Abstract:

We report on the ways in which two middle school teachers dealt with situations in which they did not understand the ideas that were being generated by their students as they solved a non-routine combinatorics problem. We share how each teacher handled the situation, and the implications for their students. In one case, the teacher tried to make sense of the ideas by asking one of the students to explain her thinking to her groupmates. However, when the teacher still couldn’t understand the ideas, he decided to tell all students to use the strategy that he himself had used when solving the problem. His hope was to lead the students toward a very predictable solution strategy. In the second case, the teacher suggested that the entire class test the idea in question. In the first case, the students did try to use the teacher’s method, but appeared to remain confused about why and how it worked. In the second, many, but not all, students succeeded in solving the problem in unique ways. During follow–up professional development sessions, the teachers shared their frustrations about how difficult it was to follow student thinking ‘in the moment’. However, after discussing the situation with their peers and project researchers, both teachers were able to formulate strategies for dealing with similar situations in the future. These strategies focused on solving the problem in a more in-depth manner—prior to implementation—with a particular emphasis on possible student thinking trajectories and the strengths and weaknesses of each. While project researchers had already emphasized this, the teachers recognized its importance only after confronting situations such as those described in this paper.

Keywords:

Math education, teacher decisions, student thinking student justification.