Examining Elementary Mathematical Argumentation Through Balacheff’s Taxonomy of Proof

• In Event: AERA Roundtable Session Sunday 9:50 am Four Seasons Ballroom 2-3
  In Roundtable Session: Studies Focused on Mathematical Reasoning and Argumentation (Table 5)

Abstract

Mathematical argumentation is a process of mathematical reasoning wherein one rationalizes truths and untruths about mathematical claims. It is seen as a precursor to formal proof and can act as a way for students to deepen conceptual understanding and reasoning skills. Despite this importance, argumentation is not frequently used in elementary mathematics. This paper presents findings from a larger study on the implementation of argumentation in elementary mathematics. Using Balacheff’s Taxonomy of Proof as a framework, we classified and analyzed samples of students’ arguments as they disproved false mathematical claims. While many students developed arguments using more concrete thinking, some engaged in abstraction and deep mathematical conceptualization, even though none had any previous experience with argumentation tasks.

Authors

• Cathy Marks Krpan, University of Toronto - OISE

• Gurpreet Sahmbi, University of Toronto - OISE

• João Paulo Attie, Federal University of Sergipe