International Electronic Journal of Mathematics Education

Representations and Conceptions of Variables in Students’ Early Understandings of Functions
AMA 10th edition
In-text citation: (1), (2), (3), etc.
Reference: 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
APA 6th edition
In-text citation: (Moss et al., 2020)
Reference: 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
Chicago
In-text citation: (Moss et al., 2020)
Reference: 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
In-text citation: (Moss et al., 2020)
Reference: 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
In-text citation: (Moss et al., 2020)
Reference: 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
Vancouver
In-text citation: (1), (2), (3), etc.
Reference: 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

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.

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