Representational fluency in calculating volume: an investigation of students’ conceptions of the definite integral

Abstract

The purpose of this study was to investigate university students’ conceptions of the definite integral in the process of finding the volume of a solid of revolution. The participants were four students enrolled in a university calculus course in Turkey. Data were obtained by task-based interviews, in which the participants had to work on a problem about calculating the volume of a solid of revolution. Representational fluency was used as a lens to analyze the conceptions of the students. Results indicated that the students imagined certain aspects of one main summation conception of the definite integral at different times in calculating the volume of the solid. They also used the conceptions of function matching and perimeter and area/boundary and volume. The students were comfortable explaining what they were doing in the solution if their conceptions of the definite integral allowed them to understand integral notation and build representational fluency. Implications based on the different conceptions that the students used and the representational fluency that they developed were discussed.

KEYWORDS:

• Calculus
• definite integral conceptions
• representational fluency
• the volume of a solid of revolution
• university students

Acknowledgements

I would like to express my great appreciation to Steven Jones for his valuable comments on the paper. I am grateful to the editor and anonymous reviewers for making constructive suggestions.

Disclosure statement

No potential conflict of interest was reported by the author.

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.

Notes

1 Although Yeliz was representing a washer in her drawing (see Figure 2(b)), she used the term ‘disks’ in her explanations. The researcher did not attempt to correct her language.

2 In English: (Shell Radius).(Shell Height).