Arguments and group discussions: middle-school students’ initial work with mathematical arguments

Abstract

This article addresses argumentation in middle-school students’ group work with conjectures in arithmetic with different epistemic states. Twenty-five episodes were analysed using G. J. Stylianides’ framework for reasoning and proving, which comprised a mathematical, psychological, and pedagogical component. The mathematical component was studied through students’ arguments. The arguments found in the study were predominantly empirical, but there are also examples of rationales and demonstrations. In addition, there were also cases displaying two different arguments. One notable finding is that the epistemic value of the conjectures is seen to affect students’ argumentation. The psychological component was seen through the characteristics of students’ discussions. Most episodes show that students agree or do not speak explicitly about how they perceive their argument, whereas in some cases, there is clear doubt or disagreement. Seeing each episode's mathematical and psychological components in tandem gave six categories of episodes, each showing potential for challenging perceptions and capitalising on doubt or disagreement, hence addressing the pedagogical component. The study provides insight into middle-school students’ initial work with argumentation and demonstrates how taking a dual perspective to students’ group work helps untangle this complex practice.