Students’ Mathematical Argumentation with Guiding Interactive Diagrams: A Case Study of Semiotic Conflict and Rebuttal Formation

This study aims to identify math students’ argumentation processes and how the design of interactive materials may serve such processes. Despite the increasing use of such materials in mathematics education, their role in shaping students’ argumentation processes remains underexplored. The case study to be reported here is part of a project aimed at examining the potential of interactive materials to support students’ argumentation processes. Three 13- and 14-year-old students were challenged by a task presented as a guiding interactive diagram centered on an animation of multi-process motion and parallel time-position graphs. The study was based on a framework for analyzing the pedagogical functionality of interactive diagrams and the Toulmin model for analyzing the argument structure. The argumentation processes evolved from claiming a discrepancy between the two hot-linked representations in the diagram. The students used backing to generate mathematical ideas and rebuttals to strengthen them by analyzing exceptional cases. The study provides evidence of the contribution of the guiding interactive diagram design to the emergence of rich argumentation processes. The students engaged in deeper argumentation and used rebuttal as a way to address the semiotic conflict prompted by the design into their broader argument structure.