In this article, we present a mathematical analysis that distinguishes two distinct quantitative perspectives on ratios and proportional relationships: variable number of fixed quantities and fixed numbers of variable parts. This parallels the distinction between measurement and partitive meanings for division and between two meanings for…

This study sought to understand how aspects of middle school mathematics teachers' knowledge and conceptions are related to their enactment of cognitively demanding tasks. I defined the enactment of cognitively demanding tasks to involve task selection and maintenance of the cognitive demand of high-level tasks and examined those two…

This study examined the effect of 2 types of mathematics content organization on high school students' mathematics learning while taking account of curriculum implementation and student prior achievement. Hierarchical linear modeling with 3 levels showed that students who studied from the integrated curriculum were significantly advantaged…

In an era when familiar categories of identity are breaking down, an argument is made for using post-structuralist vocabulary to talk about ethical practical action in mathematics education. Using aspects of Foucault's post-structuralism, an explanation is offered of how mathematical identifications are tied to the social organization of…

How issues of power and identity play out in mathematical practices are described by Na'ilah Suad Nasir and Maxine McKinney de Royston. Their article offers a perspective on how to better understand the sociopolitical nature of teaching and learning mathematics. They present data from studies of mathematics teaching and learning in…

This article shows how equity research in mathematics education can be decentered by reporting the "voices" of mathematically successful African American male students as they recount their experiences with school mathematics, illustrating, in essence, how they negotiated the White male math myth. Using post-structural theory, the…

This case study examines the practice of a full-time mathematics teacher and social activist working in a secondary school with the twin missions of college preparation and social justice. Findings detail how this teacher views the relationship between mathematics education and social justice and how her conception of teaching for social justice…

This article describes teachers' collective work aimed at learning to teach mathematics for social justice. Teacher interviews, discussions, lessons, and written reflections were analyzed using grounded theory methodology, and teachers' conversations were examined concerning the relationship between mathematical goals and social justice…

Defining what teachers need to know to teach algebra successfully is important for informing teacher preparation and professional development efforts. Based on prior research, analysis of video, interviews with teachers, and analysis of textbooks, we define categories of knowledge and practices of teaching for understanding and assessing teachers'…

This exploratory study focused on characterizing problem-solving situations associated with spontaneous metacognitive activity. The results came from connected case studies of a group of 3 purposefully selected 9th-grade students working collaboratively on a series of 5 modeling problems. Students' descriptions of their own thinking during…

The article discusses an empirical study on the use of history (as a goal) in mathematics education. A historical module was designed and implemented in a Danish upper secondary class to study how students' discussions of metaperspective issues of the historical development of mathematics may be anchored in the taught and learned subject matter of…

This study investigates 3 preservice secondary mathematics teachers' understandings of limits of sequences and their changing conceptions of limit during and after instruction involving interactive, dynamic sketches embodying the formal definition of the limit of a sequence. Manipulating a coherent visual representation of the formal definition in…

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…

Mathematics teachers' selection and implementation of instructional tasks were analyzed before, during, and after their participation in a professional development initiative that focused on selecting and enacting cognitively challenging mathematical tasks. Data collected from 18 secondary mathematics teacher participants included tasks and…

This study investigated the ways in which the technological tool, The Geometer's Sketchpad, mediated the understandings that high school Honors Geometry students developed about geometric transformations by focusing on their uses of technological affordances and the ways in which they interpreted technological results in terms of figure and…