RUME 26
2024
Omaha, Nebraska
From an Inclination to Subtract to a Need to Divide: Exploring Student Understanding and Use of Division in Combinatorics
Page: 459
In this report, we provide an initial exploration into a key but under-studied phenomenon in enumerative combinatorics – the use of division in solving counting problems. We present a case of one undergraduate student solving a combinatorics problem; this case is representative of a broader phenomenon in which students may intuitively desire to account for an overcount using subtraction, when division is a productive and useful approach. We highlight the conceptions a student demonstrated as she progressed from using subtraction to using division successfully. We frame our analysis in terms of a set-oriented perspective (Lockwood, 2014).