Grade 11 Students’ Proof Construction Ability in Relation to Classroom Resources

Abstract

Despite proof being fundamental to the mathematics discipline and its role as a means to convey mathematical content, little is known about the effect of resources on influencing students' proof construction ability. The purpose of this study was to compare two didactic environments, one regarded as resourced (favored) and the other under-resourced (disadvantaged), in relation to the construction of a mathematical proof. Motivated by the discrepancies in the literature on the influence of school resources on students' performance and the unfortunately prevalent view that the sole function of proof in mathematics is verification by using confirmatory cases, this study sought to examine the differences (if any) between resourced and under-resourced classrooms in relation to students' proof construction ability. To this end, data were drawn from a proof-related task performed by 78 Grade 11 students in the Ethekwini Metropolitan area, South Africa. A modified version of the Proof Construction Assessment tool showed that students in resourced schools significantly performed better than those in under-resourced schools in relation to proof construction. In addition, there was an observable and noticeable effect of this. Specifically, at an alpha = .05, the t-test for independent means revealed a significant difference between the two groups, t(76) = 2.749, p < .01, d = .624 SD. The practical significance of the results emphasizes the importance of taking into account the role of resources when investigating the learning and teaching of proofs. Further, preliminary results also suggested that most students struggled to even begin to prove the proposition. Recommendations and implications for the students' careers and future research are raised and discussed.

Who Should Learn Proving and Why: An Examination of Secondary Mathematics Teachers’ Perspectives

“…Finally, we think it is important to bear in mind the findings of Shongwe (2020), who also worked in a South African context. Shongwe found that so-called proof ability was not evenly distributed across various schools but that students in well-resourced, high-socioeconomic-status schools were found to be more adept at proving than students in under-resourced, lowsocioeconomic-status schools.…”

“…Third, given many of the current systems of education that function as societal gatekeepers, proof instruction can exacerbate the role that mathematics plays in inequitably sorting and excluding students from future opportunities. In South Africa, for example, Shongwe (2020) found that greater school resources correlated with greater proof performance. This suggests that a danger of instituting proof for all would be that differential success with proving could be used as a status symbol and yet it is actually a reflection of the differential resources allotted to schools.…”

“…Students have long had difficulties with proving (see Mariotti, 2006;Senk, 1985;Shongwe, 2020) but it is nevertheless seen as a worthwhile learning goal because of proof's importance to the discipline of mathematics (thus exerting a potential disciplinary obligation on teachers) and its potential to support deep learning (thus exerting a potential individual or institutional obligation on teachers). For these reasons and others, the mathematics education community has called for increases in proving opportunities.…”