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Article

전자저널 논문

2018; 28(4): 573-598

Published online November 30, 2018 https://doi.org/10.29275/jerm.2018.11.28.4.573

Copyright © Korea Society of Education Studies in Mathematics.

An Analysis of University Students’ Representational Fluency About the Derivative Concept

대학생들의 미분 개념에 대한 표현 유창성 분석

이지현

Abstract

External representations of mathematical concepts facilitate individuals’ thinking about those concepts. Multiple representations of a concept can convey different information and facilitate different cognitive processes. Students’ understanding of a mathematical concept can be revealed in their interactions with representations, and therefore the representational fluency was used as a multi focal lens to examine how and what students understand of it. In this study, 34 university students were assessed for representational fluency about the derivative concept, using items requiring translations from the input representation of function to the output representation of derivative that vary systematically algebraic, graphical, numerical and verbal representations. The students’ achievement levels of each item were analyzed, association analysis and hierarchical clustering were also conducted to infer the degree of connections between abilities to translate function-derivative representations as a connected knowledge network. Although there was high achievement of some items, the participants in this study got low achievement in several items, which involve verbal representation of derivative and applying derivative concept to functions represented non-algebraically, and there were few statistically significant associations between two translation abilities, which need to be interconnected. The finding showed students’ strength, weakness and characteristics of derivative understanding as a connected network of representational abilities. This analysis provided rich evidences about students’ conceptual understanding of the derivative and could contribute to explore the direction of improvement of calculus teaching and learning based on students’ understanding.

Keywords미분,다양한 표현,표현 유창성,Derivative,Multiple Representations,Representational Fluency

Journal Info

Korea Society of Education Studies in Mathematics

Vol.32 No.2
2018-11-30

pISSN 2288-7733
eISSN 2288-8357

Frequency : Quarterly

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