April 26, 2015

In the last few days, Robert and I returned to the workbooks we have completed twice before.

1.* Cut, Paste, & Color Logic* from Remedia Publication

As I watched Robert attempting to place four pictures in four spaces by following three or two cues, I wondered how to asses his progress. It was clear, that he would not have completed this activity if I had not been sitting next to him. I don’t know however, how exactly did he benefit from my presence. Did he observe (as he did so cleverly in the past ) my reactions to his manipulations and deduced the proper response based on what he noticed in the movement of my eyes or lips? Was it possible that my very presence did the trick by giving him psychological support as he tried to find a way to place four animals in four cages?

Nonetheless…

Whenever he read a sentence of the form, “A was not put in B”, Robert wrote in the B rectangle, “no A”. To sound less abstract: when Robert read. ” Elephant was not the last”, Robert wrote in the last rectangle, “NO elephant.” Moreover he made sure not to put elephant there. That was the progress as during our previous sessions, a year or two ago, he (and thus I) often made mistakes there. Another sign of progress was the fact that Robert slowed down and injected a few seconds of thinking between reading direction and following it. That was mostly visible when he had to choose simultaneously two out of the three spaces.

To find where to put zebras, a parrot, an elephant and a hippo, Robert read all three sentences before placing pictures in order:

1.The elephant is fed last.

2.The zebras are fed after the hippo.

3. The hippo is not fed first.

Those few seconds of hesitation squeezed between reading directions and acting upon them was the most important developmental improvement.

*Momentum Math F, Unit 1 Multiplying and Dividing Natural Numbers.*

It is an easy unit for Robert. He knows how to multiply and divide numbers. Moreover, he knew that three years ago and five years ago. well, the matter of fact, he knew that seven years ago too. But when four and five years ago Robert was working with this textbook/workbook, I decided to skip some topics. For instance, I decided not to teach him multiplying by partial products. I was afraid that learning another method might impact negatively his ability to use standard multiplication algorithm. This time, I knew that his skills were strong enough to resist possible confusion. Moreover, over the years Robert practiced writing a number in expanded form (247=200+40+7) thus he had prerequisite skills allowing mu to grasp the method of partial products.

During our previous work with Momentum Math, I introduced for the first time the prime factorization. I did it because it was a chapter in the book and I tried to follow the curriculum. I wasn’t sure if Robert would benefit from knowing it. But mainly, I wasn’t sure if Robert could grasp it. Well, it was rather easy for him to get down to the prime factors. However, he had difficulties presenting a number as a product of its prime factors – those which were on the ends of the tree. He wanted to write all factors, not only the prime ones.

This time, he didn’t make that mistake, but there is still something amiss.