Enumerative combinatorics is an area of mathematics that is both highly accessible for students and widely applicable to other sciences and areas of mathematics (Kapur, 1970; Lockwood, Wasserman, & Tillema, 2020). One important class of problems in combinatorics is combinatorial proofs of binomial identities, which is a type of proof...
Counting problems are rich in opportunities for students to make meaningful mathematical connections and develop non-algorithmic thinking; their accessible nature and applications to computer science make counting problems a valuable part of mathematics curricula. However, students struggle in various ways with counting, and while previous studies have indicated that listing...