An investigation into the effect the concept image of primary school mathematics pre-service teachers' on the teaching plant and line in three dimensional Euclidean spaces

Concepts; they enable to presenting event, object, naming ideas, express with symbols, give meaning and presentaiton. The concept image is the projection of these concepts to people's minds, that is, all the pictures, events, thoughts that come to life about the concept in the mind of people. Researchers Tall and Vinner, who introduced the concept definition and concept image structure for the first time in 1981, stated that the concept definition is the whole word used to indicate the current concept, and the concept image is used to express all the cognitive structures mentioned with the concept. Tall and Vinner (1981) argued that during the cognitive processes of remembering and manipulating a concept, a number of related processes were introduced that, either consciously or unconsciously, affect semantics and usage patterns. It would be appropriate to define the concept image for the total cognitive construction consisting of a combination of all cognitive visuals, concept-related features and processes that affect the concept consciously or unconsciously. We encounter the concept image structure in many areas. In the field of mathematics, which is our field of study, the concept image has a great importance in the analysis of students' ability to generate mathematical ideas. The concept image examines the structural features of mathematical theories and provides depth in this regard. In the thesis study, it is aimed to examine the teaching of plane and correct subjects in the three dimensional Euclidean space of primary school mathematics teaching undergraduate students in the light of concept image. Investigating the concept images of plane and correct subjects in three-dimensional Euclidean space of undergraduate students with different levels forms the basis of the research and thus, it is thought that the data obtained will contribute to the studies in the related field. Euclidean geometry, which is the subject of the study, is an area that we have encountered in our formal and informal education since primary school. The undergraduate level of the research we conducted to examine this field within the framework of the concept image was determined as the 3rd grade of primary school mathematics teaching. The thesis study was carried out in a state university of Izmir province in the 2019-2020 academic year. In the study, firstly, concept images of plane and line subjects were determined in three dimensional Euclidean space of undergraduate students. Then, in the three dimensional Euclidean space, semi-structured clinical interviews were conducted with students selected at different levels among the undergraduate students whose concept images related to plane and line subjects were examined. The pattern of the thesis study is a case study model, which is one of the qualitative research methods. In the thesis study, 6 open-ended questions were created by the researcher to determine the concept images of undergraduate students by taking expert opinions. 6 open-ended questions were asked to determine the concept images related to plane and plane subjects in the three-dimensional Euclidean space developed by the researcher to 80 elementary mathematics teaching 3rd grade undergraduate students determined by the appropriate sampling method, one of the non-random sampling methods. Afterwards, the answers of 80 undergraduate students, where open-ended questions were applied, were evaluated by applying Rubrik. Based on the results obtained in the study conducted on 80 people according to the rubric scoring key, 4 low (2 girls, 2 boys), 4 medium (2 girls, 2 boys) 4 good level with maximum diversity sampling semi-structured clinical interviews were conducted with 12 undergraduate students selected as good (2 female, 2 male). In semi-structured interviews, each student was subjected to a separate interview process. The interviews were recorded on video, and the parts deemed necessary by the researcher were recorded with written documents. At the end of our study, where we provided diversification using multiple data collection methods (Open-ended questions, semi-structured interview), all data obtained were analyzed in depth with content analysis, which is one of the qualitative data analysis methods. In our study, all four students who were at a good level in the open-ended question involving problem solving and solving were all scored full (3). Except for one student, there are no students who can pass a low level score. There is no such scoring in another open-ended question. Problem posing and solving skills have a decisive role between good level and low-level students' problem solving and solving skills in third grade undergraduate mathematics teachers. In addition, male students at the middle level get full points from the problem posing question; female students were able to get 1 point in total as 1 and 0 points. This situation shows that male students at intermediate level are better in terms of problem solving and solving than middle level female students in this study. The highest score in the study was obtained from the 3rd and 4th open-ended questions. The common feature of these open-ended questions is that they can be associated with daily life and are able to think in concrete terms. It shows that the reflection of concept images on the plane drawing is visibly affected compared to the students at the middle and good level. The best suggestion for this situation is to integrate the formal definitions used for teaching mathematics and geometry with daily life and to create a concept image with experience and experiences. Keywords: Consept, Concept Image, Euclidean Space, Line, Plane