Pre-service middle school mathematics teachers’ understanding of quadrilaterals through the definitions and their relationships

Öztoprakçı, Seçil
The purpose of this study was to examine pre-service mathematics teachers’ cognitive progress in constructing and evaluating quadrilateral definitions and the corresponding quadrilateral hierarchies under the support of the Geometer’s Sketchpad learning activities. The study employed qualitative case study design of which data was collected from 5 pre-service middle school mathematics teachers during the spring semester of 2010-2011. The main data came from one-to-one clinical interview sessions assisted with Geometer’s Sketchpad learning environment; and all sessions were hold in the Human-Computer Interaction Laboratory. The findings revealed that the Geometer’s Sketchpad supported learning tool developed in the light of related literature was effective to large extent in improving the pre-service teachers’ thinking process of identifying the critical defining properties of quadrilaterals, evaluating the mathematical value of a definition, comprehending the relations between quadrilaterals, and constructing hierarchical classification of quadrilaterals. These findings implied that Geometer’s Sketchpad assisted tasks which combined definitions, examples and figure constructions were effective enabling pre-service teachers to the definition construction process after several experiences with the concept, through which learners were able to construct meaningful geometric concept perceptions. Learning the availability of many different ways of defining a geometrical concept and discovering many different ways of classification through these definitions increased pre-service teachers’ awareness of geometrical relations between concepts. So, the developed learning material is expected to fill the gap in teacher education programs in order to handle teachers’ difficulties with concept definitions.