## Example of developing an understanding, Mathematics

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In class 1, the teacher had written down the digits 0,1, ...., 9 on the board. Then she made all the children recite the corresponding number names. Finally, she made them write the numerals in their home-work book, several times.

Some months later the teacher started teaching them how to represent two digit remember in the following way. She first reminded them of the one-digit numbers. Then she turned to the blackboard and wrote down

10

The children dutifully copied down what she'd written. Then she said the number name! Loudly one by one, while pointing to the corresponding numerals. Finally, she made the children write each of them down five times, ' saying, "Remember.1 with 0 is ten, 1 with 1 is eleven, ..., 1 with 9 is nineteen."

After some more practice, the teacher was satisfied that the children knew the numerals from 1 to 100. A year later, in the she way they were taught how to represent the numbers from 101 to 1000. And the Class 2 teacher told them that, if she asked them to write any numeral, say hundred and fifty-two, they must first write H T 0 in their books. She explained that H, T and represent hundreds, tens and ones. Since hundred and fifty-two has one hundred, five tens and two ones, the children should write it by putting 1under H, 5 under T and 2 under 0.

The teacher, then, gave them a lot of drill in writing two-and three-digit numerals.

Finally, she told the children what the place and place value of the digits in a numeral are. She did this by giving them a few examples on the board. (For example, the place values of 4, 2 and 7 in 427. are 4 x 100, 2 x I0 and 7 x I, respectively.)

Then she gave them questions of the following kind as homework: how many tens are there in 241?

Most students' answer to this question was 5. One said 25. .

Ones, Tens and More

Why do you think these different answers came forth?

Many of us tend to teach the concepts involved in H T 0 in a mechanical fashion. So, children who have been taught in this way would say that there are 5 tens in 251. We need to go further, using concrete activities, to remind them that after all, 1 hundred is I0 tens, etc. Only then could we lead them towards realising that there are 25 tens in 251.

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