PROCEEDINGS OF THE 21ST ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2018
San Diego, California
Generalizing in Combinatorics Through Categorization
Page: 311
Basic counting formulas, such as the combination (n k) and permutation n!/(n - k)!, constitute students’ initial exposure to the structure of combinatorial processes. Understanding the structure and nuance of these counting formulas is important, as more complicated processes rely on the foundation these formulas set. In this paper we describe a study in which we used a categorization task to have students focus on salient aspects of counting processes, ses of outcomes, and formulas/expressions. We describe their generalizing activity and present an instructional theory for the production of four basic counting formulas.