Preservice Mathematics Teachers' Context-Based Problems and Representations for Common Multiples and Common Divisors

Abstract

This study adopted a qualitative approach to explore how preservice mathematics teachers make sense of the concepts of common multiples and common divisors through context-based problems and the representations they use during problem-solving. The research was conducted as a case study. The participants consisted of 58 third-year preservice mathematics teachers enrolled in a public university during the fall semester of the 2025–2026 academic year. Data were gathered by asking participants to create real-life problem situations and provide explanations and justifications for their solutions. The data collected were analyzed through content analysis. The findings revealed that most preservice mathematics teachers were able to generate problems involving common multiples and common divisors. However, some participants showed a tendency to frame their problems specifically around the concepts of least common multiple and greatest common divisor. Time- and measurement-related situations emerged as the most frequently preferred contexts. In terms of representations, participants most used tables, number lines, factorization procedures, and visual models. Overall, the results highlight the importance of emphasizing not only obtaining correct answers in mathematics instruction but also encouraging learners to justify their conceptual decisions and establish meaningful connections across different forms of representation.