Construction of cyclic quadrilateral: A pre-service teacher's journey from subsets to the generic concept through instrumentation of a dynamic technology


Journal of Mathematical Behavior, vol.63, 2021 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 63
  • Publication Date: 2021
  • Doi Number: 10.1016/j.jmathb.2021.100893
  • Journal Name: Journal of Mathematical Behavior
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, EBSCO Education Source, Educational research abstracts (ERA), Psycinfo
  • Keywords: Dynamic geometry system, Instrumental genesis, Hierarchical classification, Cyclic quadrilaterals, Pre-service mathematics teacher, DEFINITIONS, CLASSIFICATION, INCLUSION, ARTIFACTS
  • Eskisehir Osmangazi University Affiliated: Yes


© 2021 Elsevier Inc.This case study examines instrumented techniques of a preservice mathematics teacher when utilising a dynamic geometry system for the construction of cyclic quadrilaterals. Equally, it investigates her understanding of the hierarchical relations between constructed cyclic quadrilaterals. For this aim, the hierarchical classification and instrumental genesis constitute the theoretical framework of our study. The data was collected through task-based interviews in which the participant was asked to construct the cyclic quadrilateral without using the circle tool in DGS. Data analysis was carried out to examine the participant's development of construction strategies related to her instrumented techniques and her reasoning regarding the properties of different cyclic quadrilaterals. Findings indicate that her initial instrumented techniques enabled her to construct subsets of the cyclic quadrilateral and the process of reaching the most inclusive cyclic quadrilateral affected both her instrumented action techniques and her understanding about the hierarchical relations between the constructed quadrilaterals.