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.





Are We Raising a Generation of Helpless Kids?

28 11 2013

Content Creator, Journalist, Memoirist

Child With Trophy
Warning signs
When a college freshman received a C- on her first test, she literally had a meltdown in class. Sobbing, she texted her mother who called back, demanding to talk to the professorimmediately (he, of course, declined). Another mother accompanied her child on a job interview, then wondered why he didn’t get the job.

A major employer reported that during a job interview, a potential employee told him that she would have his job within 18 months. It didn’t even cross her mind that he had worked 20 years to achieve his goal.

Sound crazy?

2012-02-03-download1.jpgTim Elmore with Young Gen Y Students (photo courtesy Tim Elmore)
Sadly, the stories are all true, says Tim Elmore, founder and president of a non-profit, Growing Leaders, and author of the “Habitudes®” series of books, teacher guides, DVD kits and survey courses. “Gen Y (and iY) kids born between 1984 and 2002 have grown up in an age of instant gratification. iPhones, iPads, instant messaging and immediate access to data is at their fingertips,” he says. “Their grades in school are often negotiated by parents rather than earned and they are praised for accomplishing little. They have hundreds of Facebook and Twitter ‘friends,’ but often few real connections.”

To turn the tide, Growing Leaders is working with 5,000 public schools, universities, civic organizations, sports teams and corporations across the country and internationally to help turn young people — particularly those 16 to 24 — into leaders. “We want to give them the tools they lack before they’ve gone through three marriages and several failed business ventures,” he says.

2012-02-03-download2.jpgOlder Gen Y Kids Demonstrate to Tim Elmore How to Dress the Part (Photo courtesy Tim Elmore)
But why have parents shifted from teaching self-reliance to becoming hovering helicopter parents who want to protect their children at all costs?

“I think it began in the fall of 1982, when seven people died after taking extra-strength Tylenol laced with poison after it left the factory,” he says. Halloween was just around the corner, and parents began checking every item in the loot bags. Homemade brownies and cookies (usually the most coveted items) hit the garbage; unwrapped candy followed close behind.

That led to an obsession with their children’s safety in every aspect of their lives. Instead of letting them go outside to play, parents filled their kid’s spare time with organized activities, did their homework for them, resolved their conflicts at school with both friends and teachers, and handed out trophies for just showing up.

“These well-intentioned messages of ‘you’re special’ have come back to haunt us,” Elmore says. “We are consumed with protecting them instead of preparing them for the future. We haven’t let them fall, fail and fear. The problem is that if they don’t take risks early on like climbing the monkey bars and possibly falling off, they are fearful of every new endeavor at age 29.”

Psychologists and psychiatrists are seeing more and more young people having a quarter-life crisis and more cases of clinical depression. The reason? Young people tell them it’s because they haven’t yet made their first million or found the perfect mate.

Teachers, coaches and executives complain that Gen Y kids have short attention spans and rely on external, instead of internal motivation. The goal of Growing Leaders is to reverse the trend and help young people become more creative and self-motivated so they can rely on themselves and don’t need external motivation.

Family psychologist John Rosemond agrees. In a February 2 article in the Atlanta Journal Constitution, he points out that new research finds that rewards often backfire, producing the opposite effect of that intended. When an aggressive child is rewarded for not being aggressive for a short period of time, he is likely to repeat the bad behavior to keep the rewards coming.

Where did we go wrong?

• We’ve told our kids to dream big – and now any small act seems insignificant. In the great scheme of things, kids can’t instantly change the world. They have to take small, first steps – which seem like no progress at all to them. Nothing short of instant fame is good enough. “It’s time we tell them that doing great things starts with accomplishing small goals,” he says.

• We’ve told our kids that they are special – for no reason, even though they didn’t display excellent character or skill, and now they demand special treatment. The problem is that kids assumed they didn’t have to do anything special in order to be special.

• We gave our kids every comfort – and now they can’t delay gratification. And we heard the message loud and clear. We, too, pace in front of the microwave, become angry when things don’t go our way at work, rage at traffic. “Now it’s time to relay the importance of waiting for the things we want, deferring to the wishes of others and surrendering personal desires in the pursuit of something bigger than ‘me,'” Elmore says.

• We made our kid’s happiness a central goal – and now it’s difficult for them to generate happiness — the by-product of living a meaningful life. “It’s time we tell them that our goal is to enable them to discover their gifts, passions and purposes in life so they can help others. Happiness comes as a result.”

The uncomfortable solutions:

“We need to let our kids fail at 12 – which is far better than at 42,” he says. “We need to tell them the truth (with grace) that the notion of ‘you can do anything you want’ is not necessarily true.”

Kids need to align their dreams with their gifts. Every girl with a lovely voice won’t sing at the Met; every Little League baseball star won’t play for the major leagues.

• Allow them to get into trouble and accept the consequences. It’s okay to make a “C-.” Next time, they’ll try harder to make an “A”.

• Balance autonomy with responsibility. If your son borrows the car, he also has to re-fill the tank.

• Collaborate with the teacher, but don’t do the work for your child. If he fails a test, let him take the consequences.

“We need to become velvet bricks,” Elmore says, “soft on the outside and hard on the inside and allow children to fail while they are young in order to succeed when they are adults.”

