Representations and Conceptions of Variables in Students’ Early Understandings of Functions

Diana L. Moss; Steven Boyce; Teruni Lamberg

doi:10.29333/iejme/6257

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Diana L. Moss ¹ ^* , Steven Boyce ², Teruni Lamberg ³

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¹ Utah State University, Tooele, Utah, USA² Portland State University, Portland, Oregon, USA³ University of Nevada, Reno, Nevada, USA^* Corresponding Author

Abstract

This study explored how students develop meaning of functions by building on their understanding of expressions and equations. A teaching experiment using design research was conducted in a sixth-grade classroom. The data was analyzed using a grounded theory approach to provide explanations about why events occurred within this teaching episode and what these events mean in terms of student learning of functions (Corbin & Strauss, 2014; Gravemeijer & Cobb, 2006). The findings revealed that understanding functions involved integrating their understanding of different meanings of variables such as letters representing changing values and letters representing known values to model the situation using an expression, and seeing linear relationships between the independent and dependent variable through graphing. This paper provides a learning progression for supporting early understandings of functions. We discuss implications for research on students’ conceptions of variables and implications for fostering functional thinking.

Keywords

linear relationships
functions
representations
early algebra

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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 15, Issue 2, May 2020, Article No: em0564

https://doi.org/10.29333/iejme/6257

Publication date: 28 Oct 2019

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How to cite this article

APA

Moss, D. L., Boyce, S., & Lamberg, T. (2020). Representations and Conceptions of Variables in Students’ Early Understandings of Functions. International Electronic Journal of Mathematics Education, 15(2), em0564. https://doi.org/10.29333/iejme/6257

Vancouver

Moss DL, Boyce S, Lamberg T. Representations and Conceptions of Variables in Students’ Early Understandings of Functions. INT ELECT J MATH ED. 2020;15(2):em0564. https://doi.org/10.29333/iejme/6257

AMA

Moss DL, Boyce S, Lamberg T. Representations and Conceptions of Variables in Students’ Early Understandings of Functions. INT ELECT J MATH ED. 2020;15(2), em0564. https://doi.org/10.29333/iejme/6257

Chicago

Moss, Diana L., Steven Boyce, and Teruni Lamberg. "Representations and Conceptions of Variables in Students’ Early Understandings of Functions". International Electronic Journal of Mathematics Education 2020 15 no. 2 (2020): em0564. https://doi.org/10.29333/iejme/6257

Harvard

Moss, D. L., Boyce, S., and Lamberg, T. (2020). Representations and Conceptions of Variables in Students’ Early Understandings of Functions. International Electronic Journal of Mathematics Education, 15(2), em0564. https://doi.org/10.29333/iejme/6257

MLA

Moss, Diana L. et al. "Representations and Conceptions of Variables in Students’ Early Understandings of Functions". International Electronic Journal of Mathematics Education, vol. 15, no. 2, 2020, em0564. https://doi.org/10.29333/iejme/6257