Building Thinking Classrooms in Mathematics, Grades K-12: 14 Teaching Practices for Enhancing Learning (Corwin Mathematics Series)

by Peter Liljedahl

This is because for a group to be generative, it needs to have both redundancy and diversity (Davis & Simmt, 2003). Redundancy, in this context, reflects things that a group of students has in common—language, interests, experiences, knowledge. Without these commonalities they cannot even begin to collaborate. But if all they have is redundancy, they will not achieve anything beyond what they enter the group with. To be generative, they also need diversity; the things that individual members of the group bring that are not shared by the others—different ideas, viewpoints, perspectives, representations, et cetera. Groups of three seem to have the perfect balance of redundancy and diversity.