Presents an alternative pedagogy implicit in Imre Lakatos's "Proofs and Refutations: The Logic of Mathematical Discovery." Lakatos reveals that learning mathematics is a discourse-laden activity in which it is acceptable, if not preferable, to refute conjecture. Provides examples of using a Lakatosian approach in an elementary classroom.…

This article describes constructivist principles of learning in geometry specific to children's imaginal anticipations in line measurement and fractions. Application with seven sixth grade students with learning disabilities found that students had difficulty coordinating and imagining second-order and higher nested relationships that could be…

Discusses students' progress through distinct levels in the development of their thinking as described by van Hiele levels. Focuses on the quadrilaterals and suggests some level 3 tasks and construction problems. (ASK)

A Swedish interview study of how deaf pupils reason about phenomena in a science context revealed significant variation in the extent to which pupils used scientific principles for reasoning about science phenomena, which suggests that for some pupils, school science offers little as a framework for reasoning. (Contains references.) (DB)

Comparison of area and subtest scores on the Stanford Binet Intelligence Scale (Fourth Edition) for 15 autistic retarded children and 15 nonautistic retarded children found that the children with autism scored substantially lower in the verbal reasoning area and on the subtests of Comprehension and Absurdities than did the nonautistic children.…

Examined effects of motivation and intellectual ability on adolescent reasoning. Fifty adolescents were presented "scientific" evidence relevant to their religious affiliations. A manipulation designed to motivate adolescents toward greater accuracy improved overall performance. Crystallized intellectual ability was linked to absolute level of…

A long-standing and continuing controversy exists regarding the role of induction and deduction in reasoning and in scientific inquiry. Given the inherent difficulty in reconstructing reasoning patterns based on personal and historical accounts, evidence about the nature of human reasoning in scientific inquiry has been sought from a controlled…

The notions of "abstract "and "concrete" are central to the conceptualization of mathematical knowing and learning. It is generally accepted that development goes from concrete toward the abstract; but dialectical theorists maintain just the opposite: development consists of an ascension from the abstract to the concrete. In this article, we…

Research over the past 20 years has revealed that even very young infants possess expectations about physical events, and that these expectations undergo significant developments during the first year of life. In this article, I first review some of this research, focusing on infants' expectations about occlusion, containment, and covering events,…

This article builds on two previous ones in which we presented the processes of construction and consolidation of one student's knowledge structures about comparisons of infinite sets, according to a recently proposed theory of abstraction. In the present article, we show that under slight variations of context, knowledge structures that have…

Most students in America can graduate from high school without ever analyzing a piece of art. Perhaps these students will take an art history or an art appreciation course in college that may incorporate a few references to literature and history. Math or science connections will most likely remain entirely absent. Why do we treat art analysis…

"How ScienceWorks" is now the focus of the national science specifications in English schools. This article is a brief introduction to the philosophy of science from the Greeks to the present day that underpins this notion. It consists of a brief summary of the contributions of nine philosophers and/or scientists to the debate: Aristotle, Roger…

This paper is structured in two sections. The first examines views of mathematical abstraction in two broad categories: empiricist and dialectical accounts. It documents the difficulties involved in and explores the potentialities of both accounts. Then it outlines a recent model which takes a dialectical materialist approach to abstraction in…

The question of what students gain by engaging in socioscientific inquiry is addressed in two ways. First, relevant literature is surveyed to build the case that socioscientific issues (SSI) can serve as useful contexts for teaching and learning science content. Studies are reviewed which document student gains in discipline specific content…

Our experience suggests that pre-service primary school teachers have problems with learning science, especially chemistry, and that this negative attitude towards science influences their future teaching. On that premise, the purpose of the study was to determine the level of the pre-service primary school teachers' intrinsic motivation for…