The Burdens of Gifted Children

8 03 2014

      MARCH 6, 2014

burdensofgiftedchildren

Gifted children have an unusual cross to bear; most of society sees giftedness as …… well, as a gift, but gifted children most often see it is a curse. As most who do not understand giftedness, people assume gifted children are smarter and have it made in life. For those of us who understand, teach and parent gifted children, we know otherwise. Here are 7 burdens most gifted children bear in their lives.

The Green-Eyed Monster: Some say that money is the root of all evil, but if you want my opinion, the root of all evil is JEALOUSY! Gifted children are not spared from the envious actions and words of mean-spirited, resentful people. Both same-age peers and adults deliver envy-laden insults and actions just to make sure the gifted child is knocked down a few notches. Jealousy is also a major road block to advocacy efforts for gifted children – why would a child who has it made need more? I read recently this one particularly greenish blog post written by a mom proclaiming in her title how she hates it when parents brag about their gifted child. Another blog post seen by many on the net claimed people are not born gifted, they work and create good habits in order to become gifted. Ummm … jealous much?

Bullying: Bullying could stem from jealousy, but insight into why kids bully also shows that children who become victims of bullying usually are those who stand out from the norm in some way. Sooo, you-know-who stands out among their same-age peers – Sarah Smarty-pants and Nathan the Nerd. Delivering an in-depth monologue at recess about the loss of Ancient Greek knowledge and technology when the Romans conquered the Greeks, and the resulting affect it had on the historical timing of the Industrial Revolution does call attention to oneself. Correcting a teacher in front of the class when she mispronounced a word could also lead to some retaliation. Yes, gifted children are often the victim of bullying when their intelligence shines a little too brightly.

The Race to the Middle: In the last few decades, our educational system has focused on making sure no child gets left behind, and teachers having to teach to the middle. This works well for the students who struggle and those who are performing in the average range. Excellent, right? No? Oh wait! Where does this leave our gifted learners whose voracious appetite for knowledge puts them ahead of the pack? Let me tell you – it leaves them bored, disenchanted and disengaged. While everyone in education is racing to the middle, gifted children’s love of learning is racing out the classroom door. The parents of gifted children do not escape this educational burden either, as they find themselves fighting the schools to get the education their gifted child needs and deserves.

Birds of a Feather Flock Together: Unless of course you are gifted and you are a rare bird. Gifted people make up approximately the top 1% of the population. So, if a gifted child in 6th grade attends a school with say, 200 other sixth graders, statistically there is only going to be ONE other gifted 6th grader to flock with. We know as humans, we tend to make friends with those who share our interests. The same goes for school-age kids. For gifted children, the likelihood of finding like-minded peers to make friends with are slim. Having trouble finding friends who share your interests is a significant hardship for gifted children!

Bionic Senses: Gifted children are most often born with emotional and physical intensities, sensitivities and overexcitabilities. These are known as Dabrowski’s overexcitabilities; named for the Polish psychiatrist who first noted them. An itchy tag on the back of a shirt, an odd odor no one else seems to smell or the unavoidable death of a dragonfly hitting a car’s windshield – all of these could send a gifted child into a uncontrollable spiral of emotional turmoil. These super-sensitivities easily become an unwanted burden for a gifted child, and it leads to exhausting levels of damage control for parents.

Not In Sync: Asynchronous development. While other children develop emotionally, physically, socially and intellectually in a synchronous manner, gifted children usually do not. Their intellectual and social intelligence may be light years ahead of their same-age peers, but emotionally, they could lag behind significantly. How difficult it must be for a child who has the intellectual reasoning of an adult, but not have the equivalent emotional maturity needed to handle the adult concepts he understands! As a parent of a gifted child, asynchronous development makes parenting difficult when trying to reason with the man-child who is also falling out on the floor crying like a toddler.

