A Case Study Examining Links between Fractional Knowledge and Linear Equation Writing of Seventh-Grade Students and Whether to Introduce Linear Equations in an Earlier Grade

Mi Yeon Lee

doi:10.12973/iejme/3980

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Mi Yeon Lee ¹ ^*

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¹ Arizona State University, USA^* Corresponding Author

Abstract

As a part of the larger study, a case study of two seventh grade students, Peter and Willa, was conducted. To examine links between their fractional knowledge and algebraic reasoning, the students were interviewed twice, once for their fractional knowledge and once for their algebraic knowledge in writing linear equations that required explicit use of unknowns. Peter and Willa’s fractional knowledge influenced the linear equations they wrote to represent quantitative situations. In particular, the findings showed that a reversible iterative fraction scheme is important to understand reciprocal relationships between two quantities in writing a basic linear equation of the form ax=b. Also, considering fractions as multipliers on unknowns is important to write linear equations. Implications for the possibility of introducing linear equations in an earlier grade and how to support the introduction are suggested.

Keywords

fractional knowledge
linear equation writing
reciprocal reasoning
quantitative reasoning

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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 14, Issue 1, January 2019, 109-122

https://doi.org/10.12973/iejme/3980

Publication date: 21 Dec 2018

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How to cite this article

APA

Lee, M. Y. (2019). A Case Study Examining Links between Fractional Knowledge and Linear Equation Writing of Seventh-Grade Students and Whether to Introduce Linear Equations in an Earlier Grade. International Electronic Journal of Mathematics Education, 14(1), 109-122. https://doi.org/10.12973/iejme/3980

Vancouver

Lee MY. A Case Study Examining Links between Fractional Knowledge and Linear Equation Writing of Seventh-Grade Students and Whether to Introduce Linear Equations in an Earlier Grade. INT ELECT J MATH ED. 2019;14(1):109-22. https://doi.org/10.12973/iejme/3980

AMA

Lee MY. A Case Study Examining Links between Fractional Knowledge and Linear Equation Writing of Seventh-Grade Students and Whether to Introduce Linear Equations in an Earlier Grade. INT ELECT J MATH ED. 2019;14(1), 109-122. https://doi.org/10.12973/iejme/3980

Chicago

Lee, Mi Yeon. "A Case Study Examining Links between Fractional Knowledge and Linear Equation Writing of Seventh-Grade Students and Whether to Introduce Linear Equations in an Earlier Grade". International Electronic Journal of Mathematics Education 2019 14 no. 1 (2019): 109-122. https://doi.org/10.12973/iejme/3980

Harvard

Lee, M. Y. (2019). A Case Study Examining Links between Fractional Knowledge and Linear Equation Writing of Seventh-Grade Students and Whether to Introduce Linear Equations in an Earlier Grade. International Electronic Journal of Mathematics Education, 14(1), pp. 109-122. https://doi.org/10.12973/iejme/3980

MLA

Lee, Mi Yeon "A Case Study Examining Links between Fractional Knowledge and Linear Equation Writing of Seventh-Grade Students and Whether to Introduce Linear Equations in an Earlier Grade". International Electronic Journal of Mathematics Education, vol. 14, no. 1, 2019, pp. 109-122. https://doi.org/10.12973/iejme/3980