Definitions and Student Conceptions – Mistakes, Obstacles, or Opportunities to Leverage Learning

Presenter: Darlene Kohrman PhD., Kalamazoo Valley Community College (Emeritus)

Summary: Definitions, central to the learning of mathematics, serve to create and bind the logical structure of mathematics but how do students understand definitions? This presentation shares the stories of four students’ conceptions of a mathematical definition and reveals the influences these conceptions hold on their reasoning. Through an engaging dialogue about the validity of the given mathematical definition, each student demonstrated how learning experiences and acquired knowledge influenced the miscues and implicit ideas they held that shaped their individual conceptions, understandings, and reactions to the definition. Mathematical examples and research supporting these students’ conceptions will be provided.

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