Reinforcing key combinatorial ideas in a computational setting: A case of encoding outcomes in computer programming

Counting problems are difficult for students to solve, and there is a perennial need to investigate ways to help students solve counting problems successfully. One promising avenue for students’ successful counting is for them to think judiciously about how they encode outcomes – that is, how they symbolize and represent the outcomes they are trying to count. We provide a detailed case study of two students as they encoded outcomes in their work on several related counting problems within a computational setting. We highlight the role that a computational environment may have played in this encoding activity. We illustrate ways in which by-hand work and computer programming worked together to facilitate the students’ successful encoding activity. This case demonstrates ways in which the activity of computation seemed to interact with by-hand work to facilitate sophisticated encoding of outcomes.