Door-2-Math Blog

Just the other day, as I was working with a student whom I’ll call Carl, I could almost ‘see’ how his mind was trying to formulate a question that would get him unstuck.  Tried as he might, he could not find the words to string his question together and get it out of his head and into the open space.  After what must be an eternity, he looked up at me, and just as expected, said quietly, “I’m confused.”  Thus, leaving all the work prior to the ‘I’m confused’ to dust.

“I know you are,” I calmly reaffirmed him.  “What’s more, Carl, is that I can see the question you almost found the words to ask.  Can we try to put those words into a sentence again?”

Not surprisingly, he was not willing.  The trauma of gathering words and then been forced to aborting the delivery of his sentence was too much.  Sensing the amount of frustration lurking underneath, I switched gears.  Pulling out a stack of paper, I asked Carl to split a piece of 8×11 into two identical triangles. Though not quite sure what I was up to, he complied.

This was what Carl did for the next 45 minutes: fold the paper along diagonally, starting with one end, ripping it until the tear is jagging; turn to the other end, start ripping there until the paper was hopelessly uneven; getting another one and start again.  At one point, he got so close completing the task that he sit up straight in his chair, took a deep breath, just to watch his hands torn the paper into uneven pieces.  Other students in the past had moistened the folded line (gross! But it did the trick), but no Carl.  As I sat there watching him going paper after paper, I wondered what happen to his voice – the voice that allows him to ask for the proper tools to complete the task.  A scissors to cut?  A ruler to draw a diagonal line?  Somewhere in the middle of this exercise, Carl did ask ‘do you have a scissors?’ upon hearing my answer of ‘no, I don’t have one here’, he abandoned all attempts of ever questioning me again.

Now watch carefully how I worded my answer.  Of course, I have scissors!  I don’t have one on the desk where I was working with him.  I had one sitting on my other desk not even 5 feet away!  What I’ve noticed from experience is that our kids are programmed to hear ‘no’ that they forgot to keep on asking until they get it.  Remember how your 5-year-old would ask, ask, and ask until you took him to Wal-Mart and get him that pair of

Sneakers with shining lights?!  Or how your daughter talked you into buying her yet another pack of ‘cute hair clips’?  Whatever happened to our children’s innate ‘I’m worth it’ belief??

Back to Carl.  When we finally pointed out that the point to the exercise was not ‘how to tear a piece of paper without scissors’, rather ‘ask for the proper tools’, Carl’s eyes lit up: ‘Oh, so when you said ‘I don’t have one here’, you weren’t telling me you don’t want to help?’

‘That’s right, Carl.  I merely said that I don’t have a pair of scissors on this desk.  Do you see one over there on the other table?’ Being a kid, he is, he quickly learned the next time when he found out my scissors was not a lefty one.  ‘Could you help me cut this?’ he politely asked.

‘Of course, Carl,’ was my answer.

And that was the tuning point of Carl’s math program -  as he asked more an more questions, the quality of his questions went up from ‘I’m confused, what do I do’ to ‘okay, I see I need to find this variable before solving for that.  What else have I not tried?’  The Chinese have a saying ‘how you do anything is how you do everything.’ So maybe Carl won’t grow up to be ‘I’m not lost’ type while driving his family to visit his in-laws?

Happy Zen Math!

(c) Feenix Pan, 2007. All Rights Reserved.

“Fractions? Oh, no, no, no! I can’t possible do fractions,” said the 9^th grader sitting opposite to me during his initial interactive assessment with me.

” How come?”

” Math stopped making sense when we hit fractions!”

Such is a common statement with my students when we first meet.  Intelligent as he is, the 9^th grader couldn’t tell me what a numerator was nor have any clue on what to do with the denominator.  Natural erroneous progression of addition let him believe that
1/7 + 1/8 equals 1/15.  Yet at the end of 5^th months working together, his grades went up to 90% and a confident grin emerged again with ‘I can handle math!”  On the last day of his program, his father said, ‘You know, Dr. Pan, I can tell your program worked with my son – even his little brother can tell you that much.  But I have no idea why or how worked.  It was as if you performed a magic on him.”

Magic or not, his comment got me thinking – What’s been missing in those bright young students’ mathability that made math such a formidable subject?  What’s required to succeed in math?  Drawing on my own training in mathematics and what I’ve seen worked with those students, the three building blocks of math success I come up with are:

Solid basic math foundation – This refers to an understanding of basic concepts such as how multiplication is related to addition, manipulation of signed numbers, mastery of multiplication tables, etc. these are taught up through 4^th grade.

Test taking skills – comprehension of what the question is asking and ability to verify answers through estimation, substitution or reverse operation such as the opposite of adding is subtraction and the opposite of division is multiplication.

Learning/critical thinking skills – this is the ability to break down a complex problem to bit-size known pieces and then solve it successfully.

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 10^th 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 9^th 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 3 candies is more than 5 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!

(c) Feenix Pan, 2007. All Rights Reserved.

