Investiges the mathematical behavior of graduate students and the experiences that contributed to their mathematical development and success. Students reported that a mentor facilitated the development of their problem solving abilities and continued mathematical study. When confronted with an unfamiliar task, students exhibited exceptional…

Illustrates the use of a particular situated method of interpretation in the analysis of data from three-year case studies of two schools. Analyzes various classroom incidents demonstrating that the particular constraints and affordances of formalized mathematics classrooms to which students become attuned contribute to the development of learning…

Presents a study that is interested in the teaching of geometry to primary school teachers. Defines a priori a conceptual frame that organizes geometry into three kinds of knowledge: (1) intuition; (2) experience; and (3) deduction. Illustrates this conceptual frame with examples of teaching geometry. (Contains 31 references.) (Author/ASK)

Argues that mathematics education in virtual culture should strive to give students generative fluency to learn varieties of representational systems, provide opportunities to create and modify representational forms, develop skill in making and exploring virtual environments, and emphasize mathematics as a fundamental way of making sense of the…

Interviews research mathematicians (n=70) with a focus on how they came to know mathematics. Discusses how these mathematicians understand their practices, locating them in the communities of which they claim membership, identifying the style that dominates their organization of research, and looking at their lived contradictions. Contains 14…

Explores the development of elementary school students' (n=88) understanding of comparing two datasets through the responses of students in individual interview settings. Strategies observed within the developmental cycles were visual, numerical, or a combination of the two. Contains 26 references. (Author/ASK)

Uses an evolutionary perspective of conceptual change to consider a conception in the domain of linear functions. Summarizes the results of the written assessments and presents an analysis of the discussions for two pairs of students to show that the use of the x-intercept can be framed as a transitional conception. Contains 31 references.…

Examines teachers' inner reflections and exterior manifestations as they participated in a mathematics-reform effort. Describes the analysis of three elementary mathematics teachers as they struggled with issues of reform and traditional teaching in relation to personal values and beliefs. Concludes that teachers devised personal, complex, and…

Aims to empower mathematics teachers to use interviews to understand their students' mathematical understandings as well as to prepare them to use technology-intensive curricula. Examines the influences on three high school mathematics teachers as they learned to use task-based interviews to understand students' mathematical understandings.…

Presents and investigates a theoretical perspective on the development of understandings of mathematical operations with a particular focus on addition. Presents a case study on the development of a young boy and concludes that his attainment of aspects of operation sense supported transitions into algebraic ways of thinking. Contains 46…

Focuses on the process by which children develop a formal mathematical concept of the circle by using various instruments to draw circles within the context of a goal-directed drawing task. Concludes that the use of the compass in circle drawing structures the circle-drawing operation in a radically different fashion than circle tracers and…

Proposes a framework for discussing the nature of the relationships between contexts and the formation of mathematical knowledge through model and field-of-experience concepts. Supports and illustrates this framework with references to curricular innovation and educational research. (Contains 31 references.) (Author/ASK)

Analyzes why the transfer of formal learning to outside school situations is problematical in principle and undependable in practice. Recommends an alternative approach for building bridges between practices based on analyzing the discourses involved as a system of signs and looking for appropriate points of inter-relation between them. (Contains…

Explores why learning and cognition are situated and context-dependent from the perspective of 'Embodied Cognition'. Argues that the nature of situated learning and cognition cannot be fully understood by focusing only on social, cultural, and contextual factors. Presents a case study after framing some theoretical notions of embodied cognition in…

Describes a teaching experiment conducted with fourth grade students in field of experience of gears. Identifies characteristics which, given suitable sequence of tasks and proper teacher guidance, have enabled pupils to approach theoretical thinking. Presents early findings of the teaching experiments at the external level of interpersonal…