.

Harvard-educated tutors Hunter Maats and Katie O’Brien began to notice that this belief about being born smart was creating a lot of frustration for the kids they tutored, and sometimes unwittingly reinforced by their parents. “We had sessions working with a student where the mom would walk by and say, ‘Oh, he didn’t get the math gene!’” said O’Brien. “And I’d think, Gee, give the kid a reason to never even try.”

“Try,” it seems, is the magical and operative word that has the possibility to transform how well a student does in school — once they understand a little about how to try, and a little about how learning and the brain works. How students think about learning makes a difference in what they’re able to achieve. Groundbreaking research conducted by Stanford psychologist Carol Dweck has shown that when students take on a growth mindset – one in which they believe that the brain is malleable, and they can improve at a task with effort – they handle setbacks better and improve academically.

“Kids are sent to school with no manual on how to use their brains. Not what to learn buthow to learn.”

Maats and O’Brien knew about all the research, and began sharing information about learning and the brain with their students. They turned their one-on-ones into a book, The Straight-A Conspiracy, to show teenagers that they had control, for a large part, over how they did in school, and that believing certain kids were born talented was a grand conspiracy to keep them down and stressed out (with tongue planted firmly in cheek). The authors use the latest research in psychology and neuroscience to try and convince teens, with lots of pop culture references and humor thrown in, that understanding how their brain learns can help them “totally rule the world.”

Maats explained that often students he tutored had watched another kid in class blow through an assignment and assumed they were just naturally good at it, that they didn’t even have to try. But he began clarifying the real reason they worked so fast; the student knew the answer right away because “it had become automatic,” he said. “They looked effortless, but they only became effortless through hard work.” Unlike sports or music, where students can see others practicing, much of schoolwork practice happens at home, builds slowly over time, and goes unseen. “You don’t see the work others are doing, so it looks like it never happened,” Maats said.

[RELATED: Eight Ways of Looking at Intelligence]

O’Brien said that “geniuses” also know how to focus their attention, and that’s why they may appear calm. “That overwhelmed feeling is coming from attention being focused on too many things that are not automated at once,” she said. “You can’t focus on two things you don’t know – but neither could Einstein!” Explaining one of the largest conspiracies they face with students, and parents’ biggest complaint, student multitasking, they disseminate the research for the teenage brain:

“Your attention can only deal with one unautomated task at a time. The idea that your attention can multitask is a major myth… When you’re trying to do all four of these tasks – walking, chewing gum, talking to your friend and reading Huckleberry Finn – the first two won’t be affected, because you’ve automated them. You can keep walking and chewing gum without even noticing they’re happening. But each of the new activities – holding a new conversation and reading a new book – requires your full attention in order to go well… But the more important point is that you just don’t want to put yourself through that! It’s totally manic!… The more stuff you pile on at once, the more time pressure you add to the situation, the more you start to feel really overwhelmed.”

By using concrete research in a way that speaks directly to teenagers, Maats and O’Brien hope to dispel the image of the rumpled genius, being brilliant in spite of himself. Instead, they want students to know that there are proven techniques that can improve their school performance and get parents and teachers off their back (a particular favorite is “Go Cyborg on Your Mistakes,” an extended “Terminator” metaphor that relates the idea of focused practice). And they seem to relish explaining that the straight-A student is working harder than kids think.

[RELATED: Can Everyone Be Smart At Everything?]

“You would never put a child into the driver’s seat of a car, with no license and no drivers’ ed, and expect him to be able to cruise down the highway successfully, with no fear or hesitation,” said O’Brien. “And yet kids are sent to school with no manual on how to use their brains. Not what to learn but how to learn. The result is that everyone spends their days in school guessing what might be the best approach, the most effective technique…and the questioning about the how takes a lot of time and attention away from what needs to be learned.”

The Delicate Balance

By Jill Jenkins

With school turning out more runners, jumpers, racers, tinkerers, grabbers, snatchers, fliers, and swimmers instead of examiners, critics, knowers, and imaginative creators, the word ‘intellectual,’ of course, became the swear word it deserved to be.”
― Ray Bradbury, Fahrenheit 451

                What is important for students to know?  What should our schools be teaching? If you listen to media, all the schools should be focused on is STEM: Science, Technology, Engineering, and Mathematics. Just like in the 1950’s our society is demanding that education provide more STEM education to provide a technological suave population who can produce a profit for our corporations. Are schools created to serve our corporations or the individual needs of our students?  Society certainly rewards students who perform well in science, technology, engineering and mathematics, but not every student has the desire or the aptitude to do well in those areas.  Are we doing those students a disservice? Since girls have stronger verbal skills and brains wired for an education in communications is this a subtle form of prejudice?  Before we write our curriculum, it is important to determine what is important to know to help our students become both productive citizens and principled people.  We need a more balanced approach to serve all of the needs of all of the varied students in our classes?

                Schools need to prepare students to be productive citizens, but to be honest with as rapidly as technology is changing that is not an easy task.  As a child, I remember laughing at Maxwell Smart and his shoe telephone.  Now, all of us carry telephones around in our pockets that are not only communication devices, but small computers.  The truth is there will be careers that we can’t even imagine, so we have to give students skills to be life-long learners.  To achieve they must be willing to learn new skills through-out their lives. We need to prepare students to adapt to world that we cannot conceive existing. 

                Research shows that females learn differently than males. According to the article, “How Boys and Girls Learn Differently” by Dr. Gail  Gross from the Huffington Post,boys have less serotonin and oxytocin which makes girls more sensitive to other’s  feeling subtly communicated through body language and they can sit still for longer periods of time.  Girls have larger hippocampus, where memory and language is stored.  This means they develop language skills, reading skills and vocabulary much sooner than boys. On the other hand, boys have a larger cerebral cortex which means they learn visually and have better spatial relationships.  This could improve their ability in engineering and technology.  These differences become less dramatic as the child grows older.  Perhaps schools need to focus on presenting a broad spectrum of disciplines in a variety of ways to serve all of students.

Even though our society does not value careers where communications rather than subjects like science, technology, engineering and mathematics are the primary focus, they may still be important careers for our society.  For example, teachers are essential if we want to continue to produce an educated workforce, but if pay is the measurement of value, they are not valued by society.  In the state where I taught science, engineering, technology and math teachers were all paid $5000.00 a year more than any other kind of teacher.  Still, if we want to be realistic students’ need a balance of both to be successful.  For example, my daughter is a journalist; however, she also needs to know how to write computer coding because the magazine that employs her is on-line. Most scientists must document whatever they do which means they need writing and reading skills. Furthermore, who is to say who will be the next poet laureate .   The arts, history and language arts are all equally important skills for students to master as math, science and technological based skills.

Even more important, the humanities:  literature, history and the arts force people to ask “why.”  Certainly, we can’t think about Nazi Germany without realizing, there was a reason that Hitler banned books.  We can’t read a Michael Critchton book without discussing ethics in science and medicine.  We can’t read Charles Dickens’ Oliver Twistwithout questioning the social problems caused by poverty and homelessness.  Reading, writing, history, the arts are all connected to science, math, technology and engineering. A quality education is a balance.  All of it is equally important.  Teachers should be compensated equally and students should be provided with an equal balance.  Teachers should help students develop their own individual talents, so they can become all that they can be.  Schools should prepare each student to become “all that they can be,” not a product to serve the needs of industry.

Bestowing the Gift of Self-Confidence to Students

The Gift of Self-Confidence

The moment you doubt whether you can fly, you cease for ever to be able to do it.”
― J.M. Barrie, Peter Pan

            One of the most important gifts that a teacher can impart to a student is the gift of self-confidence.  To succeed at anything, a person must believe that success is possible.  Many students lack the belief that they could possibly be successful in school or anywhere else; as a result, these same people have difficulty succeeding in life. Students who doubt their abilities often lack any motivation to try.  If a person does not try, they have no possibility of succeeding.  As a result, an educator must first impart the ability to believe in oneself before the student can begin to succeed. Educators must become Peter Pan to help students fly.

When I was teaching in an Alternative Education, I was amazed at the students who had no desire to do well in school or even to attempt to do well in school.  After getting to know these students, I discovered that most of them had suffered so many humiliating failures at school that they believed that they were not capable of learning. They found it was less painful to do nothing, than to attempt anything and fail.  To continually have the belief that they could not succeed reinforced was just too painful for them.  Some of them used outrageous behavior as a way of avoiding this failure. I remember one particular student, Juan, who would not stay in his seat, sang loudly and yelled obscenities across the room to avoid a writing assignment. To reach students like Juan, I had to break down their barriers, get to know them as individuals, persuade them that I was their advocate and I was going to show them how to be successful by celebrating even their smallest achievement.  Being successful can be  rewarding, but to convince these students of that, the teachers needs to break successful behavior into its smallest components and reward for the successful completion of each small step.  For example, I began by rewarding students for coming to class prepared.  Each student who had a pencil and paper was rewarded with a small piece of candy.  Next I created a chart on the board showing the relationship of how a student would feel if he brought this parents a report cards with all “A’s” on it compared to how he would feel if he brought his parents a report card with all “F’s” on it.  Helping a student understand that happiness is directly connected to their success in school is an important step to motivating them to want to succeed.

Students who feel socially inept are often unhappy at school.  Girls, especially, suffer from social bullying that goes unnoticed by educators.  Our society puts so much emphasis on physical beauty and social position in school that students who do not fit the norm are often isolated.  Girls often exclude these girls from social situations and do not include them even in conversations.  Shunning can be cruel treatment that can cause scars that last a lifetime.  Some of this bullying takes the form of cruel comments in social media or scathing remarks made in a classroom or a hallway.  Students who suffer from these vicious assaults lose their self-esteem and as a result, do poorly academically or feel badly about continuing their education because it is too painful.   As an educator, protecting and supporting students’ self-esteem should be one of our goals. Helping students learn to accept and embrace people who are different from them should be another. For students to do well, all students must feel safe and appreciated.

When teachers are writing goals for their classrooms, academic goals are only one dimension of education.  Helping a student feel safe and good about his ability to succeed should be high on the list of objectives. Helping a student accept that others may differ from him, but should still included  in the community without ridicule or attack.   School should prepare students to succeed in life.  If a student has doubts or is not empowered with self-confidence, he cannot succeed.  Like Peter Pan, teachers must bestow the gift of self-confidence.

Posted by Jill Jenkins 

SOME COOL FACTS ABOUT MATHEMATICS.

1. The word ‘mathematics’ comes from the Greek “máthēma”, which means learning, study, science.

2. Do you know a word known as Dyscalculia? Dyscalculia means difficulty in learning arithmetic, such as difficulty in understanding numbers, and learning math facts!

3. In America, mathematics is known as ‘math’, they say that ‘mathematics’ functions as a singular nounso as per them ‘math’ should be singular too.

4. ‘Mathematics’ is an anagram of ‘me asthmatic’. (An Anagram is word or phrase made by transposing or rearranging letter of other words or phrase.)

5. Notches (cuts or indentation) on animal bones prove that humans have been doing mathematics since around 30,000 BC.

6. The word ‘hundrath’ in Old Norse (old language from where English language originated), from which word ‘hundred’ derives, meant not 100 but 120.

7. What comes after a million, billion and trillion? A quadrillion, quintillion, sextillion, septillion, octillion, nonillion, decillion and undecillion.

8. The number 5 is pronounced as ‘Ha’ in Thai language. 555 is also used by some as slang for ‘HaHaHa’.

9. Different names for the number 0 include zero, nought, naught, nil, zilch and zip.

10. Zero ( 0 ) is the only number which can not be represented by Roman numerals.

11. The name ‘zero’ derives from the Arabic word “sifr” which also gave us the English word ‘cipher’ meaning ‘a secret way of writing’ .

12. What is the magic of No. Nine (9)? Multiply any number with nine (9 ) and then sum all individual digits of the result (product) to make it single digit, the sum of all these individual digits would always be nine (9).

13. Here is an interesting trick to check divisibility of any number by number 3. A number is divisible by three if the sum of its digits is divisible by three (3).

14. The = sign (“equals sign”) was invented by 16th Century Welsh mathematician Robert Recorde, who was fed up with writing “is equal to” in his equations.

15. Googol (meaning & origin of Google brand ) is the term used for a number 1 followed by 100 zeros and that it was used by a nine-year old, Milton Sirotta, in 1940.
16. The name of the popular search engine ‘Google’ came from a misspelling of the word ‘googol’.

17. Abacus is considered the origin of the calculator.

18. Have you ever noticed that the opposite sides a die always add up to seven (7).

19. 12,345,678,987,654,321 is the product of 111,111,111 x 111,111,111. Notice the sequence of the numbers 1 to 9 and back to 1.

20. Plus (+) and Minus (-) sign symbols were used as early as 1489 A.D.

21. An icosagon is a shape with 20 sides.

22. Trigonometry is the study of the relationship between the angles of triangles and their sides.

23. If you add up the numbers 1-100 consecutively (1+2+3+4+5…) the total is 5050.

24. 2 and 5 are the only primes that end in 2 or 5.

25. From 0 to 1,000, the letter “A” only appears in 1,000 (“one thousand”).

26. A ‘jiffy’ is an actual unit of time for 1/100th of a second.

27. ‘FOUR’ is the only number in the English language that is spelt with the same number of letters as the number itself

28. 40 when written “forty” is the only number with letters in alphabetical order, while “one” is the only one with letters in reverse order.

29. In a group of 23 people, at least two have the same birthday with the probability greater than 1/2 .

30. If there are 50 students in a class then it’s virtually certain that two will share the same birthday..

31. Among all shapes with the same perimeter a circle has the largest area.

32. Among all shapes with the same area circle has the shortest perimeter .

33. In 1995 in Taipei, citizens were allowed to remove ‘4’ from street numbers because it sounded like ‘death’ in Chinese. Many Chinese hospitals do not have a 4th floor.
34. The word “FRACTION” derives from the Latin ” fractio – to break”.

35. In working out mathematical equations, the Greek mathematician, Pythagoreans used little rocks to represent numbers. Hence the name of Calculus was born which means pebbles in Greek.

36. In many cultures no 13 is considered unlucky, well, there are many myths around it .One is that In some ancient European religions, there were 12 good gods and one evil god; the evil god was called the 13th god. Other is superstition goes back to the Last Supper. There were 13 people at the meal, including Jesus Christ, and Judas was thought to be the 13th guest.

37. Have you heard about Fibonacci? It is the sequence of numbers wherein a number is the result of adding the two numbers before it! Here is an example: 1, 1, 2, 3, 5, 8, 13, 21, 34, and so on.

38. Want to remember the value of Pi (3.1415926) in easy way ? You can do it by counting each word’s letters in ‘May I have a large container of coffee?’

39. Have you heard about a Palindrome Number? It is a number that reads the same backwards and forward, e.g. 12421.

How to turn every child into a “math person”

By Miles Kimball August 11, 2014

Miles Kimball is an economics professor at the University of Michigan. He blogs about economics, politics and religion.

The original math person. AP Photo

Last month, the US Math Team took second place in the International Math Olympiad—for high school students—held in Cape Town, South Africa. Since 1989, China has won 20 out of 27 times (including this year), and in the entire history of the Olympiad, the US Math Team has won only 4 out of 55 times, so second place is a good showing. According to the American Mathematical Association website: “team leader Loh noted that the US squad matched China in the individual medal count and missed first place by only eight points.”

Reading about the US Math Team’s performance in the Olympiad this year takes me back to my senior year of high school in 1977 when, having taken 9th place in the US Math Olympiad, I was invited to travel to the International Math Olympiad in Belgrade as an alternate to the 8-member US Math Team. I chose not to go to Belgrade because the Olympiad conflicted with the National Speech Tournament, where my team couldn’t have tied on points for first place without me—while the US Math Team won without needing my help. This profoundly shaped my perception of myself as a “math person.”

Left: an article from 1976 where Miles placed 23rd in the US Math Olympiad; top: in 1977 Miles placed 9th in the competition; bottom: questions from the 1977 USA Math Olympiad.

More than 36 years later, I have come to the view that almost everyone should think of herself or himself as a “math person.” In our column “There’s one key difference between kids who excel at math and those who don’t,” Noah Smith and I wrote this about the often-heard statement: “I’m just not a math person.”

We hear it all the time. But the truth is, you probably are a math person, and by thinking otherwise, you are possibly hamstringing your own career. Worse, you may be helping to perpetuate a pernicious myth—that of inborn genetic math ability.

Not everyone agrees with us. Noah and I got some pushback for our rejection of the idea that inborn math ability is the dominant factor in determining math skill. So I did some more reading in the psychology literature on nature vs. nurture for IQ and for math in particular. The truth is even more interesting than the simple story that Noah and I told.

Math ability is not fixed at birth 

Three facts run contrary to the idea that inborn mathematical ability is a dominantfactor in determining whether or not someone is good at math compared to others of the same age.

First, it is a reasonable reading of the very inconsistent evidence from twin studies to think that genes account for only about half of the variation in mathematical skill among kids. For example, this 2007 National Institutes of Health Public Access twin study, using relatively transparent methods, estimates that genes account for somewhere in the range from 32% to 45% of mathematical skill at age 10. That leaves 55% to 68% of mathematical skill to be accounted for by other things—including differences in individual effort. (Other estimates of the percentage of variation of mathematical skill in kids due to genes range all the way from 19% to 90%. )

Second, a remarkable fact about IQ tests, including the mathematical components of IQ tests, is that every generation looks a lot smarter than the previous generation. This steady increase in performance on IQ tests is known as “the Flynn effect” after the political philosopher James Flynn, who discovered this remarkable fact. The American Psychological Association’s official report “Intelligence: Knowns and Unknowns” says:

… performance has been going up ever since testing began. The “Flynn effect” is now very well documented, not only in the United States but in many other technologically advanced countries. The average gain is about 3 IQ points per decade.

At that rate, an IQ test from 100 years ago would put an average American today at an IQ of 130—in the top 5% of everyone back then.  The American Psychological Association’s report goes on to say:

The consistent IQ gains documented by Flynn seem much too large to result from simple increases in test sophistication. Their cause is presently unknown, but three interpretations deserve our consideration. Perhaps the most plausible of these is based on the striking cultural differences between successive generations. Daily life and occupational experience both seem more “complex” (Kohn & Schooler, 1973) today than in the time of our parents and grandparents. The population is increasingly urbanized; television exposes us to more information and more perspectives on more topics than ever before; children stay in school longer; and almost everyone seems to be encountering new forms of experience. These changes in the complexity of life may have produced corresponding changes in complexity of mind.

In other words, although people a century ago were good at many things, many of them would have struggled with the kinds of abstract problems IQ tests focus on.

(As a simple example of how math standards have risen, my father tells me that when he was in high school, people thought calculus was too advanced for high school students. Nowadays, about one of every six high school students takes calculus in the US.)

Third (and I wish the research were clearer about this for math specifically), thefraction of differences in IQ that seem genetically linked increases dramatically with age. For children, about 45% of differences in IQ appear to be genetic, while for adults, about 75% of differences in IQ appear to be genetic. Think about that. How could it be that genes matter more and more as people get older—even though the older you get, the more environmental things have happened to you? What I think is the most plausible answer, is that the genes are influencing what people do and what they do in turn affects their IQ.

The “love it and learn it” hypothesis

No one yet knows exactly how genes, environment, and effort interact to determine mathematical skill. In light of the evidence above, let me propose what I call the “love it and learn it” hypothesis. This hypothesis has three elements:

1. For anyone, the more time spent thinking about and working on math, the higher the level of mathematical skill achieved.
2. Those who love math spend more time thinking about and working on math.
3. There is a genetic component to how much someone loves math.

Despite emphasizing time spent on math as the driver of math skill, this can explain why identical twins look more alike on math skills than fraternal twins. Since time spent dealing with math matters, it allows plenty of room for the average person to be better at math now than a hundred years ago. And the effect of loving math on math experience and therefore math skill is likely to only grow with time.

To get better at math, act like someone who loves math

If the “love it and learn it” hypothesis is true, it gives a simple recommendation for someone who wants to get better at math: spend more time thinking about and working on math. Best of all: spend time doing math in the kinds of ways people who love math spend time doing math. Think of math like reading. Not everyone loves reading. But all kids are encouraged to spend time reading, not just for school assignments, but on their own. Just so, not everyone loves math, but everyone should be encouraged to spend time doing math on their own, not just for school assignments. If a kid has a bad experience with trying to learn to read in school, or is bored with the particular books the teacher assigned, few parents would say “Well, maybe you just aren’t a reader.” Instead, they would try hard to find some other way to help their kid with reading and to find books that would be exciting for their particular kid. Similarly, if a kid has a bad experience trying to learn math in school, or is bored with some bits of math, the answer isn’t to say “Well maybe you just aren’t a math person.” Instead, it is to find some other way to help that kid with math and to find other bits of math that would be exciting for their particular kid to help build her or his interest and confidence.

The way a teacher presents a mathematical principle or method in class may not work for you—or, as Elizabeth Green suggested in the New York Times, the whole American pattern of K-12 math instruction may be fatally flawed. If you loved math, you would think about that principle or method from many different angles and look up and search out different mathematical resources, until you found the angle that made most sense to you. Even if you don’t love math, that would be a good way to approach things.

Many people think that because they can’t understand what their math teacher is telling them, it means they can’t understand math. What about the possibility that your teacher doesn’t understand math? Some people are inspired to a life-long love of math by a great math teacher; others are inspired to a life-long hatred of math by an awful math teacher. If you are unlucky enough to have an awful math teacher, don’t blame math for your teacher’s failings.

Cathy O’Neil—who blogs at mathbabe.org—describes well what I like to call “slow-cooked math”:

There’s always someone faster than you. And it feels bad, especially when you feel slow, and especially when that person cares about being fast, because all of a sudden, in your confusion about all sort of things, speed seems important. But it’s not a race. Mathematics is patient and doesn’t mind.

Being good at math is really about how much you want to spend your time doing math. And I guess it’s true that if you’re slower you have to want to spend more time doing math, but if you love doing math then that’s totally fine.

I was lucky to have a dad and older brother who showed me a bit of math early on, in a way that was unconnected to school. Then in school, I spent at least as much time on math when I wasn’t supposed to be doing math as when I was. It was a lot more fun doing math when I wasn’t supposed to be doing math than when I was.

For one thing, when I did it on my own, I could do it my own way. But also, there were no time limits. It didn’t matter if it took me a long time. And nothing seemed like a failure.

I spent a lot of time doing math. And very little of that math was done under the gun of a deadline. I spent some time on literal tangents in geometry and trigonometry. But I spent a lot more time on figurative tangents, running into mathematical dead ends. When Euclid told King Ptolemy “there is no Royal Road to geometry,” it had at least two meanings:

1. Everyone—even a king or queen—has to work hard if he or she wants to learn geometry or any other bit of higher math.
2. The path to learning geometry, or math in general, is not always a straight line. You may have to circle around a problem for a long time before you finally figure out the answer.

What can be done

I feel acutely my own lack of expertise in math education for students younger than the college students I teach. Fortunately, there are a wealth of practical suggestions for teaching and learning math by others who know more than I do, or have a different perspective from their own experience.

Noah and I received many comments in response to our post but the comments I learned the most from were from these people, who let me turn their comments into guest posts on my blog:

•  Mary O’Keeffe on Slow-Cooked Math
•  Matt Waite: How I Faced My Fears and Learned to Be Good at Math
•  Marc F. Bellemare’s Story: “I’m Bad at Math”
• Marjorie Drysdale: Even When You Can Do Math, You May Not Love It 
• Kate Owino: Kenyan Women Can Love Math Too
• Jing Liu: Show Kids that Solving Math Problems is Like Being a Detective
• Matt Rognlie on Misdiagnosis of Difficulties and the Fear of Looking Foolish as Barriers to Learning
• Kevin Remisoski on Teaching and Learning Math

In Green’s article “Why Americans Stink at Math,” she talks about how differently math is taught in Japanese classrooms, and how we should hope that we might someday get that kind of math instruction in the US. The key difference is that in Japan, the students are led by very carefully designed lessons to figure out the key math principles themselves. That kind of teaching can’t easily be done without the right kind of teacher training—teacher training that is not easy to come by in the United States.

But some teachers at least encourage their students to follow a “slow-cooked math” approach where they can dig in and wrap their heads around what is going on in the math, without feeling judged for not understanding instantly. Elizabeth Cleland gives a good description here of how she does it.

Even when a student is lucky enough to have good teachers at school, a little extra math on the side can help a lot. Kids who arrive at school knowing even a tiny bit of math will have more confidence in their math ability and will probably start out liking math more. Even quite young kids will be interested in a Mobius strip made out of paper where a special twist makes what looks like two sides into just one side.  And putting blocks of different lengths next to each other as in aMontessori addition strip board is exactly how I have always pictured addition in my head.

