What’s required on the road to math success?

  These three requirements for a successful math ‘trip’ from K through 12 are no different from those required to make a successful driving trip to New York from, say Tucson:
a road to travel on is much like the basic math foundation -- more holes in basic math foundation, the bumpier the ride; a car is a vehicle just like the test-taking skill is a medium to show one’s math understanding; and a map helps us to figure out what to do if we get lost much like our critical thinking skill transforms the unknown complex problems to smaller known bits so we can solve it.

A successful math 'trip' from K through 12 is like that of a driving trip from say Tucson to New York (you cross about 12 states). Just like one needs a car, a road and a map for the driving trip, the math trip requires Basic math foundations, test-taking skills and learning/critical thinking skills.

So what happens when one of these requirements, say test-taking skills, are missing?  Much like junk car with wheels flying off, weak test-taking skills frustrate students with no end.  Take Vic, a brilliant 10th grader who came with a convection that ‘no matter how hard I study for my Trig, I can not get beyond 70% on tests.”  When I sat down and worked with him one on one, it quickly became apparent to me that Vic’s problem is not that he didn’t understand the material.  To the contrary, his understood it well.  Yet, when he started on his homework, he constantly made ‘silly mistakes’ as he

called them: 1/2 becomes 0.7, (-2) x 3 becomes +6, and list went on and on.  A problem with 5- or 6-steps to solve, by the time he got to the last step, his solution was nowhere near where he started!  

And what happens when the basic math foundation is full of ‘potholes’?  More often than th grader who aced Geometry at an alternative school one year but flunked algebra.  The multiplication table frightened him so much that he reached for his calculator for 3 x 6.  I quickly learned that too many years have gone by for me to even convince him to try.  In the end, we found a way for Kevin that allowed him to calculate 3 x 6 by building on 3 x 3 (=9) and twice of 9 is 18 so 3 x 6 is 18.   We devoted full two months to patch up Kevin’s foundation ‘potholes’ and it paid off in the end when Kevin got his first 91% on an algebra test in a long time.

Last but not least, what’s the most common symptom to a student has not had any guidance in moving away from memorizing math to understanding math?  If you guessed temporary ‘mathematic amnesia’, you’re right!  These students seemed to be able to do homework, but could not recall the formulae on exams if their lives depend on it!  Numerous students came in with 100% on their homework, and crushing experience of staying up to 2am for math exams next day, only to be awarded with a 50% exam score.  Take Megan, a studious 9th grader at a top local high school, for example.  When we met first, Megan’s confidence couldn’t have been any lower.  Apple’s eye in her teachers since grades school, Megan’s parents noticed a nosedive on her math performance once she hit high school.   With added pressure of a highly competitive environment, Megan found herself in an unfamiliar place – math phobia.  Customized to memorize her way out of math, Megan had hard time to apply what she memorized.  I remember that once we were going over collecting like-terms, Megan could see that 2x+3x=5x, but not 2(x+1)+3(x+1)= 5(x+1).  Upon asking how she know 2x+3x=5x, she said, “Oh, I memorized that a long time ago.”  I drew a big box over (x+1) and showed her that 2(x+1)+3(x+1) is no different than 2(big box) + 3(big box) which is 5 (big box) and since (big box) is (x+1), so 2(x+1)+3(x+1)= 5(x+1).  I’ll never forget that ‘Oh’ she let out as if someone just turned on a light bulb in a dark room where she’s been stranded.  Memorizing might be easier at the beginning when the material is not so demanding, but sticking to understanding math will pay in the end – like that paid off for Megan.  Two years after completing our program, Megan Mom still reports, “all A’s here!”

Build Basic Math Foundation – start early.  Whenever your child shows the first sign of interest in math, take the time to show 5 candies is more than 3 candies and that 3 candies with 5 more makes 8.  What’s important in the early years is not ‘how fast’ but ‘how consistent’.  Consistency requires patience and patience requires time.

Develop Test-taking Skills – It’s important for a child to know, from very early on, that a mistake is an opportunity to improve, not something to be frowned upon.  Mistakes are our friends not foes.  In imparting this, a child welcomes a chance to learn and sees test as a part of mastering something interesting.  Much like we take care our car (wax, wash, routine checkups), we take care our mistakes by learning from them.

Strengthen Learning/Critical Thinking Skills – “ Memorizing a bird’s name is no substitute for observing it closely and asking why it pecks its feathers constantly,” said Mr. Feynman to his young son, future Nobel Prize Winner physicist, Richard Feynman.  Look for those precious teachable-moments in your child’s life to impress him/her upon the importance of ‘getting to the bottom of things.’  Treasure those innocent questions like ‘Dad, why is sky blue?’  Behind those questions lay the human’s most precious gift – curiosity.  For centuries, many probably had asked their parents ‘why did the apple fall down’, but only Sir Newton found out!

Happy Zen Math!

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