This article proposes a taxonomy of strategies for single-digit multiplication, then uses it to elucidate the nature of the learning tasks involved in multiplication. In preceding work, it has generally been assumed that much of children's strategy development is driven by changes in their general conceptual capabilities relating to number. In…

In this article, I argue for a renewed focus in mathematics education research on procedural knowledge. I make three main points: (1) The development of students' procedural knowledge has not received a great deal of attention in recent research; (2) one possible explanation for this deficiency is that current characterizations of conceptual and…

We present here results of a case study examining the classroom practice of one thirdgrade teacher as she participated in a long-term professional development project led by the authors. Our goal was to explore in what ways and to what extent the teacher was able to build a classroom that supported the development of students' algebraic reasoning…

In this study we investigated above-average high school calculus students from Japan and the United States in order to determine any differences in their conceptual understanding of calculus and their ability to use algebra to solve traditional calculus problems. We examined and interviewed 18 Calculus BC students in the United States and 26…

Students' strategies for solving long division problems under a realistic mathematics approach (RME) at Dutch primary schools were categorized in two ways: (a) according to the level of how students created multiples of the divisor (chunking) to be subtracted from the dividend; and (b) according to their use, or nonuse, of schematic notation.…

The recent releases of two major international comparative studies that addressed mathematics--the Trends in International Mathematics and Science Study 2003 (TIMSS 2003) and the Program for International Student Assessment 2003 (PISA 2003)--provide opportunities and challenges for mathematics education researchers interested in using the…

To investigate mechanisms of failure in mathematics, we adopt the "communicational approach to cognition," which describes thinking as an activity of communication and learning mathematics as an initiation to a certain type of discourse. In the search for factors that impede students' participation in arithmetic communication, we examine…

We describe a four-level spectrum of pedagogical awareness (SPA) that emerged from the analysis of six undergraduate mathematics tutors' (1) conceptualizations of their first-year students' difficulties; (2) descriptive accounts of their strategies for facilitating the overcoming of these difficulties; and (3) self-reflective accounts regarding…

This article deals with 12th-grade students' conceptions of a mathematical definition. Their conceptions of a definition were revealed through individual and group activities in which they were asked to consider a number of possible definitions of four mathematical concepts: two geometric and two analytic. Data consisted of written responses to…

This article explores the complex relationship between language and mathematics education in multilingual settings by presenting an analysis of one lesson from a multilingual primary mathematics classroom in South Africa taught by an appropriately qualified and experienced teacher. English emerged as a dominant language in this classroom, and this…

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…