RUME 27
2025
Alexandria, Virginia
Elaboration on Lists and Listing Processes in Combinatorics
Page: 808
Lists are a foundational way to reason about and solve counting problems, yet it is unclear to what extent their role should continue for advanced learners and what that role should be. I draw on case study data of two undergraduate students who used lists repeatedly as they worked through a sequence of combinatorial tasks. I demonstrate that the students’ use of lists refined over time, and their representations developed from outcome-oriented to process-oriented, thus allowing them to draw on their knowledge of lists for increasingly sophisticated problems. Further, the forms of their solutions were impacted by their use of lists. I argue that these data shed light on broader questions of the role of representations in solutions to combinatorics problems as students develop combinatorial facility.