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

Abstract

This case study examines instrumented techniques of a pre-service mathematics teacher when utilising a dynamic geometry system (DGS) for the construction of cyclic quadrilaterals. Equally, it investigates her understanding of the hierarchical relations between the 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. The analysis showed that the participant’s initial instrumented techniques enabled her to construct subsets of the cyclic quadrilaterals. Also, the process of reaching the most inclusive cyclic quadrilateral affected both her instrumented techniques and her understanding about the hierarchical relations between the constructed quadrilaterals.