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

GÜLKILIK H.

INTERNATIONAL JOURNAL OF MATHEMATICAL EDUCATION IN SCIENCE AND TECHNOLOGY, cilt.53, sa.11, ss.3092-3114, 2022 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 53 Sayı: 11
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1080/0020739x.2021.1958943
  • Dergi Adı: INTERNATIONAL JOURNAL OF MATHEMATICAL EDUCATION IN SCIENCE AND TECHNOLOGY
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, IBZ Online, Applied Science & Technology Source, Computer & Applied Sciences, EBSCO Education Source, Education Abstracts, Educational research abstracts (ERA), ERIC (Education Resources Information Center), zbMATH, DIALNET
  • Sayfa Sayıları: ss.3092-3114
  • Anahtar Kelimeler: Calculus, definite integral conceptions, representational fluency, the volume of a solid of revolution, university students, CALCULUS, DIFFICULTIES, MATHEMATICS, CONNECTIONS, REGISTERS
  • Gazi Üniversitesi Adresli: Evet

Özet

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.