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


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.


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

Publication date: 28 Oct 2019

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Article Downloads: 1409

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