Role of formal constraints in reasoning: an approach through 2D Euclidean geometry in undergraduate mathematics

KAPLAN H. A., GÜLKILIK H., Emul N.

INTERNATIONAL JOURNAL OF MATHEMATICAL EDUCATION IN SCIENCE AND TECHNOLOGY, cilt.52, sa.6, ss.815-832, 2021 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 52 Sayı: 6
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1080/0020739x.2020.1738578
  • 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.815-832
  • Anahtar Kelimeler: Geometric reasoning, formal constraints, undergraduate, Toulmin model, ARGUMENTATION
  • Gazi Üniversitesi Adresli: Evet

Özet

The goal of this paper was to investigate the role of formal constraints (e.g. definitions, theorems) in geometric reasoning. Four students participated in a task-based interview including 2D Euclidean geometric locus problems. Data were obtained from observations, interviews, and video recordings and analyzed by Toulmin's argumentation model. The analysis of the data provided a detailed look at students' abductive, inductive, and deductive reasoning. Results revealed that formal constraints reduced the uncertainty of a claim. Students could transform abduction and induction to deduction if they could reverse the array of formal constraint usage. The co-existence of warrant and backing including formal constraints facilitated this transfer and this co-existence in reversing their usage was the key factor to eliminate the challenge of transforming abduction to deduction.