It’s a Mis – Misunderstood, Misdiagnosed, Mislabeled, Mistreated and Mistaught: The “mis” plight of our gifted children causes their lives to be unnecessarily painful. The many unique and misunderstood characteristics of our gifted children often lead to psychological misdiagnoses. The gifted child who is bored in class begins to misbehave and his teacher recommends that he be tested for ADHD. A gifted child’s underachievement in school can be misinterpreted as laziness. Teachers who misunderstand giftedness do not see the need for acceleration or differentiation when teaching gifted children. In the classroom, on the playground, at the park and in their own neighborhoods, gifted children are misunderstood and are being mistreated.

Saddled with these burdens, our gifted children struggle with self-esteem issues, feel like they don’t fit in in our world, they learn to hide or dumb down their intelligence, they may underachieve, and many end up with anxiety and depression.

Isn’t it time we alleviate these burdens? Through advocacy, all of us who love, parent, educate and work with gifted children can make positive changes in the lives of gifted children.

Advocate for gifted children and lessen the burden.





Social Board Games, Part 0: Introduction

5 03 2014

Here is a great article I found for social games

By 

As some of you already know, I am a mathematics professor at a small school in Indiana (Trine University). Despite our size, we have a very large engineering program – but more importantly, we have a class on the books called “Social Board Games”! The person who usually teaches it no longer has time, so he suggsted I take it up. No need to ask twice!

The course description says that “The object of this activity class is to expose students to the history, rules, strategies and fundamentals of a variety of social board games including Chess, Checkers, Backgammon, Cranium, Scrabble, Trivial Pursuit, Pictionary, Taboo and Monopoly.” Or, in the words of another professor, the point of the course is “to get the guys in engineering to actually talk to girls before they graduate.”

Of course, since I’m the kind of guy who runs a board gaming blog, I threw all of this out the window. While games like Pictionary and Taboo have some good social interaction and are closer to my aims for the course, games like Chess and Checkers are played in pairs and in virtual silence, and Monopoly and Scrabble can be frustrating and longish. More importantly though, I wanted to have a central goal for the course. I want students to actually learn a thing or two. The course is just 1-credit pass/fail, but that doesn’t mean it has to be a waste of time.

When I think back to my experiences in college, such as our “freshmen college experience” course that everyone college has now, I think of things I would have like to have known then, and what I want students to know now as a professor. The most important thing that came to mind was that I want students to take control of their own learning. (It amazes me the extent to which students who are confused in class will refuse to ask a question, for fear of looking stupid.) This led to me thinking about a variety of mental health issues that people don’t even realize are “issues” until it gets them fired from a job. My wife is a licensed mental health counselor, so with her help I came up with a list of ideas I wanted students to engage with and the games with which to do it. (In the future, I hope to try and get this course to count as a Social Science credit.)

What has been most amazing so far is the generosity of publishers and retailers alike. Since I was rebuilding a course from the ground up for which we already had materials (the old games), it was a safe assumption that I would have no funding from the university for new games. However, almost all of the publishers that I contacted were willing to step in and send some games to use in the course, and only a few were completely unresponsive. CoolStuffInc stepped in when I really wanted to use a game from a publisher I could not seem to contact, and I can’t be thankful enough. MeepleTown is not sponsored at all, by any publisher or retailer, but on a personal level I really want to thank (in no particular order) Rio Grande Games, Days of Wonder, Steve Jackson Games, R&R Games, FoxMind Games, North Star Games, Gamewright Games, Gryphon/Eagle Games, and Indie Boards & Cards, along with CoolStuffInc. This class as I envision it would not be possible without the generosity of every single one of you.

I am not going to share the entire syllabus, but I am going to share the flow of the course and the kind of assignments the students will have. This is a Wednesday night class, and each week students will be playing a game after I lecture a bit beforehand about the concept in mind as well as the ruleset. After about 90 minutes of play, we’ll recap the concept I want them to get and talk about how it appeared within the game. Then they have to go home and write a one-page paper on the importance of the mental health concept and how it appeared in the game. I’ll grade these out of 10 points (5 for grammar, 5 for substance) and they simply need to average a 6/10 on their assignments to pass the course. I hope to collect some important thoughts from these as I blog each week about the course, and maybe talk at some conferences about the importance of play, both psychologically and mathematically. (All that mathematical researchers do all day is goof around until something works. Play is of utmost importance.)

