The Quality of Argumentation in an Euclidean Geometry Context: A Case Study

Abstract

The research reported in this study examined the quality of argumentation of South African Grade 11 learners through the lens of Toulmin’s argument pattern (TAP). Very little research has quantified the argumentation of learners in mathematics across the school grades. The focus was on measuring the mathematical knowledge and quality of arguments formulated by learners as they engage in a reasoning task set in a Euclidean geometry investigative context. Mathematics education reform efforts have highlighted the importance of argumentation in the acquisition of mathematical knowledge. To describe these participants’ quality of arguments, a sample of 135 Grade 11 learners was drawn from a target population of high schools located in one large South African province. Using an analytical framework modified from Osborne et al. (2004), the findings suggested that although learners’ knowledge of properties of parallel lines was encouragingly satisfactory, the level of their argumentation quality was low. The implication of this finding is that mathematics initial teacher education programs need to design investigations that feature the TAP (core) in their courses. It is recommended that future studies may need to design intervention strategies to address high school learners’ lack of argumentation skills.

Investigating lower secondary school students’ geometric argumentation structure using Toulmin model

“…Apart from all that, many students are good at constructing arguments. The results differ from research by Shongwe (2022) which states that students are still categorized as low in constructing arguments because, in the arrangement of students' arguments, there are no rebuttals. Likewise, in research conducted by Andrea (2010), several groups of students and teachers used Toulmin argumentation stages where the results showed that Toulmin argumentation components in the form of claims, data, warrant, and backing could be demonstrated by students, but few could demonstrate rebuttal and qualifier (Soewardini et al, 2020).…”

“…Supporting this incident, research conducted by Basri et al (2019) also states that some students often do not understand the concept well and have difficulty understanding the entire information about the question, thus preventing students from carrying out proofs. This shows the inability of students to provide arguments and difficulty reaching higher levels of thinking (Shongwe, 2022).…”