A Montessori addition strip board.Image via jsmontessori.com

Extra math doesn’t all have to come from parents. In some towns, enough Little League soccer coaches are found for almost every kid to be on a soccer team. And even I was once drafted as a Cub Scout Den Leader. If people realized the need, many more adult leaders for math clubs for elementary and middle school kids could be found. In addition to showing kids some things themselves, math club leaders can do a lot of good just by checking out and sorting through the growing number of great math videos and articles online, as well as old-style paper-and-ink books.

I use Wikipedia regularly as a math reference. (There is no reason to think Wikipedia is any less reliable than the typical math textbook; textbooks are not 100% error-free either.)  I have a post on logarithms and percent changes that is one of the most popular posts on my blog. (Maybe it is the evocation of piano keyboards and slide rules, or the before and after pictures of Ronald Reagan.) And Susan Athey, the first woman to win the John Bates Clark Medal for best American economist under forty, highly recommends Glenn Ellison’s Hard Math for Elementary School as a resource for math clubs. All of that just scratches the surface of the resources that are out there.

The obvious issue raised by the “love it and learn it” hypothesis is that some people may not start out loving math, and some may never love math. Acting as if you love math when you don’t may work, but it can be painful. So it is important to figure out what can be done to instill a love of math. Even if they only know a little math themselves, people who can get kids who don’t start out loving math to come to love it are a national treasure. As the brilliant business guru Clay Christensen (among others) has pointed out, in an age when lectures from the best lecturers in the world can be posted online, the kind of help students need on the spot is the help of a coach.

For too long, we have depended too heavily on overburdened math teachers whohave remarkably little time in school to actually teach math, and whom the system has deprived of the kind of training they need to teach math as well as it can be taught. It is time for all of us to take the responsibility for learning math and doing what we can to help others learn math–just as we all take responsibility for learning to read and doing what we can to help others learn to read.

Most of us who participated as kids in a sport or other competitive pursuit remember a coach who got us to put in a lot more effort than we ever thought we would. Math holds out the hope of victory not just in a human competition, but in understanding both the visible universe and the invisible Platonic universe. There is no impossibility theorem saying there can’t be math coaches in every neighborhood who make the average kid want to gain that victory.

Math- When Am I Ever Gonna Use This?

by Lisa Arends

Author, wellness coach, and math teacher

 When Am I Ever Gonna Use This?

Posted: 10/21/2012 11:40 am

 “When am I ever gonna use this?” As an eighth-grade algebra teacher, I hear this refrain at least once a week. It’s a difficult question to answer. I mean, when is the last time that your employer asked you to factor a polynomial or prove two polygons congruent? The truth is that most of us will never use the myriad of math facts and algorithms in our post-school lives. However, that does not mean that math does not have some valuable lessons for us. The following are lessons that can be learned in an algebra classroom and applied in your life. No calculator required.

Mistakes

Pencils come with erasers for a reason. Mistakes in a math classroom are inevitable. In fact, they are beneficial, as they often uncover misconceptions and maladaptive beliefs. We often believe that we must write our lives in ink and that mistakes permanently mar us. We try to hide them, turn our heads in shame. There is always a lesson in every error. Rather than crossing out the mistake, examine it and learn from it.

Growth at the Edge

I always want my students to be just slightly uncomfortable; I push them a little beyond their comfort zone because this is where the learning occurs. We don’t all have algebra teachers following us around in life, but we can still push ourselves past our self-imposed boundaries. Growth occurs at the edge of comfort and panic. Find that space and embrace it.

Take Risks

I can do anything with a student who is willing to try. I have respect for those who will volunteer even when they are unsure of their answer. They have learned that taking risks can bring reward in the form of a correct answer, a deeper understanding, or the respect of their peers. Life is no different. If you never risk anything, you will never gain anything either. Don’t be afraid to raise your hand.

Break It Down

In algebra, students are presented with complex problems. One of the first skills they learn is to break a large problem into a series of simpler ones, focusing on one step at a time. When you feel overwhelmed in life by what seems to be an insurmountable obstacle, try breaking it into manageable tasks. You might just be amazed at what you can accomplish.

Eliminate the Unnecessary

“Six-year-old Suzy has four apples and 5-year-old Bobby has two. How many apples do they have together?” It’s pretty clear that this example has extraneous information, clutter that can be ignored without detracting from the answer. Examine your life. Do have unnecessary clutter that you can eliminate? Get rid of it and you will find clarity in what remains.

“See” the Effect

I train students to anticipate the effect of a step in a problem before they make it. I want their minds to always be slightly ahead of their pencil as they “see” the impact of a decision prior to carrying it out. This is beneficial in the world at large as well as it encourages thoughtful and deliberate decisions. If you understand effect, you can change the cause.

Think Logically

Every year I have students that attempt to “prove” lines parallel by stating that they look parallel. As tempting as that reasoning may be, it is simply not valid. Our minds are sometimes lazy and try to make assumptions without proof. Watch yourself and check to see if the data supports your conclusions. It’s good to listen to your gut, but don’t divorce it from your brain.

Communication

Every year I have students that can execute the mathematics perfectly, yet cannot communicate to anyone else how or why they made the decisions they did. Their work is then almost useless, as no else can understand or build upon their results. Our thoughts and ideas are only as good as our ability to communicate them to another. Learn to be clear in your words so that they may be understood.

Balance

“Whatever you do to one side, you have to do to another.” Algebra students across the country recite this line as they learn how to balance equations. Perhaps we should all be uttering this line as a reminder to create balance in our own lives. Remember that when you add something to one area of your life, you will need to make a change in another so that balance is restored.

Work Backwards

Sometimes my students face problems that feel impossible. They can’t even figure out the first step. I teach them to start from the goal and work backwards, teasing out the steps as they go along. In your life, start with your goals and figure out what you need to do to achieve them. By seeing the steps in reverse, even the loftiest dreams can be made possible. Try it.

Persevere

Math can be hard. So can life. In both cases, it takes perseverance and tenacity to see difficulties through until the end. The rewards that come from determination and dogged spirit are so much sweeter than those that come without the sweat. The only way that failure is certain is if you do not try.

Basics Matter

It’s difficult to understand algebra if you don’t know multiplication. Likewise, it’s difficult to find fulfillment if you’re not meeting your basic needs. Start at the beginning and make sure you have a strong foundation upon which to build.

Confidence

So many of my students enter my room in August convinced that they cannot “do” math. In my 11 years of teaching, I have yet to meet a student that was correct in this belief. My first job with these uncertain pupils is to convince them that they can. Until they believe in themselves, they will continue to fail. The biggest lie we tell ourselves is, “I can’t.” Stop lying. It may be scary to try, but just think of the possibilities.

Participate

One of my favorite quotes hangs right above the board in my classroom:

“Math is not a spectator sport.” — Jerry Mortensen

Neither is life. Don’t stand on the sidelines watching it unfold in front of you. Get out there and play!

Dipsticks: Efficient Ways to Check for Understanding

Dipsticks: Efficient Ways to Check for Understanding

from http://www.edutopia.org/

JULY 30, 2014

 by  Todd Finley

What strategy doubles student learning? According to 250 empirical studies, the answer is formative assessment, defined by Bill Younglove as “the frequent, interactive checking of student progress and understanding in order to identify learning needs and adjust teaching appropriately.”

Unlike summative assessment, which evaluates student learning according to a benchmark, formative assessment monitors student understanding so that kids are always aware of their academic strengths and learning gaps. Meanwhile, teachers can improve the effectiveness of their instruction, re-teaching if necessary. “When the cook tastes the soup,” writes Robert E. Stake, “that’s formative; when the guests taste the soup, that’s summative.” Formative assessment can be administered as an exam. But if the assessment is not a traditional quiz, it falls within the category ofalternative assessment.

Alternative formative assessment (AFA) strategies can be as simple (and important) as checking the oil in your car — hence the name “dipsticks.” They’re especially effective when students are given tactical feedback, immediately followed by time to practice the skill. My favorite techniques are those with simple directions, like The 60 Second Paper, which asks students to describe the most important thing they learned and identify any areas of confusion in under a minute. You can find another 53 ways to check for understanding toward the end of this post, also available as a downloadable document.

In the sections below, we’ll discuss things to consider when implementing AFAs.

Observation: A Key Practice in Alternative Formative Assessment

A fundamental element of most AFAs is observation. In her Edutopia post, Rebecca Alber says there is much to learn by taking observational notes as students work in groups. “However,” she clarifies, “if it is quiet during this talk time, and they are watching you watch them, they are most likely lost.” Another Edutopia blogger, Elena Aguilar witnessed “a fantastic first grade Sheltered English teacher” who directed his students to respond to a story by making hand gestures and holding up picture cards. “In this way, the teacher was able to immediately see who was struggling with the concepts and provide corrective feedback.”

By methodically watching and recording student performance with a focused observation form, you can learn a lot about students’ levels of understanding in just a few moments. For example, on the Teach Like a Champion blog, watch how math teacher Taryn Pritchard uses an observation sheet, and note her description of how she pre-plans to assess students’ mastery levels in only ten seconds. Pre-planning methodical observations allow instructors to efficiently and effectively intervene when it counts most — the instant students start down the wrong path.

New to Alternative Formative Assessment? Start Slow

The National Capital Language Resource Center recommends the following when introducing alternative assessment for the first time:

• Integrate alternative assessments gradually, while still using the traditional assessments.
• Walk students through the rubrics and discuss expectations when you introduce assignments.
• Learn to score alternative assessments yourself, and then gradually introduce students to self-evaluation.
• Teach students how to thoughtfully give each other feedback as you introduce them to peer-response.

A Simple Way to Gain Information from Your Students: Ask Them

When preservice teachers are confused as to why their students performed poorly on an assignment, I gently say, “Did you ask them why?” After all, having learners use their own vernacular to articulate why they are stuck can be profoundly useful for identifying where to target support.

According to the American Institute of Nondestructive Testing, the simplest tool to encourage student self-assessment is evaluative prompts:

• How much time and effort did you put into this?
• What do you think your strengths and weaknesses were in this assignment?
• How could you improve your assignment?
• What are the most valuable things you learned from this assignment?

Learners can respond to those prompts using Padlet, a virtual corkboard where many computer users can simultaneously post their responses, followed by a focused whole-class discussion of students’ answers. The instructor doesn’t always have to develop prompts — students can invent and submit one or more potential exam questions and answers on relevant content. Tell them that you’ll include the best contributions on a forthcoming quiz.

Portfolios are a more complex form of ongoing self-assessment that can be featured during student-led conferences. James Mule, principal of St. Amelia Elementary School in New York, describes how children benefit from the student-led conferences that occur at his institution: “With the student in charge and the teacher acting as a facilitator, the authentic assessment gives students practice in self-evaluation and boosts accountability, self-confidence, and self-esteem.” Pernille Ripp’s Blogging Through the Fourth Dimension provides all the handouts needed.

The biggest benefit of integrating AFAs into your practice is that students will internalize the habit of monitoring their understanding and adjusting accordingly.

We created the following list as a downloadable reminder to post by your computer. In the comments section of this post, tell us which of these 53 ways you’ve used for checking on students’ understanding — or recommend other AFAs we should know about.

53 Ways to Check for Understanding

1. Summary Poem Activity
   • List ten key words from an assigned text.
   • Do a free verse poem with the words you highlighted.
   • Write a summary of the reading based on these words.
2. Invent the Quiz
   • Write ten higher-order text questions related to the content. Pick two and answer one of them in half a page.
3. The 411
   • Describe the author’s objective.
4. Opinion Chart
   • List opinions about the content in the left column of a T-chart, and support your opinions in the right column.
5. So What? Journal
   • Identify the main idea of the lesson. Why is it important?
6. Rate Understanding
7. Clickers (Response System)
8. Teacher Observation Checklist
9. Explaining
   • Explain the main idea using an analogy.
10. Evaluate
    • What is the author’s main point? What are the arguments for and against this idea?
11. Describe
    • What are the important characteristics or features of the main concept or idea of the reading?
12. Define
    • Pick out an important word or phrase that the author of a text introduces. What does it mean?
13. Compare and Contrast
    • Identify the theory or idea the author is advancing. Then identify an opposite theory. What are the similarities and differences between these ideas?
14. Question Stems
    • I believe that ________ because _______.
    • I was most confused by _______.
15. Mind Map
    • Create a mind map that represents a concept using a diagram-making tool (like Gliffy). Provide your teacher/classmates with the link to your mind map.
16. Intrigue Journal
    • List the five most interesting, controversial, or resonant ideas you found in the readings. Include page numbers and a short rationale (100 words) for your selection.
17. Advertisement
    • Create an ad, with visuals and text, for the newly learned concept.
18. 5 Words
    • What five words would you use to describe ______? Explain and justify your choices.
19. Muddy Moment
    • What frustrates and confuses you about the text? Why?
20. Collage
    • Create a collage around the lesson’s themes. Explain your choices in one paragraph.
21. Letter
    • Explain _______ in a letter to your best friend.
22. Talk Show Panel
    • Have a cast of experts debate the finer points of _______.
23. Study Guide
    • What are the main topics, supporting details, important person’s contributions, terms, and definitions?
24. Illustration
    • Draw a picture that illustrates a relationship between terms in the text. Explain in one paragraph your visual representation.
25. KWL Chart
    • What do you know, what do you want to know, and what have you learned?
26. Sticky Notes Annotation
    • Use sticky notes to describe key passages that are notable or that you have questions about.
27. 3-2-1
    • Three things you found out.
    • Two interesting things.
    • One question you still have.
28. Outline
    • Represent the organization of _______ by outlining it.
29. Anticipation Guide
    • Establish a purpose for reading and create post-reading reflections and discussion.
30. Simile
    • What we learned today is like _______.
31. The Minute Paper
    • In one minute, describe the most meaningful thing you’ve learned.
32. Interview You
    • You’re the guest expert on 60 Minutes. Answer:
      1. What are component parts of _______?
      2. Why does this topic matter?
33. Double Entry Notebook
    • Create a two-column table. Use the left column to write down 5-8 important quotations. Use the right column to record reactions to the quotations.
34. Comic Book
    • Use a comic book creation tool like Bitstrips to represent understanding.
35. Tagxedo
    • What are key words that express the main ideas? Be ready to discuss and explain.
36. Classroom TED Talk
37. Podcast
    • Play the part of a content expert and discuss content-related issues on a podcast, using the free Easypodcast.
38. Create a Multimedia Poster with Glogster
39. Twitter Post
    • Define _______ in under 140 characters.
40. Explain Your Solution
    • Describe how you solved an academic problem, step by step.
41. Dramatic Interpretation
    • Dramatize a critical scene from a complex narrative.
42. Ballad
    • Summarize a narrative that employs a poem or song structure using short stanzas.
43. Pamphlet
    • Describe the key features of _______ in a visually and textually compelling pamphlet.
44. Study Guide
    • Create a study guide that outlines main ideas.
45. Bio Poem
    • To describe a character or person, write a poem that includes:
      • (Line 1) First name
      • (Line 2) 3-4 adjectives that describe the person
      • (Line 3) Important relationship
      • (Line 4) 2-3 things, people, or ideas the person loved
      • (Line 5) Three feelings the person experienced
      • (Line 6) Three fears the person experienced
      • (Line 7) Accomplishments
      • (Line 8) 2-3 things the person wanted to see happen or wanted to experience
      • (Line 9) His or her residence
      • (Line 10) Last name
46. Sketch
    • Visually represent new knowledge.
47. Top Ten List
    • What are the most important takeaways, written with humor?
48. Color Cards
    • Red = “Stop, I need help.”
    • Green = “Keep going, I understand.”
    • Yellow = “I’m a little confused.”
49. Quickwrite
    • Without stopping, write what most confuses you.
50. Conference
    • A short, focused discussion between the teacher and student.
51. Debrief
    • Reflect immediately after an activity.
52. Exit Slip
    • Have students reflect on lessons learned during class.
53. Misconception Check
    • Given a common misconception about a topic, students explain why they agree or disagree with it.

Other Assessment Resources

In Edutopia’s The Power of Comprehensive Assessment, Bob Lenz describes how to create a balanced assessment system.

The American Federation of Teachers (AFT) describes dozens of Formative Assessment Strategies.

The Assessment and Rubrics page of Kathy Schrock’s Guide to Everything website hosts many excellent assessment rubrics.

More Rubrics for Assessment are provided by the University of Wisconsin-Stout.

Jon Mueller’s Authentic Tasks and Rubrics is a must see-resource in his Authentic Assessment Toolbox website.

In Teaching Algebra, the Not-So-Secret Way to Students’ Hearts

from http://blogs.kqed.org/mindshift/

Katrina Schwartz | December 9, 2013 | 

Education researchers are beginning to validate what many teachers have long known — connecting learning to student interests helps the information stick. This seems to work particularly well with math, a subject many students say they dislike because they can’t see its relevance to their lives.

“When I started spending time in classrooms I realized the math wasn’t being applied to the students’ world in a meaningful way,” said Candace Walkington, assistant professor in the department of teaching and learning at Southern Methodist University. She conducted a year-long study on 141 ninth graders at a Pennsylvania high school to see whether tailoring questions to individual student interests could help students learn difficult and often abstract algebra concepts.

“We picked out the students who seemed to be struggling the most in Algebra I and we found that for this sub-group of students personalization was more effective.”

Researchers studied a classroom usingCarnegie Learning software called Cognitive Tutor, a program that has been studied frequently. In the study, half of the students chose one of several categories that interested them — things like music, movies, sports, social media — and were given an algebra curriculum based on those topics. The other half received no interest-based personalization. All the problems had the same underlying structure and were meant to teach the same concept.

Walkington found that students who had received interest-based personalization mastered concepts faster. What’s more, in order to ensure that learning was robust, retained over time, and would accelerate future learning, she also looked at student performance in a later unit that had no interest-based personalization for any of the students. “Students that had previously received personalization, even though it was gone, were doing better on these more difficult problems as well,” said Walkington.

[RELATED: Nine Tenents of Passion Based Learning]

She also found that struggling students improved the most when their interests were taken into account. “We picked out the students who seemed to be struggling the most in Algebra I and we found that for this sub-group of students that were way behind the personalization was more effective,” Walkington said. Specifically, the study tested students’ ability to turn story problems into algebraic equations — what’s called algebraic expression writing.

“That’s one of the most challenging skills to teach students because it’s a very abstract skill,” Walkington said. She hypothesizes that the abstract nature of the concepts actually allowed students to more easily generalize and apply the same knowledge to a wide variety of situations and to more difficult problems in later units.

Walkington is working to expand her study to all the ninth graders in a school district of 9,000 students. “The bigger, you make it the harder it is to tap into the interests of students,” Walkington said. But she’s confident that there are some general-interest categories that many students share, like sports and movies.

WITHOUT TECHNOLOGY

But can this tactic help a teacher with a class of 30 students that doesn’t use this particular math software? Teachers in the studied school asked this question, so Walkington developed apractical guide for them to use. She chose to conduct the study using the Carnegie blended learning curriculum because it was easy to layer on the interest-based personalization to the existing program. It also provided her with a wealth of data about how students approached the problems. That said, a teacher could use interest-driven questions without any math software.

From her guide:

Two Examples of Personalization

Personalization can be accomplished on simple mathematics story problems. For example, a typical algebra problem might read: “A particular assembly line in an automobile company plant can produce thirteen cars every hour.” Based on this scenario, students might be asked to write an expression or solve for how many cars are produced after certain numbers of hours. Below are some examples of how this problem could be personalized:

Shopping: The website of your favorite clothing store, Hot Topic, sells thirteen superhero t-shirts every hour.

Computers: A recent video blog you posted about your life on YouTube gets thirteen hits every hour.

Food: Your favorite restaurant “Steak ‘n Shake” sells thirteen caramel pretzel shakes every hour.

Music: Pandora Internet radio plays thirteen of your favorite pop songs every hour.

Cell Phones:  On your new iPhone 5 you send your best friend thirteen texts every hour.

While these problems involve relatively simple modifications, our research has shown that this type of personalization is effective for improving student learning.

 

[RELATED: How the Power of Interest Drives Learning]

Helping students see algebra in their daily lives is one way to apply this technique. In the same way, video games have point systems that allow players to level up after they’ve won a certain number of points. Students understand these systems intimately, but aren’t often asked to think about them through the lens of algebra. Similarly, students have a sense of how often they text and how their texting habits compare to others, but they aren’t often asked to express that relationship in an equation. Helping students to see the math in their own lives could get them thinking differently.

Another way teachers can personalize algebra would be to ask questions that are likely to appeal to student interests. Walkington found that students find story problems that deal with social issues of communicating with family and friends accessible. Concepts of work and business were less accessible, as were problems that dealt with physics concepts like motion, time, and space. Problems based on home references like pets were more interesting to students and garnered better results. Using these broad guidelines, teachers can try to write questions that appeal to more students.

Walkington has also experimented with having students personalize their own math instruction, writing, sharing and solving story problems in small groups. She’s found that even students with relatively little math knowledge can create complex story problems and express them with algebra if there’s interest in the topic. This is a great way to have students construct their own knowledge while applying it to their passions.

A great time to use this tactic is when introducing an abstract idea or foundational topic in algebra. That’s when educators will see the most benefit of grounding the topic in student interests, Walkington said. It’s important to elicit student interest in the math concepts, however, and not just the question’s topic. This intervention could work well with struggling students too.

“We have to layer the algebra onto those relationships that already exist,” Walkington said. “And that’s not an obvious thing because it doesn’t look anything like algebra at first. It just looks like a relationship.” She’s confident from her own experience of learning to love math that when students see its applicability to things they care about, they learn more easily and deeply.

Success in Mathematics Study Tips

Tips on how to study mathematics, how to approach problem-solving, how to study for and take tests, and when and how to get help.

Math Study Skills

Active Study vs. Passive Study

Be actively involved in managing the learning process, the mathematics and your study time:

• Take responsibility for studying, recognizing what you do and don’t know, and knowing how to get your Instructor to help you with what you don’t know.
• Attend class every day and take complete notes. Instructors formulate test questions based on material and examples covered in class as well as on those in the text.
• Be an active participant in the classroom. Get ahead in the book; try to work some of the problems before they are covered in class. Anticipate what the Instructor’s next step will be.
• Ask questions in class! There are usually other students wanting to know the answers to the same questions you have.
• Go to office hours and ask questions. The Instructor will be pleased to see that you are interested, and you will be actively helping yourself.
• Good study habits throughout the semester make it easier to study for tests.

 

Studying Math is Different from Studying Other Subjects

• Math is learned by doing problems. Do the homework. The problems help you learn the formulas and techniques you do need to know, as well as improve your problem-solving prowess.
• A word of warning: Each class builds on the previous ones, all semester long. You must keep up with the Instructor: attend class, read the text and do homework every day. Falling a day behind puts you at a disadvantage. Falling a week behind puts you in deep trouble.
• A word of encouragement: Each class builds on the previous ones, all semester long. You’re always reviewing previous material as you do new material. Many of the ideas hang together. Identifying and learning the key concepts means you don’t have to memorize as much.

 

College Math is Different from High School Math

A College math class meets less often and covers material at about twice the pace that a High School course does. You are expected to absorb new material much more quickly. Tests are probably spaced farther apart and so cover more material than before. The Instructor may not even check your homework.

• Take responsibility for keeping up with the homework. Make sure you find out how to do it.
• You probably need to spend more time studying per week – you do more of the learning outside of class than in High School.
• Tests may seem harder just because they cover more material.

 

Study Time

You may know a rule of thumb about math (and other) classes: at least 2 hours of study time per class hour. But this may not be enough!

• Take as much time as you need to do all the homework and to get complete understanding of the material.
• Form a study group. Meet once or twice a week (also use the phone). Go over problems you’ve had trouble with. Either someone else in the group will help you, or you will discover you’re all stuck on the same problems. Then it’s time to get help from your Instructor.
• The more challenging the material, the more time you should spend on it.

Problem Solving

Problem Solving (Homework and Tests)

• The higher the math class, the more types of problems: in earlier classes, problems often required just one step to find a solution. Increasingly, you will tackle problems which require several steps to solve them. Break these problems down into smaller pieces and solve each piece – divide and conquer!
• Problem types:

1. Problems testing memorization (“drill”),
2. Problems testing skills (“drill”),
3. Problems requiring application of skills to familiar situations (“template” problems),
4. Problems requiring application of skills to unfamiliar situations (you develop a strategy for a new problem type),
5. Problems requiring that you extend the skills or theory you know before applying them to an unfamiliar situation.

In early courses, you solved problems of types 1, 2 and 3. By College Algebra you expect to do mostly problems of types 2 and 3 and sometimes of type 4. Later courses expect you to tackle more and more problems of types 3 and 4, and (eventually) of type 5. Each problem of types 4 or 5 usually requires you to use a multi-step approach, and may involve several different math skills and techniques.

• When you work problems on homework, write out complete solutions, as if you were taking a test. Don’t just scratch out a few lines and check the answer in the back of the book. If your answer is not right, rework the problem; don’t just do some mental gymnastics to convince yourself that you could get the correct answer. If you can’t get the answer, get help.
• The practice you get doing homework and reviewing will make test problems easier to tackle.

