Prospective mathematics teachers' ways of reasoning on differentiability and corner points in a real-life context

KERTİL M., KÜPCÜ A. R.

INTERNATIONAL JOURNAL OF MATHEMATICAL EDUCATION IN SCIENCE AND TECHNOLOGY, cilt.52, sa.9, ss.1361-1384, 2021 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 52 Sayı: 9
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1080/0020739x.2020.1766138
  • 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.1361-1384
  • Anahtar Kelimeler: Differentiation, corner point, qualitative calculus, emergent modelling covariational reasoning, rate of change, mathematical modelling, prospective mathematics teachers, CALCULUS, KNOWLEDGE
  • Marmara Üniversitesi Adresli: Evet

Özet

This study investigates prospective elementary and secondary school mathematics teachers' ways of reasoning about differentiability at a point and corner points while working on a mathematical modelling activity. Adopting a multiple-case study design, the participants of the study were 68 prospective elementary school mathematics teachers enrolled in the 'Calculus-1' course (Case-1) and 20 prospective secondary school mathematics teachers enrolled in the 'Mathematics Teaching Methods' course (Case-2). We adapted a task from the well-known filling bottle problem and implemented it as a regular part of each course. Written group solutions, individual reflection papers and task-based group interviews were the data sources. Constant comparative analysis method was employed in analysing the data. The results from both cases indicated that prospective mathematics teachers frequently relied on roughly drawn graphs while deciding differentiability. They had difficulties in writing an algebraic model and comprehending the meaning of a corner point in the filling water context. Prospective mathematics teachers got confused when they got different results for differentiability at a critical point through the roughly sketched graph and algebraic model. The data also showed that thinking about these concepts while working on such dynamic situations fostered prospective mathematics teachers in developing more productive ways of thinking.