The evaluation of the learning environment designed for improve the geometric habits of mind of mathematic pre-service teachers

From the beginning of the humanity, people have tried to know their surroundings and keep up with the changing living conditions, which direct them to use the geometry. While geometry was used for the daily needs at the beginning, this purpose changed to increase the intellectual fund of knowledge. In this stage, human being has faced many problems. In order to solve those problems, people started to use some habits of mind such as reasoning with relationship, balancing exploration and reflection, think about the special case and generalize them, investigating the invariants. This case revealed that habits of mind should be in an important place in the geometry curriculum. The purpose of this study was to reveal the contribution of a learning environment designed centering the problem solving on the improvement of the geometric habits of mind of the pre-service teachers. In other words, designed learning environment is evaluated in the context of geometric habits of mind. In order to fulfill this purpose, habits of mind based learning environment was created by redesigning the geometry class, which is given to the bachelor degree students in the context of activities and problems that include geometric habits of mind. In the implementation process, geometric habits of mind was given by embedding the different problems through the first 4 weeks, in the next 6 weeks, they are given based on the holistic approach. In this way, with the first approach, students were made aware of those habits and learnt only one habit, with the second approach, more than one habits came into prominence. This study in which mixed method were used was conducted with 32 freshman pre-service elementary mathematics teachers. Data wer research was gathered by the pre-test and post-test problems developed by the researcher that include geometric habits of mind, belief scale for the geometric habits of mind during the problem solving process, homework problems given weekly and clinical interviews. How the learning environment developed for this research plays role on the geometric habits of mind of the pre-service teachers is tried to be revealed by pre and posttests questions, homework problems, activities during the process, observation data during the implementation and researcher field notes and clinical interviews with pre-service teachers. Qualitative data of the research were analyzed via WINSTEPS and SPSS analyze programs and were presented as statistics of the pre and posttest, linear individual scores, statistical analyzes (related t-test) done with linear scores, person-item map, item-person map, graphs of the geometric habits of mind used in the pre and posttest. In the result of this study, it is observed that geometric habits of mind of the pre-service teachers at the end of the treatment are more developed than geometric habits of mind of the pre-service teachers in the beginning. Besides, pre-service teachers started to think more dynamical in the geometry problems, within this scope; it is revealed that pre-service teachers try different strategies when they could not solve the problem. It came out with result of this study that pre-service teachers use indicator of "come up with a right answer by proportioning two or more geometric shape" within the logical framework", indicator of "in order to explain the general case in the problems, start with the special case and generalize it" within the habit of generalizing the geometric ideas by using special cases, indicator of "think a case in the problem dynamically in such a way that do not break the conditions of the problem" within the investigating the invariants and indicator of "make an additional drawing that could help the solution of the problem" within the balancing exploration and reflection. In accordance with the results of this research, it is suggested that indicators should be focused while evaluating the geometric habits of mind. Besides, according to those results, some suggestions related to teaching the geometric habits of mind and the future research about this topic were made.