Understanding and Learningtoexplain by Representing Mathematics: Epistemological Dilemmas Facing Teacher Educators in the Secondary Mathematics ``Methods'' Course
 Barbara M. Kinach
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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 eightyearlongitudinal study of secondary teachercandidates' conceptions of instructionalexplanations, this analysis of interaction inthe author's methods course and its discussionof epistemological obstacles and changescombines subjectmatter and interactionistperspectives. The author concludes thatsecondary teacher candidates can deepen theirrelational knowledge of secondary mathematicswithin a methods course by focusing oninstructional explanations.
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 Title
 Understanding and Learningtoexplain by Representing Mathematics: Epistemological Dilemmas Facing Teacher Educators in the Secondary Mathematics ``Methods'' Course
 Journal

Journal of Mathematics Teacher Education
Volume 5, Issue 2 , pp 153186
 Cover Date
 20020601
 DOI
 10.1023/A:1015822104536
 Print ISSN
 13864416
 Online ISSN
 15731820
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Authors

 Barbara M. Kinach ^{(1)}
 Author Affiliations

 1. Department of Education, University of Maryland, Baltimore County, 1000 Hilltop Circle, Baltimore, MD, 21250, USA