Knowing how and knowing why: Expert and in transition teacher understandings of representations, translations, and connections for dividing with fractions.
Item
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Title
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Knowing how and knowing why: Expert and in transition teacher understandings of representations, translations, and connections for dividing with fractions.
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Identifier
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AAI3169930
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identifier
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3169930
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Creator
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Jones, Yasemin.
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Contributor
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Adviser: Carol Kehr Tittle
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Date
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2005
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Language
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English
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Publisher
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City University of New York.
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Subject
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Education, Educational Psychology | Education, Secondary | Education, Mathematics
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Abstract
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The study is an examination of two connected forms of mathematical content knowledge: subject matter (SMK) and pedagogical content (PCK) knowledge for fractions and division with fractions. Fourteen middle school mathematics teachers "thought out loud" on division with fractions and concept map tasks. From the think alouds, eight teachers in transition (IT) and six teachers with deep knowledge (DK) were identified. Cognitive representations (i.e., models, translations, and connections) for understanding and teaching the content matter were analyzed.;The deep knowledge responses were analyzed to develop a model of content knowledge for understanding dividing with fractions. The proposed model includes the following content knowledge features of subject matter (SMK) and pedagogical content (PCK) knowledge: (1) multiple representations; (2) varied representations; (3) multiple translations; (4) emphasis on context; (5) emphasis on reference unit; and (6) fractions as sets of connected representations. The six teachers with deep knowledge evidenced well developed, organized, and connected knowledge through multiple representations, translations, and connections between and to related "big ideas" (Fosnot & Dolk, 2002) in the mathematics curriculum.;Examining differences in the qualities of "thought in action" between the two groups of teachers, deep knowledge and in transition, provided opportunities to enhance research and practical understandings of mathematics teachers' knowledge.
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Type
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dissertation
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Source
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PQT Legacy CUNY.xlsx
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degree
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Ph.D.
