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Conceptual Maps and Simulated Teaching Episodes as Indicators of Competence in Teaching Elementary Mathematics

Network representation was used to assess knowledge obtained during a teaching methodology course in elementary mathematics. Participants were the course instructor, 4 teacher educators, and 53 prospective teachers. Relatedness ratings on key terms were used to construct associative networks. Teacher educator networks shared significant similarities to the course instructor's network, and similarities between the teacher educator and prospective teacher networks were as predictive of course grades as similarity to the course instructor. Fourteen of the prospective teachers participated in a simulated teaching task. Network similarity predicted teaching for conceptual understanding, as did final course grade, and was more predictive than were either exams or lab scores. The advantage of associative networks may be in representing patterns of concept relations underlying mental models of teaching. Teaching for conceptual understanding has become one of the fundamental components of reform movements in mathematics education. Educational researchers and professional associations alike are advocating a greater emphasis