An investigation into concept image of primary school mathematics pre-service teacher's on the hyperbola

When we see or hear a concept, an image comes to our mind. This situation, though it is the definition of the image, the image that comes to our mind is not the definition.While Tall and Viner(1981) call this image that comes to our head concept image, Davis (1984) names it concept frame. In learning a concept correctly, using the knowladge of notation and the area make it easy to learn similar and related concepts. For example learning the concepts of ellipse correctly simplyfies the learnings on hyperbola. The aim of the study is to define the concept images of primary school mathematics pre-service tachers' in the lesson Analytic Geometry II on hyperbolas. These dialectics that we use to express and explain the life can be wrong or deficient and these are the misconceptions or the basis of misconceptions (Mestre,1987). Defining the concept images of teacher candidates that they grow in the process of their education life and take them to their undergraduation life will set light to their previous learning processes. Besides defining concept images of candidate teachers' on different concepts will help to remediate the misconceptions in their undergraduation process. (Gülkılık, 2008, s. 8). The survey was conducted is a state university's primary school mathematics pre-service undergraduate program by 90 candidate teachers who were on their junior year in 2019-2020 education year. The research design is case study of qualitive researches and clinical interview technique was used in the research. A poll was conducted to 90 undergraduate students in which there were open ended questions, created by the researcher, to determine the concept images on hyperbolas. This poll includes 5 open ended questions. The data aquired from the clinical interwievs, in which participants were choosen by maximum diversity, put to content analysis and primary school mathematics undergraduate students' concept images on hyperbolas were defined. In the light of the answers, we saw that the students have misconceptions and the reasons and the outcomes were assessed. Primary school mathematics undergraduate students' mistakes were also assessed as well as the misconceptions. Candidate teachers'concept images on hyperbolas are %22,2 definition of hyperbola, %60 "equation and shape" and %3,33 relation with conics. How the students can connect the ties between image definition cells and how they can improve their concept images are closely related to the learning experiences and the department they study (Bingölbali and Monaghan, 2008). The results of our research supports this situation. When you elaborate on the answers given to the question "What is hyperbola?" by candidate teachers, %80 in these answers contain concepts about mathematics.