Looking for Variables

Robert learned numbers (symbols,counting, names, order) by the time he was five years old. Soon after that he learned to add 1 to any other number.

And then for the  next five years he DID NOT LEARN  one math fact.

For five years! Nothing!

Not because he was not taught.  He was taught at school, he was taught at home.

School used not only flash cards, this antediluvian staple of American math education, but also cleverly designed program that involved cute counters and number cards.

I used counters, number line, two math curricula from SRA and yes, in my desperation, against my better judgement, and betraying my principles, I tried the  flash cards too.

Nothing worked!

Susan, the clinical supervisor of Robert’s program, sadly advised me to accept that Robert would never learn to add numbers.

Such outcome seemed both unavoidable and unacceptable.

The same week or month a parent on old ME-List advised another parent to use Saxon Math with her child.  Since the price was not prohibitive I ordered it without really knowing what I was buying.

Eureka!

The order in which  math facts were introduced seemed  counter-intuitive to me.  The first math facts to remember were additions of duplicates: 1+1, 2+2, 3+3 and so on.  It took Robert a week to add duplicates until 5+5.  It took him another week to memorize additions from 6+6 to 10+10.

Although it seemed so strange at first I quickly understood how much simpler  8+8 was than 2+4.  In the first addition there was  one number to remember.  So it sufficed to just learn that 8 was related to 16.  In the second addition there were two numbers.  You had to remember them both and that was hard for Robert. Which of the two numbers  is the  important one?  The first one or the last one?   It cannot be 4 because 1+4 is not the same as 2+4. It cannot be 2 because…

The second step in memorizing addition fact was to practice adding double plus one in the form: 1+2, 3+4, 7+8…

The problem 7+8 was written next to 7+7.  Since Robert knew the first fact and knew how to add one to any number he didn’t have much problem with 7+8.

Yet, that was just a mechanical approach.  Without seeing 7+7 first Robert was not able to solve 7+8.

I added new worksheets.  I wrote 7+8 first and 7+7 next so Robert would learn to use the second problem  as a support for the first one. Just looking to the right  was an important step.  Next, I wrote only 7+8 and next to it I drew empty squares.  Robert filled those squares with supporting addition 7+7 =14 and then solved  7+8.  In the  next step  I wrote just 7+8  and let Robert write himself   the next column.  Finally I wrote 7+8  but when Robert wanted to write 7+7 next to it I blocked the space.  He had to write an answer to 7+8 as he deduced it in his head without writing 7+7 on the paper.

So Robert knew how much was 8+9 before he knew 2+4.

Similar trick I used with practicing adding 2 to the number.

Someone (surprisingly a parent) asked me why I spent so much time on teaching addition instead of just introducing a calculator.

The answer is complicated. Of course it is nice that Robert can add, subtract, multiply and divide large numbers.  Typical people and peers with disabilities  who because of Robert  terrible problems with communication tend to  dismiss him after first encounter, might  realize that he has some relatively advanced skills.

I also believe that in this process Robert learned not just how much is 7+8 but also some strategies that he might one day apply to solving other problems.

However,  the main point of teaching Robert math facts was to LEARN how ROBERT LEARNS.  To find out what works, what doesn’t. During this process  I realized that Robert had problem with short and/or working memory. But I also discovered  that Robert learns through patterns.  Moreover, I  found out that even when he doesn’t have any visual support Robert  can still solve problems by using his mind.

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3 Comments

  1. gitasrikanth

     /  June 3, 2013

    Hi! I am working with kids who are seemingly stuck at the same level with Math. Could you elaborate a bit on the Saxon Math? You sure are inspiring!

    Reply
    • It is very hard to describe all the four books of Saxon Math. I tried to summarize reasons why I like current level 4 in the post https://krymarh.wordpress.com/2013/04/23/up-and-down-saxon-math-levels/
      At the end of that post there are descriptions of certain features which help me teach my son. But not every body would like them and not every student would respond, Depending on the needs, skills and levels of your students, you might consider other programs like Momentum Math, Singapore Math or the easiest Algebra books from Firelight Publishing.
      (They are much easier than 4th grade Saxon Math.) It you tell me more about your students’ needs, my answers might be more concrete.
      Good luck, Maria

      Reply
  1. Take It to Your Brain Part 2 | krymarh

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