Wednesday, November 12, 2008
Teaching Second Grade in Edgewood School in Scarsdale USA
For the first 15 minutes, I was worried as the children did not seem ready to engage in some difficult thinking. I had asked them to pick two 1-digit numbers from a stack of cards. Rohit volunteered and picked 3 and 3. I told them that the 3 and 3 were used to make 33 and 6 (3 + 3) and then the difference 33 - 6 was found. We used the 100-chart to help with the subtraction.
Another girl picked 8 and 6 and again we used those to form 86 and 14 and found the difference 86 - 14. I told them that even if I could not see the second number, I can still work out the difference!
This is a multi-step process problem. The children seemed lost in the many steps. They were not entirely ready for this and I had to do something to help them remember what the problem was all about. Some constantly thought that I was guessing the second number (i.e. 6 when the girl picked 8 and 6), instead of the answer to the third step - after using 8 and 6 to form 86, 8 + 6 = 14 and finding the difference between 86 and 14.
(I used the term difference very early in the lesson. I would not have done this in Singapore as I am aware that we introduce this term only in Primary 3. But I thought these kids being kids in U.S. would know the term. Clearly it was a wrong assumption - second graders who know subtraction may not comprehend the term difference.)
To help them remember, I constant got them to refer to the cases we have tried how the three numbers 86, 14 and 72 were obtained.
Each of the four groups were then invited to picked two numbers but not show the second one. I then wrote down the final answer for each case. We then checked and each time the answer was correct.
I asked the children to tell how the magic worked.
There was an early suggestion from Rohit and the boy in front of him that the answer was obtained through multiplication. However, as they had not yet learnt the multiplication tables, they struggled with this. I invited the children to checked if the answers was in their 'book of magic' which was just their exercise books which happen to have multiplicaton tables.
I gave some hints and many children could see that the tens digit in the answer is related to the first digit they chose. Someone else described that the sum of the digits in the answer is 9.
I asked Michael, who struggled with the task and seemed to start to lose interest in the lesson, to come out and helped me. Later, he told the Principal that he was nervous when he was called. I guided him and in the end he could see that the digits add to 9. He seemed more engaged after that.
I let the children try the trick among themselves and, just before we ended, gave them a few examples to try.
We had a roomful of teachers observing the children. It was a modified lesson study of sorts. The photographs of the lesson and a discussion of the mathematics will be posted here in the near future.
I did the same problem with teachers at Stamford Primary School in Singapore. The teachers came up with two ways - multiplying the first digit by 9 as well as to reduce the tens digit by 1 and making sure the sum of the digits in the final answer is 9. They could also explain method that multiply the first digit by 8 or by 10.