 

Tips on Problem Solving

• Apply Pólya’s four-step process:

1. The first and most important step in solving a problem is to understand the problem, that is, identify exactly which quantity the problem is asking you to find or solve for (make sure you read the whole problem).
2. Next you need to devise a plan, that is, identify which skills and techniques you have learned can be applied to solve the problem at hand.
3. Carry out the plan.
4. Look back: Does the answer you found seem reasonable? Also review the problem and method of solution so that you will be able to more easily recognize and solve a similar problem.

• Some problem-solving strategies: use one or more variables, complete a table, consider a special case, look for a pattern, guess and test, draw a picture or diagram, make a list, solve a simpler related problem, use reasoning, work backward, solve an equation, look for a formula, use coordinates.

 

“Word” Problems are Really “Applied” Problems

The term “word problem” has only negative connotations. It’s better to think of them as “applied problems”. These problems should be the most interesting ones to solve. Sometimes the “applied” problems don’t appear very realistic, but that’s usually because the corresponding real applied problems are too hard or complicated to solve at your current level. But at least you get an idea of how the math you are learning can help solve actual real-world problems.

 

Solving an Applied Problem

• First convert the problem into mathematics. This step is (usually) the most challenging part of an applied problem. If possible, start by drawing a picture. Label it with all the quantities mentioned in the problem. If a quantity in the problem is not a fixed number, name it by a variable. Identify the goal of the problem. Then complete the conversion of the problem into math, i.e., find equations which describe relationships among the variables, and describe the goal of the problem mathematically.
• Solve the math problem you have generated, using whatever skills and techniques you need (refer to the four-step process above).
• As a final step, you should convert the answer of your math problem back into words, so that you have now solved the original applied problem.

For Further Reading:
George Pólya, How to Solve It,Princeton University Press, Princeton (1945)

Studying for a Math Test

Everyday Study is a Big Part of Test Preparation

Good study habits throughout the semester make it easier to study for tests.

• Do the homework when it is assigned. You cannot hope to cram 3 or 4 weeks worth of learning into a couple of days of study.
• On tests you have to solve problems; homework problems are the only way to get practice. As you do homework, make lists of formulas and techniques to use later when you study for tests.
• Ask your Instructor questions as they arise; don’t wait until the day or two before a test. The questions you ask right before a test should be to clear up minor details.

 

Studying for a Test

• Start by going over each section, reviewing your notes and checking that you can still do the homework problems (actually work the problems again). Use the worked examples in the text and notes – cover up the solutions and work the problems yourself. Check your work against the solutions given.

 

• You’re not ready yet! In the book each problem appears at the end of the section in which you learned how do to that problem; on a test the problems from different sections are all together.
  • Step back and ask yourself what kind of problems you have learned how to solve, what techniques of solution you have learned, and how to tell which techniques go with which problems.
  • Try to explain out loud, in your own words, how each solution strategy is used (e.g. how to solve a quadratic equation). If you get confused during a test, you can mentally return to your verbal “capsule instructions”. Check your verbal explanations with a friend during a study session (it’s more fun than talking to yourself!).
  • Put yourself in a test-like situation: work problems from review sections at the end of chapters, and work old tests if you can find some. It’s important to keep working problems the whole time you’re studying.
  • Also:
    • Start studying early. Several days to a week before the test (longer for the final), begin to allot time in your schedule to reviewing for the test.
    • Get lots of sleep the night before the test. Math tests are easier when you are mentally sharp.

Taking a Math Test

Test-Taking Strategy Matters

Just as it is important to think about how you spend your study time (in addition to actually doing the studying), it is important to think about what strategies you will use when you take a test (in addition to actually doing the problems on the test). Good test-taking strategy can make a big difference to your grade!

 

Taking a Test

• First look over the entire test. You’ll get a sense of its length. Try to identify those problems you definitely know how to do right away, and those you expect to have to think about.
• Do the problems in the order that suits you! Start with the problems that you know for sure you can do. This builds confidence and means you don’t miss any sure points just because you run out of time. Then try the problems you think you can figure out; then finally try the ones you are least sure about.
• Time is of the essence – work as quickly and continuously as you can while still writing legibly and showing all your work. If you get stuck on a problem, move on to another one – you can come back later.
• Work by the clock. On a 50 minute, 100 point test, you have about 5 minutes for a 10 point question. Starting with the easy questions will probably put you ahead of the clock. When you work on a harder problem, spend the allotted time (e.g., 5 minutes) on that question, and if you have not almost finished it, go on to another problem. Do not spend 20 minutes on a problem which will yield few or no points when there are other problems still to try.
• Show all your work: make it as easy as possible for the Instructor to see how much you do know. Try to write a well-reasoned solution. If your answer is incorrect, the Instructor will assign partial credit based on the work you show.
• Never waste time erasing! Just draw a line through the work you want ignored and move on. Not only does erasing waste precious time, but you may discover later that you erased something useful (and/or maybe worth partial credit if you cannot complete the problem). You are (usually) not required to fit your answer in the space provided – you can put your answer on another sheet to avoid needing to erase.
• In a multiple-step problem outline the steps before actually working the problem.
• Don’t give up on a several-part problem just because you can’t do the first part. Attempt the other part(s) – if the actual solution depends on the first part, at least explain how you would do it.
• Make sure you read the questions carefully, and do all parts of each problem.
• Verify your answers – does each answer make sense given the context of the problem?
• If you finish early, check every problem (that means rework everything from scratch).

Getting Assistance

When

Get help as soon as you need it. Don’t wait until a test is near. The new material builds on the previous sections, so anything you don’t understand now will make future material difficult to understand.

 

Use the Resources You Have Available

• Ask questions in class. You get help and stay actively involved in the class.
• Visit the Instructor’s Office Hours. Instructors like to see students who want to help themselves.
• Ask friends, members of your study group, or anyone else who can help. The classmate who explains something to you learns just as much as you do, for he/she must think carefully about how to explain the particular concept or solution in a clear way. So don’t be reluctant to ask a classmate.
• Go to the Math Help Sessions or other tutoring sessions on campus.
• Find a private tutor if you can’t get enough help from other sources.
• All students need help at some point, so be sure to get the help you need.

 

Asking Questions

Don’t be afraid to ask questions. Any question is better than no question at all (at least your Instructor/tutor will know you are confused). But a good question will allow your helper to quickly identify exactly what you don’t understand.

• Not too helpful comment: “I don’t understand this section.” The best you can expect in reply to such a remark is a brief review of the section, and this will likely overlook the particular thing(s) which you don’t understand.
• Good comment: “I don’t understand why f(x + h) doesn’t equal f(x) + f(h).” This is a very specific remark that will get a very specific response and hopefully clear up your difficulty.
• Good question: “How can you tell the difference between the equation of a circle and the equation of a line?”
• Okay question: “How do you do #17?”
• Better question: “Can you show me how to set up #17?” (the Instructor can let you try to finish the problem on your own), or “This is how I tried to do #17. What went wrong?” The focus of attention is on your thought process.
• Right after you get help with a problem, work another similar problem by yourself.

 

You Control the Help You Get

Helpers should be coaches, not crutches. They should encourage you, give you hints as you need them, and sometimes show you how to do problems. But they should not, nor be expected to, actually do the work youneed to do. They are there to help you figure out how to learn math for yourself.

• When you go to office hours, your study group or a tutor, have a specific list of questions prepared in advance. You should run the session as much as possible.
• Do not allow yourself to become dependent on a tutor. The tutor cannot take the exams for you. You must take care to be the one in control of tutoring sessions.
• You must recognize that sometimes you do need some coaching to help you through, and it is up to you to seek out that coaching.

Department of Mathematics and Computer Science
SAINT LOUIS UNIVERSITY
June 1993

You can bring the Magic of Math to your school this 2014 school year!!

The Math Magician

https://www.facebook.com/pages/Math-Magician/272971359454909

http://www.odysseylearningadventures.com/

Does your school need a boost in mathematics?

Do your students need some math motivation?

Do your teachers need some new ideas in math?

Does your school need a memorable event focused on your math improvement goals?

You can bring the Magic of Math to your school this 2014 school year!!

Bob Bishop, America’s Math Magician, is back  with a newer, larger and more exciting program for 2014!

Math Magic Family Night program!!

Math should be fun, entertaining, challenging, and memorable.

The Math Magician’s programs are interactive, informative, fun  and definitely memorable!!

Total audience involvement for the entire school family!!

Participants will learn about:

•  The power and importance of mathematics
• The magic of probabilities
•  The magic of equality
•  The power of the mind and effort to achieve school success
•  The adventure and excitement of mathematics
• The power of perseverance in school
•  Escaping from Brain Chains
•  The power of  Additude

The Math Magician can visit your school and teach students, teachers and coordinate a family Magic of Math evening.  But because of availability this is on a first come first serve basis. 
Book him now!!

His schedule fills up quickly!

Contact Bob Bishop The Math Magician at:
odysseylearningadventures@gmail.com
http://www.facebook.com/pages/Math-Magician

“I have never seen my students more spellbound for 60 minutes as they were for Bob Bishop, the Math-Magician. His program generated many interesting discussions later in the classroom setting.””Mr. Bishop’s activities make math an exciting mind expanding experience.”

“I thought it was very well thought out, rich with ideas and materials, and enjoyable.”

“Fast paced with a wealth of useful information.”

“Wonderful activities to use with my students. Right on target!”

As you know, Bob Bishop has been known as Idaho’s Math Magician for more than 20 years. He has gained media notoriety as the Math Magician from television to countless newspaper articles (including the Idaho Statesman Life Section). He has won many awards for teaching and his students have also won many scholarly awards. He was awarded the GEM award for teaching Idaho’s gifted students. He has taught the gifted students in Boise for 15 years, has helped coordinate Micron’s Math Meet, has taught BSU and NNU classes in teacher development in mathematics, has taught for the Bureau of Education (BER), is a certified in Brain-based educator, has taught ICTM math conventions and Edu-fest gifted conference for 17 years. He has presented to teachers and students from Boston to Los Angeles to Taiwan to California, and in Idaho.

Education leaders in Idaho consistently hear from employers and colleges and universities in Idaho that Idaho students do not have the math skills they need to succeed in the work force or a postsecondary education setting when they graduate from high school. Scores on statewide assessments also show a troubling trend in math as students move through our K-12 system: Therefore, we must improve math education across all grades in Idaho to ensure we prepare every student to live, work and succeed in the 21st century.

“I have a vision to visit every elementary classroom  to help equip teachers and students with the art and joy of learning mathematics. There are many bored, non-engaged students who have a lack of understanding in numeracy skills. What I would like to offer is the Magic of Math to change attitudes and to ignite motivation for math success.”

Bob has coordinated his Family Math nights for more than 20 years. And for a selected few schools he will come for a week-long resident Math Magician. Bob would visit every classroom and give unique student workshops that blend hands-on activities, interactive games, and math magic that the teachers can build upon. He would also provide inservice training for the teachers by providing state and nationally aligned games and activities that will empower teachers with methods to teach the curriculum in motivating and memorable ways.

No other program comes close to the benefits of the Magic of Math!

Contact Bob Bishop, The Math Magician

odysseylearningadventures@gmail.com

http://www.odysseylearningadventures.com

http://www.facebook.com/pages/Math-Magician

208-921-7981

Motivation

Motivation for students to succeed in math.

Attitude

Attitude change in students for mathematics.

Guidance

Guidance for teacher effectiveness and student improvement.

Innovative

Innovative teaching ideas.

Competency

Competency and confidence in mathematics.

The Cost?

Family Math Night $700

Math Magic week: $500 a day of 50-60 min. classes. Teacher inservices $300 plus price of workbooks.

Be sure you ask how Tutor Doctor can help sponsor this event!!

“In my experience working with students I have noticed a continued weakness in math skills and a need to teach math in a way that will inspire elementary students to love math at an early age. “The idea that would help address this need and dovetail with your schools  Math Goals is a hands-on interactive school program for all elementary school age students. It is a vision of bringing the Magic of Math programs to every elementary classroom in Idaho to help equip teachers and students with the joy of learning and teaching mathematics. ”

What the Math Magician offers is an additional boost of excitement and enthusiasm for math.

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Magic Castle of Hollywood
Fox News
Saint Alphonsus Festival of Trees
Special Olympics World Games Fund Raiser Banquet
Muscular Dystrophy Association
Camp River Run (for kids with life threatening illnesses)
Funny Bone Comedy Club
Boise State University
Edu-fest Conference for Teachers of the Gifted Banquet
Council of Exceptional Children Teachers Banquet
Morrison Academy Schools (Taiwan)
Thunder Mountain Railroad
Boise Little Theater Public Show
Boise State University
Boy Scouts of America
Double Tree Riverside Hotel
Hewlett-Packard
Boise School District Schools
Meridian Joint School District

Boys and Girls Club of Ada Cty
Boys and Girls Club of America
Boys and Girls Club of Nampa
Boise Family YMCA
Caldwell Family YMCA
Homecourt YMCA
West Family YMCA
Applebee’s Restaurant
Chili’s Grill & Bar Restaurant
On the Border Restaurant
Boise Hawks
Awana Clubs
Boise Public Library
Boy Scouts of America (Boise)
Discovery Center of Idaho
Just For Kids Daycare
MagicFest of Twin Falls
Overland Park Cinema

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Math Magician helps Students to Want to Study Numbers USA

POCATELLO, IDAHO – A new spin has been put on mathematics as Tendoy Elementary students use some magic to study various math concepts.

Bob Bishop, the Math Magician, has delighted students in kindergarten through sixth grade and teachers with his magic skills and math abilities over the past week.

“Math is so necessary in life,” he said. “It’s not just making math fun, but it’s also trying to attach some sense of understanding for students.”

Fifth grade teacher Vicki Reeder’s class had the opportunity to spend some time with Bishop while working on problem solving skills. Students worked with calculators, the box of magic, learned how to do multiplication tables with their fingers, played a game called Fast and Loose and other activities.

During a game of fast and loose, Bishop produced a single chain and proceeded to fold it into a series of loops. Students were asked to pick a loop and place their finger inside it. If they had guessed correctly the loop would stay around their finger. However, if they guessed incorrectly, the loop would slip away.

“You will win if you know mathematics, but you’ll lose if you don’t,” Bishop said.

Students learned how to follow the loops and determine the correct place to put their fingers.

Bishop has been performing for students and other audiences for 20 years and says he continually teaches students and teachers how math can be fun.

He said many students work with arithmetic but don’t fully understand problem solving skills.

With the help of a little magic, students are forced to observe the environment around them for any changes and think about possible outcomes.

“Generally students don’t really care to do math because it’s not fun,” Bishop said. “By making it interesting and proving to them they can do it, it helps to raise their self-esteem and interest level in math.”

Bishop will perform along with Tendoy Elementary students at 6:30 p.m. today for a Math Night.

Fifth grade student Quinci Shelley is acting as Bishop’s assistant during the show and said she can’t wait to perform for other students.

“I think it’s cool and it’s a good opportunity for us,” she said. “Some people don’t like math, but when they see this show it sparks their interest.”

Fifth grade student Brant Leo will lead the audience in applause, but said working with Bishop has been great because he’s learned new things.

“He’s helping students to improve their math by using cool tricks,” he said.

“Bob Bishop is a creative and a genius at making math fun. “

“By making math fun, students will learn to enjoy it more and it will give them a sense of pride as they figure out difficult problems,” he said.

WHAT YOUR COLLEAGUES SAY ABOUT BOB BISHOP

“This has been the most energizing seminar I have ever attended in 37 years as a teacher. The book is absolutely awesome and every page is a true gem. I’ve been feeling very burned out but now I feel that I can do my best again. I wish all my administrators and teachers could benefit from Bob’s energy and message. Thank you for letting me see that there are still educators who believe in children as people and not as numbers on a chart. I have decided not to retire!”
Diena Hurtado Teacher, Anaheim, California

“Bob has a unique way on engaging his audience- whether they are children or adults. They are captivated by his humor, his intelligence, and gentle manner. Bob teaches in such a way that the participants don’t even realize they are being challenged and taught something at the same time. I would attend any workshop or class Bob taught, knowing that I will come away with more skills and knowledge than when I walked in– and have fun while doing it!”
Sue March 6th grade Cynthia Mann Elementary

“When Bob Bishop teachers he is articulate, expressive, and engages the learner in the adventure and discovery of learning. Young or old, Bob Bishop prompts the learner into new territory where learning is once again, fun, worthwhile, relevant, and meaningful.”
Scott Ziemer Teacher/Counselor

“The exposure to the wit and wisdom of Bob Bishop has indelibly impressed upon me his dedication to his students and effective teaching, his commitment to include humor in his presentations and personal interactions, and his personal high standards of achievement for himself and his students. Observing Bob will stimulate recollections of Socrates and Aristotle-Socrates for his incessant use of questions, and Aristotle for his demand for evidence for student opinions.”
Larry Rogien Education Dept. Head Boise State University

“Bob Bishop’s special skills as an educator, creative teacher, author, curriculum developer and professional magician put everything he teaches into sharp focus. His research abilities, creative style, high energy deliveries, practical applications and humor make him a sought-after presenter. This mixture of experience as a magician and educator makes his presentations a unique blend of entertainment and sound pedagogy. When you watch Bob, it is obvious that his desire goes beyond entertainment and instruction. Watching him work with a group of students, mixing magic and mathematics, is to be amazed at his ability to completely involve a very difficult audience. Nick Johnson Middle school teacher/ President of Math-Explosion

“Bob Bishop, math wizard extraordinaire, presented his hallmark math antics, games, and puzzles before parents and students at our first family math night. The cafetorium was packed with kids having fun with numbers. We gave Bob and the event a 10. The kids loved the wizard and so did we!”
Debbie Hertzog PTA President Seven Oaks Elementary

“Fantastic! Captivating! Challenging! Thorough! Creative! Very Knowledgeable! Humorous! Engaging! Committed! Gifted and talented teacher. Bob Bishop is a master teacher who makes learning come alive for his students. He can take any topic and present it in a way that allows new insights. Prepare to be both challenged and entertained.”
Cheryl Richardson Hillcrest GATE Center

“Bob’s fast paced yet calm presentations sparkle with wit and humor. His years of classroom experience and connection with children are reflected in examples to which every teacher relates. He applies his in-depth knowledge of brain-based learning in his classroom and in his presentations. Bob is a unique presenter. You will remember this presentation and use the material in it.”
Rita Hoffman, Gifted Program Supervisor, Boise School District

“Bob is energizing, motivating and …fun!!!! He makes you think, analyze, debate, and enjoy all at the same time. A session with Mr. Bishop is always worth attending because you never leave ‘empty minded’.”
Linda Stokes GATE teacher Collister Elementary School

“Bob Bishop is an amazing educator! He brilliantly enriches the lives of all children and freely gives of his time. He engages all learners in exciting, stimulating, and challenging activities that motivates, enriches, and develops their love of learning.”
Jaci Guilford 4th grade teacher

In Teaching Algebra, the Not-So-Secret Way to Students’ Hearts

• Katrina Schwartz | December 9, 2013 

Ed Yourdon/Flickr

Education researchers are beginning to validate what many teachers have long known — connecting learning to student interests helps the information stick. This seems to work particularly well with math, a subject many students say they dislike because they can’t see its relevance to their lives.

“When I started spending time in classrooms I realized the math wasn’t being applied to the students’ world in a meaningful way,” said Candace Walkington, assistant professor in the department of teaching and learning at Southern Methodist University. She conducted a year-long study on 141 ninth graders at a Pennsylvania high school to see whether tailoring questions to individual student interests could help students learn difficult and often abstract algebra concepts.

“We picked out the students who seemed to be struggling the most in Algebra I and we found that for this sub-group of students personalization was more effective.”

Researchers studied a classroom usingCarnegie Learning software called Cognitive Tutor, a program that has been studied frequently. In the study, half of the students chose one of several categories that interested them — things like music, movies, sports, social media — and were given an algebra curriculum based on those topics. The other half received no interest-based personalization. All the problems had the same underlying structure and were meant to teach the same concept.

Walkington found that students who had received interest-based personalization mastered concepts faster. What’s more, in order to ensure that learning was robust, retained over time, and would accelerate future learning, she also looked at student performance in a later unit that had no interest-based personalization for any of the students. “Students that had previously received personalization, even though it was gone, were doing better on these more difficult problems as well,” said Walkington.

[RELATED: Nine Tenents of Passion Based Learning]

She also found that struggling students improved the most when their interests were taken into account. “We picked out the students who seemed to be struggling the most in Algebra I and we found that for this sub-group of students that were way behind the personalization was more effective,” Walkington said. Specifically, the study tested students’ ability to turn story problems into algebraic equations — what’s called algebraic expression writing.

“That’s one of the most challenging skills to teach students because it’s a very abstract skill,” Walkington said. She hypothesizes that the abstract nature of the concepts actually allowed students to more easily generalize and apply the same knowledge to a wide variety of situations and to more difficult problems in later units.

Walkington is working to expand her study to all the ninth graders in a school district of 9,000 students. “The bigger, you make it the harder it is to tap into the interests of students,” Walkington said. But she’s confident that there are some general-interest categories that many students share, like sports and movies.

WITHOUT TECHNOLOGY

But can this tactic help a teacher with a class of 30 students that doesn’t use this particular math software? Teachers in the studied school asked this question, so Walkington developed a practical guide for them to use. She chose to conduct the study using the Carnegie blended learning curriculum because it was easy to layer on the interest-based personalization to the existing program. It also provided her with a wealth of data about how students approached the problems. That said, a teacher could use interest-driven questions without any math software.

From her guide:

Two Examples of Personalization

Personalization can be accomplished on simple mathematics story problems. For example, a typical algebra problem might read: “A particular assembly line in an automobile company plant can produce thirteen cars every hour.” Based on this scenario, students might be asked to write an expression or solve for how many cars are produced after certain numbers of hours. Below are some examples of how this problem could be personalized:

Shopping: The website of your favorite clothing store, Hot Topic, sells thirteen superhero t-shirts every hour.

Computers: A recent video blog you posted about your life on YouTube gets thirteen hits every hour.

Food: Your favorite restaurant “Steak ‘n Shake” sells thirteen caramel pretzel shakes every hour.

Music: Pandora Internet radio plays thirteen of your favorite pop songs every hour.

Cell Phones:  On your new iPhone 5 you send your best friend thirteen texts every hour.

While these problems involve relatively simple modifications, our research has shown that this type of personalization is effective for improving student learning.

 

[RELATED: How the Power of Interest Drives Learning]

Helping students see algebra in their daily lives is one way to apply this technique. In the same way, video games have point systems that allow players to level up after they’ve won a certain number of points. Students understand these systems intimately, but aren’t often asked to think about them through the lens of algebra. Similarly, students have a sense of how often they text and how their texting habits compare to others, but they aren’t often asked to express that relationship in an equation. Helping students to see the math in their own lives could get them thinking differently.

Another way teachers can personalize algebra would be to ask questions that are likely to appeal to student interests. Walkington found that students find story problems that deal with social issues of communicating with family and friends accessible. Concepts of work and business were less accessible, as were problems that dealt with physics concepts like motion, time, and space. Problems based on home references like pets were more interesting to students and garnered better results. Using these broad guidelines, teachers can try to write questions that appeal to more students.

Walkington has also experimented with having students personalize their own math instruction, writing, sharing and solving story problems in small groups. She’s found that even students with relatively little math knowledge can create complex story problems and express them with algebra if there’s interest in the topic. This is a great way to have students construct their own knowledge while applying it to their passions.

A great time to use this tactic is when introducing an abstract idea or foundational topic in algebra. That’s when educators will see the most benefit of grounding the topic in student interests, Walkington said. It’s important to elicit student interest in the math concepts, however, and not just the question’s topic. This intervention could work well with struggling students too.

“We have to layer the algebra onto those relationships that already exist,” Walkington said. “And that’s not an obvious thing because it doesn’t look anything like algebra at first. It just looks like a relationship.” She’s confident from her own experience of learning to love math that when students see its applicability to things they care about, they learn more easily and deeply.

The Myth of ‘I’m Bad at Math’

Basic ability in the subject isn’t the product of good genes, but hard work.

MILES KIMBALL & NOAH SMITHOCT 28 2013, 10:30 AM ET

doviende/Flickr

“I’m just not a math person.”

We hear it all the time. And we’ve had enough. Because we believe that the idea of “math people” is the most self-destructive idea in America today. The truth is, you probably are a math person, and by thinking otherwise, you are possibly hamstringing your own career. Worse, you may be helping to perpetuate a pernicious myth that is harming underprivileged children—the myth of inborn genetic math ability.

Is math ability genetic? Sure, to some degree. Terence Tao, UCLA’s famous virtuoso mathematician, publishes dozens of papers in top journals every year, and is sought out by researchers around the world to help with the hardest parts of their theories. Essentially none of us could ever be as good at math as Terence Tao, no matter how hard we tried or how well we were taught. But here’s the thing: We don’t have to! For high-school math, inborn talent is much less important than hard work, preparation, and self-confidence.

