Counting is an evolutionarily recent cultural invention of the human species. In order for humans to have conceived of counting in the first place, certain representational and logical abilities must have already been in place. The focus of this article is the origins and nature of those fundamental mechanisms that promoted the emergence of the…

Learning of the mathematical number line has been hypothesized to be dependent on an inherent sense of approximate quantity. Children's number line placements are predicted to conform to the underlying properties of this system; specifically, placements are exaggerated for small numerals and compressed for larger ones. Alternative hypotheses…

Recent studies have documented an evolutionarily primitive, early emerging cognitive system for the mental representation of numerical quantity (the analog magnitude system). Studies with nonhuman primates, human infants, and preschoolers have shown this system to support computations of numerical ordering, addition, and subtraction involving…

Despite the increasing use of the microgenetic methodology to examine change, the techniques employed to analyse microgenetic data remain fairly unsophisticated. This paper reviews the existing ways of analysing such data and describes their limitations. We use two recent studies to illustrate how modelling can avoid these problems and reveal…

The effects of two training sequences on the development of young children's logical operations and number concepts, including rational counting strategies, were investigated. Forty-five preschool children, aged 3.11 to 4.10, were randomly assigned to two treatment groups and one control group. Subjects in the treatment groups received training…