Talking about Math

Last week, I sat down with each of my grade 12 students individually and had a mathematical conversation with them. For some students, it was the first time they had to talk math and not just do math on paper.  It was also an opportunity for them to explain their knowledge and not simply regurgitate what they memorized from a textbook.

We are currently studying polynomial functions. I started the conversation by showing students a graph of a polynomial like this (I had 20 graphs to pull from so very few students saw the same graph)

Students were asked to identify if the polynomial in the graph had an even or odd degree; the sign of the leading coefficient; the x-intercepts and their order; the least possible degree of the polynomial; and the maxima and minima of the polynomial (and identify them as local or global). Following this, students were asked a deeper thinking question based on the unit. One example was “Could a polynomial have a degree of 9 and only have 4 x-intercepts?”

Many students were very nervous (a few of them actually said “I need a minute, I am so nervous”) as the conversation was marked as part of their assessment on the characteristics of polynomial functions. However, there was no time limit on their responses and they were given thinking time before they had to answer. It was illuminating to be able to more accurately see their understanding. Too often in math, at least in my career thus far and my experience as a student, many assessments are paper test and the mark is based on what the teacher sees on paper. There is no opportunity to make corrections or clarify your response – it’s a one-chance deal. As a teacher, I try to get students to show their thought-process by having them show their steps but when they make a mistake, I am left making assumptions of why they made the mistake. With conversations, I had the opportunity to ask a student to clarify their answer and not simply attempt to decipher what they really knew based on what they wrote on the test.  Furthermore, when I asked a clarifying question, many students were able to correct mistakes without being explicitly told they were incorrect.

I look forward to the next round of conversations in our next unit!