Why do students not check their solutions to mathematical problems? A field-based hypothesis on epistemological status

ABSTRACT

This study embarks on the question in the title with the construct of epistemological status, which pertains to the solver’s satisfaction with the way and the degree to which their solution had fulfilled their intellectual and psychological needs in a particular problem situation. The construct is used to hypothesize that a solver’s decision to check the solution and the act of checking itself may be shaped by the epistemological status of a developed solution. Driven by the abduction methodology, this hypothesis is supported by two empirical illustrations. The first one comes from the final exam in a large first-year course for non-mathematics majors, where many students accompanied their solutions of a low epistemological status by written checks of final answers as a way to elevate it. No such checks were found in solutions with high epistemological status. The second illustration revisits some previously reported findings to propose that an application of conventional problem-solving methods may not be sufficient for students to endow their solutions with high epistemological status.

KEYWORDS:

• checking solutions to mathematical problems
• epistemological status
• intellectual needs
• problem solving

MSC:

• 97

Acknowledgement

I am grateful to RUME and DELTA communities, and specifically to Ofer Marmur, for their insightful suggestions on earlier versions of the paper. I am grateful to Deborah King, Cristina Varsavsky and anonymous reviewers for their thorough criticism and comments. I wish to thank Lisa Kiyomoto-Fink for proofreading the paper.

Disclosure statement

No potential conflict of interest was reported by the author.

ORCID

Igor’ Kontorovich http://orcid.org/0000-0002-3353-5445

Notes

1. The richness of this data corpus has been utilized already for different purposes. In Kontorovich (2019a) it is used to discuss the reasonableness of final answers that students produce. In Kontorovich (2019b), the corpus is examined with a focus on students’ procedural knowledge in Linear Algebra. Herein, these data is used for the first time to support a theoretically developed argument about students’ decision to check their solutions.

2. This shows that not all methods employed by students were properly matched to the problems that they were intended to solve.