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!
