Believability in mathematical conditionals: generating items for a conditional inference task

This paper describes design issues for a conditional inference task with mathematical content. The task will mirror those used in cognitive psychology to study inferences from everyday causal conditionals: its items will present a conditional premise (if A then B) and a categorical premise (A, not-A, B, or not-B) and ask participants to evaluate whether a conclusion (respectively, B, not-B, A, not-A) necessarily follows. To assemble items, we asked six mathematics education researchers with expertise in conceptual understanding to generate conditionals covering a range of mathematical topics. To mirror the structure of tasks with everyday causal content, we asked that these conditionals should vary in believability. In this paper, we analyze the content and phrasing of the submitted conditionals in order to assess their suitability for use in a conditional inference task, and describe our planned use of this task to investigate the relationship between logical reasoning and mathematical expertise.