How do we know this? First of all, both of us have taught math for many years—as professors, teaching assistants, and private tutors. Again and again, we have seen the following pattern repeat itself:

1. Different kids with different levels of preparation come into a math class. Some of these kids have parents who have drilled them on math from a young age, while others never had that kind of parental input.
2. On the first few tests, the well-prepared kids get perfect scores, while the unprepared kids get only what they could figure out by winging it—maybe 80 or 85%, a solid B.
3. The unprepared kids, not realizing that the top scorers were well-prepared, assume that genetic ability was what determined the performance differences. Deciding that they “just aren’t math people,” they don’t try hard in future classes, and fall further behind.
4. The well-prepared kids, not realizing that the B students were simply unprepared, assume that they are “math people,” and work hard in the future, cementing their advantage.

Thus, people’s belief that math ability can’t change becomes a self-fulfilling prophecy.

The idea that math ability is mostly genetic is one dark facet of a larger fallacy that intelligence is mostly genetic. Academic psychology journals are well stocked with papers studying the world view that lies behind the kind of self-fulfilling prophecy we just described. For example, Purdue University psychologist Patricia Linehan writes:

A body of research on conceptions of ability has shown two orientations toward ability. Students with an Incremental orientation believe ability (intelligence) to be malleable, a quality that increases with effort. Students with an Entity orientation believe ability to be nonmalleable, a fixed quality of self that does not increase with effort.

The “entity orientation” that says “You are smart or not, end of story,” leads to bad outcomes—a result that has been confirmed by many other studies. (The relevance for math is shown by researchers at Oklahoma City who recently found that belief in inborn math ability may be responsible for much of the gender gap in mathematics.)

Psychologists Lisa Blackwell, Kali Trzesniewski, and Carol Dweck presented these alternatives to determine people’s beliefs about intelligence:

1. You have a certain amount of intelligence, and you really can’t do much to change it.
2. You can always greatly change how intelligent you are.

They found that students who agreed that “You can always greatly change how intelligent you are” got higher grades. But as Richard Nisbett recounts in his bookIntelligence and How to Get It, they did something even more remarkable:

Dweck and her colleagues then tried to convince a group of poor minority junior high school students that intelligence is highly malleable and can be developed by hard work…that learning changes the brain by forming new…connections and that students are in charge of this change process.

The results? Convincing students that they could make themselves smarter by hard work led them to work harder and get higher grades. The intervention had the biggest effect for students who started out believing intelligence was genetic. (A control group, who were taught how memory works, showed no such gains.)

Giving grades was not the most dramatic effect, “Dweck reported that some of her tough junior high school boys were reduced to tears by the news that their intelligence was substantially under their control.” It is no picnic going through life believing you were born dumb—and are doomed to stay that way.

For almost everyone, believing that you were born dumb—and are doomed to stay that way—is believing a lie. IQ itself can improve with hard work. Because the truth may be hard to believe, here is a set of links about some excellent books to convince you that most people can become smart in many ways, if they work hard enough:

• The Art of Learning by Josh Weitzkin
• Moonwalking with Einstein by Joshua Foer
• The Talent Code by Daniel Coyle
• Talent is Overrated by Geoff Colvin

So why do we focus on math? For one thing, math skills are increasingly important for getting good jobs these days—so believing you can’t learn math is especially self-destructive. But we also believe that math is the area where America’s “fallacy of inborn ability” is the most entrenched. Math is the great mental bogeyman of an unconfident America. If we can convince you that anyone can learn math, it should be a short step to convincing you that you can learn just about anything, if you work hard enough.

Is America more susceptible than other nations to the dangerous idea of genetic math ability? Here our evidence is only anecdotal, but we suspect that this is the case. While American fourth and eighth graders score quite well in international math comparisons—beating countries like Germany, the UK and Sweden—our high-schoolers  underperform those countries by a wide margin. This suggests that Americans’ native ability is just as good as anyone’s, but that we fail to capitalize on that ability through hard work. In response to the lackluster high school math performance, some influential voices in American education policy have suggested simply teaching less math—for example, Andrew Hacker has called for algebra to no longer be a requirement. The subtext, of course, is that large numbers of American kids are simply not born with the ability to solve for x.

We believe that this approach is disastrous and wrong. First of all, it leaves many Americans ill-prepared to compete in a global marketplace with hard-working foreigners. But even more importantly, it may contribute to inequality. A great deal of research has shown that technical skills in areas like software are increasingly making the difference between America’s upper middle class and its working class. While we don’t think education is a cure-all for inequality, we definitely believe that in an increasingly automated workplace, Americans who give up on math are selling themselves short.

Too many Americans go through life terrified of equations and mathematical symbols. We think what many of them are afraid of is “proving” themselves to be genetically inferior by failing to instantly comprehend the equations (when, of course, in reality, even a math professor would have to read closely). So they recoil from anything that looks like math, protesting: “I’m not a math person.” And so they exclude themselves from quite a few lucrative career opportunities. We believe that this has to stop. Our view is shared by economist and writer Allison Schrager, who has written two wonderful columns in Quartz(here and here), that echo many of our views.

One way to help Americans excel at math is to copy the approach of the Japanese, Chinese, and Koreans.  In Intelligence and How to Get It, Nisbett describes how the educational systems of East Asian countries focus more on hard work than on inborn talent:

1. “Children in Japan go to school about 240 days a year, whereas children in the United States go to school about 180 days a year.”
2. “Japanese high school students of the 1980s studied 3 ½ hours a day, and that number is likely to be, if anything, higher today.”
3. “[The inhabitants of Japan and Korea] do not need to read this book to find out that intelligence and intellectual accomplishment are highly malleable. Confucius set that matter straight twenty-five hundred years ago.”
4. “When they do badly at something, [Japanese, Koreans, etc.] respond by working harder at it.”
5. “Persistence in the face of failure is very much part of the Asian tradition of self-improvement. And [people in those countries] are accustomed to criticism in the service of self-improvement in situations where Westerners avoid it or resent it.”

We certainly don’t want America’s education system to copy everything Japan does (and we remain agnostic regarding the wisdom of Confucius). But it seems to us that an emphasis on hard work is a hallmark not just of modern East Asia, but of America’s past as well. In returning to an emphasis on effort, America would be returning to its roots, not just copying from successful foreigners.

Besides cribbing a few tricks from the Japanese, we also have at least one American-style idea for making kids smarter: treat people who work hard at learning as heroes and role models. We already venerate sports heroes who make up for lack of talent through persistence and grit; why should our educational culture be any different?

Math education, we believe, is just the most glaring area of a slow and worrying shift. We see our country moving away from a culture of hard work toward a culture of belief in genetic determinism. In the debate between “nature vs. nurture,” a critical third element—personal perseverance and effort—seems to have been sidelined. We want to bring it back, and we think that math is the best place to start.

“I Can’t Do This!” The Biggest Lie Students Tell Me (and How to Turn It Around)

The Biggest Lie Students Tell Me (and How to Turn It Around)

OCTOBER 22, 2013

Image credit: giovanni_novara via flickr (CC BY-NC-SA 2.0)

It’s easy to say that students lie to teachers all the time. Frankly, everyone, including teachers, has a lie in them, and these untruths keep the schooling process rolling along. When adults say, for instance, that they develop rules with the students, chances are that students often develop rules that teachers already thought of anyway. Or, when adults say that a student can’t use the restroom during certain parts of the day “Just because,” rather than “Because the hallways is crowded, and I don’t want you distracted from the lesson in the classroom,” that’s just one more micro-fib in a collage of fibs that we tell children.

But my push today is to talk about the lies that students tell, specifically the ones that keep them from growing into the best students possible.

“I Can’t Do This!”

This statement is perhaps the worst possible offender, and we have layers to this that we ought to unravel. If students say it often enough, they can prevent themselves from giving an honest effort toward learning the material. The student gets to fall back while the teacher explains and re-explains the material, which might have gone from a more implicit, constructivist explanation to a straight-up “This is what you do!”

Thus, it also works as a signal to the teacher that, perhaps, the student can’tlearn the material. The teacher, human and serving 30 students at a time, will focus away and leave that student to his or her own devices rather than insisting, “Try your best.” The teacher might stay away from the student, hovering over and hoping that her or she will come back into the fold again. The student often won’t.

The discussion around “I can’t do this” can be broken down into three general levels:

• They genuinely don’t understand the material.
• They’ve had a long day and just don’t have the energy to work any more.
• They have a situation at home that currently distracts them.

There are levels to “I can’t do this” that don’t get discussed, either. The current discussion around lack of effort focuses on “grit,” the cure for lack of effort — and with good reason. Paul Tough’s book How Children Succeed: Grit, Curiosity, and The Hidden Power of Character gives you a sense that he believes, with the right level of effort and conditions that help translate effort into success, any child can overcome his or her disposition.

Yet for some, the argument has taken a twist to mean that, rather than trying to address structural and pedagogical issues in our schools, we ought to focusonly on the attitudes espoused by our students. If they try hard enough, that argument goes, and if they work longer and harder than their peers, they too will surmount the incredible odds against them and acquire a proper education.

To an extent, I believe this, as I am a product of a poverty-stricken neighborhood. I was fortunate to go to good public and private schools (including Head Start) throughout my formative years. With enough effort, I made it out of the hood — only to teach in a neighborhood similar to the one where I used to live. My teaching reflects this, too. I have high expectations for my students, and I keep in mind that I should ask questions before getting emotionally bent out of shape around a student’s lack of compliance with the assignment.

Strategies for Comprehension

Thus, here are some solutions for the student who says, “I can’t do this!”

1. Ask why before all else.

Don’t just ask, “Why?” and let the answer linger. Often, the student will just say, “Because I don’t.” Your next question could be, “What part do you get?” Once you reach the point where they’re unsure, ask follow-up questions from that point onward. Push for them to answer questions rather than listen to your personal line of reasoning out the material. If they can vocalize the process and demonstrate understanding before you take them through it step by step, then let them do it. And keep asking why in the meantime.

2. Give breaks within reason.

Some of my students just need a genuine break. This isn’t about being soft, though I try not to run my classroom like a jail. If adults constantly bombard them with speeches they call lessons, then these students have had an entirely passive experience of education that doesn’t allow them to think for themselves. If you see a student who looks tired or has a hard time concentrating, firmly ask him or her to take a break just to breathe. Letting students take a small break might energize them again.

3. Make modifications to how you teach and how they learn.

The push for higher standards, rigor and accountability often means that our students’ humanness gets pushed to the wayside in some classrooms. We try to force students to see the material the way we estimate that a test-maker would, rather than developing lessons that work for as many students as possible. For instance, instead of using definitions from the textbooks, let students create explanations for the words. These explanations should come as close as possible to the definitions that you would create.

4. Teach students the art of the good question.

Unlike many of my colleagues, I do believe in smart questions (and not-so-smart questions). We ought to teach students how to ask questions that clarify, expound or enhance meaning. Students ask a lot of questions, and we ought to encourage them to get in the habit of questioning. Yet, we can differentiate between asking a question that adds value and a question that doesn’t.

All together, this means we can only control our own actions as educators in the classroom. We can teach students to persevere. We can teach students to work harder, and to see the fruits of their efforts in the learning they do. We can ask them to translate these attitudes to their lives overall.

We as educators must also keep in mind the vast personal experiences they bring into class, especially if they don’t get what we’re trying to teach them. Sometimes, there are a lot of things they’re not getting for reasons we can’t imagine, and it’s our job to provide sustenance in the meantime.

• JOSÉ VILSON’S BLOG

There’s one key difference between kids who excel at math and those who don’t

POWER OF MYTH

By Miles Kimball and Noah Smith October 27, 2013

Miles Kimball is an economics professor at the University of Michigan. He blogs about economics, politics and religion.

Noah Smith is an assistant professor of finance at Stony Brook University. His blog is Noahpinion.

People in China, Japan, and Korea are more accustomed to criticism as a means to self-improvement, whereas Westerners avoid it or resent it. Reuters/Lee Jae Won

“I’m just not a math person.”

We hear it all the time. And we’ve had enough. Because we believe that the idea of “math people” is the most self-destructive idea in America today. The truth is, you probably are a math person, and by thinking otherwise, you are possibly hamstringing your own career. Worse, you may be helping to perpetuate a pernicious myth that is harming underprivileged children—the myth of inborn genetic math ability.

+

Is math ability genetic? Sure, to some degree. Terence Tao, UCLA’s famous virtuoso mathematician, publishes dozens of papers in top journals every year, and is sought out by researchers around the world to help with the hardest parts of their theories. Essentially none of us could ever be as good at math as Terence Tao, no matter how hard we tried or how well we were taught. But here’s the thing: We don’t have to! For high school math, inborn talent is just much less important than hard work, preparation, and self-confidence.

How do we know this? First of all, both of us have taught math for many years—as professors, teaching assistants, and private tutors. Again and again, we have seen the following pattern repeat itself:

Different kids with different levels of preparation come into a math class. Some of these kids have parents who have drilled them on math from a young age, while others never had that kind of parental input.

1. On the first few tests, the well-prepared kids get perfect scores, while the unprepared kids get only what they could figure out by winging it—maybe 80 or 85%, a solid B.
2. The unprepared kids, not realizing that the top scorers were well-prepared, assume that genetic ability was what determined the performance differences. Deciding that they “just aren’t math people,” they don’t try hard in future classes, and fall further behind.
3. The well-prepared kids, not realizing that the B students were simply unprepared, assume that they are “math people,” and work hard in the future, cementing their advantage.

Thus, people’s belief that math ability can’t change becomes a self-fulfilling prophecy.

The idea that math ability is mostly genetic is one dark facet of a larger fallacy that intelligence is mostly genetic. Academic psychology journals are well stocked with papers studying the world view that lies behind the kind of self-fulfilling prophecy we just described. For example, Purdue University psychologist Patricia Linehan writes:

+

A body of research on conceptions of ability has shown two orientations toward ability. Students with an Incremental orientation believe ability (intelligence) to be malleable, a quality that increases with effort. Students with an Entity orientation believe ability to be nonmalleable, a fixed quality of self that does not increase with effort.

The “entity orientation” that says “You are smart or not, end of story,” leads to bad outcomes—a result that has been confirmed by many other studies. (The relevance for math is shown by researchers at Oklahoma City who recently found that belief in inborn math ability may be responsible for much of the gender gap in mathematics.)

Psychologists Lisa Blackwell, Kali Trzesniewski, and Carol Dweck presented these alternatives to determine people’s beliefs about intelligence:

+

You have a certain amount of intelligence, and you really can’t do much to change it.

1. You can always greatly change how intelligent you are.

They found that students who agreed that “You can always greatly change how intelligent you are” got higher grades. But as Richard Nisbett recounts in his bookIntelligence and How to Get It, they did something even more remarkable:

Dweck and her colleagues then tried to convince a group of poor minority junior high school students that intelligence is highly malleable and can be developed by hard work…that learning changes the brain by forming new…connections and that students are in charge of this change process.

The results? Convincing students that they could make themselves smarter by hard work led them to work harder and get higher grades. The intervention had the biggest effect for students who started out believing intelligence was genetic. (A control group, who were taught how memory works, showed no such gains.)

 But improving grades was not the most dramatic effect, “Dweck reported that some of her tough junior high school boys were reduced to tears by the news that their intelligence was substantially under their control.” It is no picnic going through life believing you were born dumb—and are doomed to stay that way.

For almost everyone, believing that you were born dumb—and are doomed to stay that way—is believing a lie. IQ itself can improve with hard work. Because the truth may be hard to believe, here is a set of links about some excellent books to convince you that most people can become smart in many ways, if they work hard enough:

• The Art of Learning by Josh Weitzkin
• Moonwalking with Einstein by Joshua Foer
• The Talent Code by Daniel Coyle
• Talent is Overrated by Geoff Colvin

So why do we focus on math? For one thing, math skills are increasingly important for getting good jobs these days—so believing you can’t learn math is especially self-destructive. But we also believe that math is the area where America’s “fallacy of inborn ability” is the most entrenched. Math is the great mental bogeyman of an unconfident America. If we can convince you that anyone can learn math, it should be a short step to convincing you that you can learn just about anything, if you work hard enough.

Is America more susceptible than other nations to the dangerous idea of genetic math ability? Here our evidence is only anecdotal, but we suspect that this is the case. While American fourth and eighth graders score quite well in international math comparisons—beating countries like Germany, the UK and Sweden—our high-schoolers  underperform those countries by a wide margin. This suggests that Americans’ native ability is just as good as anyone’s, but that we fail to capitalize on that ability through hard work. In response to the lackluster high school math performance, some influential voices in American education policy have suggested simply teaching less math—for example, Andrew Hacker has called for algebra to no longer be a requirement. The subtext, of course, is that large numbers of American kids are simply not born with the ability to solve for x.

We believe that this approach is disastrous and wrong. First of all, it leaves many Americans ill-prepared to compete in a global marketplace with hard-working foreigners. But even more importantly, it may contribute to inequality. A great deal of research has shown that technical skills in areas like software are increasingly making the difference between America’s upper middle class and its working class. While we don’t think education is a cure-all for inequality, we definitely believe that in an increasingly automated workplace, Americans who give up on math are selling themselves short.

Too many Americans go through life terrified of equations and mathematical symbols. We think what many of them are afraid of is “proving” themselves to be genetically inferior by failing to instantly comprehend the equations (when, of course, in reality, even a math professor would have to read closely). So they recoil from anything that looks like math, protesting: “I’m not a math person.” And so they exclude themselves from quite a few lucrative career opportunities. We believe that this has to stop. Our view is shared by economist and writer Allison Schrager, who has written two wonderful columns in Quartz (here and here), that echo many of our views.

One way to help Americans excel at math is to copy the approach of the Japanese, Chinese, and Koreans.  In Intelligence and How to Get It, Nisbett describes how the educational systems of East Asian countries focus more on hard work than on inborn talent:

             1. “Children in Japan go to school about 240 days a year, whereas children in the United States go to                              school about 180 days a year.”

2. “Japanese high school students of the 1980s studied 3 ½ hours a day, and that number is likely to be, if anything, higher today.”

3. “[The inhabitants of Japan and Korea] do not need to read this book to find out that intelligence and intellectual accomplishment are highly malleable. Confucius set that matter straight twenty-five hundred years ago.”

4. “When they do badly at something, [Japanese, Koreans, etc.] respond by working harder at it.”

5. “Persistence in the face of failure is very much part of the Asian tradition of self-improvement. And [people in those countries] are accustomed to criticism in the service of self-improvement in situations where Westerners avoid it or resent it.”

We certainly don’t want America’s education system to copy everything Japan does (and we remain agnostic regarding the wisdom of Confucius). But it seems to us that an emphasis on hard work is a hallmark not just of modern East Asia, but of America’s past as well. In returning to an emphasis on effort, America would be returning to its roots, not just copying from successful foreigners.

Besides cribbing a few tricks from the Japanese, we also have at least one American-style idea for making kids smarter: treat people who work hard at learning as heroes and role models. We already venerate sports heroes who make up for lack of talent through persistence and grit; why should our educational culture be any different?

Math education, we believe, is just the most glaring area of a slow and worrying shift. We see our country moving away from a culture of hard work toward a culture of belief in genetic determinism. In the debate between “nature vs. nurture,” a critical third element—personal perseverance and effort—seems to have been sidelined. We want to bring it back, and we think that math is the best place to start.

7 Simple, Science-Backed Ways to Boost School Success

Academic success impacts our children for the rest of their life: it influences their self-esteem, college selections, job attainment, financial success, and even their choice of spouses. It’s no wonder we go great lengths to give our kids an academic edge.

Despite our good intentions we often overlook a few simple strategies that research has proven to impact children’s academic success. Even better, these seven science-backed solutions are things that every parent can do, don’t cost a dime, and are proven to boost school success.

1. Make sure kids get enough zzz’s

In one recent study, Tel Aviv University researchers found that missing just one hour of sleep can be enough to reduce a child’s cognitive abilities by almost two years the next day. For example, a sixth grader who loses precious zzz’s the night before a big test could end up performing at a fourth grade level.

A lack of sleep can have a serious impact on children’s abilities to learn and perform at school.

Set a bedtime and keep to it every single night.

Flashing images affect REM, so be sure to turn off the computer and television at least thirty minutes prior to bedtime.

Watch out for caffeinated sleep stealers like cold medications, chocolate, and those energy-drinks.

Take away the cell phones during nighttime hours—62% of kids admit they use it after the lights go out and their parents are clueless.

2. Applaud efforts the right way

Carol Dweck’s research at Columbia University found that how we praise our kids’ schoolwork can enhance or impede achievement. For example, instead of encouraging your child to bring home straight A’s, put the emphasis on how hard she is working. This will encourage her to persist and it will help to sustain her motivation.

Kids who are praised for their persistence are more likely to blame any failure they have on not trying hard enough, rather than on a lack of ability (a belief which can discourage kids very easily).

Above all, keep in mind that the grade is not what motivates a top student to succeed-it’s their inner drive for learning.

3. Respect their learning style

If your son insists on plugging into his iPod when he studies, or if your daughter swears that flash cards are the only way she can learn her spelling words- listen up! While you may prefer a quiet room with no distractions when it comes to getting work done, that doesn’t mean it’s the best way for your kids to concentrate and get down to business.

Harvard researcher, Howard Gardner’s work shows there are eight kinds of intelligences-or ways kids learn best-which include: musical, spatial, logical-mathematical, linguistic, bodily, intrapersonal, interpersonal and naturalist.

The trick is to pay attention to how your kid learns best so you can identify their unique learn style (not yours!) and then tap into it help them be more successful. For instance, if your child learns best by remembering what she sees, point it out to her and encourage her to draw, mindmap or draw those images.

4. Pay attention to peers

Pals play an enormous part of our kids’ self-esteem, and research also reveals that who our kids befriend can affect their study habits and their overall academic success.

The truth of the matter is that peer pressure can have both positive and negative consequences on a child’s education. If your child chooses friends who believe that education is important, chances are she will adopt those attitudes and put more emphasis into hitting the books harder and focusing more in class. On the flip side, if your child is best buddies with a kid who stays distracted during class, doesn’t turn in homework assignments, and rarely studies before a big test, chances are she will fall in line with their bad habits.

An Ohio State University study found that kids are more likely to have friends with future college plans if they have a warm, positive relationship with their parents. So cultivate that kind of parenting style and you’ll help your child make the right friendship decisions! And encourage your child to seek out pals with like-minded educational values.

5. Make family meals a must

A recent study by Columbia University showed that kids whose families eat regular, relaxed meal together are not only less likely to abuse drugs and alcohol and develop eating disorders-they are also more likely to achieve higher grades.

Family dinners do not have to consist of gourmet, five-course meals. Serve simple, healthy meals, turn off the television and unplug the phone, and enjoy each other’s company. And if everyone in your family is on a different schedule and can’t make it to dinner- don’t worry!

Consider instating an evening family snack time where everyone can review their days with each other before bedtime.

The trick is to find what works best for you family and turn it into a routine. Keep in mind it’s not the macaroni and cheese dish has nothing to do with giving your kid the academic edge. It’s those informal: “How was your day?” “What are you discussing in science?” “How do you plan to study for that test?” kind of discussion topics that let your kid know your family prioritizes education.

6. Squelch the stress…at home

Research shows that the conflict kids face at home spills over into their school life and impedes their learning. In fact, family-induced stress can affect kids’ learning and behavior for up to two days following an incident.

So take a vow of ‘yellibacy.’ Make your home a stress-free zone.

Find ways to de-stress with your kids. Take longs walks, read together, do yoga, or have a family movie night.  Be a model to them on how to disagree without it ending in a screaming match. Teach your kids that it’s okay for them to walk away from an argument until they are calm enough to return. Teach your child healthy ways to reduce stress. Tune into your child’s unique stress signs, so you’ll be able to recognize when he’s on overload, help him learn to identify his own stressors (and triggers) so that you can intervene and help him to decompress before something comes to blows.

7. Tailor expectations to your child’s abilities

All parents want the very best for their kids. It’s only natural!

As a parent, you should consider your learning aspirations for your child like a rubber band: gently stretch but don’t snap.

Every child is different, and while its okay to encourage her to try hard and achieve her best, it’s also important to remember that ‘What’s best’ is different for every child. Just because your kid isn’t composing his own symphonies or writing his memoirs by age 10, doesn’t mean that he won’t still do great things with his life. Always remember this one commandment: ‘Tailor thy parenting only to thy child’. You and your children will be happier and healthier for it, as well as succeed.

Final thoughts

If you want to boost your kid’s academic performance and see lasting results, it will take a few things from you: consistency, dedication, and patience.

Form a partnership with your child’s teacher..the more you’re on the same page the better for your child.

When your child continues to struggle..get help! Those things are always better parenting tools than anything money can buy.

Remember that no two kids are the same, even if they come from the same household. If you pay attention to the individual needs of each child and do what’s right for them and for you, you’ll see the payoff in their attitudes and their report cards in no time.

