Math Talk – a powerful tool
Gopal Midha
When we think of a math classroom, the image that comes to our mind is that of students silently scribbling into a notebook with a confused look, practicing questions to become faster at solving them (aka drill work) or loud sing-along memorization of tables. What if there was another way? What if we could talk and learn math?
Math Talk is not a new idea. Lampert and Blunk wrote a wonderful book on this back in 1998. Unfortunately, it is an idea that seems to have been forgotten. It is a good time to bring this idea back to strengthen our classrooms. What is more, it is surprisingly easy to implement.
Most of us don’t talk mathematics. We did not experience it during our schooling. For most of us, math is only about using numbers in a certain way to get the right answers. That is like describing language as using consonants and vowels to spell words correctly. Both language and mathematics are more than that.
But then, how does one talk mathematics? Let us take a math question as an example:
10 – { } = [ ]
Before reading further, why don’t you figure out one value for the curly bracket and one value for the square bracket that makes the statement true.
Great!
Now let us add another equation
10 – { } = [ ]
{}+[ ]+[ ] = 13
Do your values work for both? If not, can you try and find out what could be the values for the two kinds of brackets? Be mindful of the strategies that you use. Write them down as you go about solving it. Observe how you feel as you go about it. Take your time. It is worth it.
Got the values? If so, look back and see what strategies you used to find the values. Was it trial and error or was there some reasoning? Is there more than one solution? Why not? Would you solve a similar question differently the next time?
These questions took you back to what happened within you as you solved the questions. And the answers are usually insightful. So, not only did you begin to think mathematically, you also learnt a bit more about yourself. A good education is what gives you both!
Let us try and get this kind of “talk” into a grade 4 classroom where Ms. Debbie (D) is using the same equations we solved.
Ms. D: I’d like someone to explain the solution you got, and I’ll write it on the board. Then we can see who agrees, who disagrees, who has the same answer, or who has a different answer. Jainam, what was your solution?
Jainam: Umm… I think the curly can be six, and then the other bracket is four.
Ms. D: [Writes on the board:] {} = 6, [ ]= 4. OK, so tell us what your reasoning is.
Jainam: Well, if you put them in the sentence, then ten minus six is four.
Ms. D: OK, so let’s hear what others think. Did others get the same answer or a different answer? What do the rest of you think about what Jainam said? Minal your hand is up. Did you agree or disagree with Jainam’s solution? And tell us why.
Minal: Well, I sort of disagree, because four doesn’t work.
Ms. D: Hmm, so you think four doesn’t work. But look, in this sentence here, it does work. Jainam says the square bracket is equal to six. Ten minus the curly, which is six, equals the square bracket which is four. That works, right? So what doesn’t work? I’m confused. Can someone else explain what Minal is saying? How about you, Max?
Max: I think I know what Minal is saying. She’s saying that four doesn’t work in the second sentence – that one with 13.
Ms. D: So, Minal, is that what you were saying?
Minal: Yes, because in the second sentence if you use four for the square one, then the total comes to 14 and we want 13…
Ms. D: Ok, so what did you do to find the values?
Minal: Well, I saw that we had two of the square ones in the second line, so a big number like 7 is not possible because it will already be 14 even without the curly one.
Ms. D asks Minal to come to the blackboard and show her thinking.
Ms. D: Anyone else find a different way? Zohra: I….I actually added one curly bracket to both sides, like we did in the class sometime back. I wanted to get 10 on to one side of the equation. Jainam: Why?
Zohra (turning to Jainam): Hmmm…well, the second line has a curly and square bracket as the first two items…so I thought if I could find their value, I would know what the square bracket stands for.
Zohra has shown another way of solving the equation. She has not only provided the class with another tool to solve similar equations but also reminded them how interpreting the question can lead to a way to solving it. Most of us are in a rush to solve the question by jumping to the procedure we are good at.
The example of the classroom is just one representation of how Math talk can be used.
Teachers and parents can use it to create distinct imagery to interpret the question, draw out patterns, understand the students’ reasoning and misconceptions, show respect to students’ ideas and build a way to see a discipline through the lens of an expert. That is quite a good list of benefits, is it not?
Are you game for it?
References
Lampert, M., & Blunk, M. L. (Eds.). (1998). Talking mathematics in school: Studies of teaching and learning. Cambridge University Press.
Tools of Classroom talk: Downloaded 12th July 2015 from image Sources: http://mrart.wikispaces.com and http://mathmumblings.blogspot.in/2012/02/credits-font-spicy-sushi-roll- from.html.
The author is doing his PhD at the University of Virginia, Charlottesville. Prior to this, he has worked extensively with schools, state departments and MHRD on projects to strengthen teachers and educational leaders. He may be reached at gopalmidha@gmail.com.
