Multiple pathways to mathematical proof: Toward a typology of deductive thinking

Abstract

Deductive thinking is a fundamental strategy in mathematical problem-solving that enables individuals to derive logical conclusions based on known premises or general principles. This study aimed to develop a typology of students’ deductive thinking ability in solving routine mathematical proof problems, emphasizing how they apply general principles to construct arguments and reach specific conclusions. This study employed a qualitative descriptive approach, involving 83 undergraduate students in their seventh semester from Indonesia and Malaysia. The participants were selected because they had acquired a general understanding of mathematical concepts that can be applied in proof-based problem-solving using deductive thinking, allowing them to apply deductive reasoning systematically. Data were collected through a written test and audiovisual recordings. The analysis was conducted using the Constant Comparative Procedure (CCP). The results revealed three types of students’ deductive thinking: definitive, attributive, and representative. These types illustrate different ways in which students utilize deductive reasoning in constructing mathematical proofs. No study has developed a typology of students’ deductive thinking in solving mathematical proof problems. This research introduces a new typological framework that provides a deeper understanding of how students apply deductive reasoning in structured mathematical arguments. This research provides a deeper understanding of students’ deductive thinking strategies, which serves as a foundation for the design of more effective teaching methods to enhance students’ deductive reasoning skills.