Factoring Polynomials: Explanation Quiz
Math • High School Algebra II
Selected segments with commentary below » Full video viewable here.
This Algebra II lesson centers around an explanation quiz. Students are asked to work with their group on the problem, which in many classes would mean that the student(s) who are most sure of the mathematics just give the answer to the student(s) who do not understand that mathematics. The teacher has raised the challenge level significantly, the explanation quiz will use a “spinner of death.” Any student who the spinner points to has to be able to explain how the group got the answer to the problem. Now, every student needs to work hard, and the incentives to learn skyrocket. For the students who understand the mathematics, explaining it to someone who does not understand can be a very challenging, high-level task—one that has been shown to increase the performance of the student who is doing the explaining as much or more than the student who does not initially understand. For the student who does not understand but who might be chosen by the spinner, the incentive to work seriously to gain an understanding has increased significantly. As the teacher says, “no more hiding.”
We do not see the students engaging in collaboratively solving the problem; the video picks up when they indicated they were finished with the first problem. The teacher has them spin to decide who will explain. Before the selected student explains, the teacher asks what strength she said she was going to bring to the group today. It seems that the teacher has had the students write down a strength they will bring in advance. The teacher seems to recognize that it may be uncomfortable for students who are not quick to get the answers, since they may be the weak link in the group’s success. By having the students write what they will bring to the group, he allows for the recognition of other contributions to a positive team dynamic. This student chose a mathematical contribution: “to identify and explain the polynomial and what its factors are.”
The student is able to begin explaining what she did, but when the teacher presses on understanding—“how does that help you find the zeros?”—she is not sure. The teacher addresses the whole group, not the individual student, telling them he’s going to come back because they didn’t as a group do a good job of making sure every student could explain.
In this clip we see one of the students take responsibility for explaining to the student chosen by the spinner, and then asks if she understands. The second student says she does, but practices explaining before they call the teacher over for a second time. The teacher tries to ensure that the student who explains is not just repeating what her partner said; he asks her to give an example, and she does. So, the group gets an A.
The act of explaining is a powerful contributor to learning. By having students work in small groups and requiring that a random student be able to explain the group’s work, the opportunity to learn has been expanded for every student.
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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.
