Categorizing and promoting reversibility of mathematical concepts

Simon M. A., Kara M., Placa N., Sandir H.

EDUCATIONAL STUDIES IN MATHEMATICS, cilt.93, sa.2, ss.137-153, 2016 (SSCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 93 Sayı: 2
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1007/s10649-016-9697-4
  • Dergi Adı: EDUCATIONAL STUDIES IN MATHEMATICS
  • Derginin Tarandığı İndeksler: Social Sciences Citation Index (SSCI), Scopus
  • Sayfa Sayıları: ss.137-153
  • Anahtar Kelimeler: Reversibility, Mathematical concepts, Reflective abstraction, Task design, STUDENTS, KNOWLEDGE
  • Gazi Üniversitesi Adresli: Evet

Özet

Reversibility of concepts, a key aspect of mathematical development, is often problematic for learners. In this theoretical paper, we present a typology we have developed for categorizing the different reverse concepts that can be related to a particular initial concept and explicate the relationship among these different reverse concepts. We discuss uses of the typology and how reversibility can be understood as the result of reflective abstraction. Finally, we describe two strategies for promoting reversibility that have distinct uses in terms of the types of reverse concepts they engender. We share empirical results which led to our postulation of these strategies and discuss their theoretical basis.