Classifying analogical thinking for mathematical problem-solving

Abstract

Analogical thinking is a crucial strategy for mathematical problem-solving, enabling the discovery of solutions by identifying similarities between different problems. However, existing research needs a comprehensive classification of students' use of analogical thinking in this context. This study aims to develop a new classification framework for analogical thinking in mathematical problem-solving, emphasizing the identification and utilization of analogous methods between source and target problems. The research adopts a descriptive qualitative approach involving a purposive sample of 15 high school students from Surakarta, Central Java, who demonstrated analogical thinking in solving both source and target problems. Data collection was conducted through tests, observations, and interviews, with analysis performed using the constant comparative procedure (CCP). The findings reveal three distinct classifications of analogical thinking: pattern recognition (identifying common patterns to solve both source and target problems), variable utilization (using variables as symbolic tools for problem-solving), and visualization (applying graphical representations to address the issues). This study offers significant theoretical insights for future research and practical implications for applying analogical thinking in enhancing mathematical problem-solving.

Keywords

• analogical thinking
• classification
• constant comparative procedure
• mathematical problem-solving