Pattern Generalization Processing of Elementary Students:  Cognitive Factors Affecting the Development of Exact Mathematical Structures

F. D. Rivera

doi:10.29333/ejmste/92554

Pattern Generalization Processing of Elementary Students: Cognitive Factors Affecting the Development of Exact Mathematical Structures

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F. D. Rivera ¹ ^*

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¹ Department of Mathematics & Statistics, San Jose State University, USA^* Corresponding Author

Abstract

The fundamental aim in this article is to elucidate cognitive factors that influence the development of mathematical structures and incipient generalizations in elementary school children on the basis of their work on patterns, including how they use various representational forms such as gestures, words, and arithmetical symbols to convey their expressions of generality. We describe approximate and exact pattern generalizations and three cognitive factors that mutually influence the emergence of mathematical structures, namely, competence with number relationships, competence with shape similarity, and competence with figural property construction, discernment, and justification. We also highlight various representational modes that elementary students use to capture their emergent structures and incipient generalizations, grade-appropriate use and understanding of variables via the notions of intuited and tacit variables, and ways in which their structural incipient generalizations support their early understanding of functions.

Keywords

pattern generalization
elementary students
abduction
induction
deductive closure
structural thinking in mathematics

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, Volume 14, Issue 9, September 2018, Article No: em1586

https://doi.org/10.29333/ejmste/92554

Publication date: 25 Jun 2018

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Article Downloads: 2716

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How to cite this article

APA

Rivera, F. D. (2018). Pattern Generalization Processing of Elementary Students: Cognitive Factors Affecting the Development of Exact Mathematical Structures. Eurasia Journal of Mathematics, Science and Technology Education, 14(9), em1586. https://doi.org/10.29333/ejmste/92554

Vancouver

Rivera FD. Pattern Generalization Processing of Elementary Students: Cognitive Factors Affecting the Development of Exact Mathematical Structures. EURASIA J Math Sci Tech Ed. 2018;14(9):em1586. https://doi.org/10.29333/ejmste/92554

AMA

Rivera FD. Pattern Generalization Processing of Elementary Students: Cognitive Factors Affecting the Development of Exact Mathematical Structures. EURASIA J Math Sci Tech Ed. 2018;14(9), em1586. https://doi.org/10.29333/ejmste/92554

Chicago

Rivera, F. D.. "Pattern Generalization Processing of Elementary Students: Cognitive Factors Affecting the Development of Exact Mathematical Structures". Eurasia Journal of Mathematics, Science and Technology Education 2018 14 no. 9 (2018): em1586. https://doi.org/10.29333/ejmste/92554

Harvard

Rivera, F. D. (2018). Pattern Generalization Processing of Elementary Students: Cognitive Factors Affecting the Development of Exact Mathematical Structures. Eurasia Journal of Mathematics, Science and Technology Education, 14(9), em1586. https://doi.org/10.29333/ejmste/92554

MLA

Rivera, F. D. "Pattern Generalization Processing of Elementary Students: Cognitive Factors Affecting the Development of Exact Mathematical Structures". Eurasia Journal of Mathematics, Science and Technology Education, vol. 14, no. 9, 2018, em1586. https://doi.org/10.29333/ejmste/92554