Piece of Rock

March 7, 2015

I thought it would be a piece of cake.  The task  so easy that Robert could do it without my help or even without my presence (Those are not exactly the same things for Robert as my silent presence gives him the courage to undertake more difficult problems.) Using five line segments of equal length, each divided into different parts (halves, thirds, fourths, sixths, and eights) Robert was supposed to compare fractions.  I though the problem was self-explanatory. Just decide which line is longer or if they have the same length.  It was so much simpler endeavor than comparing fractions by replacing them with equivalent fractions with the same denominators.  That Robert could do.  He might  need one example as a reminder, but then he can follow with the same algorithm and find the correct answers.

Using the number lines, however, seemed so much simpler and quicker for ME, so I was led  to the conclusion that it would be also easier and faster for Robert. It wasn’t.

Five parallel number lines completely confused him.  I was not able to detect what exactly was a reason for his errors and I was not able to help him get on track.  I was telling him, that the longer segments represent larger fractions, that the same length segments represent equivalent fractions. that didn’t help.

Moreover, I knew that without those five number lines, Robert would easily point to the pairs of equivalent fractions.  Still, he couldn’t do that WITH the visual HELP of number lines.  I am still not sure why, but I might consider these reasons:

1. Robert was looking not at the length of segments assigned to the whole fraction (for instance 3/4) but at the length of one part – that is 1/4.  And thus decided than 2/3 was larger than 3/4 because 1/3 segment was longer than 1/4/

If that was the case, I should have asked him to measure the length of the segment starting from 0.

2. Placing the equivalent fractions on top of each other might have suggested to him that those which were on top were larger than those on the bottom. Again, I should have asked Robert to measure the segments starting from 0.

I also could ask him to draw vertical lines through some of the fractions.

I am not sure what was the reason for Robert’s confusion.  I am sure, however, that I  should refrain from deciding for Robert what is easy and what is not as he processes signs differently than I do.


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