Context and Implications Document for: Secondary students’ proof constructions in mathematics: The role of written versus oral mode of argument representation

Abstract

The concept of ‘proof’ is fundamental to deep learning in mathematics and in various countries it is considered to be important for students’ mathematical experiences across all the levels of education, as early as the primary school (e.g. National Governors Association Center for Best Practices & Council of Chief State School Officers [NGA & CCSSO], 2010; Department for Education, 2013). The concept of proof is also hard-to-teach and hard-to-learn, and thus over the past few decades it has attracted significant attention internationally by researchers in the field of mathematics education (for a review of the state of the art in this area, see Stylianides, Stylianides, &Weber, 2017). A main research strand has focused on secondary (i.e. post-primary) students’ constructions of mathematical arguments, showing that many secondary students fail to produce arguments that meet the standard of proof. However, the studies in this strand have tended to only consider secondary students presenting their perceived proofs in written form, primarily in the context of survey studies. The lack of consideration by these studies of secondary students presenting their perceived proofs orally —in tandem with students’ written proofs for the same claims—might have resulted in an incomplete or a skewed picture of the potential of students’ constructed proofs, and this raises concern about the validity of research findings. In this article I aimed to contribute to this area by exploring the role of the mode of argument representation in secondary students’ proof constructions. Using classroom data to compare the written arguments (perceived proofs) constructed by students in two secondary mathematics classrooms with the oral arguments that the students presented in the front of their class for the same claims, I derived findings that suggest