Classroom Collaboration Supports Mathematical Generalizations

Amy Ellis

In mathematics classrooms, generalization is an important part of the curriculum.
When students know how to generalize they can identify commonality across cases, extend their reasoning beyond the range in which it originated, and derive broader results from particular cases. But generalization remains difficult for students to do, and for teachers to support.
UW-Madison education professor Amy Ellis studies the processes that support students’ productive generalizing in their math classrooms. She considers generalization a dynamic social process as well as an individual cognitive activity.
In a recent study she studied an 8th-grade math class during a 3-week unit on quadratic growth. The class sessions focused on relationships between the height and area of growing rectangles (see illustration). As they grew, the rectangles retained the same height-to-length ratio.