The chapter presents a case study of a student’s (Nat’s) developing understanding of differential equations as reflected through his progressive concept maps and Vee diagrams (maps/diagrams). Concept mapping and Vee diagramming made Nat realized that there was a need to deeply reflect on what he really knows, determine how to use what he knows, identify when to use which knowledge, and be able to justify why using valid mathematical arguments. Simply knowing formal definitions and mathematical principles verbatim did not necessarily guarantee an in-depth understanding of the complexity of inter-connections between mathematical concepts and procedures. The presentations of his ideas and understanding of differential equations, Nat found, was greatly facilitated by using his individually constructed concept maps and Vee diagrams. The external projection of his ideas visually on maps/diagrams also facilitated social critiques and mathematical communication during seminar presentations and one-on-one consultations with the researcher. The chapter discusses some implications for teaching mathematics.
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Afamasaga-Fuata’i, K. (2009). Concept Mapping and Vee Diagramming “Differential Equations”. In: Afamasaga-Fuata'i, K. (eds) Concept Mapping in Mathematics. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-89194-1_14
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