RUME 26
2024
Omaha, Nebraska
Conceptualizing Students’ Ways of Understanding Bijections in Combinatorics
Page: 959
Pairing and one-to-one correspondences are natural activities, which can be formalized using bijections. Despite bijections being central to mathematics, few studies have explicitly attended to how students construct, understand, and use them. Because bijections show up naturally in combinatorial arguments, I situate this work in combinatorics. In this theoretical paper, I propose three ways of understanding bijections in combinatorics—relabeling, representational, and relational bijections—and discuss possible affordances and constraints of each. I also provide combinatorial examples using binomial coefficients to exemplify each way of understanding.