The goal of this study is to uncover the successes and challenges that preservice teachers are likely to experience as they unpack lesson-level mathematical learning goals (i.e., identify the subconcepts and subskills that feed into target learning goals). Unpacking learning goals is a form of specialized mathematical knowledge for teaching, an…

Using case study analysis and a cognitive theoretical orientation, we examine elements of knowledge for teaching needed by a mathematician to orchestrate whole-class discussions in an undergraduate mathematics classroom. The instructor, an experienced teacher and mathematics researcher, used an inquiry-oriented curriculum to teach a differential…

Recent federal education policies and reports have generated considerable debate about the meaning, methods, and goals of "scientific research" in mathematics education. Concentrating on the critical problem of determining which educational programs and practices reliably improve students' mathematics achievement, these policies and reports focus…

This "Research Commentary" addresses the quality of statistical research in mathematics education. To do so, 10 years of Journal for Research in Mathematics Education (JRME) articles were analyzed on the basis of criteria suggested by the American Educational Research Association, American Psychological Association, and National Council for…

Although preservice elementary school teachers (PSTs) lack the understanding of multidigit whole numbers necessary to teach in ways that empower students mathematically, little is known about their conceptions of multidigit whole numbers. The extensive research on children's understanding of multidigit whole numbers is used to explicate PSTs'…

Although students of all levels of education face serious difficulties with proof, there is limited research knowledge about how instruction can help students overcome these difficulties. In this article, we discuss the theoretical foundation and implementation of an instructional sequence that aimed to help students begin to realize the…

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…

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…

This study investigated introductory calculus students' spontaneous reasoning about limit concepts guided by an interactionist theory of metaphorical reasoning developed by Max Black. In this perspective, strong metaphors are ontologically creative by virtue of their emphasis (commitment by the producer) and resonance (support for high degrees of…

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…

The author responds to the recent work of Kaminski, Sloutsky, and Heckler (2008) and advances two major concerns about their research and its applicability to learning mathematics: a confounding variable that arises from the mathematical differences between the generic examples and concrete examples poses a threat to the construct validity of the…

The author clarifies his position regarding what features of the examples used by Kaminski, Sloutsky, and Heckler (2008a) constitute substantive differences affecting performance. I also reiterate my hesitancy to extrapolate their findings to the broader realm of mathematics.

The purpose of this study was to investigate children's construction of 10s out of the 1s they have already constructed. It was found that, for many younger children, a dime was something different from 10 pennies even though they could say with confidence that a dime was worth 10 cents. As the children grew older, their performance improved.…

This article examines 3 models for developing and analyzing culturally responsive teaching in mathematics teacher education. The models were developed from and are illustrated by findings from a series of exploratory research studies conducted to evaluate various methods for preparing preservice teachers to address the educational implications of…

Previous research has shown that when confronted with missing-value word problems, primary school students strongly tend to use proportional solution approaches, even if these approaches are inappropriate. The authors investigated whether (besides the missing-value formulation of word problems) the numbers appearing in word problems are part of…