An Undergraduate Student's Understanding of Differential Equations through Concept Maps and Vee Diagrams

Abstract

The paper presents the case of a student (Nat) who participated in a semester long study which investigated the impactof using concept maps and vee diagrams on students' understanding of advanced mathematics topics. Through the constructionof concept maps and vee diagrams, Nat realized that there was a need for him 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 mathematicalarguments. He found that simply knowing formal definitions and mathematical principles verbatim did not necessarily guaranteean in-depth understanding of the complexity of inter-connections and inter-linkages between mathematical concepts and procedures. During seminar presentations and one-on-one consultations, Nat found that using the constructed concept maps and vee diagrams greatly facilitated discussions, critiques, dialogues and communication. The paper discusses the results from this case study and some implications for teaching mathematics.