Learners’ Functional Understandings of Proof (LFUP) in Mathematics: A Qualitative Approach

Abstract

The purpose of this study was to present a revision and validation of the Learners’ Functional Understandings of Proof (LFUP) scale in mathematics using data collected from Grade 11 learners (n = 87) in a high school in South Africa. The LFUP scale was linked to the five-factor model (verification, explanation, communication, discovery, and systematisation) whose items were derived from existing literature on proof functions. Unlike the previous version of the scale, the new scale being validated here blends Likert-scale and constructed-response items to evaluate learners’ conceptions of the essence of the functions of an aspect central to mathematical knowledge development: proof. It is my contention that the LFUP instrument can be used as either a summative or a formative assessment tool, given the argument that learners often require motivation as to why they are required to write proofs. In short, this study provided an instrument to introduce learners to the concept of mathematical proof. Multiple regression analysis revealed that all five LFUP tenets correlated significantly with the total sum of all the functions of proof taken together. In the qualitative analysis, a substantial number of learners (52%) were found to hold hybrid beliefs about the functions of proof in mathematics.