 





21 Habits of Happy People

16 11 2013

Posted in  Self Improvement on January 30, 2013Comments: 162 comments

 

“Happiness is a habit – cultivate it.” ~ Elbert Hubbard 

Happiness is one aspiration all people share. No one wants to be sad and depressed.

We’ve all seen people who are always happy – even amidst agonizing life trials. I’m not saying happy people don’t feel grief, sorrow or sadness; they just don’t let it overtake their life. The following are 21 things happy people make a habit of doing:

1. Appreciate Life

Be thankful that you woke up alive each morning. Develop a childlike sense of wonder towards life. Focus on the beauty of every living thing. Make the most of each day. Don’t take anything for granted. Don’t sweat the small stuff.

2. Choose Friends Wisely

Surround yourself with happy, positive people who share your values and goals. Friends that have the same ethics as you will encourage you to achieve your dreams. They help you to feel good about yourself. They are there to lend a helping hand when needed.

3. Be Considerate

Accept others for who they are as well as where they are in life. Respect them for who they are. Touch them with a kind and generous spirit. Help when you are able, without trying to change the other person. Try to brighten the day of everyone you come into contact with.

4. Learn Continuously

Keep up to date with the latest news regarding your career and hobbies. Try new and daring things that has sparked your interest – such as dancing, skiing, surfing or sky-diving.

5. Creative Problem Solving

Don’t wallow in self-pity. As soon as you face a challenge get busy finding a solution. Don’t let the set backs affect your mood, instead see each new obstacle you face as an opportunity to make a positive change. Learn to trust your gut instincts – it’s almost always right.

6. Do What They Love

Some statistics show that 80% of people dislike their jobs! No wonder there’s so many unhappy people running around. We spend a great deal of our life working. Choose a career that you enjoy – the extra money of a job you detest isn’t worth it. Make time to enjoy your hobbies and pursue special interests.

7. Enjoy Life

Take the time to see the beauty around you. There’s more to life than work. Take time to smell the roses, watch a sunset or sunrise with a loved one, take a walk along the seashore, hike in the woods etc. Learn to live in the present moment and cherish it. Don’t live in the past or the future.

8. Laugh

Don’t take yourself – or life to seriously. You can find humor in just about any situation. Laugh at yourself – no one’s perfect. When appropriate laugh and make light of the circumstances. (Naturally there are times that you should be serious as it would be improper to laugh.)

9. Forgive

Holding a grudge will hurt no one but you. Forgive others for your own peace of mind. When you make a mistake – own up to it – learn from it – and FORGIVE yourself.

10. Gratitude

Develop an attitude of gratitude. Count your blessings; All of them – even the things that seem trivial. Be grateful for your home, your work and most importantly your family and friends. Take the time to tell them that you are happy they are in your life.

11. Invest in Relationships

Always make sure your loved ones know you love them even in times of conflict. Nurture and grow your relationships with your family and friends by making the time to spend with them. Don’t break your promises to them. Be supportive.

12. Keep Their Word

Honesty is the best policy. Every action and decision you make should be based on honesty. Be honest with yourself and with your loved ones.

13. Meditate

Meditation gives your very active brain a rest. When it’s rested you will have more energy and function at a higher level. Types of meditation include yoga, hypnosis, relaxation tapes, affirmations, visualization or just sitting in complete silence. Find something you enjoy and make the time to practice daily.

14. Mind Their Own Business

Concentrate on creating your life the way you want it. Take care of you and your family. Don’t get overly concerned with what other people are doing or saying. Don’t get caught up with gossip or name calling. Don’t judge. Everyone has a right to live their own life the way they want to – including you.

15. Optimism

See the glass as half full. Find the positive side of any given situation. It’s there – even though it may be hard to find. Know that everything happens for a reason, even though you may never know what the reason is. Steer clear of negative thoughts. If a negative thought creeps in – replace it with a positive thought.

16. Love Unconditionally

Accept others for who they are. You don’t put limitations on your love. Even though you may not always like the actions of your loved ones – you continue to love them.

17. Persistence

Never give up. Face each new challenge with the attitude that it will bring you one step closer to your goal. You will never fail, as long as you never give up. Focus on what you want, learn the required skills, make a plan to succeed and take action. We are always happiest while pursuing something of value to us.

18. Be Proactive

Accept what can not be changed. Happy people don’t waste energy on circumstances beyond their control. Accept your limitations as a human being. Determine how you can take control by creating the outcome you desire – rather than waiting to respond.

19. Self Care

Take care of your mind, body and health. Get regular medical check ups. Eat healthy and work out. Get plenty of rest. Drink lots of water. Exercise your mind by continually energizing it with interesting and exciting challenges.

20. Self Confidence

Don’t try to be someone that you’re not. After all no one likes a phony. Determine who you are in the inside – your own personal likes and dislikes. Be confident in who you are. Do the best you can and don’t second guess yourself.

21. Take Responsibility

Happy people know and understand that they are 100% responsible for their life. They take responsibility for their moods, attitude, thoughts, feelings, actions and words. They are the first to admit when they’ve made a mistake.

Begin today by taking responsibility for your happiness. Work on developing these habits as you own. The more you incorporate the above habits into your daily lifestyle – the happier you will be.

Most of all: BE TRUE TO YOURSELF.








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