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"ERIC ED623252: Thinking About Quantity: The Intertwined Development Of Spatial And Numerical Cognition" and the language of the book is English.


“ERIC ED623252: Thinking About Quantity: The Intertwined Development Of Spatial And Numerical Cognition” Metadata:

  • Title: ➤  ERIC ED623252: Thinking About Quantity: The Intertwined Development Of Spatial And Numerical Cognition
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  • Language: English

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  • Internet Archive ID: ERIC_ED623252

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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, mass). Moreover, space can be broken down into more specific dimensions (e.g., length, area, density) and number can be conceptualized discretely or continuously (i.e., natural versus 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. [This paper was published in "Wiley Interdisciplinary Reviews: Cognitive Science" v6 n6 p491-505 2015.]

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