Dr. Michele Borba, Parenting Expert

I am an educational psychologist, parenting expert, TODAY show contributor and author of 22 books including The Big Book of Parenting Solutions: 101 Answers to Your Everyday Challenges and Wildest Worries.

You can also refer to my daily blog, Dr. Borba’s Reality Check for ongoing parenting solutions and late-breaking news and research about child development.

Finding the Beauty in Math

Holly Korbey | October 1, 2013 |

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Flickr: Cuyahoga jco

Math has a bad rap, writes math professor Manil Suri in a recent New York Times op-ed, and would be better geared to students as a playful and stimulating subject of ideas. Unfortunately, that’s not at all what our culture currently embraces.

“Sadly, few avenues exist in our society to expose us to mathematical beauty,” Suri writes. “In schools, as I’ve heard several teachers lament, the opportunity to immerse students in interesting mathematical ideas is usually jettisoned to make more time for testing and arithmetic drills. The subject rarely appears in the news media or the cultural arena.”

While research suggests that improving self-efficacy and providing math-positive role models can help spark interest and stave off math anxiety, what some mathematicians and teachers are looking for reaches beyond surviving or tolerating math class, but helping connect students to mathematics beauty. Suri wants students to “fall in love” with math, and suggests that maybe our entire approach to math is upside down, and deserves to be righted.

But how does a person fall in love with math? For too many, math class conjures up anxious worksheets filled with rows of unanswered problems. Students go along, seeming to perform the steps required — plug in the formulas, solve for x — without ever understanding what they’re doing, or why.

“We have defined math rather narrowly in the U.S. to mean memorizing procedures and performing them accurately and quickly.”

 

Cornell Math Professor and New York Timescolumnist Steven Strogatz, author of The Joy of x, said much of middle and high school math curriculum (which covers not basic arithmetic, but higher math) doesn’t appeal to students’ hearts, instead offering answers to questions that kids would never ask — which he calls “the definition of boredom.”

“When people want to learn about music, they’ve reacted to it, they love it and naturally want to learn more about it. They have their own questions,” Strogatz said. When introducing higher math to a group of curious young students, he suggests first “showing them math’s greatest hits” and allowing them to become fascinated; students then naturally come up with their own questions. Suri was on the right track, Strogatz said, when he suggested students learn something like theorigin of numbers — because the first step is falling in love with the mathematical ideas behind the formulas and procedures.

Strogatz acknowledges that grasping the concepts of higher math can pave the way to many wonderful careers — many in the popular and highly needed STEM fields. But rationalizing to students that math improves reasoning skills or that “you’ll need it in the real world” are two strategies doomed to fail, he said, because they not-so-subtly suggest that math isn’t worth learning for its own sake, but parallels something more akin to “mental push-ups.”

“Have you ever asked why you need music?” Strogatz said. “You don’t need music. It’s nice to know about music. Why do you need to look at Picasso?” Perhaps when presented first as the story of how the universe works, math can become beautiful.

[RELATED: Important Facts About Teaching Math]

Grabbing students’ hearts, however, is only the first step to falling in love with math. High school math teacher Dan Meyer realized his algebra classes needed a makeover, the subject of an inspiring TED talk in which Meyer takes a larger look at how math is taught. “We have defined math rather narrowly in the U.S. to mean memorizing procedures and performing them accurately and quickly,” he said. “Those are certainly important parts of mathematics, but they aren’t the only parts, or even the most important parts. We need to define math to include skills like prediction, argumentation, and systematic thinking. These are important skills to have whether you go into a STEM field or not.”

Instead of trying to make math less boring by inserting more interesting, youthful details, said Meyer, like “‘Justin Bieber’ or loosely pasting real-world contexts into word problems from the 1960s,” math needs to be accessible far more than it needs to be relevant. One large part of providing access to math concepts, he said, is helping students understand that math makes sense with or without the teacher, and that students can create and solve new problems without a textbook.

But would he go so far to try and convince his high school students that math is beautiful? “Math involves creation,” Meyer said. “You can add up different sets of numbers or attach different kinds of shapes together and create theories about the patterns you’re seeing. Math is personal. Those theories and how you express them is personal to you. ‘Beautiful’ is the sort of word that makes a lot of people who do math for a living seem crazy to those who don’t, but when you’re creating something that’s personal to you, I suppose that’s rather beautiful.”

 

Measurement conversions made easy

For those who thought the hardest part of Physics 101 was the constant conversion from feet and inches to the metric system, including all its Newtons, Joules, and Watts, here are some other useful conversions:

Ratio of an igloo’s circumference to its diameter:

Eskimo Pi

2000 pounds of Chinese soup:

Won ton

1 millionth of a mouthwash:

1 microscope

Time between slipping on a peel and smacking the pavement:

1 bananosecond

Time it takes to sail 220 yards at 1 nautical mile per hour:

Knot-furlong

16.5 feet in the Twilight Zone:

1 Rod Serling

Half of a large intestine:

1 semicolon

1000 pains

1 kiloahurtz

Basic unit of laryngitis:

1 hoarsepower

Shortest distance between two jokes:

A straight line

454 graham crackers:

1 pound cake

1 million microphones:

1 megaphone

1 million bicycles:

2 megacycles

2000 mockingbirds:

two kilomockingbirds

10 cards:

1 decacards

1 kilogram of falling figs:

1 Fig Newton

1000 milliliters of wet socks:

1 literhosen

1 millionth of a fish:

1 microfiche

1 trillion pins:

1 terrapin

10 rations:

1 decoration

100 rations:

1 C-ration

2 monograms:

1 diagram

8 nickels:

2 paradigms

2.4 statute miles of intravenous surgical tubing at Yale University Hospital:

1 I.V. League

100 Senators:

Not 1 decision

Classroom Sneak Peek – Common Core Mathematical Practice #1

Posted January 18th, 2012 by Michelle Flaming

The common core standards are here and it’s time we start reflecting about the necessary changes that will be needed to meet these standards in the classroom.  This blog is designed to first look at the mathematical practice and then to put into what the classroom should look like, feel like, and sound like.  Teacher questioning will be critical to the success of the CCSS vision, so we will also explore this.  If you are interested in this process to facilitate this discussion with your staff, read What Do the Common Core Standards Look Like in the Classroom.

1. Make sense of problems and persevere in solving them.

-Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution.  They analyze givens, constraints, relationships, and goals.

-They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt.

-They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution.

-They monitor and evaluate their progress and change course if necessary.

-Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need.  Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem.

-Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.

Explain, analyze, make conjectures, monitor, evaluate, check their answers.

So what does this really look like?  The chart below is a work in progress.  I’ve designed this with the expertise of many classroom teachers.  If you have other ideas, please don’t hesitate to email me and share your expertise as well.

Mathematical Practice: #1 Make sense of problems and persevere in solving them.

Student Actions:	Teacher Actions:	Open-Ended Questions:
Feel like a detective or mathematician, look for clues and evidence on how to solve the problem Believe they are a mathematician and can solve the problem and understand that mistakes are the way we learn. Talk to other students about how they might solve the problem. (Partner, small group, or whole group discussion) Think about and tries several ways to solve the problem Use a variety of mathematical tools to solve the problem Reflect about what the problem is asking Write about how they solved the problem Listen to other students and may change their own strategy based upon the thinking of others Understand other student strategies Share their thinking and solution.	Create a classroom climate where struggle is expected and that making mistakes are OK. Provide students with word problems and real-world scenarios and encourage a variety of tools and strategies. Discuss appropriate behavior for respectful dialogue. Give students individual think time before discussing with a partner. Set a timer for three minutes for individual think time. Frame math challenges that are clear and explicit. Check in periodically to check student clarity and thought process. If students are stuck, scaffold the problem to a simpler problem. Ask students, how the problems are similar and how they are different. Set up structures requiring students to connect different forms of the problem (equation to graph, table, etc.) Students share out different strategies for solving the problem.	What do you know about the problem? What is being asked? What problems have we solved before like this problem? How might talking to ______ help you? What might be another way to solve this problem? How is ____ strategy like yours? How is it different? How might a number line help you? How is your graph connected to your equation? How does your equation match the problem? How might acting out the story help you solve the problem? What made you decide to use that strategy? What made you choose that operation?

Possible Activities:

1.     Be a math detective – Discuss the job of detectives, ” To look for clues/evidence and solve mysteries.” 2.     Provide story problems and allow students to struggle with solutions. 3.     Ask students to show three ways to solve the problem  (Give individual think time prior to   group) 4.     Look at different student work (remove names and replace with Student 1 and Student 2)  Ask, “what is this mathematician thinking or trying to figure out.” 5.     Provide real world, high quality tasks. 6.     Keep in mind the level of cognitive demand from this practice: – Explain, analyze, make conjectures, monitor, evaluate, check their answers.

“Struggling in mathematics is not the enemy any more than sweating is in basketball, it’s a clear sign you are in the game.”  – Kim Sutton

– See more at: http://michellef.essdack.org/?q=node/156#sthash.GhNCvjhY.dpuf

WE ONLY GET STRONGER WHEN IT’S DIFFICULT!

Photo by Barney Moss

Gifted kids, by their nature, often breeze through the early years of school, not facing a real challenge until high school or college. They get used to succeeding without putting in the work. Then, when things get difficult, they can flounder. Even in 6th grade, I’d see this starting.

So, here’s a great opening week discussion that sets up a year-long expectation. Teach your students that we only get stronger when it’s difficult.

How To Grow A Muscle

I showed my students this image:

Photo from the US Navy

After waiting for the commotion to die down, I asked:

“Do you know how his muscles got so large?”

They knew that lifting weight was involved, but didn’t know about whymuscles grow.

Push ‘Em To Their Limits

I explained: muscles only grow when we work them just more than what they’re used to. This causes “micro-tears,” damaging the muscle just slightly. This is why our muscles hurt after a workout.

The muscle then thinks, “Uh oh! We’re doing harder work, I better get stronger!” and uses protein to repair the micro-tears, building itself backa little bit bigger.

Then, we repeat.

Work the muscle past its ability, it hurts, and then it rebuilds itself stronger. Eventually, this is how bodybuilders get huge muscles! Little bit by little bit, they push their muscles just past their limits.

We Only Get Stronger When It’s Difficult

I’d emphasize, if we did nine pushups, but stopped because the tenth got tough, then the muscle won’t grow! It’s only the difficult repetitions that cause growth. We only get stronger when we push ourself through that final, tough pushup.

Of course, I’d dramatically act out the final repetition of a bicep curl, wincing with the imaginary effort.

Our Thinking Muscle

All of this is true for thinking and learning as well. When it’s difficult, when it’s uncomfortable, when it’s getting frustrating, that’s when we’re pushing our brain. That’s when we’re learning and growing.

So many of my students would give up just as things got hard. They don’t like the way it feels. They’re not used to it. But the longer they wait, the more difficult it will be to push themselves.

This difficult part could apply to:

• finishing the word problems in math homework
• writing out answers in complete sentences
• taking notes while reading
• citing sources in a research paper
• pushing through a challenging book

It Gets Easier!

And, as many athletes will say, you don’t just get used to the idea of pushing past a barrier, you actually start to like it! Runners, bodybuilders, and swimmers all profess how good they feel after a tough workout. It’s getting started that’s so hard.

Beyond The Brain

I’m sure your students will come up with many different situations where struggling past the difficult part is important. Do a class brainstorm and capture these examples.

A Year’s Motto

I printed out the statement “We Only Get Stronger When It’s Difficult” and stuck it to the board, referencing it constantly. If I saw the class being academically lazy, I’d point to the weight-lifter and recite the motto: we only get stronger when it’s difficult!

Here’s an image I made using PasuKaru76‘s hilarious Lego photo. Feel free to download, print, and use it in your class:

Download here in color or here 

’10 big brain benefits of playing chess’

Not for nothing is chess known as “the game of kings.” No doubt the rulers of empires and kingdoms saw in the game fitting practice for the strategizing and forecasting they themselves were required to do when dealing with other monarchs and challengers. As we learn more about the brain, some are beginning to push for chess to be reintroduced as a tool in the public’s education. With benefits like these, they have a strong case.

1. It can raise your IQ
Chess has always had an image problem, being seen as a game for brainiacs and people with already high IQs. So there has been a bit of a chicken-and-egg situation: do smart people gravitate towards chess, or does playing chess make them smart? At least one study has shown that moving those knights and rooks around can in fact raise a person’s intelligence quotient. A study of 4,000 Venezuelan students produced significant rises in the IQ scores of both boys and girls after 4 months of chess instruction.

2. It helps prevent Alzheimer’s
Because the brain works like a muscle, it needs exercise like any bicep or quad to be healthy and ward off injury. A recent study featured in The New England Journal of Medicine found that people over 75 who engage in brain-stretching activities like chess are less likely to develop dementia than their non-board-game-playing peers. Just like an un-exercised muscle loses strength, Dr. Robert Freidland, the study’s author, found that unused brain tissue leads to a loss of brain power. So that’s all the more reason to play chess before you turn 75.

3. It exercises both sides of the brain
In a German study, researchers showed chess experts and novices simple geometric shapes and chess positions and measured the subjects’ reactions in identifying them. They expected to find the experts’ left brains being much more active, but they did not expect the right hemisphere of the brain to do so as well. Their reaction times to the simple shapes were the same, but the experts were using both sides of their brains to more quickly respond to the chess position questions.

4. It increases your creativity
Since the right hemisphere of the brain is responsible for creativity, it should come as no surprise that activating the right side of your brain helps develop your creative side. Specifically, chess greatly increases originality. One four-year study had students from grades 7 to 9 play chess, use computers, or do other activities once a week for 32 weeks to see which activity fostered the most growth in creative thinking. The chess group scored higher in all measures of creativity, with originality being their biggest area of gain.

5. It improves your memory
Chess players know — as an anecdote — that playing chess improves your memory. Being a good player means remembering how your opponent has operated in the past and recalling moves that have helped you win before. But there’s hard evidence also. In a two-year study in 1985, young students who were given regular opportunities to play chess improved their grades in all subjects, and their teachers noticed better memory and better organizational skills in the kids. A similar study of Pennsylvania sixth-graders found similar results. Students who had never before played chess improved their memories and verbal skills after playing.

6. It increases problem-solving skills
A chess match is like one big puzzle that needs solving, and solving on the fly, because your opponent is constantly changing the parameters. Nearly 450 fifth-grade students were split into three groups in a 1992 study in New Brunswick. Group A was the control group and went through the traditional math curriculum. Group B supplemented the math with chess instruction after first grade, and Group C began the chess in first grade. On a standardized test, Group C’s grades went up to 81.2% from 62% and outpaced Group A by 21.46%.

7. It improves reading skills
In an oft-cited 1991 study, Dr. Stuart Margulies studied the reading performance of 53 elementary school students who participated in a chess program and evaluated them compared to non-chess-playing students in the district and around the country. He found definitive results that playing chess caused increased performance in reading. In a district where the average students tested below the national average, kids from the district who played the game tested above it.

8. It improves concentration
Chess masters might come off like scattered nutty professors, but the truth is their antics during games are usually the result of intense concentration that the game demands and improves in its players. Looking away or thinking about something else for even a moment can result in the loss of a match, as an opponent is not required to tell you how he moved if you didn’t pay attention. Numerous studies of students in the U.S., Russia, China, and elsewhere have proven time and again that young people’s ability to focus is sharpened with chess.

9. It grows dendrites
Dendrites are the tree-like branches that conduct signals from other neural cells into the neurons they are attached to. Think of them like antennas picking up signals from other brain cells. The more antennas you have and the bigger they are, the more signals you’ll pick up. Learning a new skill like chess-playing causes dendrites to grow. But that growth doesn’t stop once you’ve learned the game; interaction with people in challenging activities also fuels dendrite growth, and chess is a perfect example.

10. It teaches planning and foresight
Having teenagers play chess might just save their lives. It goes like this: one of the last parts of the brain to develop is the prefrontal cortex, the area of the brain responsible for planning, judgment, and self-control. So adolescents are scientifically immature until this part develops. Strategy games like chess can promoteprefrontal cortex development and help them make better decisions in all areas of life, perhaps keeping them from making a stupid, risky choice of the kind associated with being a teenager.

This article was cross-posted with permission from OnlineCourses.com.

Qualities of Engaging Student Work

A critical factor for improving learning lies in providing high-quality work for students- work that engages students, work that enables

• 

students to learn what they need in order to succeed in the world.

The traits of engaging student work listed below evolved from Dr. Phillip Schlechty’s book, Working on the Work. (Note: each of the listed qualities of engaging work below is a hot-link that will scroll down the page to a short description of the trait, along with some examples of what the trait looks like in the hands of the learner – paired with non-examples, for clarity.)

• Persona Response – More than one right answer
• Clear/Modeled Expectations – Student knows what success “looks like”
• Emotional/Intellectual Safety – Freedom to take risks
• Learning with Others (Affiliation) – Learning has asocial component
• Sense of Audience – Student work is shared
• Choice – Students have meaningful options
• Novelty and Variety – Learning experiences are unusual or unexpected
• Authenticity –Connections to experience or prior learning

Personal Response – More than one right answer

Work that engages students almost always focuses on a product or performance of significance to students.  When students explain their answers (or the logic and reasoning behind those answers), they are invested in their personal response.

What it looks like:

• Supported predictions
• Opinions
• Remembrances
• Connections
• Comparisons
• Analogies
• Summary Statements
• Strategies
• “I think…because…”

It is not: Recall of answers, Only one answer possible, Only one answer accepted

Caution: Optimal personal response is based upon activities that force all students to articulate their ideas (rather than four or five students).  For that reason, written personal response may be more powerful than oral response.

Clear/Modeled Expectations – Student knows what success “looks like”

Students prefer knowing exactly what is expected of them, and how those expectations relate to something they care about.  Standards are only relevant when those to whom they apply care about them.

What it looks like:

• Clear objective of activity & learning
• Models of expectation and strategy
• Visual exemplars that persist
• Rubrics & self-assessment
• Clear formats & procedures
• Sources
• Quantity & quality required in personal response activities
• “I included…”

It is not: Oral explanations by teacher; Inconsistent expectations; “Grading”

Emotional/Intellectual Safety – Freedom to take risks

Students are more engaged when they try tasks without fear of embarrassment, punishment, or implications that they are inadequate.  Personal response activities that students must support with logic, reasoning or explanation require more intellectual safety than answering a question that has only one right answer.

What it looks like:

• Students explain why/how their answer is plausible
• Students take risks with “unpopular” or more subtle answers
• Sources, evidence & examples are cited
• Reasoning first, answers second
• Answers questioned or defended
• “I disagree with the author because…”

It is not: Answering single-answer questions, answers without explanation, students being “correct” or “incorrect,” students critiqued

Learning with Others (Affiliation) – Learning has a social component

Students are more likely to be engaged by work that permits, encourages, and supports opportunities for them to work interdependently with others.  Those who advocate cooperative learning understand this well, and also recognize the critical difference between students working together and students working together independently on a common task (which may look like group work, but isn’t).

What it looks like:

• Think, pair, share
• Literature circles
• Small group discussion
• Reciprocal teaching
• Peer revision or review
• Student A reports/paraphrases student B’s thoughts
• “When David talked about the symbolism, I thought…”

It is not: Taking turns talking, group grades in isolation

Sense of Audience – Student work is shared

Students are more highly motivated when their parents, teachers, fellow students, and “significant others” make it known that they think the student’s work is important.  Portfolio assignments- which collect student work for scrutiny by people other than the teacher- can play a significant role in making student work “more visible.”

What it looks like:

• Increased level of concern
• Connections to audience/purpose
• Voice
• Responsibility to the group
• Proficient work posted
• Student work as exemplars
• The ballgame, the concert, the play
• “When I finish this business letter, I will mail it to…”

It is not: Being “singled out”

Choice– Students have meaningful options

When students have some degree of control over what they are doing, they are more likely to feel committed to doing it.  This doesn’t mean students should dictate school curriculum, however: schools must distinguish between giving students choices in what they do and letting them choose what they will learn.

What it looks like:

• Tiered assignments
• Self-selected reading material
• Product
• Selecting tasks from a list
• Meaningful options
• Decision-making
• “I chose to present my thoughts in graphic form”

It is not: Opting out of standards; avoiding an assignment; overwhelming choices

Novelty and Variety – Learning experiences are unusual or unexpected

Students are more likely to engage in the work asked of them if they are continuously exposed to new and different ways of doing things.  The use of technology in writing classes, for example, might motivate students who otherwise would not write.  New technology and techniques, however, shouldn’t be used to create new ways to do the same old work- new forms of work and new products are equally important.

What it looks like:

• Variety of products
• Diverse perspectives
• Integrated fun
• Layered interests
• Games
• Simulations and role-play
• Competitions
• Responding “in the voice of…”
• “Rather than working problems in math, we wrote two new work problems”

It is not: Chaos; lack of procedure or protocols

Sense of Audience – Student work is shared

Students are more highly motivated when their parents, teachers, fellow students, and “significant others” make it known that they think the student’s work is important.  Portfolio assignments- which collect student work for scrutiny by people other than the teacher- can play a significant role in making student work “more visible.”

What it looks like:

• Increased level of concern
• Connections to audience/purpose
• Voice
• Responsibility to the group
• Proficient work posted
• Student work as exemplars
• The ballgame, the concert, the play
• “When I finish this business letter, I will mail it to…”

It is not: Being “singled out”

 Authenticity- Connections to experience or prior learning

This term is bandied about quite often by educators, so much that the power of the concept is sometimes lost.  Clearly, however, when students are given tasks that are meaningless, contrived, and inconsequential, they are less likely to take them seriously and be engaged by them.

What it looks like:

• Relevance to age group
• Tasks that represent the personalities of the learners
• Real-life activities
• Inquiry or discovery learning
• Hands-on manipulative
• Current events/issues
• “Learn, then label”
• Transfer or synthesis beyond content
• Extension of workplace activities
• Use of workplace or home technology

It is not: Vocabulary in isolation; Contrived activities; Practice without context; Repetition of low-level work

 

 

Mr. X and Wild Thing

The Math Magician Expand your brain with Mr. X!!

Bob Bishop is internationally known as the Math Magician. He visits many school each year to share the wonder of math. He has traveled from Boston to Los Angeles to Taiwan amazing and motivating teachers and students.Appearing as Mister X (The Illusionist), The Math Magician, Einstein, or even the Zany Dr. Lamebrain, he teaches teachers with keynotes and workshops and gives students long remembered workshops and assemblies. His classroom experience and training in brain-based education gives him unique insight into the vital need for quality math education to keep our country on the innovative edge.Bob Bishop, creator of Odyssey Learning Adventures, has loved math, games, and puzzles since he was a child. He shares from his passion to motivate students to love math. He has been a classroom teacher for Elementary, High School and Middle school for over 20 years.

Bob’s commitment and passion for math are obvious as he teaches. Bob’s programs are fun, dynamic and intellectually engaging.

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Mr. X, The Math Magician

Mr. X, The Math Magician, is now booking school family math nights for the Fall and Winter. Bob Bishop is internationally known as America’s Math Magician. He visits many school each year to share the wonder of math. He has traveled from Boston to Los Angeles to Taiwan amazing and motivating teachers and students.

Danica McKellar’s 5 tips to conquer math phobia, for your kids’ sake

Danica McKellar, author of “Girls Get Curves: Geometry Takes Shape”

Aug. 13, 2012 at 7:00 AM ET

She gained fame as Winnie Cooper on “The Wonder Years,” and now actress Danica McKellar is a mom and serious mathematician with four books and a published theorem to her name (the Chayes-McKellar-Winn Theorem). She’s on a mission to demystify math, especially for girls. Here are her tips for ensuring your children grow up to love math, not fear it.

Danica McKellar /

So if you smear 20 percent of the beets on your face, and scatter 30 percent on the floor, and arrange 20 percent on your tray, how much do you actually eat? Danica McKellar’s son, Draco, enjoying a tasty math lesson.

Much like how moms can model positive body image, we can influence our kids’ outlook on math in healthy ways. Math is a crucially important subject that all too often gets rejected, especially by girls, and then they risk missing out on the brain-building, confidence-boosting gifts that tackling math has to offer. Here are some tips for how to start your kids off on the right foot, and keep math phobia away!

1. Starting when they are toddlers, point out math in everyday life.

Introduce addition (“more”) and subtraction (“take away” and “less”) with their cereal O’s or crayons. As they get a little older, explain what unit prices are at the store and how they compare to the total price — this is multiplication and division. It’s OK if they don’t fully “get” it right away. As they get into middle school, find math challenges from outside resources like online sites  or books (see the Reality Math sidebars in my books). The main point is to train them from an early age to see math as a normal part of life. It’s harder to develop a phobia of something that is part of your everyday life!

