Exploring cognitive pathways of mathematics education students in solving contextual modular arithmetic problems - Metia Novianti; Dede Suratman; Christy Oktavany Siambaton Munthe (FKIP Universitas Muhammadiyah Prof. DR. HAMKA, 2026)
Understanding how university students grasp modular arithmetic in real-world contexts remains underexplored, particularly regarding their use of cognitive pathways in solving contextualized problems. This study aims to examine the cognitive pathways utilized by mathematics education students when solving context-based modular arithmetic problems. 32 undergraduate students in the early stage of a mathematics education program who had successfully completed course in Number Theory were asked to solve three real-world-based problems involving work cycle patterns, container multiples, and congruence systems. The tasks were designed to represent fundamental real-world structures of modular arithmetic and to explore how contextual representations influence students’ cognitive pathways. The analysis was conducted using a descriptive qualitative approach through Cognitive Task Analysis (CTA) to identify five key cognitive pathways: quantitative reasoning, linguistic processing, working memory, pattern recognition, and cognitive flexibility. The result show that the first three pathways were consistently used across all task, indicating stable patterns in numerical reasoning, language processing, and information management. In contrast, pattern recognition and flexibility varied depending on how the problems were presented. Contextual narratives encouraged more reflective and adaptive thinking, whereas symbolic forms tended to limit exploration and reduce conceptual engagement. These results highlight the importance of problem design in supporting diverse cognitive approaches. The study's practical implications include the development of assessments and learning strategies that foster flexible and meaningful thinking, especially when understanding abstract mathematical concepts. Future research is encouraged to explore the integration of digital technologies and multiple representations to enhance students' cognitive flexibility.