The Design of Learning Trajectory for Parabola Equation in Geometry STEM-Based Learning for Flexibility Skills

Nopriyanti, Tika Dwi
Zulkardi, Zulkardi
Putri, Ratu Ilma Indra
Aisyah, Nyimas

JTAM (Jurnal Teori dan Aplikasi Matematika)
Vol 9, No 4 (2025): October

The flexibility of mathematical thinking among prospective mathematics teachers remains relatively low, primarily due to learning approaches that do not meaningfully connect mathematical concepts with real-world contexts. This study aims to design and implement a STEM-based learning trajectory on the topic of parabolic equations to foster the development of mathematical thinking flexibility in prospective teachers. The research employs a design research approach consisting of two stages: a pilot experiment to test and refine the learning trajectory, and a teaching experiment to implement and evaluate its effectiveness. The participants were students who had completed an Analytical Geometry course. Data were collected through activity sheets, Desmos documentation, video recordings, and interviews. Data were analyzed using a retrospective analysis method, which involved three main steps: (1) organizing data from various sources, (2) conducting within-case analysis to trace students' thought processes throughout each activity, and (3) synthesizing patterns across cases to identify the development of mathematical flexibility. The results show that the learning trajectory consisting of four main activities: video analysis, elevation angle experiments, graphing parabolas using Desmos, and determining parabolic equations effectively facilitated the development of mathematical flexibility in three aspects: representational, conceptual, and procedural. Students demonstrated the ability to shift between different representations, understand the interconnections among mathematical concepts, and adapt problem-solving strategies to contextual situations. The teaching experiment also revealed increased student engagement, higher quality of discussion, and a greater diversity of strategies employed. This study recommends the integration of real-world contexts, such as football throw-ins, to support STEM-based mathematics instruction aimed at developing flexible mathematical thinking in prospective teachers.