Most problems students are given in math classrooms have a single answer. In this video, a clever tactic is employed by the teacher: students are given an answer and asked to develop a problem situation for which it would be the solution [serpinstitute.org/sensemaking]. The reversal makes the task more conceptual: students need to think about the equation in terms of a set of relationships in order to generate a situation. It’s a more challenging task than simply solving the problem, creating value in discussing with a partner.
The students quickly agree on a problem situation, and reveal an important piece of information: while the topic the class is learning about has switched from single variable problems to solving problems with two variables, students are still thinking in terms of mathematics learned earlier. It is not uncommon for students to use lower-level mathematics to try to solve problems that the teacher expects students to solve using newly-learned mathematics (again, multiplication problems can be solved using repeated addition as long as the numbers are small enough and the time allotted long enough). In this type of problem, in which students are much less constrained—they can propose many situations that can be characterized by the equation. This pair of students reveal both that they have mastered the earlier mathematics and that they have not yet grasped the concept of a two variable problem.
You’ll see in this discussion between the pair that they are equally engaged. This is aided by the small group size, in a pair no student can hide. The students are also working off of a shared resource (a single worksheet) and the teacher sets the expectation at the outset that they are expected to be able to explain their thinking.
In this segment the teacher joins the pair of students and has them explain their work. The discussion leads to some misconceptions around the mathematics, namely the students created two constants in their equation, when it should be two variables. This mid-task discussion helps the student locate where their thinking has gone astray so that they can use the remaining time to revise their problem situation and chart.
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The Academically Productive Talk Project was made possible by a grant from the Spencer Foundation #202000131. The views expressed here are those of the authors and do not necessarily reflect the views of the Spencer Foundation.
