When Less is More

June 4, 2015

For the last couple months, Robert and I were rushing through units in Level F Momentum Math. Why shouldn’t we?  After all, we were ONLY reviewing what Robert already knew or what I ASSUMED he knew. So each day, we did one whole unit – nine pages of definitions, examples, and problems.  Then one day, Robert was lost when the tasks required placing fractions on number lines. Since I believed he knew how to do it, I tried to rush him through that unit as well. With every problem Robert became more and more bewildered, but I still pushed forward thinking that the next problem would clarify the whole concept. Instead of stopping and reworking the problem again so Robert could better understand the issues involved, and so I could understand the nature of Robert’s confusion, I presented the next task as if it would provide a better  opportunity to learn.  It didn’t.

It couldn’t as each problem became more complex and thus more difficult.

No wonder, Robert grew tense.

I had to rethink the strategies.

Every day, I presented Robert with one page of 4-5 easy exercises of placing halves, thirds, fourths, or fives on the number lines. 1/2,  2/3,  1/4, or 3/5.

I noticed that instead of counting segments into which one unit was divided, Robert was counting marks on number line starting with the first. The remedy was simple, Robert was asked to draw and count small arches connecting ends of the segments.

The second errors Robert kept making was not to count all the parts in one whole unit, but only up to the first letter representing a fraction (part of the unit). So we went back and I only drew one unit at a time for instance from 3 to 4 divided into a few parts.  This way, the end was clearly visible. Then I extended the number line to include next (or previous) whole number.

For the last three days, Robert and I worked on placing fractions and decimals on number lines. We went slowly, very slowly.  For every example in the book, I prepared a few similar ones. Before any example or problem in the book, we reviewed changing fractions to decimal and vice versa.

We didn’t hurry. Robert solved very few problems from this chapter, and yet he learned something.  That “something”  meant ” a lot more.

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