Argumentation Analysis for Early Career Researchers

Abstract

Proving processes in mathematics classrooms follow their own peculiar rationale, which raises the question of how to reconstruct and analyse the complex argumentative structures that arise in classroom discussion. In this chapter we describe a method of analysis of argumentation processes in the mathematics class, following the structure of our workshop at the ICME-13 Early Career Researcher Day. The method builds on Toulmin's theory of argumentation (Toulmin 1958) and allows the description of both global argumentation structures and local argumentations. A three stage process is followed: reconstructing the sequencing and meaning of classroom talk; analysing local argumentations and global argumentation structures; and finally comparing these argumentation structures and revealing their rationale. The second stage involves two moves, first analysing local arguments on the basis of Toulmin's functional model of argumentation, and second analysing the global argumentative structure of the proving process. We provide an example of the use of the method to analyse a transcript from a mathematics classroom. Keywords Argumentation Á Argumentation processes Á Argumentation structures Á Proof Á Proving Á Mathematics classrooms Á Model of argumentation 1.1 Toulmin's Functional Model of Argumentation We make use of Toulmin's (1958) functional model of argumentation which has the important characteristic that it was developed to reconstruct arguments in different fields, such as law or medicine. As Toulmin (1958) investigates the functional

An interview with Anthony Brown, Ohio State University, Columbus, OH, USA

“…long proofs have been broken up into series of shorter lemmas" (Hales et al, 2017, 11). The educationists Christine Knipping and David Reid have proposed more fine-grained subdivisions of parallel arguments in mathematics (Knipping and Reid, 2019; for further discussion, see Section 1.3.1 below. )…”

Design of Classroom Discussions and the Role of the Expert in Fostering an Effective and Aware Use of Examples as a Means of Argumentation

“…The tool we chose to interpret students' use of examples (in particular, LCEs) as means to support argumentation and to model and analyze students' argumentative processes was a simplified Toulmin model of argumentation (Fig. 1), which represents a fundamental reference to the study of argumentative processes in mathematics (Knipping & Reid, 2019). Toulmin (2003) distinguished between the claim or conclusion being sought and the facts used as a foundation for the claim, in other words, the data.…”

Argumentasi Siswa Dalam Pembuktian Konjektur

“…Hal ini disebabkan oleh munculnya sub argumen karena warrant yang digunakan perlu dibuktikan (Conner et al, 2014). Knipping & Reid (2016) menyebut sub argumen tersebut sebegai local argument. Pada bukti formal, warrant yang digunakan merupakan aturan yang telah ditetapkan dan tidak memerlukan bukti lebih lanjut.…”