Abstract
Summary The principal aim of this report has been to clear the air with regard to number development theory and research. We began with a brief overview of the status of the number concept in pure mathematics and psychology. It was argued that although there are clear methological differences between pure mathematical and psychological approaches to the study of number, the two approaches are substantively complementary. Both are attempts to found the number concept on underlying psychological processes. Three influential mathematical theories of number and three metamathematical criteria by which such theories are judged (consistency, completeness, categoricalness) then were summarized. The first theory, originally proposed by Peano (30) and von Neumann (49), postulates that the number concept may be reduced to a wholistic property of the natural numbers: viz., their inherent ordering. It was found that Peano-von Neumann's ordinal theory allows one to construct natural numbers without contradiction (cons...
Published Version
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