For the purpose of clarity and consistency, the term e-learning is used throughout the paper to refer to technology-enhanced learning and information technology (IT) in teaching and learning. IT depicts computing and other IT resources. Research into e-learning has changed in focus and breadth over the last four decades as a consequence of…

There is a strong push from within mathematics education reform to incorporate representations in math classrooms (Behr, Harel, Post, & Lesh, 1993; Kieren, 1993; NCTM, 2000). However, questions regarding what representations should be used (for a given topic) and how representations should be used (such that students gain a deep understanding of…

This article reflects on the author's experience in teaching courses in mathematics content and methods in teacher preparation programs. It shows how technology-enhanced inquiry into a seemingly mundane task on situated addition found in a popular textbook for prospective elementary teachers, can reveal hidden properties of integers associated…

Argues for "post-structural Marxism" as the pedagogical practice of reading and rereading Marx in a critical manner. Briefly discusses the concept of the social in the post-modern condition before reviewing relations between post-structuralism and Marxism. Provides an account of Deleuze's Marxism, using it to analyze education as a form…

Presents an alternative perspective that conceives of graphing as observable practices employed to achieve specific goals rather than as knowledge represented in students' minds. Highlights the nature of graphs as semiotic objects, rhetorical devices, and conscription devices. Illustrates the plausibility and fruitfulness of the new perspective in…

A study of students' understandings of the nature of science makes science itself the focus of inquiry. This book is an account of a research project undertaken to elicit and to describe the range and nature of school students' understandings of the nature of science. The features of students' representations which are focused on include their…

A discussion of the papers, "Representation, Vision and Visualization: Cognitive Functions in Mathematical Thinking. Basic Issues for Learning" (Raymond Duval) and "On the Development of Human Representational Competence from an Evolutionary Point of View: From Episodic to Virtual Culture" (James J. Kaput), is presented. Kaput…

New forms of mathematical knowledge are growing in importance for mathematics and education, including tacit knowledge, knowledge of particulars, language, and rhetoric in mathematics. Highlights the importance of attending to rhetoric and the range of rhetorical styles in school mathematics, and the need for explicit instruction in this area.…

Considers the cognitive mechanisms available to individuals which enable them to operate successfully in different parts of the mathematics curriculum, such as children's arithmetic shows divergence in performance. Explains how students cope with the transition to advanced mathematical thinking in different ways, leading once more to a diverging…

Shares perspectives on the history and current status of ethnomathematics. Speculates as to whether this field is revisionist and discusses the features of ethnomathematics that distinguish it from mathematics. (DDR)

Argues that the challenge for teachers of algebra in Australia is to find ways of making the structural aspects of algebra accessible to a greater percentage of students. Uses the zero product principle to provide an example of a common student error grounded in the difficulty of understanding the structure of algebra. (DDR)

Reviews the history of the epistemological and ontological underpinnings of science education and surveys other selected articles with this theme. (DDR)

This paper contains the comments of a discussant reviewing the paper, "The Role of Visual Representations in the Learning of Mathematics" (Abraham Arcavi). A research-based evaluation is made that focuses on the ideas of stochastics and the epistemological triangle. (Contains 28 references.) (DDR)

Proposes that the adoption of the notion that students should be taught so that they think like mathematicians leads to a number of enticing questions but ignores some important educational issues. Argues that a new course must be charted for mathematics education. (DDR)

Presents a summary of teaching practices that are successful in promoting conceptual change based on a study of Grades 4, 8, and 10 and on the research literature. Proposes improvements in teaching methodology. Contains 31 references. (DDR)