John was doing his homework on vertical addition, and had to compute :

5 3+ 3 4  and 6 8 +45

He did the first one easily, just the way his teacher had taught him. He first added 3 and 4,.and wrote 7 beneath 4. Then he added 5 and 3, and wrote 8 beneath 3.

The next sum was also manageable. While doing it he could be heard mumbling to himself, "8 + 5 = 9, 10, 11, 12, 13. So I write 13 here (below 5). Then 6 + 4 is 7, 8, 9, I0 and so 1 write 10 (below 4)." He was satisfied with his answer, 1013. But, next day, his teacher wasn't !

His teacher tried to quickly repeat the method; he had given the class on the previous day, namely, in 68+45, since 8+5 is 13, write 3 below 5, and write 1 on the right of the problem. Then, 6 + 4 is 10, plus the 1 on the side is 11 [see Fig. 3(b)], so write 11 below 4. So the answer is 113.

Quite a few of John's classmates had made a mistake in the sum. The teacher thought it was just a matter of practice. So she gave them more exercise$ to do over a period of time. And then she moved on to discussing other concepts. Some students managed to cope with what she was teaching, and some fell by the wayside.

The following exercise is about the situation given above.

2.  According to you, what are the reasons for John's, and the other children, inability to solve the sums correctly?

If you look closely at the children's problem in Example 3, you may feel that they faced it because of their poor understanding of what the ones ten hundreds places denote. My neighbour's child, who is in Class 3, also seemed to have the same problem. I tried a method with her, which 1 shall share with you now.