Creating a classroom environment where students publicly disagree with one another is often a challenging endeavor. During this class, my class of Integrated Math 1 students were finding the rate of change (ROC) from graphs, tables, and two points. Students had been introduced to slope triangles and the slope formula, but the majority of the work had been solo as students worked on finding the ROCs. In this extended warm up, I asked students to evaluate each “student’s” claim.
Activity adapted from colleague Thach D.
This is an instance of some fictional students making mathematical claims. I gave this task because I wanted students to continue working on critiquing arguments while being removed from the person itself. I have noticed that my students seem to avoid constructing critiques about students in class because they do not want to be the one to “hurt” someone’s feelings.
First, I had students write down their ideas independently for Damon, Mari, and Anika’s claims using the sentence frame. After about 2 minutes of writing independently, I asked students to share with their elbow partners as a “turn and learn.”
As I walked around, some pairs were still reluctant to share with their elbow partners (about 3 of these pairs also had little written down. I think they were struggling to form an opinion). For these pairs, I asked more directed questions such as, “Do you see a rise of 1 and a run of 2 anywhere on the graph?” Then, that was usually enough for students to try and evaluate Mari’s and Anika’s claims.
I then asked for volunteers to share for the whole class. For Damon’s claim, one student said, “Damon’s wrong because he switched the 1 and the 2. He has run over rise, but it should be 2 over 1.”
With this, I jumped in and continued to clarify that we have been defining slope as rise over run. I wonder if I could have let students expand further. For Mari’s claim, another student said, “I agree with Mari because there’s a rise of 2 and a run of 1.” The students who shared were both volunteers who typically share often. However, I believe using “fictional” students helped students feel more comfortable in critiquing the displayed mathematical claims. The multiple representations (graph, words, equation) also opened access for more students to evaluate the claims.