Investigates 10-year-old children's abilities to reason by analogy in solving addition and subtraction comparison problems involving unknown compare sets and unknown reference sets. Children responded in a consistent manner to the tasks involving the basic addition problems, indicating substantial relational knowledge of these but responded in an…

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…

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…

We applied a mixed-method research design to investigate the patterns of reasoning used by novice undergraduate chemistry students to classify chemical substances as elements, compounds, or mixtures based on their particulate representations. We were interested in the identification of the representational features that students use to build a…

Science classes are full of abstract or challenging concepts that are easier to understand if an analogy is used to illustrate the points. Effective analogies motivate students, clarify students' thinking, help students overcome misconceptions, and give students ways to visualize abstract concepts. When they are used appropriately, analogies can…

In his influential book "Dialogues with Children" (1984), Gareth Matthews presents strong evidence that children as young as six can and should engage in philosophical discourse. His findings form the basis of this article, a theoretical and practical guide for parents and teachers seeking respectful and creative ways to encourage…