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August 15, 2014

On confusions and clarity...

Its interesting how small things can confuse or clarify things for children. At times the children dwell in their confusion and come out with clarity and growth. At other times they reach the end of their patience and look for adult intervention. I often relying on giving time, peer learning, but sometimes peers are unable to fix the problems because they don't have the same problem and can't find the patience to understand the problem. Here something that happened this week at Udavi (6th Grade) and Isai Ambalam (5th Grade)...

We had been working with the weighing balance to apply addition, subtraction, multiplication and division with using things that could be put into pencil boxes. As I was weighing some working with different blocks I noticed that the hand made blocks were not all the same and for a change we went into a puzzle to identify a heavy block among three blocks. In time, I talked about the use of math to document what we learn and create processes. We numbered the blocks so we could distinguish between them and know what you did with them. When the children were comfortable having observed the process with real blocks we thought of ways of writing it out and came up with the following flowchart.

This chart confused quite a few kids. I asked what they had not understood and if they would like me to repeat with the blocks. The children said that they understood the physical measurements. I spent some time revisiting >, < signs and a couple of children did have difficulty with that, but for most that was not the problem. They just felt they didn't understand and something was off. I stared at the picture myself and then some clarity dawned and I drew this one...

Logically it was the same flowchart. Only it had when one is used on the left and when 2 was used on the right with the corresponding >, < signs reversed. This clarified the issue for almost all children instantly. A couple of children go it once they were able to discuss it with their classmates who had now understood.

It was interesting that when the children were working on finding the lighter block they actually switched the signs again to get 1 continuing on the left and 2 on the right. 

Its also interesting that as they started dwelling into more complicated problems of not knowing if the ball was lighter or heavier and with 4 balls they got quite good at the symbols and were able to play around with any order.

I took the same problem with the 5th graders in Isai Amlalam. Having learnt from my experience I did not want them to fall into the same trap and once they were comfortable with what physically happens with 3 balls I went to the pic that I found was flowing in class. 

Apparently the pic didn't make sense to some kids. I went over the signs >, < but still there were 4-5 kids who looked puzzled and few others who seemed to have got it were also a little uncomfortable applying it to another puzzle. Finally, one child articulated that he didn't understand how 2 could be greater than 1. I told him that its only a name to keep track of the balls, but then I took the names of three of the kids in the first row and used these for the name of the balls. I wrote their initials V, D, A and this put the children at ease to work on these puzzles.

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