Enhancing Students' Proof Competencies in Secondary Mathematics Classrooms

A primary objective of secondary school mathematics is to develop students' proof competencies, that is, their abilities to investigate whether and why "things work" in mathematics by means of the logical structure of the mathematical system rather than by appeal to the authority of the teacher or the textbook. Proficiency in proof can provide secondary students with a solid basis for conceptual understanding and prepare them for a smooth transition to advanced mathematical studies.

Yet, prior research showed that even high-attaining secondary students have difficulties with proof and that there is only modest growth in these students' proof competencies over time. These findings are worrisome for they suggest that existing classroom practices fail to support students' learning of proof.
This study was organised as a design experiment in two high-attaining secondary mathematics classes over a period of two school years (when the students were in Years 10 and 11), and aimed to generate research knowledge about how secondary classrooms can better support students' learning of proof. Specifically, the study was concerned both with the practical issue of improving students' learning of proof and with the theoretical issue of developing more generalised research understandings about the means by which this learning was supported.