In this article, I used a discourse analytic framework to examine the “voice” of a middle school mathematics unit. I attended to the text's voice, which helped to illuminate the construction of the roles of the authors and readers and the expected relationships between them. The discursive framework I used focused my attention on particular language forms. The aim of the analysis was to see whether the authors of the unit achieved the ideological goal (i.e., the intended curriculum) put forth by the NCTM's Standards (1991) to shift the locus of authority away from the teacher and the textbook and toward student mathematical reasoning and justification. The findings indicate that achieving this goal is more difficult than the authors of the Standards documents may have realized and that there may be a mismatch between this goal and conventional textbook forms.
Beth A. Herbel-Eisenmann
David H. Haimes
This article reports a case study set in the context of a “function” curriculum approach to introductory algebra and involving a teacher and her ninth-grade class in a high school in Western Australia. The expectation that the teacher's actions would reflect the teaching philosophy implied in the curriculum was not supported by the study's findings. Instead, the teacher gave priority to curriculum content coverage, emphasized methods and procedures, and adopted teacher-focused pedagogical practices.
Dung Tran, Barbara J. Reys, Dawn Teuscher, Shannon Dingman and Lisa Kasmer
This commentary highlights the contribution that careful and systematic analyses of curriculum or content standards can make to questions and issues important in the mathematics education field. We note the increased role that curriculum standards have played as part of a standards-based education reform strategy. We also review different methods used by researchers to compare and analyze the Common Core State Standards for Mathematics, each method designed for a particular purpose. Finally, we call upon mathematics education researchers to engage in careful analysis of curriculum standards and to share their findings in ways that can inform public debate as well as support education professionals in improving student learning opportunities.
Denisse R. Thompson, Sharon L. Senk and Gwendolyn J. Johnson
This article addresses the nature and extent of reasoning and proof in the written (i.e., intended) curriculum of 20 contemporary high school mathematics textbooks. Both the narrative and exercise sets in lessons dealing with the topics of exponents, logarithms, and polynomials were examined. The extent of proof-related reasoning varied by topic and textbook. Overall, about 50% of the identified properties in the 3 topic areas were justified, with about 30% of the addressed properties justified with a general argument and about 20% justified with an argument about a specific case. However, less than 6% of the exercises in the homework sets involved proof-related reasoning, with developing an argument and investigating a conjecture as the most frequently occurring types of proof-related reasoning.
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. Specifically, we analyze videorecorded 1st- and 2nd-grade classroom lessons in terms of students' opportunities to reason and communicate about mathematics. This analysis indicates that the level of fidelity to the written curriculum differs from the level of fidelity to the authors' intended curriculum during lesson enactments. Drawing on this analysis, this article explores how curricula support and hinder teachers as they engage students in opportunities to learn mathematics and how teachers' instructional moves and choices impact the enactment of curricula.