The challenge for education in today's knowledge age is developing students' capacity for sustained creative work with ideas. Although even the youngest students don't fear the abstract, working to improve ideas is an acquired disposition. Creative production is a progressive design process. Software is described in which students, as a community,…

Builds on the results of earlier research that investigated principles that facilitate higher levels of learning in Internet-based distance learning university courses. Explores how these can be applied to Internet-based distance learning environments, using results of questionnaires from experts and scholars that considered complex abstracted…

Interviews 60 Japanese children between the ages of 3 and 7 years to investigate the relationship between levels of abstraction and representation. Indicates that abstraction and representation are closely related. Implies that educators need to focus more on the mental relationships children make because the meaning children can give to…

A review of groundbreaking studies in child development by Piaget, Vygotsky, Baillargeon, Premack, and Woodruff suggests that the ideal learning environment would need to have developmentally appropriate and challenging activities; nurturing experts; plenty of social interaction; and opportunities for problem solving, thoughtful reflection, and…

Conventional instruction in critical thinking may ignore the creative and intuitive functions of rationality, thereby encouraging a mechanically rote approach to textual analysis, problem solving, and problem construction. Such an overemphasis upon logical "calculus of justification" functions has epistemological weaknesses and pedagogical…

Refutes Peter Mueser's criticisms of the author's position on formalistic research approaches. Restates that statistical significance is virtually useless. Claims mathematical economists take their intellectual positions from mathematics departments bringing irrelevant intellectual values into economics. (NL)

Too much classroom work is teacher-initiated, labor-intensive, abstraction-rich, and experience-lean. In contrast, science centers offer students a learner-initiated, discovery-rich opportunity to explore stimulating experiences, especially when second trips are made. Optimal learning occurs with a dynamic blending of abstract and experiential…

Considers Richard Ohmann's argument that composition texts which instruct students to emphasize concrete details over abstract concepts encourage conformity with the dominant order. Suggests that Ohmann failed to consider the effects of teachers' and students' viewpoints. Cites methods that encourage students to use detail as a device of broader…

Investigates the effects of two context variables on the performance of seventh-grade students on a qualitative and numerical proportional reasoning test. Explores the nature of the relationships between rational number skills, qualitative reasoning about ratios, and numerical proportional reasoning. (Author/YP)

Investigates the effect of cognitive style on the performance of college students on proportional reasoning tasks. Reports that students having proportional reasoning can be misled by the presence of field effects and that there was a significant correlation between the test of field independence and the items of proportional reasoning. (Author/YP)

The problem of finding all topological spaces is considered. Two characterizations are presented whose proofs involve only elementary notions and techniques. The problem is appropriate for students in a beginning topology course after they have been presented with the Embedding Lemma. (DC)

A theory of deductive reasoning is presented for inferences that depend on multiply quantified premises. It is argued that reasoners construct mental models based on their knowledge of the meaning of the quantifiers. Three experiments, with 54 university students and adults, corroborated the theory. (SLD)

The origins of the emphasis on formal proof are discussed as well as more recent views. Factors in acceptance of a proof and the social process of acceptance by mathematicians are included. The impact of formal proof on the curriculum and implications for teaching are given. (DC)

Modified dilemmas from the Kohlberg Moral Judgment Instrument were administered to 15 hearing-impaired students, aged 12-15. Analyses indicated that subjects reasoned at Stages 1-2, whereas Kohlberg's norms indicate that hearing peers reason at Stages 2-4. A positive correlation was found between subjects' average scores for moral reasoning and…

Studied 100 adolescents' approaches to problem-solving proofs and reasoning competence tasks. Found that a formal level of reasoning competence is associated with a deductive approach. Results support the notion of a cognitive development progression from an inductive approach to a deductive approach. (ETB)