Quadrilateral definitions and classifications of mathematics teachers

Purpose: The aim of this study is to examine the definitions and classifications of special quadrilaterals that mathematics teachers created as a result of mathematical discussions based on the criteria of being definitions. Method: The research was qualitative and a case study pattern was used. While the study was carried out with a total of nine mathematics teachers working at the se-condary or high school level, the data were collected through focus group discussions. Deductive content analysis was performed to analyze the collected data. Coding proces-ses were conducted by two coders and Miles and Huberman reliability test were applied to ensure validity. Data triangulation and participant confirmation were made. Results: As a result of the related analyzes, it was observed that the participants generally made definitions that fit the economic definition criteria in the context of qu-adrilaterals other than deltoids and trapezoids. On the other hand, it produced erroneous definitions of the participants' deltoid and trapezoidal definitions that did not comply with various definition criteria. In addition, it was observed that the teachers were not sure of the accuracy of the answers they gave about the place of trapezoid and deltoid in hierarchical classifications. While defining rectangle and square, in some definitions they sadisfied the necessary conditions but failed to satisfy the sufficient conditions. Higher conceptual definitions of special quadrilaterals have been largely uneconomical. In the hierarchical classification models of special quadrilaterals, except for one group, the correct answers were obtained through group discussions. Conclusion and Suggestions: In the results, it was observed that both middle school and high school mathematics teachers had knowledge about the hierarchical clas-sification of quadrilaterals at the beginning of the interviews. When the definitions for special quadrilaterals were examined during the research process, deltoid and isosceles trapezoid were the quadrilaterals in which the participants made the most mistakes. It is thought that the definitions made by adhering to the prototype drawings cause errors. It was observed that secondary school teachers produced more than one alternative defini-tion. It was determined that the participants frequently focused on angle and edge pro-perties, and thought less on diagonal and symmetry properties while producing definiti-ons of special quadrilaterals. Based on these results, it is thought that written and visual resources can be pre-pared to support the reasoning processes of mathematics teachers about defining special quadrilaterals and creating their hierarchical classification. It is also recommended to carry out practical professional development studies in order to increase the aforementi-oned skills. Keywords: Special Quadrilaterals, Definition Criteria, Classification Of Quadri-laterals, Economic Definition, Mathematic Teachers