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Explicating the Role of Mathematical Tasks in Conceptual Learning: An Elaboration of the Hypothetical Learning Trajectory
Simon's (1995) development of the construct of hypothetical learning trajectory (HLT) offered a description of key aspects of planning mathematics lessons. An HLT consists of the goal for theExpand
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An Integrated Study of Children's Construction of Improper Fractions and the Teacher's Role in Promoting That Learning
In this constructivist teaching experiment with 2 fourth graders I studied the coemergence of teaching and children's construction of a specific conception that supports the generation of improperExpand
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Explicating the Teacher's Perspective From the Researchers' Perspectives: Generating Accounts of Mathematics Teachers' Practice
In this article we articulate a methodology for studying mathematics teacher development in the context of reform. The generation of accounts of teachers'practice, an adaptation of the case study,Expand
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Becoming a Mathematics Teacher-Educator: Conceptualizing the Terrain Through Self-Reflective Analysis
My purpose in this article is to contribute tothe conceptualization of the complex terrainthat often is indiscriminately termedmathematics teacher educator development.Because this terrain is largelyExpand
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Explicating a Mechanism for Conceptual Learning: Elaborating the Construct of Reflective Abstraction
We articulate and explicate a mechanism for mathematics conceptual learning that can serve as a basis for the design of mathematics lessons. The mechanism, reflec- tion on activity-effectExpand
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An Account of a Teacher's Perspective on Learning and Teaching Mathematics: Implications for Teacher Development
This report presents an account of one teacher's mathematics teaching and a perspective that underlies his teaching. Nevil was a fifth grade teacher participating incurrent mathematics educationExpand
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Distinguishing Two Stages of Mathematics Conceptual Learning
In this theoretical article, we distinguish two stages of learning a new mathematical concept – participatory and anticipatory. We use a recently developed mechanism for explaining mathematicalExpand
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Fine grain assessment of students’ mathematical understanding: participatory and anticipatory stagesin learning a new mathematical conception
This study addressed a twofold problem – the soundness of a theoretical stage-distinction regarding the process of constructing a new (to the learner) mathematical conception and how such distinctionExpand
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Characterizing a Perspective Underlying the Practice of Mathematics Teachers
We postulate a construct, perception-based perspective, that we consider to be fundamental to the practices of many teachers currently participating in mathematics education reform in the UnitedExpand
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Teacher and Students' Joint Production of a Reversible Fraction Conception.
Abstract Within a constructivist perspective, I conducted a teaching experiment with two fourth graders to study how a teacher and students can jointly produce the reversible fraction conception.Expand
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