This article examines a "calculus graphing schema" and the triad stages of schema development from Action-Process-Object-Schema (APOS) theory. Previously, the authors studied the underlying structures necessary for students to process concepts and enrich their knowledge, thus demonstrating various levels of understanding via the calculus graphing…

The authors use data from a large-scale Brazilian national assessment to discuss the relation between reform teaching and equity in mathematics education. They study the dimensionality of teaching style to better qualify what reform teaching means. Full Description of the Continuous Variables Included in the Analysis are appended. (Contains 2…

Research on the impact of Standards-based, K-12 mathematics programs (i.e., written curricula and associated teaching practices) and of reform calculus programs has focused primarily on student achievement and secondarily, and rather ineffectively, on student attitudes. This research has shown that reform programs have competed well with…

The current study examined the mathematical achievement of high school students enrolled for 3 years in one of three NSF funded "Standards"-based curricula (IMP, CMIC, MMOW). The focus was on traditional topics in mathematics as measured by subtests of a standardized achievement test and a criterion-referenced test of mathematics achievement.…

Research investigating algebra students' abilities to generalize and justify suggests that they experience difficulty in creating and using appropriate generalizations and proofs. Although the field has documented students' errors, less is known about what students do understand to be general and convincing. This study examines the ways in which…

Many researchers and curriculum frameworks recommend that the concept of "proof" and the corresponding activity of "proving" become part of students' mathematical experiences throughout the grades. Yet it is still unclear what "proof" means in school mathematics, especially in the elementary grades, and what role the teacher has in cultivating…

In this article, we deal with students' algebraic generalizations set in the context of elementary geometric-numeric patterns. Drawing from Vygotsky's psychology, Leont'ev's Activity Theory, and Husserl's phenomenology, we focus on the various semiotic resources mobilized by students in their passage from the particular to the general. Two small…

This ethnographic study investigated the mathematical disposition of engineers. Structural engineers in two firms were observed in everyday practice. Observation and interview data were analyzed to elucidate the role of mathematics in solving engineering problems and the engineers' perceptions of the status of mathematics relative to other…

This article describes a subset of results from a larger study (Rubel, 2002) that explored middle school and high school students' probabilistic reasoning abilities across a variety of probabilistic contexts and constructs. Students in grades 5, 7, 9, and 11 at an urban, private school for boys (n = 173) completed a Probability Inventory,…

In this experimental study, prospective elementary school teachers enrolled in a mathematics course were randomly assigned to (a) concurrently learn about children's mathematical thinking by watching children on video or working directly with children, (b) concurrently visit elementary school classrooms of conveniently located or specially…

The purpose of this article is to sketch a hypothetical descriptive framework of statistical knowledge for teaching. Because statistics is a discipline in its own right rather than a branch of mathematics, the knowledge needed to teach statistics is likely to differ from the knowledge needed to teach mathematics. Doing statistics involves many…

After evaluating a proposal by Jon Star (2005) that mathematics educators reconceptualize the construct of procedural knowledge, we offer an alternative reconceptualization based on an extension and amalgamation of his and other conceptualizations of procedural knowledge and conceptual knowledge. We then propose some implications for research…

This study evaluated the efficacy of a preschool mathematics program based on a comprehensive model of developing research-based software and print curricula. Building Blocks, funded by the National Science Foundation, is a curriculum development project focused on creating research-based, technology-enhanced mathematics materials for pre-K…

Government agencies and members of the educational research community have petitioned for research-based curricula. The ambiguity of the phrase "research-based", however, undermines attempts to create a shared research foundation for the development of, and informed choices about, classroom curricula. This article presents a framework for the…

Using data from the Longitudinal Study of American Youth (LSAY), we examined the extent to which students' mathematics coursework regulates (influences) the rate of growth in mathematics achievement during middle and high school. Graphical analysis showed that students who started middle school with higher achievement took individual mathematics…