Related: Read an excerpt of “Girls Get Curves: Geometry Take Shape”

2. Hide your math phobia, if you have any.

My mom didn’t want to pass along her fear of spiders to me and my sister, so she pretended not to be afraid of them, and it totally worked. Same thing works for math. If you have a fear or phobia about numbers, don’t let your kids know! Letting them hear things like, “Oh I never did well in math,” or “I’m just not a numbers person” at a young age is likely to lower the bar in their own minds, and subconsciously allows them to give up on math as soon as they struggle with it.

3. Use money.

No, I don’t mean pay them to do their math homework! From an early age, kids understand that money makes the world go round. As soon as they start to get an allowance, teach them about saving money by asking things like, “If you don’t spend any allowance for two months, how much will you have saved?” or “How long will it take you to save up for that toy you saw on TV?” And have them keep track. As they get older, you could tell them about percentages in the context of APR’s for credit cards, and how a late payment actually increases the amount you paid for an item. The value of money is a great motivator to think about numbers, and this is also an opportunity to start fiscally responsible habits, too!

Related: How’s your body image? Check out our survey

4. Provide support and encouragement during rough patches.

Pay attention, and if your child is floundering in math class, get him or her additional support, whether it’s finding supplemental resources like books, tutors, or helping them yourself. Math is cumulative — unlike most subjects in school, each new concept is built upon the ones before it, so if an important concept gets missed, it can be much harder to understand the following lessons.

5. Brush up on your own math skills.

This will strengthen all of the above strategies, and as a bonus, will improve your life, too!

Danica McKellar — actress, author and mathematician — is mom to son Draco, who turns 2 next month. You can find her on Twitter and on her website, danicamckellar.com. Her latest book, “Girls Get Curves: Geometry Takes Shape,” and her three other books about math are available in stores.

 

7 Tips to Learn to Love Mathematics

WE OFTEN HEAR THE REMARK, “I hate Mathematics!” But do we really realize how relevant and interesting to make it as significant part of our daily routines?

Learning mathematics is like learning another language, so at first it will be hard but it will get progressively easier. Being not able to get the correct answer should not discourage you; it is a natural part of the learning process. So, keep on studying Math.

Here are some points to consider when learning to love Mathematics:

1. Have a positive mindset.

Believe on the power of positive thought as one of the most potent forces. Set your mind that learning Mathematics is a great fun and beneficial.

2. Dedicate some time to learning Math.

Make sure to allot at least an hour a day to study mathematics.

3. Become familiar with the vocabulary.

Having a math dictionary at your side is a huge help. There are many technical mathematical terminologies that need to be understood. It will be a relief to be able to quickly look up the meanings as you study.

4. Have reference books.

This will provide different explanations that will help in your study.  One of the explanations may make better sense to you than the other; or a combination of both may help you to get it.

5. Practice and practice more.

It makes perfect. Solve as many math problems as you can. In this way, you may get good feelings and get used to solving various Math problems.

6. Consult the more knowledgeable. You can always seek for help on something confusing and things you don’t know yet.

7. Never stop studying.

Grab every opportunity to learn. Sooner or later, you’ll learn to love Math. Happy learning!

Maya Elaine Paler, the contributor, is a BS Accountancy student from Caloocan City, Philippines.

A Worksheet for Math-Phobic Parents

By Sue Shellenbarger

Parents who hate math often fear raising kids who will feel the same.

Many parents who loathe math fear raising kids who feel the same. This is becoming a more urgent concern as the fastest-growing occupations increasingly require skills in either math or science. Sue Shellenbarger on Lunch Break discusses how parents overcome math phobias.

Tammy Jolley is one of them—”a horrible math-phobic,” she says. After struggling through algebra and statistics in high school and college, helping her 9-year-old son Jake with math homework makes her “feel like saying, ‘Aaarghh, this is hard! I know why you don’t get it,’ ” says the Madison, Ala., state-court official. Instead, she forces herself to encourage Jake.

Ongoing research is shedding new light on the importance of math to children’s success. Math skill at kindergarten entry is an even stronger predictor of later school achievement than reading skills or the ability to pay attention, according to a 2007 study in the journal Developmental Psychology.

The issue is drawing increasing attention as U.S. teens continue to trail their global peers in math, performing below average compared with students in 33 other industrialized nations, based on the most recent results of the Program for International Student Assessment in 2010.

Parents play a pivotal role in kids’ math attitudes and skills, starting in toddlerhood. Those who talk often to their youngsters about numbers, and explain spatial relationships in gestures and words, tend to instill better math skills at age 4, according to a long-term, in-home study of 44 preschoolers and their parents led by Susan C. Levine, a professor of psychology and comparative human development at the University of Chicago.

Jason Schneider

Yet many parents unconsciously teach children to fear math. A parent who reacts to a child’s math questions or homework by saying, “I have never been good in math,” or, “I haven’t done math in 20 years,” conveys to kids that math is daunting and they probably can’t do it either, says Bon Crowder, a Houston-based teacher, tutor and publisher of MathFour.com, a website on math-teaching strategies.

It is possible for a math-phobic parent to raise a quant, but parents need to change their behavior, researchers and educators say. This means halting negative talk, mixing math games and questions into daily life just as they do reading and spelling, and encouraging kids to dive into tough math problems and not be afraid to struggle.

Encouraging children’s instinctive curiosity is a good place to start. Adam Riess, who won the 2011 Nobel Prize in physics, peppered his parents with questions about math as a child, and they treated his curiosity as natural. On car trips with his family at age 8, “instead of asking the proverbial, ‘Are we there yet?’ I’d look at mile markers and the speedometer and figure out how much time we needed to get there,” says Dr. Riess, a professor of astronomy and physics at Johns Hopkins University. “Math seemed powerful to me.”

Parents don’t have to know math to help kids get off to a good start. Teaching youngsters to make connections between numbers and sets of objects—think showing a child three Cheerios when teaching the number three—helps children understand what numbers mean better than reciting strings of numbers by memory, Dr. Levine says. Doing puzzles together or using gestures to help describe spatial relationships such as “taller” and “shorter,” can instill spatial abilities, which are linked to better math skills, she says.

Jason Schneider

Something as simple as playing with blocks side-by-side and encouraging a child to replicate your stacks and structures can teach spatial skills, says Kelly Mix, a professor of educational psychology at Michigan State University.

Although Fiona Cameron struggled with math in school, she is trying to teach her children Iain, 5, and Mhairi, 3, to enjoy it. Snuggling with them at bedtime, she encourages them to spot patterns in picture books, such as the “stripe-stripe-dot” on an eel, says Ms. Cameron, a Pasadena, Calif., financial adviser. She also poses daily problems from Bedtime Math, a nonprofit website launched last February to help parents integrate math into their children’s lives.

The site posts a playful math question each day related to daily life and current events, such as the Olympics, and pushes “kids to wrestle with it in their heads, while talking with their parents about how to do it,” says founder Laura Bilodeau Overdeck of Summit, NJ, a former high-tech strategy consultant.

Baking in the kitchen, Ms. Cameron explains fractions while having each of her children crack half the eggs. Filling muffin cups becomes a subtraction problem: “If we fill eight muffin cups and there are 12 in all, how many more do we have to fill?” Thanks to this “stealth math” approach, her kids are having fun solving problems, she says.

When kids start bringing math homework home, many parents have to break old habits of emphasizing good scores and grades, and praise them instead for trying hard and using multiple approaches to figure out problems. In Dr. Levine’s study, 9-year-old children were more eager to tackle new math challenges if their parents focused on the process of problem-solving, rather than correct answers.

Struggling alongside your child can actually be helpful, says Suzanne Sutton, a Rockville, Md., math consultant and founder of NewtonsWindow.com, a website to help parents and students with math. A parent who is comfortable with trying and failing can teach a child how to look up things and grapple with challenges.

If you haven’t a clue how to help, Ms. Crowder says, avoid voicing your anxiety or frustration. Instead, tell your child your time together would better be spent in other ways, and offer to get a tutor or another person to help.

Another option: Hire your child to tutor you in math. A parent asked Ms. Sutton years ago how to help her teenage son tackle a tough algebra course when she couldn’t even understand the syllabus. Ms. Sutton told her to pick the toughest topic and offer to pay her son for writing a report on it and teaching it to her. The mother picked logarithms.

When her son gave her only a superficial explanation, Ms. Sutton says, the mother told him, “You didn’t meet the terms of our agreement. I don’t understand what it means.” The teen dug deeper and tried again, and finally got the concept across to his mom, Ms. Sutton says.

Secure knowing that he had already mastered one of the toughest topics in the course, the teen went on to do well in the class.

Write to Sue Shellenbarger at sue.shellenbarger@wsj.com

Introducing Mr. X The Math Magician

Mr. X, The Math Magician, is now booking school family math nights for the Fall and Winter. Bob Bishop is internationally known as America’s Math Magician. He visits many school each year to share the wonder of math. He has traveled from Boston to Los Angeles to Taiwan amazing and motivating teachers and students.

Mathematics: 1,000 Years Old, and Still Hot

Michael Morgenstern for The Chronicle

By Bryna Kra

President Obama’s 2014 budget request includes programs for research, development, and education in STEM (science, technology, engineering, and mathematics) fields. He has called for 100,000 new STEM teachers and one million new STEM graduates over the next 10 years, increased participation by groups historically underrepresented in these fields, and additional resources to support networks focused on STEM education. Mathematics is a major component of improving and expanding the STEM-literate work force.

But mathematicians, and the profession as a whole, are under scrutiny and attack. In 2012, the President’s Council of Advisors on Science and Technology labeled mathematics the “bottleneck that is currently keeping many students from pursuing STEM majors” and called for teaching of college-level mathematics courses “by faculty from mathematics-intensive disciplines other than mathematics.” E.O. Wilson recently claimed that “many of the most successful scientists in the world today are mathematically no more than semiliterate.” Paul Krugman agreed that researchers do not need much math and writes that “higher math isn’t usually essential; arithmetic is.”

Not only are these statements misguided, they also reinforce popular negative stereotypes. When someone learns that I am a mathematician, the inevitable comment is, “I was never good at math,” often accompanied by a dismissive chortle. Society accepts such comments but would never accept the analogous “I was never good at reading.” We accept the use of a calculator to add small numbers but not the use of software to read basic English. We accept T-shirts advertising how hard math is, popular caricatures of math geeks, and scientists who claim they are mathematically ignorant, but we do not condone illiteracy, and we work hard to eradicate it.

Unfortunately, these discussions are a distraction from the main issue: We need to train more people to be scientifically literate, and mathematics is a core component of such training. The precise nature of mathematics provides a framework for scientific advances. Without proficiency in the language of logical reasoning and quantifiers, it is impossible to work in a STEM field. The study of mathematics is thousands of years old, yet it is still a hot field.

Mathematics provides a tool box for the sciences. Mathematical models are used to explain and predict events around us, and rigorous mathematical thinking organizes ideas. Mathematics is used to model the spread of infectious diseases and then as a tool to halt the spread. It is used to develop rigorous standards for testing in drug trials that lead to major improvements in treatment, and it is used to design buildings that can withstand earthquakes and other natural disasters.

But mathematics is much more than a tool box. Its logical reasoning underpins all scientific discoveries, and it has transformed the way we understand our world. Long before experimental evidence was available, Galileo used mathematics to predict that the earth revolves around the sun. Centuries later, Albert Einstein used mathematics to show that the universe is curved, not flat; his theories were only experimentally verified years later.

Mathematics plays a role in the design of satellites, whose applications include communications, weather prediction, Internet access, and military uses. Before public encryption codes, a theorem of Pierre de Fermat established a rigorous foundation for a commonly used cryptographic system. Without Alan Turing’s fundamental work, the modern computer would not be possible. Numerical analysis, modeling, and statistics—all branches of mathematics—played a significant role in mapping the human genome. This is mathematical theory turned into applications, but applications that developed long after the theory.

Sometimes mathematical theory turns into practice much more quickly, as happened with the use of complex analysis to develop sophisticated coding techniques that protect the transmission of personal data.

Simpler mathematical concepts are implicitly used in numerous other professions: A plumber computes volumes and understands angles; a nurse calculates doses and drip rates; and a mechanic understands torque, ratios, and volumes.

This is not to say that every scientist needs a degree in mathematics. But every scientist needs the rigorous language and logic afforded by mathematics. Equating this knowledge with the ability to do calculus is as nonsensical as equating a biologist’s ability to hunt with the ability to map a genome. Mathematics should not be used as a gatekeeper for the sciences, but one cannot excel in science without basic mathematical reasoning.

Increasingly, students arrive at colleges without sufficient background to take basic mathematics courses. Nonetheless, we are expected to teach them the higher-level concepts they need for classes in biology, statistics, physics, and chemistry. But mathematics builds on a previous foundation and cannot be taught starting at the end. It is like asking a student unable to read a newspaper to analyze Shakespeare.

From an early age, children are directed to books appropriate to their individual reading levels. Working within guidelines for a third grader, a good teacher or librarian directs a student to appropriate material, and schools are equipped with reading material at a wide range of levels. But elementary education in mathematics does not have specialists like librarians to present students with appropriate-level material. The result is that we bore the good students and lose the weaker ones, helping only some in the middle. Improving the STEM work force starts early—focusing on individual needs and teaching the language of mathematics.

With all our debating, we have lost sight of the main issues: We need to support mathematics research at all levels and train more people to be mathematically literate. Does every scientific discovery depend on mathematics? Of course not. Can any scientist function without mathematics? Absolutely not.

Bryna Kra is a professor of mathematics at Northwestern University.

In Defense of Algebra

Nicholas Warner

Professor of Physics, Mathematics and Astronomy, University of Southern California

Posted: 08/09/2012  3:42 pm

   

   An apocryphal joke has a medical student failing physics and questioning why he should ever have to solve useless mechanics problems that he will never again see in his life.  The physics professor reassures the hapless student.

“These problems are terribly important: They save lives.”

“How?” cries the student.

“They keep thousands of idiots like you out of medical school.”

There are many reasons why we teach various parts of Physics and Mathematics but not all of them are obvious.  Physics centers around finding a simple set of universal laws that govern the universe at the most basic level. The skill set that physics is trying to teach medical students is the ability to disassemble a complicated problem into smaller, more easily solvable component parts, use some of those laws to understand the parts and then reassemble the pieces into a whole.  The human body is one of the most complicated machines we have ever studied and, if a doctor cannot understand the workings of a simple mechanics problem, then he really will kill people.

Andrew Hacker recently argued with some force, in the New York Times, that we should not be torturing the minds of high-school students with algebra.  The primary burden of the piece is to catalog the abysmal performance of US students and to evoke sympathies of the vast majority of people who never use algebra after high school. While recognizing the need for an intellectual elite that can do algebra, Dr. Hacker goes on to argue that something that is so useless should not be holding back students who might be able to make remarkable contributions elsewhere in our culture.  He advocates that students should be taught things that are more real, like how the CPI is constructed and the meaning of statistics. “This need not involve dumbing down. Researching the reliability of numbers can be as demanding as geometry.”  So presumably another set of differently-abled people will be held back and many more useless (and annoyingly difficult) things like Shakespeare, French and Astronomy can safely be dropped from the curriculum. I sympathize with the critical need for everyone to know what statistics and margins of error mean and for them to be able to compute their mortgage payments, but I also believe it is crucial that high-school students also learn very basic algebra.

One of the less obvious goals in algebra is to get people to think more abstractly.  Very elementary mathematics is all about “real things” and initially employs realia to help us add, subtract and multiply. From this experience we learn the language and some of the basic rules of mathematics.  We abstract and generalize the experience and learn that, when we manipulate one side of an equals sign then the equality is only true if we do the same thing to the other side.  Algebra makes a major intellectual leap: It names and labels things that we do not immediately know and that sometimes lie outside our direct experience. There are certainly other studies that involve abstractions like love, empathy and ethics, but in algebra we learn to handle abstractions that are not part of visceral human experience. We learn not only to be comfortable with such external unknowns but how to master them.

In algebra we develop essential life skills. We learn dispassionate analysis of external realities:  how to simplify the things that we know and reduce the things that we do not; to see that some problems are unsolvable as presented; to identify exactly what data is needed to solve a problem entirely; to recognize extraneous data that is irrelevant to our problem; to identify data that conflicts with what we already know about a problem.  By learning algebra we all become far better thinkers and even the majority who never use algebra again will still have enriched their life experience and expertise by grappling with difficult abstraction.

A limited understanding of one’s passions and of the real things that can be manipulated by hand were sufficient to the needs of peasantry in medieval times.  Today’s society requires us to think in abstractions, to understand why an invisible, odorless gas that we breathe out every moment of our lives might be killing us all through climate change. We need to manipulate these abstractions to reasonably determine whether something is a fad or whether we must change our life-style. Does vaccination cause an unacceptable risk of autism?  Does your body mass index affect your long-term health? What further data do we need to make an informed decision? What are the unknowns we should try to corral and eliminate before we make a critical decision or before we vote?

Algebra was developed by the Arab cultures as Western Europe was emerging from the Dark Ages.  Algebra is not just the language of mathematical elites, it is one of the cornerstones by which we have emerged from a peasant society, ruled by the small elites sometimes capable of abstract thought, to become a complex, vibrant democracy.  Algebra has helped us to rise beyond the simple understanding of immediate, tangible experiences and frame questions and look for the essential data that will give us deeper understanding. Only authoritarian and reactionary politicians benefit from a population for whom abstractions have no meaning. Such a population will be satisfied by sound bites and flag waving and will be placated by bread and circuses while their economy is subverted and their democracy implodes. Like mechanics problems in physics, the study of algebra, and the skills it develops, are not just critical to our long-term health individually but to our survival as a society.

Your Brain on Math

By Maia Szalavitz @maiaszApril 23, 2013

Getty Images

 Among the 100 million or so nerve cells in the brain,  it turns out there is a group dedicated to making sense of numbers.

 No one is born knowing their 1, 2, 3’s or  A, B, C’s. However, the brain clearly handles these  uniquely human but culturally varied types of knowledge differently. Many  people, for example, are far stronger in one area or another, showing a  propensity for verbal skills over numerical ones or vice versa.

So understanding how the brain codes these different systems could not only  aid children with language disabilities, for instance, or those who struggle  with processing numbers, but could also help to reveal more about how the brain  works to process new information and acquire knowledge.

In a new study, which was  published in the Journal of Neuroscience, researchers tested seven people  with epilepsy who had electrodes implanted in their  brains to determine the source of their seizures. Researchers have learned a great deal about the  brain with the help of such patients, including more about how the brain works  to produce speech and the effect of anesthesia on consciousness. The electrodes help inform doctors about the  source of electrical disturbances that contribute to the seizures; some of these patients may then be eligible for additional surgery to remove the damaged region. Because of the unusual circumstance of having electrodes in their brain that can track neural activity, these patients are often approached to volunteer for clinical  trials of brain function.

In the first experiment aimed at determining the brain’s “numeral area,”  participants looked at single digits, letters, foreign numeral symbols from  languages they didn’t know and at images of distorted numbers and letters that  were unreadable. They were asked to press keys on the computer indicating  whether or not they could read each symbol. In a second test, the volunteers saw  either numbers, the words depicting numerals (one instead of  1) or words that sounded similar to number words (won instead  of one), which they read aloud.

The researchers pinpointed a group of around 1 million to 2 million cells,  located in a region called the inferior temporal gyrus that extends into both  sides of the head near the ear canals. These cells responded much more strongly  when the participants processed actual numbers than number words, meaningless  symbols resembling the numbers or the numbers written in an unknown foreign  language.

“This is the first ever study to show the existence of a cluster of nerve  cells in the human brain that specializes in processing numerals,” Dr. Josef  Parvizi, associate professor of neurology at Stanford University and the lead  author of the study, said in a statement. “It’s a dramatic demonstration of our  brain circuitry’s capacity to change in response to education. No one is born  with the innate ability to recognize numerals.”

(MORE: The  Math Gender Gap: Nurture Trumps Nature)

Because the second experiment asked the participants to distinguish between  phonetically similar words for the numbers (too instead of  two) and the numerals, the researchers could determine that different  brain regions were activated by the idea of the number, not just the sound of  the word.

The authors say that the region of the brain that preferentially processes  numerals is close to the area that is responsible for interpreting language,  which makes sense since people often read words and numbers together. That could  explain why previous work showed that some types of brain damage, for example,  can interfere with reading letters but leave numeral reading unaffected, or can  cause verbal dyslexia but not numerical confusion.

Interestingly, however, the cells responding to numerals seem to be  physically close to those that process distorted numbers and to foreign number  symbols, suggesting they might share a common origin and could be specialized  versions of cells that generally process visual images of lines, angles and  curves. Additional research on this region of cells could inform how education  and learning tease out this subgroup of these cells to process numerals in  particular.

(MORE: Can’t  Do Math? How the Brain Makes Tradeoffs in Favoring Some Skills Over  Others)

The study may also explain why such regions have not appeared in imaging  studies of the brain that did not have the advantage of the implanted electrodes  to track physiological activity. Since the inferior temporal gyrus is so close  to the ear canals, functional MRI machines, which detect changes in oxygen use  and blood flow by nerve cells, may not be as sensitive to the activity of  neurons tucked away in that area.

However, say the researchers, combining different techniques should lead to  deeper understanding of the brain’s inner workings and start to reveal some of  its seemingly inscrutable mysteries.

Maia Szalavitz @maiasz

Maia Szalavitz is a neuroscience journalist for TIME.com and co-author of  Born  for Love: Why Empathy Is Essential — and  Endangered.

Read more: http://healthland.time.com/2013/04/23/your-brain-on-math/#ixzz2ZDnQrfbe

Why Algebra is Important

 written by: William Springer   • edited by: Trent Lorcher                       • updated: 1/20/2012

Math is the least popular school subject; because it constantly involves learning entirely new ways of thinking about things, it provides more of a mental challenge than most people care for. However, algebra is such a large part of our daily lives that is important for everyone to understand. So what are the applications of high school algebra? Exactly why is algebra important?

• Algebra is the Key to Advancement

• Planning to go to college? Chances are you’re going to need algebra. Obviously the hard sciences (such as physics and chemistry) are extremely mathematical, but you might not realize how much other fields depend on math as well. Computer science? You need algebra to analyze how quickly programs run. Psychology? Requires statistics, which comes after algebra. Art? Algebra is useful to calculate the correct proportions which will lead to an aesthetically pleasing result. Music? The underlying structures of music are basically mathematical.

  Planning to start working right out of high school rather than going on to college? A 2006 ACT study found that occupations that pay enough to support a family but do not require a four year degree, such as becoming a plumber or electrician, also require basic algebra skills.

  Because of its importance, algebra is often referred to as a gateway subject; those who do not understand it find themselves unprepared for college and the workforce.

  Applications of High School Algebra in Everyday Life

• But suppose you won’t be going to college and plan to clean bathrooms for a living. Does that mean you don’t need to know algebra?

  Well, sure. Unless you plan to go grocery shopping. (The same item from different companies tends to be packaged in different units, so you need to do a quick calculation if you want to know which is cheaper). You don’t need anything particularly complex – just set x to be the price per unit and solve – but this is a simple application of high school algebra.

  Real-World Example

• Suppose you want to buy a new television, but you want it to fit on your current TV stand. If your TV stand is 19 inches wide, how large of a TV can you get?

  Because TV size is measured by the length of the diagonal, this is a great example of a time when you’d use the Pythagorean Theorem. You could carry a tape measure to the store and measure how wide each TV is. Or you can simply calculate how large of a TV you can buy!

  If you plan to buy a traditional (non-widescreen) television, the width to height ratio is 4:3; plugging this in to the pythagorean theorem, we get 4x² + 3x² = y², where x is the width of your TV stand and y is the largest TV you can buy. For a widescreen tv, replace 4 and 3 in the above formula with 16 and 9.

   Necessary for Success In Business

• I run an online toy store, so why is algebra important to me as a business owner? I need to be able to calculate my profit margin on any given item and decide whether it’s worthwhile to stock it in my store. I also need to calculate what’s the lowest price I can sell an item for and still make enough money to cover expenses.

  Again, this is not complicated math, but once you’re used to it, algebra really isn’t that complicated, and it makes a lot of things in everyday life much easier. Although I use algebra and graph theory for my work in computer science, I find that understanding applications of high school algebra makes the day to day things much simpler and less time-consuming. That means less time spent and more money earned…and who can say no to that?

This is why Algebra matters

A sportswriter sarcastically wrote that an opening preseason basketball game will “become about as significant as algebra formulas learned in high school.” The writer may not realize it, but nearly all sports statistics are produced using algebraic equations. Average points per game are used to determine the Most Valuable Player. Winning percentages are used to determine top rankings. These are calculated with concepts learned in Algebra.

 There are some significant reasons why Algebra matters so much in life.  Student success in algebra can help predict salary earning, math confidence, high school courses and college readiness.

Zalman Usiskin, the director of the University of Chicago School of Mathematics, writes in “Why is Algebra Important to Learn” that without a knowledge of Algebra, students:

• are kept from doing many jobs or even entering programs that will get you a job;
• are more likely to make unwise decisions, financial and otherwise; and
• will not be able to understand many ideas discussed in chemistry, physics, the earth sciences, economics, business, psychology, and many other areas.

