Using concept maps to mediate meaning in undergraduate mathematics

Abstract

The chapter presents the concept map data from a study, which investigated the use of concept maps and Vee diagrams (maps/diagrams) to illustrate the conceptual structure of a topic, its relevant problems and common procedures. Students were required to construct comprehensive topic maps/diagrams as ongoing exercises throughout the semester and to present these for critique before individuals finalized them. With improved mapping proficiency and on-going social critiques, students' mathematical understanding deepened, becoming more conceptual as a result of continually revising their work as the validity of each map is dependent on how effective it illustrated the intended meanings and correct mathematics structure. Students also developed an appreciation of the crucial inter-linkages between mathematical principles, common procedures and formulas, and how all of these mutually reinforce each other conceptually and methodologically. Incorporating concept mapping as a normal mathematical practice in classrooms can potentially alter the learning of mathematics, making it more meaningful and conceptual to supplement the predominantly procedural proficiency practised in many mathematics classrooms. © 2009 Springer-Verlag US.