Analyzing Structural Gaps in Mathematical Argumentation: A Toulmin-Based Study on Graph Theory - Zulkarnaen, Rafiq; Aziza, Asya Khaula (FKIP Universitas Lampung, 2025)
This research project sought to explain the format and quality of students' mathematical argumentation in graph theory by examining how students built and defended arguments using the Toulmin model. Although research on mathematical argumentation has been extensive, studies that explicitly examine the structure of students' argumentation in graph theory are still very limited, especially in the context of Discrete Mathematics courses in Indonesian higher education. The qualitative descriptive design has been used to investigate students' written responses to graph theory problems in a Discrete Mathematics course. The sample consisted of 22 undergraduate students from the Mathematics Education Study Program at Universitas Singaperbangsa Karawang, selected purposively and classified into high-, medium-, and low-ability groups. Inductive and deductive analysis methods were applied to the data to identify patterns in the reasoning and to assess whether the students' arguments were complete and logically consistent. Data analysis was conducted by combining inductive and deductive approaches supported by a Toulmin model-based coding framework to identify the structure and completeness of arguments, particularly the presence and thickness of claims, data, and warrants, and to compare patterns across levels of ability. The findings showed clear differences in mathematical argumentation across ability levels. Students with high ability presented more coherent arguments with correct and justified claims and logical warrants, whereas medium- and low-ability students produced incomplete or no arguments. The results of this study suggest that ways to enhance the reasoning and argumentation of mathematics instruction, especially by using tasks that encourage justification and conceptual learning in discrete mathematics, need to be reinforced. Keywords: mathematical argumentation, reasoning, Toulmin’s model, graph theory, discrete mathematics, mathematics education.