This article examines a classroom discussion of multiple interpretations of the scales on two distance versus time graphs. The analysis describes how two students and a teacher used multiple meanings for phrases of the form "I went by" and coordinated these meanings with different views of the scales. Students' ambiguous and shifting meanings did…

Explores the growth of mathematical knowledge and the relationship between abstraction and context. Builds on work to construct a viable model of the micro-evolution of mathematical knowledge in context whose central feature is the visibility of its mechanisms. Illustrates a case study of 10-11-year-old children's construction of meanings for…

Provides an overview of research on transfer, highlighting its main tenets. Looks at interviews of two grade 5 students learning about mathematical concepts regarding operations on positive and negative quantities. Focuses on how their learning is influenced by prior knowledge and experience. (Author/MM)

Introduces a special issue on the ways in which symbolic tools enable, mediate, and shape mathematical thinking while being themselves a product of these processes. (Author/MM)

Describes a methodology for analyzing the collective learning of the classroom community in terms of the evolution of classroom mathematical practices. In developing the rationale for this approach, grounds the discussion in work of mathematics educators who conduct classroom-based design research. Frames sample analysis as a paradigm case in…

Proposes an account of mechanisms by which students develop knowledge structures for modeling the physical world with algebra. (Author/CCM)