THE EARLY DEVELOPMENT OF ARITHMETIC REASONING: NUMERATIVE ACTIVITIES AND LOGICAL OPERATIONS (NUMBER, COUNTING, REPRESENTATION).
Item
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Title
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THE EARLY DEVELOPMENT OF ARITHMETIC REASONING: NUMERATIVE ACTIVITIES AND LOGICAL OPERATIONS (NUMBER, COUNTING, REPRESENTATION).
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Identifier
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AAI8409404
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identifier
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8409404
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Creator
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KLEIN, ALICE S.
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Contributor
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Harry Beilin
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Date
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1984
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Language
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English
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Publisher
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City University of New York.
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Subject
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Psychology, Developmental
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Abstract
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This study addressed the role of numerative activities in the development of children's reasoning about arithmetic operations. The theoretical approach of this study was based on two proposals. First, children's ability to solve an arithmetic problem is influenced by both the numerative activities that they employ on a problem and their logical operations of addition and subtraction. Second, children's knowledge of addition and subtraction constitutes a system of interrelated operations.;Preschool children between 4 and 6 years of age participated in two experiments, a counting experiment and a figural correspondence experiment. Each experiment comprised tasks that assessed two fundamental arithmetic abilities: (1) the ability to make an inference about the outcome of an arithmetic operation (judgment task), and (2) the ability to "undo" the outcome of an arithmetic operation (inverse task). The main difference between these two experiments concerned the numerative activities (counting objects or establishing one-to-one correspondence between objects) by which children constructed numerical representations of the arithmetic problems.;A set of arithmetic problems was presented to children in both experiments, and these problems varied on two principal dimensions: (1) the logical form or the arithmetic operations, and (2) the quantitative relationship between the initial collections. Children received an initial interview and a final interview (judgment and inverse tasks) on each problem. In addition, a pretest was administered in order to determine children's level (I-III) of number development with respect to their logical operations and their understanding of the numerative activities in the study.;The results indicate that children in the two experiments constructed different forms of numerical representation of the arithmetic problems through their activities of counting objects or establishing one-to-one correspondence between objects. Furthermore, the particular properties (cardinal values or correspondence relations) of each form of numerical representation of the problems influenced how children solved the judgment task and the inverse task. The results also indicate that the dimensions of the arithmetic problems influenced children's ability to reason about these problems. Children solved one-way function problems earlier than two-way function problems, and equality problems earlier than inequality problems. Finally, the findings in both experiments reveal that children's arithmetic reasoning changed qualitatively over levels, both in their understanding of different numerative activities and in their ability to solve different types of arithmetic problems. These results are discussed in relation to the theoretical proposals of the study.
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Type
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dissertation
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Source
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PQT Legacy CUNY.xlsx
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degree
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Ph.D.
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Program
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Psychology
