Linking Prior Knowledge to New Learning: Mathematical Connections in Complex Number Instruction
DOI:
https://doi.org/10.26877/ijre.v6i2.3830Keywords:
Mathematical connections, Complex Numbers, Secondary Mathematics Teachers, Prior KnowledgeAbstract
The introduction of complex numbers represents a significant conceptual transition for students, making it essential to understand how teachers connect new mathematical ideas to prior knowledge in order to promote coherent and meaningful learning. This study investigates how secondary mathematics teachers create meaningful instructional connections (Instruction-Oriented Connections, IOC) when introducing complex numbers to Grade 12 students. Drawing on Businskas’ framework and subsequent research, we focus on Linking with Prior Knowledge (LinkPK) connections, links between newly introduced concepts and previously learned material that are not immediately apparent to students unless explicitly highlighted by the teacher. Six experienced teachers’ online lessons were analyzed through an abductive approach, combining deductive analysis informed by the theoretical framework with inductive identification of emergent themes. Two new subcategories of LinkPK connections emerged: Extensional Connections, where new concepts are presented as natural extensions of existing knowledge, and Structural Connections, where teachers highlight how underlying properties or structures remain consistent across old and new concepts. Findings show that both types of connections play a critical role in fostering conceptual understanding by integrating new content into students’ existing mathematical frameworks. Without such connections, new ideas risk being perceived as isolated facts rather than part of a coherent system. This study contributes to the Extended Theory of Connections (ETC) by refining its typology and offers pedagogical insights for advancing conceptual learning in mathematics classrooms.
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