From Computational to Analytical: Designing Learning Trajectory through Creative Mathematical Thinking in Numerical Methods Learning - Atmaja, Satriya Adika Arif; Zaenuri; Isnarto; Dewi, Nuriana Rachmani (Mathematics Education Journal, 2026)
Courses in numerical methods at the tertiary level are often delivered through algorithm-oriented instruction. Students should be encouraged to move beyond routine computational procedures and engage in deeper analytical processes. This study aims to design a learning trajectory to foster students’ creative mathematical thinking in numerical methods learning. It employed a design research approach consisting of three main stages: preliminary design, design experiment, and retrospective analysis. The study involved three students from the Mathematics Education Department at Universitas Islam Negeri (UIN) Sunan Kudus who were enrolled in the Numerical Methods course in the odd semester of the 2024–2025 academic year. The use of a small number of participants aimed to examine students’ thinking processes in depth and to validate the learning design. Data were collected through written tasks, classroom observations, video recordings, and semi-structured interviews. The data were analyzed by identifying episodes that reflected students’ thinking processes. The learning trajectory includes four main stages, namely Warming Up with Newton-Raphson Problem Solving, Reinforcing the Newton-Raphson Concept, Exploring Numerical Reasoning through Newton Interpolation, and Tracking Cognitive Changes (Reflection). The results indicate that students actively engaged with the tasks across the four activities and components of creative mathematical thinking emerged during the problem-solving process. This study highlights that the designed learning trajectory supported the development of students’ creative mathematical thinking in numerical methods learning. Future research is recommended to explore a different computational context of numerical methods to further investigate the development of creative mathematical thinking.