PROCEEDINGS OF THE 21ST ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2018
San Diego, California
Generalizing in Combinatorics Through Categorization
Page: 1048
In this report we discuss students generalizing within a combinatorial setting. To facilitate reflection on prior activity, we prompted students in a teaching and a design experiment to categorize a myriad of problems they had previously engaged in. We will discuss the combinatorial underpinnings behind the students’ generalizations according to Lockwood’s (2013) model for combinatorial understanding. We saw that the students were able to produce generalizations of various basic combinatorial problems while each maintaining different understandings of the combinatorial structures. We conclude by discussing uniformity in the students’ reasoning pertaining to combinations and the productive nature of such discussions.