This commentary reviews each of the three content chapters in the integers section and offers questions to promote further discussion. In addition to the themes raised in the three chapters, I introduce the role of formal mathematical structure in generalizing systems of number, from natural numbers to integers, and analogously, from real numbers…

Wertsch's clarification of Vygotsky's claims about the role of social interaction in the development of children's thinking made an important contribution to educational research. Revisiting that clarification, I suggest that "talk" instead of "speech" best describes Vygotsky's concern with the functional dynamics of dialogue rather than the…

A scientific definition of the meaning of human creative thought is pursued. (JD)

The article reviews six conceptions of genius and offers a seventh. Three types of genius (analytic, synthetic, and integrated) are defined. Common to all three is the sustained ability to use analysis and synthesis (i.e., to be both linear and creative in approaching complex problems). (Author/DB)

Reviews and discusses Piaget's recent work on abstract reasoning. Piaget's distinction between empirical and reflective abstraction is presented; his hypotheses are considered to be metaphorical. (Author/DB)

Examines Paul H. Hirst's concept of reason as implied in his theory of the forms of knowledge. Explains Hirst's view of the temporal nature of knowledge and analyzes his key concepts of objectivity, judgement, the given, and facts. (Author/DMM)

Major themes from the previous light articles on literacy, reasoning, and education are highlighted. Common inferences about the needs for organizational change, loosening of governmental rules and controls, and field-initiated research are described. The general exclusion of the affective domain from this discussions of higher order reasoning is…

This paper argues that morality is essentially a matter of rational reflection and judgment and has little to do with feelings or affections. The notions of reason and justification are analyzed. Four types of feelings are defined and shown to provide inadequate bases for moral judgment. (Author/SJL)

Considers the cognitive mechanisms available to individuals which enable them to operate successfully in different parts of the mathematics curriculum, such as children's arithmetic shows divergence in performance. Explains how students cope with the transition to advanced mathematical thinking in different ways, leading once more to a diverging…

This paper presents two puzzles that have emerged in a series of completed and ongoing studies at Queen's University, Ontario. These puzzles concern teachers' professional knowledge, a term used to refer to the non-propositional forms of knowledge assumed to be of importance to professional action. This research assumed that the professional…

A theory of adult cognitive development which includes two post-formal operational stages is described. The paper is divided into three sections. The first section provides background for discussion of the theory. A case study in which various employees in a hypothetical organization react to a problem is provided. Examples of pre-logical,…

Discussed are the concepts of intuition, the general properties of an intuitive knowledge, and the classification of intuitions as problem solving of affirmative. An example of intuition using multiplication and division is described in some detail. (MNS)

A brief survey of models in dealing with various types of understanding is given. Then a hybrid model, which proved inadequate for describing understanding, is outlined. Finally, four levels of understanding are discussed: intuitive, procedural, abstract, and formal. The concept of number is used to illustrate these levels. (MNS)

Descries professional overspecialization and education's overemphasis on the acquisition of formalized information. Discusses the capabilities of the hemispheres of the brain and the problems caused by focusing on only the left hemisphere. Illustrates intuition and abstract patterns. Suggests that recognition of laterality will advance education…

Comments on Flavell's paper (PS 522 962) presented in the same issue. Stresses some of the positive aspects of preschoolers' conception of thinking, and raises questions about the relatively negative portrait of young child's introspective abilities. Discusses evidence of introspection among preschoolers, and underlines the special, and…