PROCEEDINGS OF THE 17TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2014
Denver, Colorado
Reinventing Permutations and Combinations
Page: 842
Counting problems provide an accessible context for rich mathematical thinking, yet they can be surprisingly difficult for students. While some researchers have addressed these difficulties, more work is needed to uncover ways to help students count effectively. In an effort to foster conceptual understanding that is grounded in students’ thinking, we had two undergraduate students engage in guided reinvention in a ten-session teaching experiment. In this experiment, the students successfully reinvented four basic counting formulas. In follow-up problems, combinations proved to be the most problematic for them, however, suggesting that the learning of combinations may require special attention. In this presentation, we describe the students’ successful reinvention, and we discuss potential reasons for the students’ issues with combinations. We additionally present potential implications and directions for further research.