Hello friends,

Our First "Maths Teachers Study Group" meet on 18th May was fantastic. I will soon share its proceedings. Thanks to all the teachers who participated in this initiative :)

Yesterday night, I saw the video of Deborah Ball where she shares some interesting insights about the competency required by the maths teachers to spot the error in their students’ work. I don’t want to spoil your excitement by narrating her video and hence would recommend you to first watch this video and then resume your reading. https://www.youtube.com/watch?v=nrwDM4ejNqs

Who is Deborah Ball?

Deborah shows three multiplication problems to the committee members and asks them if they can figure out the errors made by the three students. You may call me crazy but, something drove me next day to pose the same challenge to my class-7 students J I wrote these 3 problems as it is on the board. Believe me, it was a real pleasure and a rich learning experience to watch and hear them analyze these problems - hunt for others’ mistakes and base reason on their arguments. I strongly felt the need to video record these conversations. We will discuss about this process at length during our next ‘Maths Teachers Study Group’ scheduled on **Sunday, 31**^{st} May.

But in this email, I want to share with you some equally (if not more) interesting observations that came out as a by-product of the discussions on the above problem.

The students were very happy (and even surprised) to come across one of the new ways of doing multiplication. I leave this up to you now to figure out (and tell me) the reason for their excitement. You will have to watch the video for this.

In fact Poonam was so thrilled by this experience that she wanted to test/ apply this method (‘new’ method - according to her) on a different problem now. This is how she did it.

She asked me to check if it’s correct. (Hold on - What do you feel about her way of doing multiplication this way?)

Now, they have heard enough from me that it is not the teacher’s business to check if the student’s work is correct. But my experiences have taught me that the Undoing and Unlearning effect takes some time J

She got the message. “I can cross-check this answer by using division. Shall I?”

“Go ahead.”

And this is how she did.

I noticed that she has erred.

“Sir, how come the quotient is 154? Shouldn’t I get 198?”

“How do I know dear?” I see to it that my pretended innocence is not caught J

Perplexed, she thought for a while, and decides to solve the same problem using the ‘old’ multiplication method now.

She errs again and gets the product (3770) which is different than the one she had got in the former one (4950)
“Oh sir, it means I have some done some mistake in the first multiplication process. Or, is it that the ‘new’ method doesn’t work?”

“What do you feel?”

“But we had seen earlier that we get the same and correct answers using both the methods....because they are actually similar methods.”

(We had already discussed about the use of commutative property in these two methods.)

“Hmm....So what do we do now?”

She thinks for a while.... And I was so happy to hear her say, “Shall I cross-check the product that I have got using division?”

(Of course, there were other smarter ways for verifying the correctness of product, but talking about all that at this juncture had the potential danger of disturbing her present flow. Hence I choose to just let her go - her way(struggle)).

So this is how she did it.

“Oh my god! Sir, I am getting a remainder of 20 now!”

I also noticed that her process of division was not complete. Look at the quotient. (In fact, it’s one of the most common mistakes made by most of the students (why so?) However, I choose to ignore this error as of now. And I will surely bring this to her notice, but later, and with the help of this snap :-) ...To continue to read, click on 'Read More' below...