Saturday, May 27, 2017

The Wonder of Working Memory

I was first introduced to the concept of working memory by the author of the COGAT.  I was reading his papers in the hopes that he would give hints on the design of test questions so I could reverse engineer the test.  He mentions repeatedly that working memory is important.

OK, whatever this working memory is, I set out to create a training program for it.  My goal was simple - take average or below average kids and put them through my training program so that they measure at the genius level on both the COGAT and academic work.  (Both of these measures are equivalent because the COGAT measures academic skills.)  I really wanted to work with kids with 'the math gene' but apparently 'the math gene' doesn't exist in this house.

My success was 300% of my original goals.

My starting point was the COGAT.  Almost all of the COGAT questions appear to have 2 things going on, so I would have 3 (it turns out that 4 don't work so I used 3) and on top add complexity so that the student has to keep these 3 subjects in the brain for as long as possible while she sorts out the complexity.

Before 2nd grade, it's easy to find age appropriate training material.  Just grab 2nd grade math.  After 5th grade, easy.   There's pre-algebra, 8th grade math, and the SAT.  The problem is the 2nd to 4th grade age range where the brain should be on the verge of a skill explosion but the material in school is so dumbed down as to be useless.  This, in a nutshell, was the motivation behind Test Prep Math.

I created word problems heading toward 3 equations to be solved.  These 3 equations are buried in a complicated word problem.  Not only does it take a while to sort out the equations and solve them, but I like to put 'something extra' in the problem, whether it's grammar that's a bit twisted or a missing element.  It's hard, but it's just 1 problem a day to begin with, and the math itself isn't that hard.  That's the first section in Test Prep Math.  Then I followed that up with a problem design that is just equations and is meant to make the COGAT quantitative section look like a walk in the the park. That's the second section.  Easy math, really hard thinking.  The section section didn't exist at first, but after doing the first problem, it's almost doable.

Here's what I found.

First, I witnessed the brain creating 3 brain buckets where before there was only 1 brain bucket.  On top of that, I ended up with kids who could spend a lot of time reading questions and don't get upset by mistakes, because they made mistakes repeatedly on the way to the correct answer.  If you have a kid who learns to concentrate on the material at hand and is not emotionally crushed by mistakes then you have a kid who will succeed.  Being able to take in 3 times more material at once while they sort it all out is a huge advantage.  That was 100% of my goals and pretty awesome.

What surprised me was that Working Memory is not just a shorter term version of Short Term memory.  There's a reason why it has Working in the name.   It's not just that kids learn to take in 3 problems at once and solve them.  It's too hard.  Instead, as they take in the material they are filing, organizing, classifying, regrouping, simplifying and who knows what else in order to take short cuts.

I didn't realize how powerful Working Memory is, especially at its new level, until we graduated from Test Prep Math and started to crush what followed, including pre-algebra, competitive math, 8th grade math, algebra and trig.

"Today we'll look at the sign and cosine functions and calculate adjacent angles".   Unless the child is a sophomore in high school, I just used a sentence with 3 new terms, and we're about to make things harder.  Even worse, "what's the 5th digit of a 9 digit number that starts and ends with 6 and every 3 consecutive digits sums to 14".  What?  When I watched a third grader actually solve this problem, I realized the working memory exercises took us to 200% of my goals.

When we were decomposing SAT reading comprehension questions, I admired the level of complexity in these questions, including the use of words, the logic underlying the structure of phrases.  It dawned on me that I had never seen anything so convoluted since I wrote Test Prep Math. I ran to my shelves of curriculum and started comparing elementary school curriculum to Test Prep Math and realized that none of it was remotely comparable.

While the rest of the country is doing 2nd to 4th grade math, which is spoon feeding, or even accelerated math, which is spoon feeding next year's material, my kids where trying to sort out insane word problems some of which don't have a satisfying answer, and some don't really have an answer.

Is this really what we should be doing at this age?  Shouldn't we just practice decimals and long division?  But long division and decimals are useless and boring.  Why not teach your child to think and let math take care of itself?

I'm waiting for end of year MAP math test results.   This year is not a high stakes year.  I'm not sure how things went and don't really care.  Would my children be in the zone and execute, or would they get bored half way through the test and just go through the motions?  The older one told me by the end all he was doing was solving triangles using trig.  He stinks at trig.  His approach is trial and error with lots of errors. but I have reason to think that his test score is going to be good this year because he's only in 6th grade.  Who's dumb idea for a test format is giving trig to 12 year olds?  The 8 year old came out of his MAP test asking what x is in pi*x = 24.62.  He asked what is the decimal value of pi.  Oops, I never told him (because I hate decimals) before the MAP test even though we're beyond simple algebra.

Reading is a different matter.  There will be hell to pay if either child doesn't do well on the reading comprehension part of the MAP, now that I know that the 2 years I invested in writing Test Prep Math pays off on reading comprehension in a big way.  It wasn't possible to jump from Test Prep Math in 3rd or 4th grade to SAT reading comprehension practice.  I didn't even realize that this was an option until after 5th grade.  But now that I've discovered the link I expect results.


  1. Hi Norwood:

    I am an avid follower of your post, and a professor myself. I wanted to thank you for the tips that you shared with me. I do credit your help to a large extent that got my 3rd grader into GATE this year. She is in the 99 percentile, and though schools always make you believe that a child should see the test for the first time, and ace it, I actually see the benefits of practice both in my profession, and with my child.
    Thank you and hope we can collaborate some day on related research.

    1. I'm glad to hear things are going so well with your child.
      The correlation between highly skilled children and high test scores only works in large enough sample sizes, not for an individual child. The recommendation not to do any preparation is in the best interest of a school and not the best interest of a parent.
      Anyway, thanks for the encouragement. I'm convinced that every child is a potential genius. My research is now squarely focused on parents who seem to be at the heart of success or failure.