Recognition of deep-seated conceptual crosslinks in mathematics is often weak or nonexistent among students and faculty who view and study mathematics merely in procedural terms. Too often mathematical course content is presented as an approach to a currently considered problem with the mediation of deeper meaning and the connections to other mathematical ideas left unaddressed. The development of mathematical mindfulness requires that educators substantively address the topics they teach by locating the conceptual essence of fundamental ideas from a cultural-historical context. This important pedagogical work can be enhanced through the skilful use of concept mapping. This chapter provides an in-depth look at how concept mapping can be used in the development of a meaningful secondary mathematics’ curriculum that avoids rote learning and favors transcendent cognitive development. The implications presented emerge from several related uses of concept mapping. The chapter illustrates an approach to mathematics’ education that first uses concept maps in conjunction with a direct effort to locate the historically grounded conceptual essence of a significant mathematical concept. Without historical context, mathematics′ educators may easily be unaware of the conceptual essence of the concepts they teach. Concept mapping is shown to address this shortcoming. Empirical research is then guided by concept mapping in order to expose the “operating understanding” among students and their teachers revealing specific metonymic inadequacies that exist. By comparative use of concept maps, weak or missing crosslinks are readily identified. Together, these uses of concept mapping inform and guide the design of mathematics′ lessons that mediate mathematical understanding in a profound way. Concept mapping is thus shown to provide a useful approach to secondary mathematics′ education curricular reform aimed at meaningful learning.

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