Fostering a Student’s Abstraction of the Relationship Between Parallelogram and Trapezoid Within Quadrilateral Hierarchy

Abstract

This article provides an analysis of a data set coming from a two-phase qualitative study that focused on fostering primary students’ abstraction of interrelations among quadrilaterals (squares, rectangles, parallelograms, rhombuses, trapezoids). The pilot study consisted of work with eight primary students operating at van Hiele level 2 (e.g., understanding quadrilaterals without interrelations). We benefitted from the teaching experiment methodology to develop a task sequence applied in a dynamic geometry environment and a paper-pencil environment to help each participant develop quadrilateral hierarchy at van Hiele level 3 (e.g., understanding quadrilaterals with their interrelations). The main study used a case study approach to investigate two primary students’ progress (Efe and Ayla, age 10). After the pre-interviews, each participant was taught the developed task sequence individually during seven up-to-one-hour teaching sessions, followed by a post-interview. This article only details Efe’s case as he worked on developing the relationship between parallelogram and trapezoid. We analyzed Efe’s data (from the pre-interview, Teaching Session-7, and the post-interview) to describe how the different parts of the task sequence fostered his abstraction of the interrelation between parallelogram and trapezoid as he moved from van Hiele Level 2 to 3. This article provides initial evidence for the classification process.