The evaluation of the learning environment designed for improving pre-service mathematics teachers' proving skills

The concept of proof is considered to be the heart of mathematics by many mathematicians and mathematics educators. Traditionally perceived as verifying a mathematical expression, proof has various functions such as explaining, associating, and discovering. Proof is an important phase in the development of mathematical thinking. An individual displays such high-level mental activities through proof as discovering, conjecturing, generalizing, and associating. In a way, all these mental activities included in proof reflect the formation process of mathematical knowledge. However, despite such important roles it plays in learning mathematics, proof is considered to be a difficult activity by most students and pre-service teachers. Previous research also shows that most college students cannot make an absolute sense of concepts related to mathematical proving and are not competent at writing a proof and checking the validity of these proofs. In this regard, it is important to design a learning environment that will allow students to experience the actions existing in the very nature of proof. The purpose of this study is to determine whether the designed learning environment is influential on pre-service mathematics teachers' proving and conjecturing and how it affects their perspectives regarding the roles of proof. To this end, a teaching model that has foundations such as engaging in group work and classroom discussions and using dynamic geometry software and involves activities existing in the very nature of proof was designed and named as Mathematical Proof (ISMAT). Quasi-experimental research method was employed in the study, which was carried on two groups consisting of pre-service primary school mathematics teachers: experimental group and control group. The experimental group members were exposed to a learning environment in which worksheets prepared based on the ISMAT Model were followed whereas the control group members just continued their current teaching process in which no intervention was made in the existing practices. The research data were collected through Proving Achievement Pretest, Proving Achievement Posttest, Conjecturing Test, clinical and semi-structured interviews, field notes, and video records taken in the proving process. The administered tests were evaluated based on the categorical scoring tables developed, and the obtained data were exposed to statistical analyses (Mann-Whitney U test, analysis of covariance, chi-square test). The video records taken in the proving process were analyzed based on a form developed through determination of indicators concerning the behaviors expected at the stages of the ISMAT Model. Moreover, content analysis was made to determine the change in the pre-service teachers' perspectives regarding the roles of proof. It was seen that the learning environment designed based on the ISMAT Model had a positive effect on the pre-service teachers' reasoning and using the mathematical language in the proving process. There was no difference between the groups of preservice teachers in terms of producing conjectures and using mathematical language while expressing conjectures. In addition, the pre-service teachers turned out to have a wider variety of perspectives regarding the roles of proof and evaluated proof in a wider range. Based on the results obtained in the study, recommendations were put forward in regard to the points to be considered by teachers and instructors wishing to conduct lessons by using the ISMAT Model.