Counting Errors. His and Mine

Robert was making many mistakes today (November 6) as he was trying to solve word problems that required adding and subtracting fractions. The word “more” confused him again when it was a part of a phrase, “How much more?”, so he wanted to add the quantities that should be subtracted. Although he found common denominators without problems, he kept forgetting the whole numbers when they were part of the mixed fractions.  He couldn’t understand the way he had to regroup the fractions and change one whole into a fraction of a given denominator so it could be added to the fraction’s part of the mixed number.  He made too many mistakes for me to address at the same time.

The best solution would be to put the packet of 5 worksheets away and return to it after practicing separately or in a  chain of related problems of increasing difficulties all the skills required for successful completion of those worksheets.

I couldn’t do that, because when Robert starts working on a packet of worksheets, he has to finish working on the worksheets. So I led Robert through each and every problem from the beginning to end.  That didn’t make any educational sense.  Robert was not learning anything about solving word problems that required adding and subtracting fractions.  Even worse, I was teaching him not to trust himself, be passive, and helplessly wait for others to solve problems for him.

Yes, Robert was making many errors but his errors were results of a giant blunder I had committed by asking him to work on this folder.

I miscalculated, to put it gently.

I should have known that asking  Robert to solve the problem that had two steps would lead to errors even if he could fluently address each step separately. I was asking him to put together three skills, each very different from the other: choosing the proper operation (a sum or a difference), finding common denominators, not forgetting the whole numbers in the process, and changing one whole number into a fraction.

I cannot even say, that before I started working with Robert on this unit,  I was not aware of difficulties he (and I)  might encounter.  Almost one year ago, I worked with Robert on the same packet, just for diagnostic purposes.  I wanted to know how far he could go on his own; how difficult would it be for him to follow all the steps. I found out that was very hard.

Consequently, a year ago, I designed a pretty good, step by step program to help Robert learn.

1. Robert worked on worksheets that only had problems of the format 1-2/3. Subtracting a fraction from 1.

2.Robert worked on worksheets on which each problem of the form 1-2/3 was followed by a few problems of the form 2-2/3 or 5-2/3

3.Robert worked on problems in which he had to change mixed fraction into the improper fraction: 2 and 3/4= 11/4

4. Robert worked on problems where he had to change just 1 out of the whole number into the fraction: 3 and 1/4= 2and 5/4

5.  I made worksheets which required Robert to do the three steps in a row: 1-2/3 followed by (4-2/3),then by (4 and 1/3 – 2/3), and  finally by (4and 1/3- 2and 2/3)

I am using the word “and” as well as the parenthesis in the above expressions only for the purpose of this writing. 

This is exactly what I should have done today. Instead of rushing to complete one more chapter in the book on fraction I should have planned to practice those, well, prerequisite skills over a few more days or weeks.

I know Robert  well enough, to predict that  my errors would lead to his.

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