Understanding and Learning-to-explain by Representing Mathematics: Epistemological Dilemmas Facing Teacher Educators in the Secondary Mathematics ``Methods'' Course

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Abstract

Building on the work of Ball and McDiarmid,this study provides an equivalent at thesecondary level to the work of Liping Ma at theelementary level in that it provides a betterunderstanding of the conceptual knowledge ofschool mathematics held by prospectivesecondary teachers, along with examples of thesorts of knowledge needed to teach forunderstanding within the domain of integersubtraction. Part of an eight-yearlongitudinal study of secondary teachercandidates' conceptions of instructionalexplanations, this analysis of interaction inthe author's methods course and its discussionof epistemological obstacles and changescombines subject-matter and interactionistperspectives. The author concludes thatsecondary teacher candidates can deepen theirrelational knowledge of secondary mathematicswithin a methods course by focusing oninstructional explanations.