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Thinking about quantity: the intertwined development of spatial and numerical cognition
Author(s) -
Newcombe Nora S.,
Levine Susan C.,
Mix Kelly S.
Publication year - 2015
Publication title -
wiley interdisciplinary reviews: cognitive science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.526
H-Index - 49
eISSN - 1939-5086
pISSN - 1939-5078
DOI - 10.1002/wcs.1369
Subject(s) - number line , numerical cognition , dimension (graph theory) , separable space , natural number , mathematics , space (punctuation) , point (geometry) , number sense , proportional reasoning , development (topology) , sequence (biology) , computer science , arithmetic , theoretical computer science , cognition , discrete mathematics , mathematics education , pure mathematics , geometry , mathematical analysis , psychology , neuroscience , biology , genetics , operating system
There are many continuous quantitative dimensions in the physical world. Philosophical, psychological, and neural work has focused mostly on space and number. However, there are other important continuous dimensions (e.g., time and mass). Moreover, space can be broken down into more specific dimensions (e.g., length, area, and density) and number can be conceptualized discretely or continuously (i.e., natural vs real numbers). Variation on these quantitative dimensions is typically correlated, e.g., larger objects often weigh more than smaller ones. Number is a distinctive continuous dimension because the natural numbers (i.e., positive integers) are used to quantify collections of discrete objects. This aspect of number is emphasized by teaching of the count word sequence and arithmetic during the early school years. We review research on spatial and numerical estimation, and argue that a generalized magnitude system is the starting point for development in both domains. Development occurs along several lines: (1) changes in capacity, durability, and precision, (2) differentiation of the generalized magnitude system into separable dimensions, (3) formation of a discrete number system, i.e., the positive integers, (4) mapping the positive integers onto the continuous number line, and (5) acquiring abstract knowledge of the relations between pairs of systems. We discuss implications of this approach for teaching various topics in mathematics, including scaling, measurement, proportional reasoning, and fractions. WIREs Cogn Sci 2015, 6:491–505. doi: 10.1002/wcs.1369 This article is categorized under: Psychology > Development and Aging Psychology > Learning