Students who leave middle school with a strong understanding of Algebra have more confidence in math and consequently envision themselves as more likely to go on to college, according to research from The National Center for Educational Statistics, Early Childhood Longitudinal study data published in 2010.  At Flagstaff, our goal in middle school is for every student to successfully pass Algebra by the end of 8th grade. To achieve this goal, we have two different ways we approach learning Algebra.  Typical Algebra students at Flagstaff take Algebra over the course of 7th and 8th grades.  By taking two years to study Algebra, we ensure students have the time necessary to fully master the content.  Some students who have proven ready to master the content in a single year take the full Algebra course in one year and go on to take more advanced classes in subsequent years.

By taking Algebra in middle school, students can take more advanced math classes in high school. Students who take advanced math classes in high school are more likely to enter into a Science, Technology, Engineer and Mathematics (STEM) profession later in life.  According to the 2011 study “STEM: Good jobs now and for the future,” published by the U.S. Department of Commerce, this is important for two reasons.  First, STEM occupations are projected to grow by 17 percent from 2008-2018, compared to 9.8 percent growth for non-STEM occupations.  Second, STEM workers command higher wages, earning 26 percent more than their non-STEM counterparts.

Algebra is helpful for many reasons.  The mind develops new ways of thinking through the process of learning algebra.   It helps us understand and make sense of patterns in life.  As educators, we are committed to helping students master Algebra, because Algebra matters in life.

In Defense of Algebra

By JESSICA LAHEY

Jessica Lahey Algebra homework, the second time around.

I admit it: I am one of the millions of Americans who suffer from math anxiety, and my math phobia runs deep. I shudder when the check arrives after dinner, then surreptitiously slide it toward my math-proficient husband. I love all aspects of my teaching job save for grading, which requires me to perform addition and division, and worse, assign inflexible numbers to my students’ aptitude. I am happy to report that I have never, not once, used algebra in my everyday life.

Given my history with math, Prof. Andrew Hacker’s Op-Ed article “Is Algebra Necessary?” should have prompted cheers and fist-bumps with my teenage son. What I got instead was wisdom from the mouth of babes. “Who says algebra isn’t useful?” my son demanded as I slid him the headline. “It’s useful — I mean, it’s not useful now, but I don’t know what I’m going to be. What if I want to be an engineer?”

Professor Hacker’s article has clearly hit a nerve. His opinion piece has accumulated hundreds of comments, many from educators, engineers and mathematicians arguing for the merits of algebra. I claim no such expertise; my perspective is personal.

I know precisely where I lost my battle with math, the moment I was informed clearly and unequivocally that I simply wasn’t “a math person.” My seventh-grade math teacher, an otherwise lovely man, called each of his students up to his desk one by one in order to write a “1” (for the honors track) or “2” (for the standard track) on the school’s official math placement forms. As I watched from over his hunched and courduroyed shoulder, he wrote a beautiful, decisive and neat “1” on my form.

There it was, in permanent ink. I was good at math.

“Jess, could you come back up here for a minute?” he asked as I floated back to my seat.

He reclaimed my form, and carefully overlaid that beautiful “1” with a dark, clumsy “2,” pressing hard with his black pen in order to make sure the ink obliterated any evidence of his indecision.

And from then on, I wasn’t good at math anymore.

From the moment I was relegated to standard math, I knew I was never going to be an engineer. I went through the motions of my math education, but never put any heart into the subject. My teachers didn’t push back very hard because the evidence was in: I just wasn’t a math person. I’d make it through to the day I could opt out of math forever, and I would never look back.

Except, I did. For years, I have eyed my colleague Alison Gorman’s math classroom with wary suspicion. I peek in on her class when I hear laughter, wondering what could possibly inspire mirth in algebra class. I have watched with wonder during recess when her MathCounts students show up with their lunches, willing to spend valuable leisure time challenging each other to think through math problems.

At the same time, my son was beginning to come home with math work I could not understand, let alone help him with, and my math deficits had become a household joke. When Ben started to have trouble with the occasional math problem, I realized he had hit a crucial moment in his education. It was time for me to rewrite my own past in order to set an example and protect his future, whether or not he decides to become an engineer. I took my chance — and “enrolled” in Mrs. Gorman’s Algebra I.

Alison Gorman knows about my history with math, but she steadfastly refused to view me as a “2.” She has taught me much more than the quadratic formula and the fact that (x² + y²)² = (x² – y²)² + (2xy)². I have learned discipline and the importance of linear, organized thinking. I have learned patience, diligence and shockingly, I have learned that I am good at math. Even my teenage son has been impressed by my efforts, and believe me, very little impresses him these days.

Algebra class has made me a better student, but more important, it has made me a better teacher and parent. I will be far less likely to impose fixed values and expectations on children, because you know what I learned in algebra class? Even the simplest equations can contain more than one variable. And for that lesson alone, algebra is necessary.

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Jessica Lahey is a middle-school teacher. She blogs about education and parenting at Coming of Age in the Middle.

How to be good at Mathematics?

by Math-O-Mania (Notes) on Sunday, November 7, 2010 at 6:45am

I love this question. Most people think that either you’re good at mathematics or you’re not…..period….end of story. But this is such a defeatist attitude, to say the least. And worse than that, it can be a self-fulfilling prophecy. If you think you aren’t good at mathematics (or anything else for that matter), if you’ve always been told that you’re not good at mathematics, if even your parents say that THEY were not good at mathematics, well then what chance do you have? The answer is, none. But I believe that all of this is a fallacy. There are several key elements necessary to be good at mathematics, and these are available to anyone who desires them.

1. You must be interested in mathematics. You must want to be good. If you find that after a while you start to see the beauty in mathematics this is all the better.

2. What many people don’t realize is that mathematics does not come easily to anyone – not even to mathematicians. If it did, they would lose their interest in a heartbeat. My absolute favorite quote of all time comes from Albert Einstein – “Do not worry about your difficulties in Mathematics. I can assure you mine are still greater.” Anyone who pursues mathematics reaches a point where it becomes difficult. But as they say about physical exercise – “No pain, no gain.” The important thing to realize is that just because you don’t understand a mathematical concept at first, or don’t know how to solve a problem this doesn’t mean you are not good at it. Imagine if Einstein had thrown up his hands and said “Oh, I’m just not good at this!” when he ran into his first difficulty!

3. Don’t get hung up on thinking that every step you take as you are learning has to make sense to you; that you have to understand what it means, why you are doing it, where it will lead. I picture myself back in high school, loving my math and not caring in the least if I didn’t know “why.” And sometimes, I even felt like saying “Don’t bother me with WHY – just let me do it.” I’ve found that lots of other mathematicians and math teachers say the same thing. But the cool part is that as your knowledge deepens and broadens you probably will find that “why?” begins to become clearer. Sometimes you have to have a larger perspective to be able to step back and see how it all fits together. This comes with time. And don’t worry – there’ll always be a new”why?” on the horizon.

4. Don’t equate being quick with math to being better at math. Slow doesn’t mean “not good.” I remember my moment of epiphany when I was in graduate school. I was so intimidated by other students in the class who shouted out the answer right away when the professor posed a problem. I couldn’t do that. But then I realized that just because I was not as quick as some didn’t mean I was not as good as they were. I needed time, and quiet to concentrate. I got an A in the course – some of those “quick” students probably didn’t. Being quicker certainly did not make them better.

5. Don’t be afraid to “get your hands dirty”. Imagine that your car isn’t running. You lift up the hood and stand there staring into the engine trying to figure out what’s wrong, and wondering how to fix it. Standing and looking will never get it fixed. You have to get in there and check things out, try different things, get your hands dirty – until you find and then fix the problem. Well math is the same way. If someone who is “good at math” sees a problem they are not familiar with it would be very rare that they would see the whole solution laid out in their mind before they even start step one. But they are not afraid to start – anything that seems like it might lead somewhere. Then take the next step, and the next step in a similar manner. And if they find that it is not leading anywhere, well then they crumple up the page and start over again trying something different.

6. Step away for a while from a problem that is perplexing you. I do some of my best thinking while I’m driving, before I fall asleep, scribbled on napkins in restaurants. You never know when the light bulb will suddenly turn on and illuminate the way.

So go ahead; try it. Expect some frustration, and great gratification once you’ve solved the problem. Revel in the gratification for a bit, and then challenge yourself to begin the process again with a new problem. And try to relax about it and maybe even enjoy it!

By nadp. Source – Hubpages

Stanford online course for teachers, parents: Helping students to love math

Stanford Report, June 28, 2013

Already some 20,000 people have enrolled in a free online class, beginning July 15, that offers a new approach to engaging students in mathematics.

By Jonathan Rabinovitz

The 18 freshmen in Professor Jo Boaler‘s seminar had demonstrated the academic promise needed to gain admission to Stanford, so it was striking that they shared a similar fear: mathematics.

“I subconsciously thought either you were or you weren’t good at math,” said one student, Chloe Colberg, echoing the views of many in the class. Indeed, that notion prevails in schools across the nation, and Boaler, a professor of education, has made it her mission to change that attitude.

Lisa F. Young / ShutterstockProfessor Jo Boaler’s new online course provides teachers and parents with a different way to teach mathematics, an approach that her research has shown helps students to overcome their fear of the subject while also improving their academic performance.

The seminar that she offered last fall emphasized that math demands creativity, collaboration and discussion more than memorization, drills and just hurrying to get the right answers. According to Boaler, the way math is traditionally taught reinforces the idea that it’s an innate talent.

“Coming into this class, I realized, oh, OK, that had been the mindset I had for my whole life,” Colberg said. “This class allowed me to see that’s not really how it is.”

She and her classmates said that they finished the course last year with a new appreciation of math.

Such dramatic transformations spurred Boaler to look for a new way to reach more people with her lessons. The result is a free online course, How to Learn Math, for K-12 teachers and parents that aims to help them improve students’ engagement with math, as well as help teachers prepare to implement the new Common Core standards. The course covers topics such as “Knocking Down Myths About Math,” “Mistakes, Challenges and Persistence” and “Appreciating Algebra.”

It will be offered, beginning July 15, through the university’s new open-source platform, OpenEdX. Already more than 20,000 people have enrolled. A course listing on the Stanford Online website provides further detail about the lessons and how to register. Boaler will also offer a version of the course designed especially for students from ages around 10 to adult in the 2013-14 school year.

Boaler has devoted her career to studying math teaching and learning why math evokes such strong negative feelings among so many. One survey of adults found that four out of 10 hated math in school, twice as many as any other subject. Her research presents evidence that an approach to teaching math that includes problem solving, mathematical discussions and the use of real-life examples can not only make students more enthusiastic about the subject but also improve their performance.

Emma DugganEducation Professor Jo Boaler

Boaler said that the other important strand in her work is the mindsets students come to math with – and the ever-present myth that only some students can be good at math. She has presented her ideas and findings in peer-reviewed journals as well as in a book for a general audience, What’s Math Got to Do With It? How Parents and Teachers Can Help Children Learn to Love Their Least Favorite Subject.

“Math teaching is often too procedural,” Boaler said. “There’s a lot of drill and practice.

“I want students to understand the importance of conceptual thinking in math. In this class, for instance, when we work on number problems, we’ll look at how they can be solved in many ways, not just one. And we’ll explore how to represent and understand them visually.”

In Boaler’s approach, a teacher could ask a class of students how they can solve the problem 18 times 5, without pen and paper. The teacher then collects the different methods and compares them. There are several different ways of solving the problem, including multiplying 20 x 5 and subtracting 2 x 5; multiplying 18 x 10 and halving the answer; or adding 8 x 5 and 10 x 5 – all ways to reach 90.

The course will feature interviews with successful users of math in different, interesting jobs – a filmmaker and an inventor of self-driving cars – to demonstrate the importance of conceptual math and the types of mathematical relationships that may benefit students.

It will also include an interview with Carol Dweck, professor of psychology at Stanford, whose research showing the impact of having a “growth mindset – a belief that math is learned, not an innate talent – underlies Boaler’s approach to teaching math.

Boaler said that her approach encourages students to think of themselves as capable of math, and to see math as an interesting, visual subject that is all around them. Her research has shown that when students approach math in these ways they enjoy their learning and achieve at higher levels.

The course consists of eight sessions of one to two hours. About 15 to 20 minutes of each session features video of Boaler introducing ideas; the rest of the time involves exercises and other activities that engage participants. In addition, the class promotes interactivity through an online forum where students can discuss the lessons with each other.

Participants can also engage in a live video session with Boaler where she will answer questions that course participants submit.

“Teachers at many schools are taking it together and planning to discuss and do all the activities in groups,” Boaler said.

The new course will be one of the first to debut on OpenEdX, which replaces Stanford’s previous online learning platform, Class2Go.

In April, Stanford and edX, the nonprofit online learning enterprise founded by Harvard and MIT, announced they would collaborate on future development of the edX online platform.

Boaler’s course is particularly timely, given that 45 states, including California, are adopting the Common Core, which sets higher standards for K-12 students’ mastery of math and reading. The math standards call for better conceptual understanding and fluency in problem solving.

“Many districts are really worried about how unprepared their math teachers are for the Common Core,” said Boaler. “The key is for teachers to learn to teach the concepts at the heart of mathematics and to help learners understand they are all capable of high-level math.”

Jonathan Rabinovitz is the director of communications at the Graduate School of Education.

In Defense of Algebra

by    Nicholas Warner

Professor of Physics, Mathematics and Astronomy, University of Southern California

An apocryphal joke has a medical student failing physics and questioning why he should ever have to solve useless mechanics problems that he will never again see in his life.  The physics professor reassures the hapless student.

“These problems are terribly important: They save lives.”

“How?” cries the student.

“They keep thousands of idiots like you out of medical school.”

There are many reasons why we teach various parts of Physics and Mathematics but not all of them are obvious.  Physics centers around finding a simple set of universal laws that govern the universe at the most basic level. The skill set that physics is trying to teach medical students is the ability to disassemble a complicated problem into smaller, more easily solvable component parts, use some of those laws to understand the parts and then reassemble the pieces into a whole.  The human body is one of the most complicated machines we have ever studied and, if a doctor cannot understand the workings of a simple mechanics problem, then he really will kill people.

Andrew Hacker recently argued with some force, in the New York Times, that we should not be torturing the minds of high-school students with algebra.  The primary burden of the piece is to catalog the abysmal performance of US students and to evoke sympathies of the vast majority of people who never use algebra after high school. While recognizing the need for an intellectual elite that can do algebra, Dr. Hacker goes on to argue that something that is so useless should not be holding back students who might be able to make remarkable contributions elsewhere in our culture.  He advocates that students should be taught things that are more real, like how the CPI is constructed and the meaning of statistics. “This need not involve dumbing down. Researching the reliability of numbers can be as demanding as geometry.”  So presumably another set of differently-abled people will be held back and many more useless (and annoyingly difficult) things like Shakespeare, French and Astronomy can safely be dropped from the curriculum. I sympathize with the critical need for everyone to know what statistics and margins of error mean and for them to be able to compute their mortgage payments, but I also believe it is crucial that high-school students also learn very basic algebra.

One of the less obvious goals in algebra is to get people to think more abstractly.  Very elementary mathematics is all about “real things” and initially employs realia to help us add, subtract and multiply. From this experience we learn the language and some of the basic rules of mathematics.  We abstract and generalize the experience and learn that, when we manipulate one side of an equals sign then the equality is only true if we do the same thing to the other side.  Algebra makes a major intellectual leap: It names and labels things that we do not immediately know and that sometimes lie outside our direct experience. There are certainly other studies that involve abstractions like love, empathy and ethics, but in algebra we learn to handle abstractions that are not part of visceral human experience. We learn not only to be comfortable with such external unknowns but how to master them.

In algebra we develop essential life skills. We learn dispassionate analysis of external realities:  how to simplify the things that we know and reduce the things that we do not; to see that some problems are unsolvable as presented; to identify exactly what data is needed to solve a problem entirely; to recognize extraneous data that is irrelevant to our problem; to identify data that conflicts with what we already know about a problem.  By learning algebra we all become far better thinkers and even the majority who never use algebra again will still have enriched their life experience and expertise by grappling with difficult abstraction.

A limited understanding of one’s passions and of the real things that can be manipulated by hand were sufficient to the needs of peasantry in medieval times.  Today’s society requires us to think in abstractions, to understand why an invisible, odorless gas that we breathe out every moment of our lives might be killing us all through climate change. We need to manipulate these abstractions to reasonably determine whether something is a fad or whether we must change our life-style. Does vaccination cause an unacceptable risk of autism?  Does your body mass index affect your long-term health? What further data do we need to make an informed decision? What are the unknowns we should try to corral and eliminate before we make a critical decision or before we vote?

Algebra was developed by the Arab cultures as Western Europe was emerging from the Dark Ages.  Algebra is not just the language of mathematical elites, it is one of the cornerstones by which we have emerged from a peasant society, ruled by the small elites sometimes capable of abstract thought, to become a complex, vibrant democracy.  Algebra has helped us to rise beyond the simple understanding of immediate, tangible experiences and frame questions and look for the essential data that will give us deeper understanding. Only authoritarian and reactionary politicians benefit from a population for whom abstractions have no meaning. Such a population will be satisfied by sound bites and flag waving and will be placated by bread and circuses while their economy is subverted and their democracy implodes. Like mechanics problems in physics, the study of algebra, and the skills it develops, are not just critical to our long-term health individually but to our survival as a

Chess and Math? Improving math skills one move at a time

From Deb Russell

First of all, Math provides the building blocks and foundation that children will need throughout their lives. If you think that the basics are adding, subtracting, multiplying and dividing – think again! Today, we live in an information age where it’s reported that information is doubling at a rate less than every two years. The basic skills need to function in the workplace today are decision making, problem solving, critical thinking and deductive and inductive reasoning along with the ability to make judgements and good estimates. We haven’t loved math but we’ve certainly loved our games. That’s when Chess comes into the picture.

Chess is a game that requires problem solving. Math requires problem solving, it makes good sense then to become a good problem solver means you’ll do better in math. Chess (and other games) require a mental workout, thinking ahead, planning, being systematic, and determining the outcomes of certain moves. Chess moves can’t be memorized, weakness in math often stems from an over emphasis on memory skills instead of thinking skills. Research studies have indicated that students playing chess have improved problem solving skills over the group that have not been involved in the playing of chess. Ollie LaFreniere, the Washington Chess Federation’s statewide Coordinator for Scholastic Chess, said in a Seattle Post-Intelligencer interview on May 31, “Chess is the single most powerful educational tool we have at the moment, and many school administrators are realizing that.” There are also studies that indicate that many students’ social habits improved when playing chess.

The late Faneuil Adams (president of the American Chess Foundation (ACF). believed that chess could enhance learning, especially for the disadvantaged. He with the ACF founded the Chess in Schools Program which initially began in New York’s Harlem School district. Early in the program, the focus was on improving math skills for adolescents through improved critical thinking and problem solving skills. Remarkably “test scores improved by 17.3% for students regularly engaged in chess classes, compared with only 4.56% for children participating in other forms of enriched activities.”

The ACF reports that chess improves a Child’s:

Visual memory

Attention span

Spatial reasoning skills

Capacity to predict and anticipate consequences

Ability to use criteria to drive decision making and evaluate alternatives

Many countries are following suit. In Canada, a growing number of elementary schools have incorporated chess into the regular school curriculum. Looking specifically at Quebec, 10 years ago their math scores were the lowest in the country, Chess became a school subject and now the children in quebec have the highest average math scores in Canada.

Overcoming Math Phobia through Chess

Why is it when we ask the majority of people what they think of math or if they’re good at math, they immediately show a look of distaste? Think of what happens when a group of people are at a restaurant and the bill comes on one check instead of on separate checks. Usually, you’ll hear ‘here, you figure it out, I was never any good at math.’ I’m sure you’ve been in this situation yourself at times. However, do they ever say, here you figure it out – I can’t read. When we take a look at why people don’t like math, we’re told it’s because it makes them feel stupid, or that they just don’t understand it because there are too many rules, formulas and procedures to remember. But, can you think of a situation where there are rules, procedures and such that we enjoy? Games!!! Perhaps if our math instructors treated math like a game, more individuals would excel and would like mathematics. A more favorable attitude in math leads to better performance. Let chess pave the way to better math scores and improved problem solving strategies!

Mathematics and the game of chess

by Enrique Diaz G.

Our purpose for writting this article is to attempt to answer the question: Is there any relationship between thinking mathematically and thinking in the game of Chess? In other words, must a person possessing an active mind in Mathematics become necessarily a good Chess player have skills in Mathematics?

It is necessary to point out that due to the subject complexity, our efforts will be to explain basic characteristics of both Mathematics and Chess which have been posed by well-known Mathematicians and Chess players. Accordingly, we are not interested in exposing facts, for example, from the Theory of Knowledge, Psychology, Epistemology or going further into the technical and sophisticated aspects of Chess.

To begin with, let us examine some qualities of Mathematics.

People having poor experience in Mathematics believe that knowing how to add, subtract, multiply or divide enables them to say that they could master Mathematics. Others possessing some skill in performing quick calculations think they are “Mathematicians”. In both cases, they indicate they do not know about the meaning of Mathematics:

Mathematics as an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generality and individuality. Though different traditions may emphasize different aspects, it is only the interplay of these antithetic forces and the struggle for their synthesis that constitute the life, usefulness, and supreme value of mathematical science. (Courant& Robbins, 1941).

Even though at the beginning this definition seems difficult to understand, it is the best approximation to comprehend the whole sense of mathematics.

The first major step which the Greeks made was to insist that Mathematics must deal with abstract concepts… On the basis of elementary abstractions, mathematics creates others which are even more remote from anything real. Negative numbers, equations involving unknowns, formulas, and other concepts we shall encounter are abstractions built upon abstractions. Fortunately, every abstraction is ultimately derived from, and therefore understandable in terms of, intuitively meaningful objects or phenomena. The mind does play its part in the creation of mathematical concepts, but the mind does not function independently of the outside world. Indeed the mathematician who treats concepts that have no physically real or intuitive origins is almost surely talking nonsense .² (Kline, 1962).

After this brief glance at the meaning of Mathematics, let us seethe most commonly methods used in this science. According to Kline (1962), the major method of obtaining knowledge is reasoning, and within the domain of reasoning there are several forms. One can reason by analogy, which consists of finding a similar situation or circumstance and to argue that what was true for the similar case should be true of the one in question. Of course, one must be able to find a similar situation and one must take the chance that the differences do not matter.

Another common method of reasoning is induction. People use this method of reasoning every day. Inductive reasoning is in fact the method must commonly used in experimentation. An experimentation is generally performed many times, and if the same result is obtained each time, the experimenter concludes that the result will always follow. The essence of induction is that one observes repeated occurrences of the same phenomenon and concludes that the phenomenon will always occur.

There is still a third method of reasoning, called deduction. Let us consider an example. If we accept as basic facts that honest people return found money and that John is honest, we may conclude unquestionably that John will return money that he finds. In deductive reasoning we start with certain statements, called premises, and assert a conclusion which is a necessary or inescapable consequence of the premises.

All three methods of reasoning, analogy, induction, and deduction, and other methods, are commonly employed. There is one essential difference, however, between deduction on the one hand and all other methods of reasoning on the other. Where as the conclusion drawn by analogy or induction has only a probability of being correct, the conclusion drawn by deduction necessarily holds. Despite the usefulness and advantages of induction and analogy, mathematics does not rely upon these methods to establish its conclusions. All mathematical proofs must be deductive.

Each proof is a chain of deductive arguments, each of which has its premises and conclusion.

Finally, we point out that Mathematics must not be considered only as a system of conclusions drawn from premises or postulates. Mathematicians must also discover what to prove and how to go about establishing proofs. These processes are also part of Mathematics and they are not deductive:

In the search for a method of proof, as in finding what to prove, the mathematician must use audacious imagination, insight, and creative ability. His mind must see possible lines of attack where others would not. In the domains of algebra, calculus, and advanced analysis especially, the first-rate mathematician depends upon the kind of inspiration that we usually associate with the creation of music, literature, or art.³ (Kline, 1962).

Let us consider now the game of Chess showing some of its characteristics and trying to find out any special method of reasoning that Chess players could use. First of all, we are not going to explain the game as accurately as in a Chess book. Instead, we will describe the game in a rather general form.

A Chess game is a war between two medieval Kingdoms. In medieval times, when Kingdoms were small, absolute monarchies, if the King was imprisoned or captured the war was over. So it is in the game of Chess. The game is finished when one of the Kings is captured. It may here be noted that Chess is not necessarily a game of elimination but rather a game of tactics. However, elimination of the opponent’s pieces plays an important part since by so weakening or wearing down your opponent the end is hastened. A general definition is given by Mason: “Chess is a process of thought conditioned and limited by the Institutes and Rules of the Game. The judgments of thought are certified or visibly expressed upon the chessboard in movements of various forces”.⁴ (Mason, 1946)

The invention of Chess had been credited to the Persians, the Chinese, Arabs, Jews, Greeks, Romans, Babylonians, Scythians, Egyptians, Hindus, Irish and the Welsh. Although the precise origin has been lost in obscurity, it continues to excite the speculation of men of learning at one end of dilettantes at the other. Careful research has called it an “ancient” game; the foolhardy are quite ready to underwrite exact dates. Other characteristics are pointed out by Mason (1946).

