Connections between Empirical and Structural Reasoning in Technology-Aided Generalization Activities

Xiangquan Yao; John Elia

doi:10.29333/iejme/9770

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Xiangquan Yao ¹ ^* , John Elia ¹

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¹ Department of Curriculum and Instruction, The Pennsylvania State University, University Park, PA 16802, USA^* Corresponding Author

Abstract

Mathematical generalization can take on different forms and be built upon different types of reasoning. Having utilized data from a series of task-based interviews, this study examined connections between empirical and structural reasoning as preservice mathematics teachers solved problems designed to engage them in constructing and generalizing mathematical ideas aided by digital tools. The study revealed closer connections between naïve empiricism and result pattern generalization, between naïve empiricism and recognizing a structure in thought, between reasoning by generic example and process pattern generalization, and between reasoning by generic example and reasoning in terms of general structures. Results from this study imply that the ability to generalize based on perception and numerical pattern does not necessarily lead learners to generalize based on mathematical structure.

Keywords

empirical reasoning
structural reasoning
mathematical generalization

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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

INT ELECT J MATH ED, Volume 16, Issue 2, May 2021, Article No: em0628

https://doi.org/10.29333/iejme/9770

Publication date: 07 Mar 2021

Article Views: 1891

Article Downloads: 1360

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Declaration of Conflict of Interest: No conflict of interest is declared by author(s).

Data sharing statement: Data supporting the findings and conclusions are available upon request from the corresponding author(s).

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How to cite this article

APA

Yao, X., & Elia, J. (2021). Connections between Empirical and Structural Reasoning in Technology-Aided Generalization Activities. International Electronic Journal of Mathematics Education, 16(2), em0628. https://doi.org/10.29333/iejme/9770

Vancouver

Yao X, Elia J. Connections between Empirical and Structural Reasoning in Technology-Aided Generalization Activities. INT ELECT J MATH ED. 2021;16(2):em0628. https://doi.org/10.29333/iejme/9770

AMA

Yao X, Elia J. Connections between Empirical and Structural Reasoning in Technology-Aided Generalization Activities. INT ELECT J MATH ED. 2021;16(2), em0628. https://doi.org/10.29333/iejme/9770

Chicago

Yao, Xiangquan, and John Elia. "Connections between Empirical and Structural Reasoning in Technology-Aided Generalization Activities". International Electronic Journal of Mathematics Education 2021 16 no. 2 (2021): em0628. https://doi.org/10.29333/iejme/9770

Harvard

Yao, X., and Elia, J. (2021). Connections between Empirical and Structural Reasoning in Technology-Aided Generalization Activities. International Electronic Journal of Mathematics Education, 16(2), em0628. https://doi.org/10.29333/iejme/9770

MLA

Yao, Xiangquan et al. "Connections between Empirical and Structural Reasoning in Technology-Aided Generalization Activities". International Electronic Journal of Mathematics Education, vol. 16, no. 2, 2021, em0628. https://doi.org/10.29333/iejme/9770