Matematik öğretmenliği öğretmen adaylarının mühendislik tasarımı aktiviteleri ile belirli integrali öğrenmeleri: Bir tasarım deneyi

The aim of the current study is to investigate the pre-service mathematics teachers' developments in the concept images about integral through a design experiments that was designed engineering design process activities. In this design experiment, a sequence of engineering design process activities was developed, tested, and evaluated in a real classroom environment in two cycles. Data were collected from three pre-service mathematics teachers enrolled and attending an elective course at a public university in Ankara during the spring semester of 2017-2018. In the data collection process multiple data collection sources were used. Qualitative methods were used in analyzing the data. On the other hand during the analyzing the data a new method was used which is linkograph. The linkograph enabled researcher to see that what processes students went through while constructing a concept individually and within a group and how they constructed it. In this way, the stages of students' process of reaching mathematically accurate concept images were analyzed in more detail. moreover, thanks to the linkograph, students were visualized where and after which event and which link they made. The data indicated that pre-service mathematics teachers various concept images such as partial-primitive, discrete and a hybrid concept image. In the progress of the design experiment sessions significant improvements were observed in preservice mathematics teachers' concept images about integral. Namely, they developed mathematically accurate concept images about integral. Furthermore, they enriched their concept images about integral. Moreover, engineering design process activities provided them to experience the mathematics in the real life application. By this way their interpretation of the authentic problems and solving them become easier. The data also showed that engineering design process activities promoted pre-service mathematics teachers contextual understanding about integral and its sub-concepts. Keywords: Engineering Design Process, Design- Based Research, Concept Image and Concept Definition, Integral, Mathematics Education