RUME 28
2026
Alexandria, Virginia
Expert Perspectives on the Set of Outcomes for a Non-Standard Presentation Counting Problem
Page: 755
The objective of a counting problem is to determine the cardinality of a set of outcomes, but there is never a singular, unique way to conceive of those outcomes. I report on data of combinatorics experts solving a counting problem whose numerical solution is 2^6, a standard expression to see in combinatorics, but whose set of outcomes is not standard. I demonstrate four distinct models that the participants used to conceive of the outcomes, and how each of those led to different ways of explaining the solution. I argue that these differences among experts reflect the challenging nature of articulating what the set of outcomes for a counting problem is, and how to approach a solution using this set. These data may inform how counting could be presented to learners when adopting a wide view on the multiple possible sets of outcomes for any given problem.