Defining and Classifying Skills of Pre-service Secondary School Mathematics Teachers in Quadrilaterals: The Example of Trapezoid

In this study, it is aimed to describe the problems in defining, drawing and hierarchical classification with other quadrilaterals of the concept of trapezoid with their reasons. Among the interactive patterns of the qualitative approach, the case study method was used. The study group consisted of 61 fourth-class pre-service mathematics teachers who were under education in the Department of Secondary School Mathematics Teacher Training of the Faculty of Education in 2016-2017 educational year. As the data collection tool, two information forms including open-ended questions were developed. The content analysis method was used in the data analysis. As a result, it was determined that only 15% of the pre-service teachers made inclusive definition during defining the trapezoid, the rest of them made exclusionary definition or missing or incorrect definition. As the drawings of the pre-service teachers related to the concept of trapezoid were investigated, it was found that most of the pre-service teachers had made prototype drawings like the drawing related to the trapezoid stated in the books without considering the family relationship of trapezoid with other quadrilaterals. Related to the classification of trapezoid with other quadrilaterals, it was noticed that most of the pre-service teachers had a misconception that rectangular and parallelogram were not trapezoid. A considerable number of pre-service teachers were determined to have a misconception about that the unequal quadrangular was trapezoid. It is recommended that at least one side of the parallel state should be emphasized and not to confused with the concept of trapezoid used in daily life during teaching the concept of trapezoid. In addition, except from the prototype drawings of teachers and pre-service teachers, their learning and teaching drawing considering the family relationships of the quadrilaterals has great significance in terms of the students’ acknowledging of the hierarchical structure of the quadrilaterals