The purpose of the study reported in this article was to explore the mathematical discourse in which four dyads engaged while sharing the storybook "One Snowy Night" (Butterworth, 1989) while at home or in other locations (e.g., day care centers). Each dyad consisted of a mother and her four-year-old child. Various discourse patterns were evident,…

Fourth-grade students who participated in a yearlong, whole-class teaching experiment not only reconceptualized natural numbers but also generated flexible solution strategies to perform numerical computations mentally and in writing. Students' reconceptualization of number was mediated by their perceived resemblance between the physical action of…

With great interest the author read the May 2002 editorial in the "Journal for Research in Mathematics Education (JRME)" (King, 2002) regarding changes to the 5th edition of the "Publication Manual of the American Psychological Association" (APA, 2001). Of special note to him, and of great import to the field of mathematics education research, are…

The transformation to reform mathematics teaching is a daunting task. It is often unclear to teachers what such a classroom would really look like, let alone how to get there. This article addresses this question: How does a teacher, along with her students, go about establishing the sort of classroom community that can enact reform mathematics…

The study reported in this article examined relations between ethnicity, out-of-school activities, and arithmetical achievements in Latin American and Korean American children in first, second, and third grades. Three types of data were collected: parents' educational attitudes and beliefs, parents' reports of children's everyday activities with…

All fields of research need to reconsider, on an ongoing basis, their standards for research quality. At the present time in mathematics education, such discussion is particularly critical to the ongoing growth and strength of the field. Mathematics education research has evolved significantly in the last 20 years. The most sweeping change has…

In this article we investigate how preservice elementary school (K-7) teachers understand the concept of prime numbers. We describe participants' understanding of primes and attempt to detect factors that influence their understanding. Representation of number properties serves as a lens for the analysis of participants' responses. We suggest that…

Many children read mathematics word problems and directly translate them to arithmetic operations. More sophisticated problem solvers transform word problems into object-based or mental models. Subsequent solutions are often qualitatively different because these models differentially support cognitive processing. Based on a conception of problem…

Information processing researchers have assumed that algebra symbol skills depend on mastery of the abstract rules presented in the curriculum (Matz, 1980; Sleeman, 1986). Thus, students' ubiquitous algebra errors have been taken as indicating the need to embed algebra in rich contextual settings (Kaput, 1995; National Council of Teachers of…

This article considers the question of what specific actions a teacher might take to create a culture of inquiry in a secondary school mathematics classroom. Sociocultural theories of learning provide the framework for examining teaching and learning practices in a single classroom over a two-year period. The notion of the zone of proximal…

Some years ago, Gila Hanna offered the very insightful and useful distinction between mathematical proofs that prove and those that also explain. Proofs that explain not only state the deductive logic that justifies their mathematical claims, they lay bare the mechanisms and structures that underlie that logic, making content and logic more…

We articulate and explicate a mechanism for mathematics conceptual learning that can serve as a basis for the design of mathematics lessons. The mechanism, reflection on activity-effect relationships, addresses the learning paradox (Pascual-Leone, 1976), a paradox that derives from careful attention to the construct of assimilation (Piaget, 1970).…

Widespread agreement exists that U.S. teachers need improved mathematics knowledge for teaching. Over the past decade, policymakers have funded a range of professional development efforts designed to address this need. However, there has been little success in determining whether and when teachers develop mathematical knowledge from professional…

One of the greatest challenges to a peace education curriculum is preparing young people to deal with conflicts over issues central to identity. These kinds of conflict can threaten beliefs derived from authority and, accordingly, may be characterized by cognitive rigidity. Various factors central to constructive conflict resolution are…

Reviewed here are approaches to peacebuilding citizenship education in Northern Ireland and the USA, where social education has been responding to intergroup and structural violence. Strategies for peacebuilding have been developed and implemented in response to societal conflicts, government mandates, and available funding. Government support for…