Evaluation of the learning environment designed basing on using analytical, synthetic and vectorial approaches together

It is approved that geometry problems which are used during the process of developing students' problem solving skills that is among the objectives of geometry education, can be handled with different ways. The solution of these problems can be done by using Euclidian geometry as well as using analytical plane and vectorials. This situation proves that various approaches can be use in geometry. Within the scope of the study, the geometry class instructed synthetic geometry oriented in the secondary school mathematics teaching program was designed basing on using analytical approach, synthetic approach and vectorial approach together, and it was aimed to find out what kind of differences this designed geometry lesson created on the problem solving process of prospective secondary school mathematics teachers. In line with this purpose, this study designed as quasi experimental study was carried out with 20 experimental group and 21 control group prospective teachers. While prospective teachers in the experimental group were provided experience during the geometry lessons that were designed according to different approaches, the prospective teachers in the control group were involved in the geometry classes instructed with synthetic based approach. Before and after the 10 weeks practices, prospective teachers were administered tests whose validity and reliability were investigated: a test for using different types of approaches and a test for determining their approach preferences. These tests were evaluated with the scoring key adapted within the scope of the study. Before and after the application, clinical interviews were carried out with totally 6 each prospective teachers from the experimental group chosen from different success levels that formed in accordance with the points which were gotten from the tests. It was established that according to the findings obtained from the research, the designed geometry lesson has a positive effect on the success of experimental group prospective teachers in all of the approaches they used during the problem solving process. While it was proven that the most preferred approach by the experimental and control group before and after the application was synthetic approach, there was an increase in the rate of preferring analytical and vectorial approaches for problem solving in the experimental group before and after the application. Regarding these results, the study was completed with the suggestions for using different approaches in geometry teaching and for future studies. Key Words: Geometry Teaching, Analytical Approach, Synthetic Approach, Vectorial Approach, Problem Solving.