Answers Burn's question related to a previous study on the nature of knowledge about abstract algebra. Claims that a previous paper presents research that attempts to contribute to knowledge of how students' understanding of certain group concepts may develop instead of teaching abstract algebra with the computer software ISETL. (ASK)

The negotiation of meaning presupposes a taken-to-be-shared understanding of a situation. Uses an example to illustrate how negotiation of meaning and task may be linked in ways inappropriate to the learning of modeling and critical reflections. Contains 16 references. (Author/ASK)

Discusses the problem in the relationship between schemata and intuitions. Analyzes the hypothesis that intuitions are always based on certain structural schemata. Concludes that intuitions, even when expressed as instantaneous guesses, are in fact manipulated behind the scenes by schemata. Contains 27 references. (Author/ASK)

Presents a study in which Chinese students were given items from the math subtest of the Scholastic Aptitude Test (SAT) which were found to produce the largest gender differences in American students. Concludes that, consistent with differential coursework view but contrary to several others, results revealed no difference in performance on the…

Discusses ways to improve the understanding of problems involving combination and complementation. Analyzes three children's initial mental representations, procedures, and reflections when presented with four different situations. Concludes with the impacts of the logico-mathematical relation of inclusion in these processes. Contains 31…

Describes and analyzes a short teaching episode in a multilingual secondary mathematics classroom in South Africa where the teacher uses a participatory-inquiry approach. Argues that such an approach to teaching and learning mathematics creates dilemmas of mediation for teachers. (AIM)

Presents an alternate perspective for utilizing the action/process/object framework when discussing student development of conceptions of function. Describes a property-oriented view of function based on visual aspects of functional growth. Less emphasis is placed on how the variables are changing and more emphasis is placed on the properties that…

Addresses the initial understanding that advanced undergraduate mathematics students exhibit when presented with a new concept in an environment requiring self-generation and self-validation of examples of the concept. Concludes that students who used an example generation learning strategy were more effective in attaining an initial understanding…

Examines the possibility that at times imagery might be a disadvantage in certain tasks. For example, the notion of a persistent image may be so vivid as to actually block other creative thought. Describes one calculus student's images supporting high levels of mathematical functioning which occasionally became so powerful as to obscure more than…

In an article from the July 1995 issue of Educational Studies in Mathematics, Even and Tirosh claim that the quantity (-8)1/3 is undefined. This article presents arguments as to why the reasoning of Tirosh and Even is flawed. Attempts to convince educators of the importance of applying a mathematical definition precisely. (AIM)

Discusses two possible approaches to (-8)1/3. Considers the pros and cons of each of these approaches and specifies some implications to teacher education. (AIM)

Reports on the case study of a high school student using a computer-based tool called the Contour Analyzer to create graphs of height versus distance and slope versus distance for a flat board positioned with different slants and orientations. Focuses on visually recognizing the mathematical behavior of the slope versus distance function which…

Presents two case studies of learners attempting to understand the concept of normal distribution, specifically why physical phenomena such as height fall into normal distributions. Draws conclusions about a Connected Mathematics learning environment that enables confrontation with epistemological anxiety and the features of modeling languages…

Explores the relationship between learners' actions, visualizations, and the means by which these are articulated. Describes a microworld called Mathsticks which is designed to help students construct mathematical meanings by forging links between the visual and symbolic representations they develop and their actions. Presents a case study of two…

Suggests a theoretical framework to address some phenomena of mathematical behavior. Defines the terms "pseudo-conceptual" and "pseudo-analytical" and analyzes examples from classrooms, exams, and homework within the framework. (Author/AIM)