To pick games for this course, I needed them to satisfy some pretty important criteria. They needed to have a relatively short playtime – some games like Ticket to Ride will take a bit longer, but I was really aiming for 20-30 minute games that could be played several times in a row. It was also very important that they had a simple ruleset – the toughest game is probably Dominion, but I’ll be setting out the simplest Kingdom Cards in the basic set when they play, and that’ll be towards the end of the semester. I’ll also be walking around the room to answer rules questions as they play. Most importantly, they had to model some sort of important mental health concept that would be useful later in life as well as right now in college. To that end, the first unit is the most important one for college: realizing that it’s okay to be a little ignorant, and that everyone is a little ignorant too. The point of college is to become educated, which you can’t do if you won’t admit that youaren’t completely educated. The second unit is about communication, whose importance is hopefully obvious, although we will focus on several different types of communication. The third unit is on applying strategic thinking to life in general (which is, of course, a game, although we’re all a little fuzzy on the rules and victory conditions). The last unit is on separating play from reality – students (and even children) need to learn not to huff and puff and scream and stomp out of the room when they lose when they are still young, lest they act the same way at a board meeting.

I’ll talk more about the individual games chosen in detail as they come up each week, and I’ll also talk about responses from the students and what I lectured about. But for now, here is the list of games along with the mental health goals and writing prompts. (The game synopses are straight from BoardGameGeek and included for the students, who have probably never played or heard of most of these, since my Finite Math students at IUPUI did not even know the content of a deck of standard playing cards.) Check back next Friday for Part 1!

UNIT 1: Getting Out of Your Comfort Zone

The goal of this unit is for students to get comfortable with their own limitations. No one – even a genius – knows that much about the world compared to everything there is to know, and not everyone has the same skill set. It’s okay to be wrong or not know something! It’s more than okay to ask a question during classes! These games are meant to illustrate that.

TelestrationsWeek 1 (1/8) Telestrations

Game Synopsis: Telestrations is the award winning, laugh-out-loud party game that has players simultaneously draw what they see, then guess what they saw to reveal hilarious and unpredictable outcomes. In this fun, modern twist on the classic “telephone game,” there are multiple words being passed around between players, with everyone sketching and guessing at the same time! But the real fun and laughter is the big reveal, where players get their own books back and get to share how “this” became “that”!

Mental Health Goal: Learning to laugh at yourself.

Focus for Review: Were your drawings guessed correctly? When the meaning was entirely lost, was everyone (including you) able to laugh at the errors? How can you apply those aspects of the game to failures in everyday life?

wwfamilyWeek 2 (1/15) Wits & Wagers Family

Game SynopsisWits & Wagers is the trivia game you can win without knowing any trivia! All you do is bet on the answer you think is the closest. Get lucky and your team will be cheering like they hit the jackpot!

Mental Health Goal: Learning to properly assess how knowledgeable other people are.

Focus for Review: When answers revealed, was your answer ever far from the rest? How did players react to “out there” answers? Did anyone lose self-confidence for that reason? Was an “out there” answer ever right? Were ever you afraid to bet on your own answer, but then it turned out to be right? How would you apply those aspects of this game to real-life situations?

faunaWeek 3 (1/22) Fauna

Game Synopsis: Do you know where the panda lives (… you most likely know)? Do you know where the babirusa lives (… you are less sure about that)? Some of us are not entirely sure what a babirusa is? In Fauna, you are not expected to know all the answers, simply gather your wits and make an educated guess. You are right on target? Great! You are close? That’s good too, since you score partial points. Playing Fauna involves some fun betting for points, but don’t get cocky, as this may cost you your hide!

Mental Health Goal: Learning to strategize and assess a situation with imperfect knowledge.

Focus for Review:  A big difference between this game and Wits & Wagers is the way you play the game on the board. Did you ever make a tactical move that wasn’t really related to what you know? Were you able to still strategize and accomplish things without knowing exactly what the right answer was? How did you use what you thought other players knew? How could this idea be applied in a real-life situation?

timesupWeek 4 (1/29) Time’s Up!

