An investigating of the reasonsof middle school mathematics teachers' use of examples for irrational numbers

This study conducted with 16 mathematics teachers working in Kocaeli province in order to determine the types of examples used by middle school mathematics teachers to teach the concept of irrational numbers and their purposes. The study utilized the qualitative research method of case study. Data for the study were collected through semi-structured interviews and classroom observations. The types of examples used by teachers were analyzed with respect to representation type and example type. It was observed that teachers preferred generic examples when teaching the concept of irrational numbers, with very few teachers using non-example examples, and counter examples being used by only one teacher. When examples were examined in terms of representational type, it was determined that opaque representations were preferred more than transparent representations. Additionally, it was found in the interviews that teachers' choice of examples was significantly influenced by auxiliary resources, their digital applications, the academic achievement level of the class, and the High School Transition Exam (LGS). While teachers stated that they mostly used examples to prevent misconceptions, they also frequently used them to concretize abstract concepts, demonstrate differences between concepts, reinforce what was taught, and recall past knowledge. A small number of teachers listed their purposes for using examples as showing exceptional situations, encouraging generalizations, or establishing connections with everyday life. Observations indicated that teachers frequently used examples and generally obtained them from a single source. Furthermore, teachers mentioned that they predetermined the examples they would use.