An Integrative Theory of Numerical Development

Understanding of numerical development is growing rapidly, but the volume and diversity of findings can make it difficult to perceive any coherence in the process. The integrative theory of numerical development posits that a coherent theme does exist-progressive broadening of the set of numbers whose magnitudes can be accurately represented-and that this theme unifies numerical development from infancy to adulthood. From this perspective, development of numerical representations involves four major acquisitions: (a) representing magnitudes of nonsymbolic numbers increasingly precisely, (b) linking nonsymbolic to symbolic numerical representations, (c) extending understanding to increasingly large whole numbers, and (d) extending understanding to all rational numbers. Thus, the mental number line expands rightward to encompass larger whole numbers, leftward to encompass negatives, and interstitially to include fractions and decimals.