Game Synopsis: Time’s Up! is a party game for teams of two or more players (best with teams of two). The same set of famous names is used for each of three rounds. In each round, one member of a team tries to get his teammates to guess as many names as possible in 30 seconds. In round 1, almost any kind of clue is allowed. In round 2 no more than one word can be used in each clue (but unlimited sounds and gestures are permitted). In round 3, no words are allowed at all. Time’s Up! is based on the public domain game known as Celebrities.

Mental Health Goal: Being comfortable with acting like a fool (in an appropriate situation).

Focus for Review:  Did you have trouble “loosening up” and acting silly in this game? Why or why not? Do you think that the ability to act silly is an actual, important real-life skill? Why or why not?

 Were you able to get your teammates guess the correct words? When you were not able to use words, how were you able to still indicate the card? Were you able to reference what happened in the previous rounds? How could you use this to communicate in real life?

UNIT 2: Communicating Effectively

The goal of this unit is to get students to communicate effectively with each other. This means working together as a team, as well as learning to interpret and use both verbal and nonverbal communication.

Week 5 (2/5) Dixit

dixitGame Synopsis: Every picture tells a story – but what story will your picture tell? Dixit is the lovingly illustrated game of creative guesswork, where your imagination unlocks the tale. In this award-winning board game, players will use the beautiful imagery on their cards to bluff their opponents and guess which image matches the story. Guessing right is only half the battle – to really succeed, you’ll have to get your friends to decide that your card tells the story!

Mental Health Goal: Making mental and emotional connections with strangers and acquaintances.

Focus for Review: Was it difficult to make up appropriate clues? How did you respond when your clue was too easy, too hard, or just right? Were you able to make mental or emotional connections with other players via the clues? How can you apply this idea to real life social situations with new people?

forbislandWeek 6 (2/12) Forbidden Island

Game Synopsis: Dare to discover Forbidden Island! Join a team of fearless adventurers on a do-or-die mission to capture four sacred treasures from the ruins of this perilous paradise. Your team will have to work together and make some pulse-pounding maneuvers, as the island will sink beneath every step! Race to collect the treasures and make a triumphant escape before you are swallowed into the watery abyss!

Mental Health Goal: Working together as a team.

Focus for Review: The game requires that you cooperate with other players to win. Did anyone try to be the “alpha player” and tell everyone what to do? How did you decide on what actions to take? What was different when you played with hidden cards? How does this correspond to working on a team or a committee at a real job, or on a group project? Did you win or lose? Why do you think you won or lost? What lessons did you take away from playing the game?

hanabi_productshotWeek 7 (2/19) Hanabi

Game Synopsis: An intriguing and innovative card game. Race against the clock to build a dazzling fireworks finale! Trouble is, you can see the cards that everyone holds…except your own.  Working together, you must give and receive vital information in order to play your cards in the proper launch sequence. Build and light each firework correctly to win the game and avoid a fizzling fiasco!

Mental Health Goal: Learning to properly intonate and infer silent communication.

Focus for Review: Were you able to correctly guess what your teammates were trying to say? Did they infer what you wanted them to when you gave clues? What changed when you did not allow intonation? What are some real-life situations where you need to pick up on silent clues?

labocaWeek 8 (2/26) La Boca

Game Synopsis:  In shifting teams of two that sit across from one another, players try to create skylines on challenge cards – but the players can see the completed image only from their point of view, so they must consult with one another constantly to make sure each colored block ends up in the right location while racing against the timer. The faster the players complete their building, the more points they score. Then the next team takes a seat, breaks down the blocks, then begins building anew. Whoever has the most points after a certain number of rounds will stand atop La Boca and glory in the cheers of the Argentinian public!

Mental Health Goal: Communicating effectively under pressure.

Focus for Review: Now that you have communicated with your classmates for a few weeks, was this easier or harder other communication games? Do you think that made a difference? Were you able to communicate under pressure? Did you work better with some teammates than others? Why or why not?

UNIT 3: Applying Strategy to Real Life:

So far, many of the games we have played have been party games, and maybe not what people typically think of when they think of board games. In this unit, we will play some strategy-based board games that will challenge your brain, but more importantly, we’ll talk about how to apply strategy to the game of life (metaphorically, not the board game Life).

