Preservice Teachers' Perspectives on Connections Within Mathematical Concepts: A Qualitative Study
Keywords:
common content knoweldge, specific content knowledge, horizon content knowledge, mathematics content connections, preservice teachersAbstract
This study explores how preservice secondary mathematics teachers comprehend and apply advanced mathematical concepts to the content they will teach in K–12 classrooms. Responding to student inquiries and guided by the Mathematical Education of Teachers II recommendations, an innovative capstone course was developed and integrated into the mathematics education program to bridge the gap between college level mathematics and secondary instruction. The course was designed to foster meaningful mathematical connections through assignments and guided reflection, enhancing preservice teachers’ ability to connect advanced concepts to secondary teaching. Employing a generic qualitative research design with thematic analysis, written reflections from five preservice teachers in their final semester of a teacher preparation program at Northwest Missouri State University were analysed. The purpose of the written reflection was to help these teachers examine their evolving mathematical thinking and instructional planning. The findings indicate that participants transitioned from procedural to conceptual reasoning, developed heightened awareness of mathematical interconnectivity, and gained confidence in designing lessons that integrate advanced mathematics. These results suggest that purposefully designed capstone courses can strengthen preservice teachers' pedagogical effectiveness and promote curricular coherence. Further, it is recommended teacher preparation programs prioritise connecting advanced mathematics to school level instruction.
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