Samples of children and young adolescents were asked what the word "Change" meant to them and their responses were analyzed to discover the degree of understanding shown by different age groups. Results are reported and discussed. (Author/CT)

Twenty-one male and 21 female adolescents were tested individually for conservation of mass, weight, and volume. (CM)

Discusses how people bridge chasms of thought with insubstantial but named fictions to make it possible to cross them in imagination. (HOD)

Discusses two meanings of abstract: abstract-apart, ideas removed from reality; and abstract-general, ideas general to a wide variety of contexts. Suggests that greater interest in abstraction as a process, instead of just a product, would be beneficial to mathematics education theory and practice. (48 references) (MKR)

Identifies and explores the difficulties in the novice mathematician's encounter with mathematical abstraction. Observes 20 first-year mathematics undergraduates and extracts sets of episodes from the transcripts of the tutorials and interviews within five topics in pure mathematics. Discusses issues related to the learning of one mathematical…

The fundamental relations that underlie cognitive comparisons--''same'' and ''different''--can be defined at multiple levels of abstraction, which vary in relational complexity. We compared response times to decide whether or not two sequentially-presented patterns, each composed of two pairs of colored squares, were the same at three levels of…

Four experiments explored participants' understanding of the abstract principles governing computer simulations of complex adaptive systems. Experiments 1, 2, and 3 showed better transfer of abstract principles across simulations that were relatively dissimilar, and that this effect was due to participants who performed relatively poorly on the…

An apparent "crisis" of youth at-risk is a key marker in contemporary debates about young people among a range of intellectuals, social commentators and experts in various domains and centres of expertise. Drawing on aspects of the reflexive modernization, governmentality and feminist literatures, this paper explores how risk discourses emerge as…

The current study compared the effects of technological environments with that of the paper-and-pencil environment on reasoning about the concept of derivatives in the context of maximum and minimum problems. The data consisted of clinical interviews conducted with three pre-service secondary mathematics teachers and a newly registered graduate…

This study focussed on how secondary school students construct and use mathematical models as conceptual tools when solving word problems. The participants were 511 secondary-school students who were in the final year of compulsory education (15-16 years old). Four levels of the development of constructing and using mathematical models were…

The present study contrasts mathematical knowledge that two sixth-grade teachers apparently used when teaching fraction multiplication with the Connected Mathematics Project materials. The analysis concentrated on those tasks from the materials that use drawings to represent fractions as length or area quantities. Examining the two teachers'…

This paper will examine an unresolved tension inherent in the question of art and argue for the idea of a singular rule as a natural resolution. In so doing, the structure of a singular rule will be fully outlined and its paradoxical constitution will be resolved. The tension I mention above unfolds both as a matter of history and as a product of…

This study examines the development of children's ability to reason about proportions that involve either discrete entities or continuous amounts. Six-, 8- and 10-year olds were presented with a proportional reasoning task in the context of a game involving probability. Although all age groups failed when proportions involved discrete quantities,…

The study of literature such as Orwell's works will not solve issues in contemporary culture and thought, but it can help one detect abstract language in the discussion and formulation of issues.

Based on an M.A. thesis (Snow) submitted to McGill University.