Week 9 (3/12) Ticket to Ride

ttrGame Synopsis: Ticket to Ride is a cross-country train adventure in which players collect and play matching train cards to claim railway routes connecting cities throughout North America. The longer the routes, the more points they earn. Additional points come to those who can fulfill their Destination Tickets by connecting two distant cities, and to the player who builds the longest continuous railway.

Mental Health Goal: Learning to adapt your strategy after short-term setbacks.

Focus for Review: Did someone ever claim a route that you wanted? Did you claim a spot someone else wanted? What happened afterwards? Were you able to recover and do your best, anyway? How did you react to winning or losing?

Week 10 (3/19) Dominion

DominionGame Synopsis: In Dominion, each player starts with an identical, very small deck of cards. In the center of the table is a selection of other cards the players can “buy” as they can afford them. Through their selection of cards to buy, and how they play their hands as they draw them, the players construct their deck on the fly, striving for the most efficient path to the precious victory points by game end.

Dominion is not a CCG, but the play of the game is similar to the construction and play of a CCG deck. The game comes with 500 cards. You select 10 of the 25 Kingdom card types to include in any given play—leading to immense variety.

Mental Health Goal: Learning to understand long-term consequences of your actions.

Focus for Review: How often did you see a card that you bought early? What was different about a card you bought in the first few turns, compared to the cards you bought at the end of the game? When do you think you should buy the action and money cards – early, or at the end? What about the victory cards? How does this idea of a game decision having long-term consequences translate into real life? As you approach the end of the game, the consequences of your choices don’t last as long – is there an analog to this in real life? Why or why not?

Week 11 (3/26) Skull & Roses, Coup

skullGame Synopsis: Skull & Roses is the quintessence of bluffing, a game in which everything is played in the players’ heads. Skull & Roses is not a game of luck; it’s a game of poker face and meeting eyes.

In Coup, you are head of a family in an Italian city-state, a city run by a weak and corrupt court. You need to manipulate, bluff and bribe your way to power. Your object is to destroy the influence of all the other families, forcing them into exile. Only one family will survive…

Mental Health Goal: Understanding the moral, psychological, and strategic implications of lying and bluffing.

coupsmallFocus for Review: How often did you and your opponents lie in these games? Was it absolutely necessary to tell some lies to win? Were you comfortable with doing so? Do you think it is ‘okay’ to lie to get ahead? On the other hand, is it sometimes correct or even moral to withhold truth? Is it lying to tell the truth in a way that paints it as a lie? Is it important to be able to recognize a liar when you see one? Can this be done without lying yourself and putting yourself in a liar’s shoes?

UNIT 4: Emotions During Gaming

We’ve all been there. Someone won the last game, so you don’t want to cooperate with them in this game. Someone attacked you within the game, so you want to punch them in the face. The goal of this unit is to get students comfortable with competition, so that they can properly separate play from reality, and deal with competition at their future jobs.

Week 12 (4/2) Hearts

heartsGame Synopsis: Hearts is a trick taking, standard deck playing card game, without trumps, which has been played popularly for generations and has many variations. The object is to avoid capturing hearts at one (1) point apiece and (in the most commonly played version today) the queen of spades, at thirteen (13) points, the card on which the whole game pivots. But to make it interesting, it is also possible to “shoot the moon,” taking all the hearts and the queen, a coup that gives 26 points to each of your opponents!

Mental Health Goal: Separating frustration and “mean” play within a game from the reality outside of the game.

Focus for Review: Did you ever feel targeted or attacked during the game? How did you react? What would you do in a social situation where you became angry because of the game being played? What’s a good way to avoid getting in this kind of situation in the first place?

Week 13 (4/9), Part 1 Zombie Dice

zombiediceGame Synopsis: You are a zombie. You want braaains. More brains than any of your zombie buddies. Zombie Dice is fast and easy for any zombie fan (or the whole zombie family). The 13 custom dice are your victims. Push your luck to eat their brains, but stop rolling before the shotgun blasts end your turn! Two or more can play. Each game takes 10 to 20 minutes, and can be taught in a single round.

