Mathematics, as a Dialogue
May 7, 2012 § Leave a comment
People would do music or skating for leisure, but I don’t know anyone who would do mathematics for leisure. If there is a recreational mathematics club for adults, I wonder how many(besides me) would attend. I am very curious whether this is because the way mathematics is taught in school, or due to the nature of mathematics itself.
I teach mathematics part time. But I do not like mathematics as a question. I like it as a dialogue, a conversation. I like to ‘dance’ with my students. It is too hard for me to do it this way in a group, so I only teach 1 to 1. For example, one day I gave a student this question:
“You are given a triangle made of paper. Can you find out the center of the inscribed circle? How can you do this with as little tools as possible?”
To give you some background, the student is sec 2 from a local(Singapore) school, and was never trained for competitions. It is interesting to see all kinds of responds students will give when they feel safe. It is like a drawing assignment when everybody will turn up something different and creative.
Except that in mathematics, there is logic.
He cut out a triangle (right angled isosceles triangle to be exact) and started folding, and told me that he found the center. When I give my students questions like that, I don’t really know what they will throw back at me. How he folded is different from how I knew I would fold, but at that moment it wasn’t clear whether he has in fact found another way of folding, or he is just being wishful. So I asked him why (to buy myself some time). He couldn’t explain, so jokingly he said, “because I feel like this is the center.”
Now, if he had given me some reasons, it will be easy for me to (either agree, or) point out what is wrong with them. My hunch was telling me that what he proposed will not get the required center. But how can I show that he is wrong when he(mathematically) did not say anything?
How do I entertain his thoughts and intuition, without discouraging his creative input? I need to be at the top of my wits and be careful not to appear like I am trying to outsmart him. That is the challenge that I always love about these dialogues.
I think that a mathematics recreational programme for adults — where every participant is made clear of the choice that the value lies in the dialogue, not the answer — will be very interesting. Maybe then people would start to do mathematics for leisure.