Charting the Links Between Mathematics Content and Pedagogy Concepts: Cartographies of Cognition

Links between content knowledge in the mathematics domain and in pedagogical reasoning were compared for university mathematicians, mathematicsmethods professors, high school teachers, middle school teachers, and elementary school teachers. Because of their experience in both mathematical content and pedagogical concepts, mathematics-methods professors were expected to integrate those domains into a coherent pedagogical content-knowledge structure. That was the case. Although university mathematicians possessed integrated content-knowledge structures, they tended to represent teaching as transmission of knowledge and learning as accumulation of knowledge. Mathematics-methods professors, high school teachers, elementary school teachers, and, in most instances, middle school teachers appeared to conceptualize teaching as facilitation of conceptual change and learning as an interactive process. In addition, pathfinder network analysis showed concept maps to yield more logically coherent representations of content-knowledge structure than did similarity judgments of all pairwise comparisons.