Mental Health Goal: Learning firsthand the risks of “gambler’s logic.”

Focus for Review: Did you ever get greedy while rolling, and refuse to stop? If it paid off, did you begin to think that that is “okay” to always do? If you busted after being greedy, how did that make you feel? How do the experiences you had during the game apply to real-life gambling?

Week 13 (4/9), Part 2 For Sale

forsaleGame Synopsis: Bid and bluff your way to purchase the most valuable real estate for the lowest amount of money. Then turn around and sell those houses (and shacks) for cold hard cash. Be the richest mogul at the end of the game to win this Stefan Dorra classic. Considered one of the finest bidding games of all time, For Sale has a devoted following of fans that is about to grow much, much larger.

Mental Health Goal: Learning when to back down from a “fight.”

Focus for Review: You see it quite often in television and movies – someone is angry about being overbid and won’t back down from an auction. Did this happen in your games? Did you feel the urge to overpay for a property because someone outbid you? How do you calm yourself down and convince yourself to walk away? How can this be applied to real life?

Week 14 (4/16) Bohnanza

bohnanzaGame Synopsis: This great card game is about planting, trading, and selling beans – 11 kinds of beans! Players try to collect large sets of beans to sell for gold. There is limited growing space and always new beans to plant. To avoid planting unwanted beans, players trade them to other players who want them for their bean fields

Mental Health Goal: Balancing cooperation with competition.

Focus for Review: How often did you trade or donate within the game? How shrewd were you and the other players? How did cooperating and trading work into your strategy and/or the strategy of the winners? How important was the emotional metagame (the game outside the game)? What kinds of situations in real life require you to cooperate with your competitors?

COMBINING ALL 4 UNITS

Week 15 (4/23) The Resistance

resistance2ndGame SynopsisThe Resistance is a very intense social deduction game for 5-10 players.  While it shares similarities with games like Werewolf,Mafia and even Battlestar Galactica, it has many very unique features such as a quick 30 minute play time, no moderator required and no player elimination.

Mental Health Goal: Learning how to read people’s tells, and to recover from misguided trust.

Focus for Review: Were you loyal or a spy? How did this affect your actions? What did you do to figure out whom to trust, or to trick people into trusting you? What verbal and nonverbal clues did you use? How did you and the other players react when the truth was revealed? Was anyone upset? Were you able to pretend to know things, or otherwise make use of your partial information? How could you apply what happened in the game to real-life situations?





Success in Mathematics Study Tips

4 01 2014

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





~We are All Teachers~

1 01 2014
~We are All Teachers~

“We are all teachers at all times – with everything we do, with everything we don’t do, with everything we say, with everything we don’t say and with our beliefs, with our attitudes – all of us.

When you hold a door for someone, you are being a teacher. When you honk and yell obscenities while driving, you are being a teacher. When you walk about with a furrowed brow and pursed lips, you are being a teacher. When you smile at those who cross your path, you are being a teacher.

It all spreads. It is all felt. The energy that you are walking around with, whether you say anything to anyone or not, is felt. What are you carrying around? What are you spreading out into the world? It is all within your control. You are choosing it all. The thoughts that come into your brain you may not get to control, but you can choose which ones stay and which ones you are projecting out into the world.

I invite you to pay more attention to what is going on up there. I invite you to pay more attention what is going on with you. Are you feeling tension in your body? Well, what is going on upstairs? Is your stomach upset? What is taking up space in your head? What are you holding onto? If it doesn’t serve you, let it go. Kick it out. Laugh it at.

You may think that it’s no big deal, that you can ignore it, that you can push it down, but it doesn’t go away, it won’t leave you. It will just multiply into the Universe. So, maybe you have a hard time thinking about yourself; you think, “Oh, I’m fine.” “It really doesn’t bother me”, but consider that you are not just poisoning yourself, but all of those around you.

Let it go and live it up. Do it for you and do it for them. Do it for the ones that you know and love and the ones that you may never speak to. Really, do it for all of humankind.