But there is a mischievous imagination abroad that it is a difficult game. It takes time. Its intricacies and profundities are not rightly within mastery of the average human intellect. This, in a sense, is true enough, else Chess would not be Chess. That it cannot be all known and mastered by anybody is truly its chiefest, crowning merit. It is an instrument all may play, no two precisely alike, and yet everyone his best. Too much time may be devoted to it. Chess is a science as well as an art. In its exercise the tendency is to premature mechanical facility, rather than to a clear perception of principles; though upon this, of course, all true and lasting faculty necessarily depends.

Now, after these rough explanations about Chess, let us see what attributes a person must possess in order to become a good Chess player. In other words, what is the pattern of intellectual skills that makes one man a good chess player while the other remains a duffer?

In the first place, topnotch Chess requires visual imagery. Before you make a contemplated move, you have to visualize how the board will look after you make it, and then how it will be changed by your opponent’s response, and how it will look after you meet another possible answer. You also need patience and restraint.

The quick thinker is often a fool. You need a good memory too. Memory has two components: ability to retain, and ability to recall. The chess player needs both. Finally, Chess calls for a certain kind of “reasoning”. This reasoning consists of joining together the above elements in order to give an appropriate response to any move. This, then, is the “putty” which holds the “blocks” together. The “blocks” are memory, patience and imagery. The putty is associative reasoning. In daily life you use some of these processes, but you also use other intellectual techniques. For instance, inductive reasoning is not much used in chess, but it pays dividends in business and professional life.

Now, let us consider a mathematician with all his capacity to think abstract concepts; with all his methods of reasoning, that is, reason by analogy, induction, and deduction. Will he become a good Chess player? One of the greatest mathematicians, Henri Poincare, denies this possibility:

In the same way I should be but a poor chess player; I would perceive that by a certain play I should expose myself to a certain danger; I would pass in review several other plays, rejecting them for other reasons, and then finally should make the move first examined, having meantime forgotten the danger I had foreseen. In a word, my memory is not bad, but it would be insufficient to make me a good chess player. Why them does it not fail me in a difficult piece of mathematical? Evidently because it is guided by the general march of the reasoning.⁵ (Binet, 1946).

Also, we have Binet’s thinking about this matter:

Conversely, mathematicians have after been interested in Chess. However, few famous mathematicians have been first-rate chess players … I will readily admit that a similarity exists between chess and mathematics, especially between chess and mental arithmetic, without, however, ascribing to them identical mental operations. Chess and Mathematics follow parallel lines. In other words, the two types of study have a common direction; they presuppose the same taste for complex mental operations which are both abstract and precise; and they both require a strong dose of patience and concentration.⁶ (Binet, 1966).

Now, let us consider a good Chess player, for example, the so-called, chess master. Could he become a good mathematician also? One categorical, answer is expressed by Horowitz and Rothenberg. ,

As strange as it may seen, the chess player’s skill may have no relationship whatever to any other facet of his personality or activity. The common belief that expert chess players are good mathematicians is fiction. On the other hand, good mathematicians may turn out to be good chess players … One conclusion and one only is a safe one: Expert Chess-players are able to play Chess expertly.⁷ (Horowitz & Rothenberg, 1963).

Again Poincare points out that:
…, but, however extraordinary he (a chess player) may be, he will never prepare more than a finite number of moves; if he applies his faculties to arithmetic, he will not be able to perceive its general truths by a single direct intuition; to arrive at the smallest theorem he can not dispense with the aid of reasoning by recurrence, for this is an instrument which enables us to pass from the finite to the infinite, (Poincare, 1946).

Another interesting point of view concerning this point is set up by Abrahams:

The Chess process, being intuitive, Is not mathematical in the normally accepted sense of that term. The fact that the Chess player is controlled by rules makes him comparable to the user of a language with a grammar rather than to those who explicitly use rules and formulate deductively. The Chess player is sometimes in a position to be aided by learning and memory. But essentially each Chess act is a fresh application of mind to data. Than which nothing is less mathematical or less inferential.⁸ (Abrahams, 1951).

To summarize then, we can say that up to now there is not any valuable reason to support the theory that a Chess player must possess abilities related to Mathematics. Lastly, we will indicate some ideas about Chess as a mental process.

Why has Chess remained the world’s most popular game for fifteen centuries? Some authorities attribute the game’s fascination to its mimicry of war and all the other struggles of “real life’ , others see Chess as a convenient escape from reality. Some have found in Chess an admirable schooling for the mind; others would agree with Ernest Cassirer that “what Chess has in common with science and fine art is its utter uselessness” … The great Chess masters, like the great poets, the great composers, the great artists, the great mathematicians, the great mystics, have the faculty of immersing themselves in some creative process with a concentration, a finality, that is beyond most of us… Chess concepts, like mathematical concepts, depend on formal relations, and therefore exist forever, independent of the capacity of this or that human brain to grasp them.

Now nobody, according to Abrahams (1951), has succeeded in explaining, in casual terms, how the mind apprehends in the first place, or why it falls to apprehend, whether in Chess or in any department of mental activity. The working of the mind is a fact common to intelligent human beings, and Chess has no exclusive claim of vision; for an element of vision or intuition, however slight, is involved in any mental process which is distinguishable form reflex action. But Chess is important because in it the functions of the mind are relatively clear and the mental process is less assisted than inmost other activities by positive rules. Within limits set by the material (the pieces, the board, and the matrix of paths available to pieces on the board) the mind is moving freely. Its scope is the possibility of the material, limited only by the degree of vision available to the player. Its methods, whatever they are, do not resemble the mechanical use of formula, which is the essence of mathematics. The appearance of simplicity that characterizes effective mental action is as deceptive in Chess as it is in any other department of science or art. Imagination traces its own paths and develops idiosyncrasies. Through seeing a clever maneuver, an improving Chess player may find himself quicker at apprehending an analogous idea; and, more remarkably, quicker at apprehending a different clever possibility in a different setting.

Where Chess differs from many other activities is in that, in Chess, the mind is “influenced” by notions and ideas that it has appreciated, rather than “stocked” with them, or guided by them as one is guided by a signpost.

As to Chess ability, at the present stage of psychology, the nature of imagination remains obscure. Therefore, it is impossible to speak about special faculties for Chess, or even to establish any cognate relationship between skill at Chess and other abilities. Certainly, famous Chess masters have excelled in other, and various activities – from the music of Philidor and the Shakespearian researches of Staunton to the medicine of Tarrash and the engineering of Vidmar. Nor is there evidence of the transmission of Chess skill, innate or acquired. Why some persons are good at Chess, and others bad at it, is more mysterious than anything on the Chess board. “Chess can never reach its height by following in the path of science … Let us, therefore, make a new effort and with the help of our imagination turn the struggle of technique into a battle of ideas” ( Jose Raoul Capablanca).

REFERENCIAS

Abrahams, Gerald. (195 1) The Chess Mind. London.

Binet, Alfred. (1966). Mnemonic virtuosity. New York.

Courant, Richard and Herbert Robbins. (194 1). What is Mathematics?. New York.

Horowitz, I.A. and P.L. Rothenberg. (1963). Personality of Chess. New York.

Kline, Morris. (1962). Mathematics. A Cultural Approach.

Mason, James. (1946). The Principles of Chess in Theory and Practice. Philadelphia.

Poincare, Henri. (1946). The Foundations of Science. Lancaster

No Ordinary Genius: BBC Captures Richard Feynman’s Legacy

by Maria Popova

Explaining the scientific process with chess, or why childlike wonder is key to getting unstuck in science.

As physicists write another inconclusive chapter in the epic hunt for the “God particle” this week, it’s time to revisit one of the scientists whose work shaped modern physics. Richard Feynman, known as the “Great Explainer,” is one of my big intellectual heroes and a Brain Pickings frequenter — from his timeless insights on beauty, honors, and curiosity to his wonderful recent graphic novel biography, among the best science books of 2011 and a fine addition to our favorite masterpieces of graphic nonfiction.

In 1993, five years after Feynman’s death, BBC set out to capture his spirit and his scientific legacy in a fantastic documentary titled Richard Feynman: No Ordinary Genius, part of their excellent Horizon program, which has also brought us such fascinations as the nature of reality, the age-old tension between science and religion, how music works, and what time really is. The film was subsequently adapted into the book No Ordinary Genius: The Illustrated Richard Feynman, and the documentary is now available on YouTube in its entirety — enjoy.

When Feynman faces a problem, he’s unusually good at going back to being like a child, ignoring what everyone else thinks… He was so unstuck — if something didn’t work, he’d look at it another way.” ~ Marvin Minsky, MIT

http://youtu.be/Fzg1CU8t9nw

 

At around minute 39, Feynman gives a fantastic analogy-turned-explanation that captures what’s essentially the heart of the scientific process:

In the case of the chess game, the rules become more complicated as you go along, but in the physics, when you discover new things, it looks more simple. It appears, on the whole, to be more complicated because we learn about a greater experience — that is, we learn about more particles and new things — and so the laws look more complicated again. But if you realize all the time, what’s kind of wonderful is as we expand our experience into wilder and wilder regions of experience, every once in a while we have these integrations in which everything is pulled together in a unification, which turns out to be simpler than it looked before.”

Tender and intelligent, the film reveals some of Feynman’s defining qualities: his intense cross-disciplinary curiosity and determination (he taught himself to be a skillful artist, studying drawing like he studied science); his thoughtful, caring character (the anecdote Joan, Feynman’s younger sister, recounts at about 9:04 is just about the most poetic expression of nerd-affection I’ve ever encountered); and, perhaps above all, the remarkable blend of humility and genius that made him able to see error and wrongness as an essential piece of intellectual inquiry and truth itself.

ASTONISHMENT IS OUR NATURAL STATE OF MIND

Paul Harris

“If you take any activity, any art, any discipline, any skill, take it and push it as far as it has ever been pushed before, push it into the wildest edge of edges, then you force it into the realm of real magic”-Tom Robbins

ASTONISHMENT IS OUR NATURAL STATE OF MIND.

What?

The magic arena is a place of infinite possibilities and there’s room to play whatever game you want. But just for a moment let’s play the game of pushing the art into the wildest edge of edges.

All right. Here we go. Think back to your first magical encounter. The seed experience that first excited you then compelled you to do magic yourself. Someone did a trick for you that made you gasp. For me it was when my uncle Paul smashed a newspaper-covered glass through a table top. A moment of ecstatic bliss where every thought was pulled from my face leaving nothing more then empty space.

My first instinct was not to hear a joke or to be entertained or to be told a story or to make small talk but to experience that moment again and again. And it’s natural to think if you could learn to do magic yourself, then…well, you could have this experience all the time. But then about three seconds later you realize that it’s fun to know secrets and to do things for people that they can’t figure out. And suddenly you’re out of the astonishment game and into the ego game and with hard work and some good jokes and maybe even into the money game.

So now you’re a long way from home and from that virgin gasp that motivated the journey. And now you’re performing some of your high-entertainment-value effects and despite yourself a profound moment of astonishment is unleashed. It doesn’t happen every time but when the moon is right and the conditions are just so…there it is, a moment of total white-light astonishment. And you look at those astonished faces and maybe you’re not sure what to say, or you feel a little guilty, or a bit uncomfortable because it’s stopped the flow of your show or changed your easy relationship with the audience. Something powerful has happened. But everyone knows its just a trick and you’re “just a magician” so there’s this dysfunctional relationship going on and no one’s sure what to do with this strange experience including yourself.

But in general you’re pretty happy because on some level you realize this is a big win until someone says, “I wish the children were here to see this.” And for a moment you feel your whole game fall apart. Doing magic for children can be glorious. But the frequently voiced opinion that the experience of astonishment is a childish thing makes you wonder about what’s really going on.

If you listen carefully you’ll also hear things like “that made me feel like a child again” or “you made me feel like a little kid at the circus.” And if you think about this, you’ll see that what these astonished adults are really trying to say, even though they’re not consciously aware of it, is that for a brief moment, they experienced a clear, primal state of mind that they associate with a child’s state of mind. Somehow the adult experience of astonishment triggered some feeling of what it felt like to be a child.

I’m going to say this again because it’s so much fun using the italics button: The experience of astonishment is the experience of a clear, primal state of mind that they associate with a child’s state of mind. It’s the same experience that seduced you into performing magic in the first place. And if you follow these footprints it takes you right up to the crumbling edge of everything we think we are…and just beyond to a state of mind we experienced naturally as small children but that society devalued then made taboo as we became adults.

Here’s basically how it works, give or take a few metaphors.

You came into this world a blank slate. No ideas about who you are or what anything is. You’re just being. And it feels great…because there are no options, or opinions or judgments. There is no right or wrong. Everything is everything. That’s what you see in a baby’s eyes. Pure child’s mind. Then, very quickly, we learn stuff. The names of ten thousand things, who we are, what we’re supposed to be, what’s good and bad according to the current rules of the game. And you organize all of this information into little boxes. And when any new information comes along you file it into the appropriate box.

Right now you might be filing these very thoughts into the whack-o ideas box. I understand. You’re just doing your job. You’ve been trained to do this since birth. You have thus created your world-view.

There’s no particular reality to any of this. But it’s in your head and you know the territory and its where all of your thoughts do their thinking. But we quickly forget what was there in the first place because these thousands of little thought-boxes are stacked up so tight that the original clear space of child’s mind is completely covered up. It’s not gone. It’s just blocked by this wall of overstuffed boxes.

And then along comes a focused piece of strange in the form of magical effect. Let’s say this book vanishes from your hands. “Poof” no book. Your trained mind races into action and tries to put this piece of strange into one of its rational boxes. But no box will hold it. At that moment of trying to box the unboxable your world-view breaks up. The boxes are gone. And what’s left? Simply what was always there. Your natural state of mind. That’s the moment of astonishment. The sudden experience of going from boxes to no boxes. If you can keep the fear-response from arising you have the experience of going from a cluttered adult mind to the original clear space. Gee, it almost makes you feel like a kid again.

For most people the moment lasts less then ten seconds. Then because we crave the security of our missing world-view, we quickly build a new box. The “it-went-up-his-sleeve” box or the “it-was-all-done-with-mirrors” box or even the “I-don’t-know-what-happened-but-I-know-it-was-a-trick” box. And that’s all it takes. One thought, one guess, even a wrong one, and the boxes all come back, natural mind gets covered up, and the moment of astonishment is over.

Astonishment is not an emotion that’s created. It’s an existing state that’s revealed.

So what’s the point?

This new model redefines the magician’s valuable role in our culture as an “astonishment guide” who can help others experience their natural state of mind. This is a galactic leap from the magician’s current role as a novelty entertainer, or super con-man or Mr Ego. The centre or magic has always been the therapeutic experience of our natural state of mind. But that primal experience is so powerful and the taboo of “loosing” our mind is so great that we water down the experience with jokes and excuses and “hey, it’s just a trick.”

When the experience of astonishment starts to be recognized as a highly-valued destination, the win/lose magician vs. spectator game starts to dissolve. Suddenly you’re both on the same team…equally responsible for getting the most out of the moment.

More experienced astonishee’s who’ve learned to surrender to the moment and sink into the astonishment will be rewarded with a deeper, more sustained experience. Others who feel compelled to fight the moment or treat it as a puzzle to be figured out will get what they pay for…non-astonishment.

There is a genuine difference in the quality of peoples experience of magic once they understand the new model and take responsibility for the moment. I’ve had the participants who “get it” trying to explain it to those who don’t. One astonishee said it was like the difference of tossing down a beer and savoring a fine wine. Someone else referred to it as “gourmet astonishment.”

This model reshapes the perceptions of people who feel “I was astonished but I know it was just a trick, so what I experienced couldn’t have been real or very valuable.” Because now it’s understood that the astonishment and the tricks are not the same thing. The astonishment is real. It’s a brief flash of our natural state of mind. A place we should all experience more often.

The tricks are helpful tools to help unleash the moment.

You and your astonishee can still have fun and tell jokes and play together, but now there’s an understandable therapeutic value t the game. A definite win for all players.

In a nutshell: You’re using magical illusions to dissolve cultural illusions in order to experience a moment of something real.

The art of astonishment, when pushed into the wildest edge of edges, is the art of doing real magic.

What Research Can Help Your Students Score Higher on the Upcoming BIG Tests?

Posted by                Eric Jensen                in                Brain-Based Learning                on                04 3rd, 2012

This month, we’ll focus on how to prepare for existing state and national tests. I’ll focus on three things that can help your students improve their chances to score up to their potential. By the way, kids never score above their potential; they’re just not going to randomly make enough lucky right answers time after time after time (in statistics, it’s called regression to the mean).

But, they often underperform for a host of reasons, even when they should perform much better. While we could focus on dozens of variables that influence standardized testing, we’ll focus on these three: 1) brain chemistry, 2) priming, and 3) episodic memory triggers. Some of these suggestions got so many rave reviews that they are reproduced from an earlier bulletin!

The Research

Ten Minutes to Better Scores

Two laboratory and two randomized field studies tested a psychological intervention designed to improve students’ scores on high-stakes exams. These simple ten-minute activities can raise test scores. One well-designed study showed that writing about testing worries prior to taking the exam boosts exam performance in the classroom.

The study authors expected that sitting for an important exam leads to worries about the situation and its consequences that undermine test performance. What the authors tested was… whether having students write down their thoughts about an upcoming test could improve test performance.

This simple intervention, a brief expressive writing assignment that occurred immediately before taking an important test, significantly improved students’ exam scores, especially for students habitually anxious about test taking. Simply writing about one’s worries before a high-stakes exam can boost test scores. It does it by more than 10% and it’s quick and free (Ramirez G, Beilock, SL., 2011).

Brain Chemistry and Testing There are three chemicals to focus on for optimal testing results: 1) dopamine (it generally facilitates informational transfer within limbic and cortical networks to promote working memory and reward-seeking behavior, says Luciana, et al. 1998), 2) noradrenaline (it generally promotes a more narrowed focus, sharper attention and improved memory. This system plays a specific role in the regulation of cognitive functions, including sustained attention, working memory, impulse control, and the planning of voluntary behavior), and 3) glucose (it provides short term energy and, in low to moderate doses, promotes enhanced memory (Krebs DL, Parent MB., 2005).

The Power of Suggestion

Can you influence testing outcomes by “prepping” their brain for success? It has long been proposed that motivational responses that were subtle could serve as priming to effect academic performance. A recent study showed that yes, it can be done and they can show you how to do it. “You can prep the brain several ways. One is by showing them the letter “A” in advance.” (I’ll tell you “how” in a moment.) The other one of our two “prepping” studies is to give peppermints to all kids for your final review, then use them again at the time of the big test. (Barker, et al. 2003). This raises attentional levels and provides glucose.

Location of the Test Itself

I have always advocated that we ensure that students taking the test take it in the room in which they studied for it. That’s the power of episodic or content memory. But, there’s more to it. Stress is an issue, too. Stress impaired memory when assessed in the unfamiliar context, but not when assessed in the learning context (Schwabe L., and Wolf OT, 2009). In short, if your students can’t be in the test-givers room to learn the material, at least bring them into the testing room and do a review there days before the event.

Practical Applications

Let’s “flesh out” each of the studies listed above. The first category is about enhancing brain chemicals. This is fairly easy to do.

Dopamine can be strengthened by 1) voluntary gross motor repetitive movements, like marching, relays, playing a game. It is enhanced by strong positive feelings like reunions and celebrations. Most of all, it’s enhanced by looking forward to something very good.

Norepinephrine is enhanced by 1) risk, like a student speaking in front of his/her peers, 2) urgency, like serious deadlines for compelling tasks, and 3) excitement, like theater, competition, comedy, the arts.

Glucose is enhanced by 1) food sources: complex carbs are best, but almost any source can do in a pinch, 2) physical activity: glucose is stored in the liver in the form of glycogen and released in the form of glucose, and 3) any time we are experiencing emotions.

The study that I mentioned earlier used peppermint odor during simple skill practice, performance, memorization, and alphabetization. Participants completed the protocol twice–once with peppermint odor present and once without. Analysis indicated significant differences in the gross speed, net speed, and accuracy on the task, with odor associated with improved performance. The study results suggest peppermint odor may promote a general arousal of attention, so participants stay focused on their task and increase performance.

The Power of Suggestion

You can influence testing outcomes by “prepping” their brain for success with a positive suggestion. Sound like Star Trek “Vulcan” Mind Control? Or, is it more like “Obi Wan Kenobe”? It’s neither. It has long been proposed that motivational responses that were subtle could serve as priming to affect academic performance. The research study I mentioned above was conducted at a large research university in the USA. Here is what they started with:

23 undergraduates participated in Group 1 (were conducted in classroom settings) 32 graduate students in Group 2 (were conducted in classroom settings) 76 undergraduates in Group 3 (were conducted in laboratory setting)

The “mind games” manipulation came in the form of a “Test Bank ID code” (completely phony) on the cover of a test. The ID Code was needed because participants were prompted to view and write it on each page of their test. The letters used were “A” (the positive priming for group 1), “F” (the negative priming for group 2) and “J” (the neutral, control group 3). Students who got the “A” on their ID Code outperformed BOTH the “F” on the code and the “J” control group. Students are vulnerable to evaluative letters presented before a task, these results support years of research highlighting the significant role that our nonconscious processes play in achievement settings.

Location of the Test Itself

Stress before retention testing impairs memory, whereas memory performance is enhanced when the learning context is reinstated at retrieval. As a general rule, low-moderate stress is best for encoding and for retrieving, it is best to match the encoding stress level. I have always advocated that we ensure that students taking the test take it in the room in which they studied for it. That’s the power of episodic or content memory.

But there’s more to it. Stress is an issue, too.

The study examined whether the negative impact of stress before memory retrieval can be attenuated when memory is tested in the same environmental context as that in which learning took place. These results suggest that the detrimental effects of stress on memory retrieval can be abolished when a distinct learning context is reinstated at test.

Stress impaired the student’s memory when assessed in the unfamiliar context, but not when assessed in the learning context (Schwabe L., and Wolf OT., 2009). In short, if your students can’t be in the test-givers room to learn the material, at least, bring them into the testing room and do a review there days before the event.

Combine for Positive Synergy

Remember, the science is solid when you consider each strategy separately. But combined, these strategies may help you get to the next level. As Chef Emeril would say they could give you “BAM!” power.

BONUS: Here’s what to do after the interim tests (but before the big “Standards Tests”). We know that reflection and meta thinking can be powerful. Debbie Barber, a sixth grade teacher at Ackerman Middle School in Canby, Oregon says, “My kids have a chance to improve their scores by doing a test autopsy. They correct their mistakes and then write a half page reflection on why they did so poorly and what they should have done differently. They earn a half point for each corrected answer. Not only do the parents love it, the test scores have improved and the students are really taking ownership of their work!”

This is the potential of smarter, targeted teaching. But you have to commit to the process and ensure that it gets done. Don’t let anyone say, “I’ve heard of all that!” Get your staff on board and start making miracles. Is this awesome or not?

Let’s cut to the chase: everything you do in your classroom is likely to have SOME effect on the brain. Brain-based education says, “Be purposeful about it.” Now, go have some fun and make another miracle happen!

Research:

• Barker S, Grayhem P, Koon J, Perkins J, Whalen A, Raudenbush B. Improved performance on clerical tasks associated with administration of peppermint odor. Percept Mot Skills. 2003 Dec;97(3 Pt 1):1007-10.
• Arnsten AF. Through the looking glass: differential noradrenergic modulation of prefrontal cortical function. Neural Plast. 2000;7:133–46. [PubMed]
• Ciani KD, Sheldon KM. (2010) A versus F: the effects of implicit letter priming on cognitive performance. Br J Educ Psychol. Mar;80(Pt 1):99-119.
• Fulkerson, F. E.; and G. Martin. 1981. Effects of exam frequency on student performance, evaluations of instructor, and test anxiety. Teaching of Psychology; April, 8(2): 90-93.
• Krebs DL, Parent MB. (2005) The enhancing effects of hippocampal infusions of glucose are not restricted to spatial working memory. Neurobiol Learn Mem. Mar;83(2):168-72.
• Luciana, M., Collins, PF and RA Depue (1998) Opposing roles for dopamine and serotonin in the modulation of human spatial working memory function Cerebral Cortex Volume 8, Number 3, Pp. 218-226.
• Schwabe, L, Wolf OT. (2009) The context counts: congruent learning and testing environments prevent memory retrieval impairment following stress. Cogn Affect Behav Neurosci. Sep;9(3):229-36.
• Ramirez G, Beilock, SL. Writing about testing worries boosts exam performance in the classroom. Science. 2011 Jan 14;331(6014):211-3.