Introducing a measure of perceived self-efficacy for proof (PSEP): Evidence of validity

Abstract

It is widely recognized that students encounter difficulties with proof across all grades and beyond, yet standardized instruments related specifically to students’ perceived self-efficacy for mathematical proof have not been readily available. The purpose of this study was to develop and investigate preliminary validity evidence for a new instrument for measuring self-efficacy for mathematical proof that can be of importance to the field. The new Perceived Self-Efficacy for Proof (PSEP) questionnaire is a self-administered, 8-item questionnaire that quantifies experimentation, conjecturing, inductive reasoning, justification, and validation. To validate the PSEP, two studies with 260 eleventh grade students—recruited from three Dinaledi schools in EThekwini metropolitan area, South Africa—were conducted. In Study 1 (n=128), face and content validity were evaluated, and an exploratory factor analysis (EFA) was performed. In Study 2 (n=132), a confirmatory factor analysis (CFA) was conducted and external validity was investigated. In both samples, the PSEP was found to possess good internal consistency reliability with relatively high factor loadings on a single component. Although the findings in this report represent preliminary validation evidence, it can be concluded that the PSEP is a valid, reliable and sensitive measure of 11th grade students’ perceptions of their ability to construct a proof and may serve as a meaningful outcome in mathematical proof research and classroom proof education.

Keywords

• calibration, factor analyses, instrument development, self-efficacy for proof