The Korea Society Of Educational Studies In Mathematics

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Journal of Educational Research in Mathematics - Vol. 30 , No. 2

[ Article ]
Journal of Educational Research in Mathematics - Vol. 30, No. 1, pp.39-66
Abbreviation: JERM
ISSN: 2288-7733 (Print) 2288-8357 (Online)
Print publication date 28 Feb 2020
Received 10 Jan 2020 Revised 10 Feb 2020 Accepted 18 Feb 2020

University Students’ Understanding of the Process-object Layers of Derivatives at a Point Through the Lens of Representational Fluency
Lee, Jihyun*
*Professor, Incheon National University, South Korea (


Representational fluency refers to the ability to easily and accurately interact with multiple representations of a concept. This study focused on a specific representation fluency about derivatives at a point: the ability to represent derivatives at a point algebraically, graphically, numerically, and verbally from the functions given by formulas, graphs, tables, and verbal descriptions. Thirty-four Korean university students participated in the representational fluency assessment consisting of 16 tasks, and their written responses were analyzed by using the qualitative content analysis method to explore their understanding of the process-object layers of derivatives at a point from their interactions with given representations of each task. The emergent students’ derivative conception categories indicate that a substantial portion of the students did not fully understand a derivative as a rate of change of a dependent variable with respect to an independent variable, and lacked understanding of the ratio, limit, and function process underlying the concept of the derivative. Students’ diverse responses to the representational fluency tasks and qualitative analysis of such tasks demonstrate what students’ interactions with the given multiple representations of derivatives involve and what possibilities multiple representations tasks have as a tool for assessing and facilitating students’ understanding of the complex concept structure of derivatives.

Keywords: derivatives, multiple representations, representational fluency, process-object theory, a rate of change

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