Prospective Math Teacher Students' Graphical Shape Thinking: Is it Static or Dynamic?

Graphical reasoning is a fundamental skill in mathematics education, particularly for prospective teachers who must interpret and construct mathematical representations effectively. This study examines graphical thinking tendencies among prospective mathematics teachers, distinguishing between static and dynamic approaches. Using a mixed-methods approach, data were collected through quantitative surveys and qualitative interviews to analyze students' reasoning patterns. The findings reveal that while many students exhibit emergent dynamic thinking, a significant portion remains undecided, relying on visual structures rather than conceptual relationships between variables. The persistence of static reasoning suggests a need for pedagogical interventions to enhance students' transition toward dynamic graphical understanding. The study underscores the importance of inquiry-based learning, technology-enhanced graphing tools, and real-world applications in fostering deeper engagement with mathematical representations. Future research should explore longitudinal studies to assess the long-term impact of instructional strategies on graphical reasoning development.