TY - JOUR

T1 - Using task-based interviews to generate hypotheses about mathematical practice

T2 - mathematics education research on mathematicians’ use of examples in proof-related activities

AU - Mejía-Ramos, Juan Pablo

AU - Weber, Keith

PY - 2020/1/1

Y1 - 2020/1/1

N2 - Mathematics education researchers frequently use task-based interviews to gain insight into mathematicians’ practice. However, there are a number of factors that should prevent mathematics educators from extrapolating how individual mathematicians respond to researcher-generated tasks in laboratory conditions, to how mathematicians practice their craft in authentic settings. In this paper we critically analyze the rationality of using task-based interviews to investigate mathematical practice, focusing on how task-based interview studies have been used to inform our understanding of mathematicians’ use of examples in mathematical practice. We discuss four specific generalizations about mathematical practice drawn from these studies, and suggest other types of studies that can be used to corroborate or challenge those generalizations.

AB - Mathematics education researchers frequently use task-based interviews to gain insight into mathematicians’ practice. However, there are a number of factors that should prevent mathematics educators from extrapolating how individual mathematicians respond to researcher-generated tasks in laboratory conditions, to how mathematicians practice their craft in authentic settings. In this paper we critically analyze the rationality of using task-based interviews to investigate mathematical practice, focusing on how task-based interview studies have been used to inform our understanding of mathematicians’ use of examples in mathematical practice. We discuss four specific generalizations about mathematical practice drawn from these studies, and suggest other types of studies that can be used to corroborate or challenge those generalizations.

KW - Conjecturing

KW - Examples

KW - Mathematical practice

KW - Proof

KW - Task-based interviews

UR - http://www.scopus.com/inward/record.url?scp=85085972719&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85085972719&partnerID=8YFLogxK

U2 - https://doi.org/10.1007/s11858-020-01170-w

DO - https://doi.org/10.1007/s11858-020-01170-w

M3 - Article

JO - ZDM - International Journal on Mathematics Education

JF - ZDM - International Journal on Mathematics Education

SN - 1863-9690

ER -