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Siegler, Robert S.; Braithwaite, David W. – Grantee Submission, 2016
In this review, we attempt to integrate two crucial aspects of numerical development: learning the magnitudes of individual numbers and learning arithmetic. Numerical magnitude development involves gaining increasingly precise knowledge of increasing ranges and types of numbers: from non-symbolic to small symbolic numbers, from smaller to larger…
Descriptors: Numeracy, Numbers, Arithmetic, Fractions
Braithwaite, David W.; Tian, Jing; Siegler, Robert S. – Developmental Science, 2018
Many children fail to master fraction arithmetic even after years of instruction. A recent theory of fraction arithmetic (Braithwaite, Pyke, & Siegler, 2017) hypothesized that this poor learning of fraction arithmetic procedures reflects poor conceptual understanding of them. To test this hypothesis, we performed three experiments examining…
Descriptors: Fractions, Addition, Arithmetic, Hypothesis Testing
Braithwaite, David W.; Tian, Jing; Siegler, Robert S. – Grantee Submission, 2018
Many children fail to master fraction arithmetic even after years of instruction. A recent theory of fraction arithmetic (Braithwaite, Pyke, & Siegler, in press) hypothesized that this poor learning of fraction arithmetic procedures reflects poor conceptual understanding of them. To test this hypothesis, we performed three experiments…
Descriptors: Fractions, Addition, Arithmetic, Mathematics
Siegler, Robert; Lortie-Forgues, Hugues – Grantee Submission, 2014
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 is present, however--progressive broadening of the set of numbers whose magnitudes can be accurately…
Descriptors: Numbers, Theories, Individual Development, Cognitive Development
Kamii, Constance – 1994
Equivalent fractions are usually introduced in fourth grade and reviewed repeatedly in the subsequent grades as the four arithmetical operations are taught. In spite of this repeated instruction, the results are disappointing. This paper reviews some data from previous research documenting the difficulty of equivalent fractions, explains this…
Descriptors: Arithmetic, Cognitive Development, Elementary School Mathematics, Fractions
Cheek, Helen – 1981
Bilingual mathematics competencies and competency-coordinated activities are provided in the four sections of this curriculum guide for kindergarten (pre-operational) and grades 1-3 (concrete-operational) children. Topic areas for kindergarten include: classification (logic); comparing/ordering/graphing; quantitative; measurement; geometry;…
Descriptors: Algorithms, Arithmetic, Bilingual Education Programs, Classification
Davydov, V. V., Ed. – 1991
This is volume 6 of the series of translations of books from the Soviet literature on research in the psychology of mathematics instruction and on teaching methods influenced by the research. This book contains both a theoretical examination of the connection between instruction and the development of children, and experimental data on a definite…
Descriptors: Algebra, Arithmetic, Cognitive Development, Concept Formation
New York State Education Dept., Albany. Bureau of Curriculum Development. – 1990
This guide describes 20 learning activities that can be used with elementary school students on the topic of probability and statistics. These activities have been developed using the mathematics laboratory approach. This publication is designed to serve as a stimulant to encourage teachers to open their minds and employ their imagination in…
Descriptors: Arithmetic, Cognitive Development, Computation, Concept Formation