We are all teaching, at all times. What are you teaching? How about teaching love and acceptance to all beings at all times, yourself included! Deal?”

Much Love & Gratitude
Your Joyologist, Tricia Huffman

http://www.yourjoyologist.com/





10 Unbelievable Facts About Human Brain That Everyone Should Know.

30 12 2013
  1. Nerve impulses to and from the brain travel as fast as 170 miles per hour. Ever wonder how you can react so fast to things around you or why that stubbed toe hurts right away? It’s due to the super-speedy movement of nerve impulses from your brain to the rest of your body and vice versa, bringing reactions at the speed of a high powered luxury sports car.
  2. The brain operates on the same amount of power as 10-watt light bulb. The cartoon image of a light bulb over your head when a great thought occurs isn’t too far off the mark. Your brain generates as much energy as a small light bulb even when you’re sleeping.
  3. The human brain cell can hold 5 times as much information as the Encyclopedia Britannica. Or any other encyclopedia for that matter. Scientists have yet to settle on a definitive amount, but the storage capacity of the brain in electronic terms is thought to be between 3 or even 1,000 terabytes. The National Archives of Britain, containing over 900 years of history, only takes up 70 terabytes, making your brain’s memory power pretty darn impressive.
  4. Your brain uses 20% of the oxygen that enters your bloodstream.The brain only makes up about 2% of our body mass, yet consumes more oxygen than any other organ in the body, making it extremely susceptible to damage related to oxygen deprivation. So breathe deep to keep your brain happy and swimming in oxygenated cells.
  5. The brain is much more active at night than during the day.Logically, you would think that all the moving around, complicated calculations and tasks and general interaction we do on a daily basis during our working hours would take a lot more brain power than, say, lying in bed. Turns out, the opposite is true. When you turn off your brain turns on. Scientists don’t yet know why this is but you can thank the hard work of your brain while you sleep for all those pleasant dreams.
  6. Scientists say the higher your I.Q. the more you dream. While this may be true, don’t take it as a sign you’re mentally lacking if you can’t recall your dreams. Most of us don’t remember many of our dreams and the average length of most dreams is only 2-3 seconds–barely long enough to register.
  7. Neurons continue to grow throughout human life. For years scientists and doctors thought that brain and neural tissue couldn’t grow or regenerate. While it doesn’t act in the same manner as tissues in many other parts of the body, neurons can and do grow throughout your life, adding a whole new dimension to the study of the brain and the illnesses that affect it.
  8. Information travels at different speeds within different types of neurons. Not all neurons are the same. There are a few different types within the body and transmission along these different kinds can be as slow as 0.5 meters/sec or as fast as 120 meters/sec.
  9. The brain itself cannot feel pain. While the brain might be the pain center when you cut your finger or burn yourself, the brain itself does not have pain receptors and cannot feel pain. That doesn’t mean your head can’t hurt. The brain is surrounded by loads of tissues, nerves and blood vessels that are plenty receptive to pain and can give you a pounding headache.
  10. 80% of the brain is water. Your brain isn’t the firm, gray mass you’ve seen on TV. Living brain tissue is a squishy, pink and jelly-like organ thanks to the loads of blood and high water content of the tissue. So the next time you’re feeling dehydrated get a drink to keep your brain hydrated.




Unbelievable Facts

30 12 2013

Unbelievable Facts

Top 50 Unbelievable Facts
(General)

You see,as much as some people hate to be taught and trained, there are few of us who
can resist learning something interesting. It’s in our blood. The need to know.
As a way to keep my young man’s interest alive, I spent the rest of that course trawl up as many interesting and credibility-busting
facts as I could. Even if I had to stretch their relevance to the subject of my course.
And it’s a trick you can keep up your sleeve too. Just make a
file on your computer called “Strange Facts” and put in it any fascinating facts that you come across while surfing or
training.

Here are 50 outstanding ones to  start you off…

1. If you are struck by lightning, your skin will be heated to 28,000 degrees Centigrade, hotter than the surface of the Sun.

2. If you trace your family tree back 25 generations, you will have 33,554,432 direct ancestors – assuming no incest was involved.

