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July 2009, Volume 40, Issue 4

FEATURES

Brief Report: Measuring Curriculum Implementation
Mary Ann Huntley
Using curriculum-specific tools for measuring fidelity of implementation is an essential yet often overlooked aspect of examining relationships among textbooks, teaching, and student learning. This “Brief Report” describes the variety of ways that curriculum implementation is measured and argues that there is an urgent need to develop curriculum-sensitive tools for analyzing classroom practice. It also outlines the use of the Concerns-Based Adoption Model (CBAM) theory to develop analytical tools for measuring implementation of two middle-grades reform mathematics curricula: Connected Mathematics and MathThematics. The report also presents next steps in this program of research.

Reconceiving Fidelity of Implementation: An Investigation of Elementary
Stacy A. Brown, Kathleen Pitvorec, Catherine Ditto, and Catherine Randall Kelso
Recent research on mathematics reforms in the United States indicates that the reforms are not yet widely implemented. Generally, this claim results from looking at the extent to which teachers use curricular materials or engage in particular classroom practices. This article moves beyond disparate questions of use and practice to examine interactions between teachers and curricula as evidenced by their enactments of whole-number lessons from a Standards-based curriculum.

Collapsing Dimensions, Physical Limitation, and Other Student Metaphors for Limit Concepts
Michael Oehrtman
This study investigated introductory calculus students’ spontaneous reasoning about limit concepts guided by an interactionist theory of metaphorical reasoning developed by Max Black. Students’ reasoning had significant implications for the images they formed and the claims and justifications they provided about multiple limit concepts.

Seeing a Colleague Encourage a Student to Make an Assumption While Proving:
Talli Nachlieli and Patricio Herbst with Gloriana González
This article reports on an investigation of how teachers of geometry perceived an episode of instruction presented to them as a case of engaging students in proving. Confirming what was hypothesized, participants found it remarkable that a teacher would allow a student to make an assumption while proving. But they perceived this episode in various ways, casting the episode as one of as many as 10 different stories. Those different castings of the episode make use of intellectual resources for professional practice that practitioners could use to negotiate the norms of a situation in which they had made a tactical but problematic move.

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