“Anyone can become angry, that is easy…but to be angry with the right person, to the right degree, at the right time, for the right purpose, and in the right way…that’s not easy.”  – Aristotle

So you’ve had a long day at your day job and finally, you got your tired, over-worked under-paid body back home.  You’ve been doing good at the home-front lately, ‘emotionally depositing’ here and there, wife is happy, kids have enough attention from you and even the dog is smiling when you approach him.  Life is good until you sit down, thinking it’s a piece of cake, to help your son on his math homework.

He is a good kid, smart, caring and popular at school.  It’s just this math ‘thing’ he could not get the hang of it.  Math is the only subject where his performance is anything but consistent.

Here’s what my clients tell me usually happens next:

With good intention of helping him on his homework and getting him through this rough spot, you start your explanation.  He didn’t get it.

No problem, so you repeat what you’ve just said, bit more slowly this time.  He still didn’t get it.

Getting a bit annoyed, you say to yourself, ‘I can do this. It’s not that hard.” And you try again.  He patiently listens to your explanation the third time, nodding his head along the way, and you think ‘there we go’ until at the end of your explanation, he asks a totally irrelevant question or even worse, to your horror, he claims ‘well, Mrs. Terron at school taught us to do it this way!”  In your mind, you can see how the two approaches are the same, but by now you can feel the anger flaring up and the last thing you want to do is to hear is what Mrs. Terron did or did not do!!

If you’ve been there trying to help your child on his math homework after a tired day at work, you probably know how this ends up: he is in tears and a helping session turns into a yelling match.  Both of you get frustrated and if there is such thing called ‘lose-lose’, this is it!

Having worked with many Dads and Moms to overcome this ‘lose-lose’ situation, there is hope and a “win-win” is possible!

What is required is a ground rule and practice with two communications skills:

1. Ground Rule – Agree to a time limit BEFORE you start.  This gives both you and, more importantly, your child a sense of control.  Children are natural at keeping their parent in line with ‘but I thought you said this will only last one hour!”  Invest in a timer with a loud beep, punch in the agreed amount of Dad-helping time, and leave it where both of you can see/hear it.  Knowing there is an end to this, your child will much more likely to, at least try to, stay focused.  And on your part, under no circumstances, should you extend the session without his agreement.  Your ability to stick to your words will lay the foundation for the next helping session. Remember, Rome wasn’t built in one day and as the Chinese say “A thousand-mile journey starts with one step’.

2. Communication Skill #1 – Rely more on non-verbal communications.  I’m an engineer by training and so is my husband.  So you can imagine the amount of work we had to go through to pick up this ‘thing’ called ‘non-verbal communication’ when we first got married almost ten years ago!  But the reward is well worth the investment (time, books, seminars and endless practice).  Unlike the grownups, children are natural at both picking up and sending non-verbal communications.  Given the potential stress in helping  your child understand a concept/problem in a subject he is already stressed out about, what often works is not more explanation (verbal communication) but writing (non-verbal communications).  What you can try is this: write down your steps to a question your son asked about, in as much detail as humanly possible (pretend this is the last thing you’ll leave your child with before your trip on Richard Branson’s Virgin Galatic) and then WALK OUT OF THE ROOM. Give him the space to read (non-verbal communication) and invite him to find you when he has had the time to formulate his questions.  Children crave for ‘space/freedom’, and the ironic thing is that once we the parents grant them that, they don’t know what to do with it and they come back for our help — only this time, they are receptive to what we have to say.  Understanding this and utilizing this can be tremendously helpful in transforming a ‘lose-lose’ situation to a ”win-win’ situation.

3. Communication Skill #2 – Make an emotional currency deposit.  By the time they are in the 6th, 7th grade, our children spend an average of  6 1/2 hours at school.  During those hours, there is peer pressure, academic pressure, pre-teen hormone pressure, uncomfortable chairs, constant noises, big grownups telling them what to do, what not to do, how to do it right (or their way) and sadly for some, enduring racial or sarcastic remarks and the list just goes on and on.  So when they come home, they are just as burned out as we are after a day of work — only we get paid they don’t.  True that they get an education, but how many of us at their age, appreciated the value of the education?  From our children’s prospective, they are putting up with all that school stuff because we told them it’s important for their future and they’ve placed their trust in our words and our values.  In a way, we send them out to school as ‘buyers’ ( to get an education), they do what they were told to do at the shopping place (school) by spending their emotional reserve as the currency.  At night, ideally, we give them more emotional currency to go out again the next day to get more ‘education’.  Only the shopping place is stressful and a ‘lose-lose’ helping session depletes their reserve. So connect to your child first, school always comes after connection.  It doesn’t matter if it’s 5 minutes of quality time or 30 minutes of one-on-one, so long both your and your child are doing something you both enjoy.  In engineering terminology, the amount of emotional investment and the amount of time spend in achieving such investment is “not on a linear scale’ but more of a ‘logarithmic’ by nature.  Like we Chinese say, if you can keep the green mountain (their self-esteem) in good shape, why worry about running out of fire wood (good grades)?

Happy Zen Math!!
(c) Feenix Pan, 2007.  All Rights Reserved.