There is a well-established area of work in mathematics education focusing on mathematics for social justice. Much of the work, however, is concerned with "individual" students' understanding the world symbolically -- as evident in the notions of reading and writing the world using mathematics -- while failing to address a transformative…

Standard approaches to thinking in the mathematics curriculum depict it as the result of some stable constructions in the mind of the person, constructions that are the results of individual efforts in the mind of subjects or of collective efforts that are then appropriated by and into the mind of individuals. Such work does not appreciate what…

Rhythm is a fundamental dimension of human nature at both biological and social levels. However, existing research literature has not sufficiently investigated its role in mathematical cognition and behavior. The purpose of this article is to bring the concept of "incarnate rhythm" into current discourses in the field of mathematical learning and…

Cultural-historical activity theory--with historical roots in dialectical materialism and the social psychology to which it has given rise--has experienced exponential growth in its acceptance by scholars interested in understanding knowing and learning writ large. In education, this theory has constituted something like a well kept secret that is…

In this article, we present a sociocultural alternative to contemporary constructivist conceptions of classroom interaction. Drawing on the work of Vygotsky and Leont'ev, we introduce an approach that offers a new perspective through which to understand the "specifically human" forms of knowing that emerge when people engage in joint activity. To…

Current conceptualizations of knowing and learning tend to separate the knower from others, the world they know, and themselves. In this article, we offer "relationality" as an alternative to such conceptualizations of mathematical knowing. We begin with the perspective of Maturana and Varela to articulate some of its problems and our alternative.…

In this article, I (1) argue for approaching processes, events-in-the-making, by means of process categories--to learn, to teach--not by means of categories that denote differences in state and (2) exemplify doing and writing research consistent with process philosophy. To understand process we must not think, research, and write them in terms of…

Much of the evidence provided in support of the argument that mathematical knowing is embodied/enacted is based on the analysis of gestures and bodily configurations, and, to a lesser extent, on certain vocal features (e.g., prosody). However, there are dimensions involved in the emergence of mathematical knowing and the production of mathematical…

This study examines the origins of geometry in and out of the intuitively given everyday lifeworlds of children in a second-grade mathematics class. These lifeworlds, though pre-geometric, are not without model objects that denote and come to anchor geometric idealities that they will understand at later points in their lives. Roth's analyses…

There is mounting research evidence that contests the metaphysical perspective of knowing as mental process detached from the physical world. Yet education, especially in its teaching and learning practices, continues to treat knowledge as something that is necessarily and solely expressed in ideal verbal form. This study is part of a funded…

Examined eighth graders' approaches to contextual word problems. Subjects were observed in two situations: open-inquiry field studies that included production of convincing representations (inscriptions) to support students' findings and; word problems with stories and student-produced data based on field studies. Analysis of mathematical…

Provides a rationale for a learning environment in science classrooms that integrates science, mathematics, and technology while solving authentic problems. Describes activities that can be used in such an environment and presents data regarding students' attitudes toward the described activities. (MDH)

The notions of "abstract" and "concrete" are central to the conceptualization of mathematical knowing and learning. Much of the literature takes a dualist approach, leading to the privileging of the former term at the expense of the latter. In this article, we provide a concrete analysis of a scientist interpreting an unfamiliar graph to show how…

The notions of "abstract "and "concrete" are central to the conceptualization of mathematical knowing and learning. It is generally accepted that development goes from concrete toward the abstract; but dialectical theorists maintain just the opposite: development consists of an ascension from the abstract to the concrete. In this article, we…

Provides an example of the integration of science and mathematics learning of one high school physics student in a constructivist classroom. Discusses the student's integration of mathematical and nonmathematical representations and of different mathematical representations in a nonuniform acceleration experiment. Describes a model for integrating…