The NCTM's Research Committee has prepared this article as a means to raise the awareness about equity and issues surrounding equity from a research perspective as well as to support the NCTM's commitment to the Equity Principle. The committee discusses the concept of equity from three perspectives: as a subject of research, as a "critical lens"…

We address the telling/not-telling dilemma in mathematics education. Telling is instructionally important, but has been downplayed because of (a) perceived inconsistencies between telling and constructivism, (b) increased awareness of the negative consequences of relying too heavily on telling, and (c) a focus on "non-telling" actions as…

This study had two purposes: (a) to investigate the developmental relationship between students' uses of fractions notation and their understandings of part-whole relations; and (b) to produce an analysis of the role of fractions instruction in students' use of notation to represent parts of an area. Elementary students (n = 384) in 19 classes…

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 the…

In the study reported here, I examined the diagrams that mathematically capable high school students produced in solving applied calculus problems in which a diagram was provided in the problem statement. Analyses of the diagrams contained in written solutions to selected free-response problems from the 1996 BC level Advanced Placement Calculus…

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 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…

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…

This study investigated Catholic and Protestant students' ideas about historical significance in Northern Ireland. The research was conducted in two secondary schools in a medium-sized rural town, and data were derived from a ranking task and semi-structured interview with 40 students, aged 12-17, equally divided between the two communities.…

Educators across academic environments seek to prepare students for participation in the development of a more just and caring society and world. In this paper, I explore the value of "art" and "aesthetics," broadly defined, as means of addressing these issues through citizenship education. After a brief historical review of the social studies, I…

Skills of argument are important for effective consideration of social issues and participation in democratic institutions. Such skills applied to a juror-reasoning task have been found to have a relationship with how well possible verdict choices might be considered. As justice in the jury system requires that jurors give full consideration to…