Secondary students’ proof constructions in mathematics: The role of written versus oral mode of argument representation

Prior research showed that many secondary students fail to construct arguments that meet the standard of proof in mathematics. However, this research tended to use survey methods and only consider students presenting their perceived proofs in written form. The limited use of observation methods and the lack of consideration of students presenting their perceived proofs orally—in tandem with their written proofs for the same claims—might have resulted in a skewed picture of the potential of students’ constructed proofs, and this raises concern about the validity of research findings. The research reported in this article substantiates this concern. Using data from a design experiment in two secondary mathematics classrooms (14–15‐year‐olds), I explored the role of the written versus the oral mode of argument representation in students’ proof constructions. Findings from the comparison between the written arguments (perceived proofs) that the students produced during small group work and the oral arguments that the students presented in front of the class for the same claims showed that the oral mode of representation is more likely than the written mode to be associated with the construction of arguments that meet the standard of proof. Thus if a study had analysed students’ written arguments only (as in survey research), it would have reported a less favourable picture of the potential of students’ constructed proofs than another study that would focus only on students’ oral arguments (as in observational research). Implications for methodology, research and practice are discussed in light of these findings.