How positioning as teacher or student may change validation of the same proofs

Recent results such as by Wasserman, Weber, and McGuffey (2017) show the promise of using a particular type of task in undergraduate mathematics courses for secondary teachers: tasks that situate mathematics in pedagogical context. Yet their design deviated from previous recommendations that tasks necessitate pedagogical knowledge; some of their tasks can be solved with purely mathematical knowledge, even if pedagogical knowledge may be beneficial. We examine the phenomenon they observed, that the presence of pedagogical context appears to change the work of a mathematical task. We presented 17 practicing secondary teachers with the same set of proofs to validate, once in the context of teaching secondary mathematics, and then in taking a university mathematics course. We argue that the construct of social positioning – as a student or teacher – explains differences in secondary teachers’ proof validations as well as the problem of disconnect between undergraduate mathematics and secondary teaching.