3. The average distance between the stars in the sky is 20 million miles.

4. It would take a modern spaceship 70,000 years to get to the nearest star to earth.

5. An asteroid wiped out every single dinosaur in the world, but not a single species of toad
or salamander was affected. No one knows why, nor why the crocodiles and tortoises
survived.

6. If you dug a well to the centre of the Earth, and dropped a brick in it, it would take 45 minutes to get to the bottom – 4,000 miles.down.

7. Your body sheds 10 billion flakes of skin every day.

8. The Earth weighs 6,500 million tons.

9. Honey is the only food consumed by humans that doesn’t go off.

10. The Hawaiian alphabet has only 12 letters.

11. A donkey can sink into quicksand but a mule can’t.

12. Every time you sneeze your heart stops a second.

13. There are 22 miles more canals in Birmingham UK than in Venice.

14. Potato crisps were invented by a Mr Crumm.

15. Facetious and abstemious contain all the vowels in their correct order.

16. Eskimoes have hundreds of words for snow but none for hello.

17. The word “set” has the most definitions in the English language.

18. The only 15 letter word that can be spelled without repeating its letters is uncopyrightable.

19. Windmills always turn counter-clockwise.

20. The “Sixth Sick Sheik’s Sixth Sheep’s Sick” is the hardest tongue-twister.

21. The longest English word without a vowel is twyndyllyngs which means “twins”.

22. 1 x 8 + 1 = 9; 12 x 8 + 2 = 98; 123 x 8 + 3 = 987; 1234 x 8 + 4 = 9876; 12345 x 8 + 5 = 98765; 123456 x 8 + 6 = 987654; 1234567 x 8 + 7 = 9876543; 12345678 x 8 + 8 = 98765432; 123456789 x 8 + 9 = 987654321

23. The word “dreamt” is the only common word in the English language that ends in
“mt”.

24. Albert Einstein never wore any socks.

25. The average human will eat 8 spiders while asleep in their lifetime.

26. In space, astronauts cannot cry because there is no gravity.

27. Hummingbirds are the only creatures that can fly backwards.

28. An ostrich’s eye is bigger than its brain.

29. Cockroaches can live 9 days without their heads before they starve to death.

30. A flamingo can eat only when its head is upside down.

31. The lighter was invented before the match.

32. The average left-handed person lives 7 years LESS than a right-handed person.

33. The average person has over 1,460 dreams a year!

34. Scientists with high-speed cameras have discovered that rain drops are not tear shaped
but rather look like hamburger buns.

35. The first Internet domain name ever registered was Symbolics.com on March 15,1985.

36. When Alexander Graham Bell invented the telephone back in 1876, only six phones were
sold in the first month.

37. Approximately 7.5% of all office
documents get lost.

38. Business.com is currently the most expensive domain name sold: for $7.5 million.

39. In 2001, the five most valuable brand names in order were Coca-Cola, Microsoft, IBM, GE, and Nokia.

40. In Canada, the most productive day of the working week is Tuesday.

41. In a study by the University of Chicago in 1907, it was concluded that the easiest colour to spot is yellow. This is why John Hertz, who
is the founder of the Yellow Cab Company picked cabs to be yellow.

42. It takes about 63,000 trees to make thenewsprint for the average Sunday edition of The New York Times.

43. On average a business document is copied 19 times.

44. The largest employer in the world is the Indian railway system in India, employing over 1.6 million people.

45. Warner Chappel Music owns the copyright to the song “Happy Birthday.” They make over
$1 million in royalties every year from the commercial use of the song.

46. All babies are colour-blind when they are born.

47. Children grow faster in the springtime than any other season during the year.

48. Each nostril of a human being registers smells in a different way. Smells that are made from the right nostril are more pleasant
than the left. However, smells can be detected more accurately when made by the left nostril.

49. Humans are born with 350 bones in their body, however when a person reaches adulthood they only have 206 bones. This
occurs because many of them join together to make a single bone.

50. May babies are on average 200 grams heavier than babies born in other months.





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

26 12 2013

interests300

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:
ShoppingThe 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.








Follow

Get every new post delivered to your Inbox.

Join 64 other followers