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Presentation 2C1. Teachers' Conceptions and Constructions of Pedagogical Representations in Teaching Statistics: A Case of Arithmetic Average

Jinfa Cai (USA)


Presentation Abstract

Pedagogical representations are the representations that teachers and students use in their classroom as both carriers of knowledge and thinking tools to explain a concept, a relationship, a connection, or a problem-solving process. Although there is no universal agreement about what constitutes "good pedagogical representation" in mathematics teaching, no one questions the idea that the construction of desirable pedagogical representations is influenced by teachers' beliefs, conceptions, and knowledge of mathematics. This paper will present results from a study investigating 12 experienced and 12 inexperienced math teachers' conceptions and construction in their teaching of arithmetic average. This study used interviews and analyses of lessons to examine teachers' conceptions and constructions of pedagogical representations. The interviews and analyses of lessons weave together pedagogical representations in mathematics teaching from three aspects: knowing students' representations and strategies in problem solving, evaluating students' representations and solution strategies, and generating pedagogical representations for classroom instruction. Any representation will express some, but not all, of the information; it will stress some aspects and hide others. Hopefully, the results of this study will not only help us understand desirable pedagogical representations for teaching arithmetic average, but also help us establish a balanced view of using various representations in mathematics instruction.


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