Philosophy in the Mathematics Classroom
Martin, Christopher, Mathematics Teaching
Christopher Martin found that he needed to persevere when attempting to set up a climate of discussion in his classroom.
"We are going to have a discussion about what we have just heard. To do this, we need to have some rules. The first is that you may only speak when you are holding this [a pot of drawing pins]; the second is that when you wish to speak you must raise your hand."
The Y7 students entered the room to find a layout different from what they were used to. Some students asked what was going on, but the questions were ignored as I welcomed them in. The desks were all pushed to the side of the class and the chairs were in a ring. I asked for some volunteers to read and handed out four copies of the first chapter from The Mathematical Adventures of Michelle and Damian (Tiles and Jackson, 2002). They did so and then we paused.
The chapter had the characters thinking about the nature and existence of cubes. This gave a very rich source for us to investigate. We began by trying to come up with various drawings that could represent cubes. The students were asked to work independently and to come up with as many ideas as they could.
As I walked around the room, I saw that the students had ideas such as nets, isometric drawings and real-life occurrences of cubes (eg, dice). As well as these, there were algebraic suggestions such as n^sup 3^ and n × n × n. Links that I had not anticipated were already forming and we were yet to begin the discussion!
After five minutes, I asked the class 'Are your drawings themselves cubes or do they just look like cubes?" and put down the 'talking pot'. The class were given a few minutes to think about the question. I then passed the 'talking pot' to a member of the group, who, after thinking for a while, passed it to the next person, who passed it, who passed it, who passed it, etc.
Then there was silence; for five minutes no-one said a thing. I felt agitated. I had an urge to take the pot and rephrase or re-question or reiterate. I was being observed and I wanted the observer to see something; but I did nothing - I just waited. Believing that my role is that of 'facilitator' helped me keep my nerve.
At this point, the observer raised her hand for the pot (she was sitting in the ring) and offered an idea based on her own drawings. She made no statements of fact; her comments were in the language of conjecture: "I think ..." and "I'm not sure about this but ..." This appeared to be a catalyst for change in the group: as she spoke, five hands were slowly raised into the air. After each new comment, more people wanted to speak, and from then on there was always a hand raised. Students responded to each other as well as posing new questions and putting forward hypotheses. It is clear that the class were demonstrating important mathematical behaviour before we even consider the substance of what was said. …