Building a Case-Based Curriculum to Enhance the Pedagogical Content Knowledge of Mathematics Teachers

Little attention has been given to research on cases in specific disciplines or on the development of an integrated case-based curriculum. In this article, I discuss how the cognitive flexibility and knowledge transfer theory proposed by Rand Spiro and his colleagues frames the design of a case-based curriculum for use in mathematics teacher education. The paper includes a sample mathematics teaching case and presents an analysis of four discussions based on that case. In the analysis, the dominant themes of those case discussions are identified and a framework for selecting and sequencing cases for an integrated curriculum is discussed. The analysis also shows the potential of subject-specific cases for enhancing mathematics teachers' pedagogical thinking and reasoning.

[1]  Bruce K. Britton,et al.  Executive Control Processes in Reading , 1987 .

[2]  Walter P. Vispoel,et al.  Knowledge Acquisition for Application: Cognitive Flexibility and Transfer in Complex Content Domains. Technical Report No. 409. , 1987 .

[3]  Rand J. Spiro,et al.  Multiple analogies for complex concepts: antidotes for analogy-induced misconception in advanced knowledge acquisition , 1988 .

[4]  Stella Vosniadou,et al.  Similarity and analogical reasoning: Similarity and Analogical Reasoning , 1989 .

[5]  R. Lesh,et al.  Acquisition of mathematics concepts and processes , 1983 .

[6]  Walter Doyle,et al.  Case Methods in the Education of Teachers. , 1990 .

[7]  Judith H. Shulman Case Methods in Teacher Education , 1992 .

[8]  Richard Lesh,et al.  Rational number concepts , 1983 .

[9]  本家 優子 デュ-イにおけるsubject matterの意義 , 1984 .

[10]  J. Kleinfeld Doing research on effective cross‐cultural teaching: The teacher tale , 1983 .

[11]  J. Kleinfeld,et al.  Changes in Problem Solving Abilities of Students Taught through Case Methods. , 1991 .

[12]  D. Schoen The Reflective Practitioner , 1983 .

[13]  D. Ball The Subject Matter Preparation of Prospective Mathematics Teachers: Challenging the Myths. , 1988 .

[14]  Rand J. Spiro,et al.  Cognitive flexibility theory : advanced knowledge acquisition in ill-structured domains , 1988 .

[15]  L. Shulman Those Who Understand: Knowledge Growth in Teaching , 1986 .

[16]  Judith H. Shulman Case Writing as a Site for Collaboration. , 1990 .

[17]  G. Leinhardt,et al.  Expertise in mathematics instruction: Subject matter knowledge. , 1985 .

[18]  Richard Lesh,et al.  ORDER AND EQUIVALENCE OF RATIONAL NUMBERS: A CLINICAL TEACHING EXPERIMENT , 1984 .