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• W1646204749 endingPage "48" @default.
• W1646204749 startingPage "1" @default.
• W1646204749 abstract "Abstract Psychological research on the development of children's mathematical reasoning has focused either on their understanding of quantities or on their knowledge of number. A synthesis between these two different kinds of theory can be achieved by acknowledging that numbers have two meanings: a representational meaning, defined by their use as signs for quantities or relations between quantities, and an analytical meaning, defined by the conventions in the number system. In the introduction, this chapter introduces these two meanings of numbers and explores the vital connections between them. The subsequent sections analyze how children's mathematical knowledge develops by their increasing ability to use different numerical representations (e.g., from the use of fingers to represent quantities to the use of conventional signs), by their growing understanding of invariant relations between quantities (e.g., realizing that, given a fixed number of cookies, the more people sharing the cookies, the less each one receives) and by their increasing awareness of the relevance of specific concepts to different situations (e.g., understanding the relevance of division to the solution of situations more readily connected to multiplication). Throughout the chapter, the connection between the nature of quantities and their numerical representations is explored. The final substantive section focuses on the use of numbers to quantify space and relations between spatial dimensions, and argues that understanding relations between different dimensions in space (e.g., length, width, and area) is crucial to quantifying space. The chapter ends with a brief discussion of directions for future research." @default.
• W1646204749 created "2016-06-24" @default.
• W1646204749 creator A5018055006 @default.
• W1646204749 creator A5043088088 @default.
• W1646204749 date "2015-03-23" @default.
• W1646204749 modified "2023-10-16" @default.
• W1646204749 title "The Development of Mathematical Reasoning" @default.
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