Evaluation of the effectiveness of dynamic geometry software on pre-service teachers and teachers' skills in making nonverbal proofs

This research was carried out to evaluate the effectiveness of a training program designed to improve proof skills with the dynamic geometry software GeoGebra on nonverbal proof making skills of mathematics teachers and pre-service teachers and to reveal the opinions of the participants about this training process. Due to the use of various quantitative and qualitative data collection tools in the research, the sequential explanatory method, one of the mixed research method, was used. The study was carried out with a total of 41 participants, including 35 third-year mathematics teacher candidates studying in Primary School Mathematics Teaching at a state university in a state university in the Central Black Sea Region in the 2019-2020 academic year, and 6 mathematics teachers doing a master's degree in Mathematics Education. First of all, a five-week GeoGebra nonverbal proof skills development training was conducted with the participants. Then, 9 participants were selected among the participants by criterion sampling method and the study group was formed. The data of the research consisted of the answers given by the participants to the proof skill test, the camera recordings taken during the GeoGebra training process, the evaluation forms and the interviews made by taking the audio recordings. In this study, the triangulation method was used because it was thought that supporting the quantitative findings with qualitative findings would be more effective in making sense of the results. As a result of the quantitative findings of the study, a significant difference was found between the pre-tests and post-tests of the participants in favor of the post-test. For this reason, it is possible to say that a training program designed to develop proof skills with GeoGebra, a dynamic geometry software, supports the development of nonverbal proof skills of mathematics teachers and teacher candidates. In addition, it was concluded that this training program, which was designed to develop proof skills with GeoGebra, improved the proof skills of mathematics teachers statistically significantly more than the proof skills of prospective teachers. A case study was used in the qualitative data of the study. According to the findings that emerged from the qualitative data of the research, it was seen that the participants' opinions about the training on developing non-verbal proof skills with GeoGebra were generally positive, that the proofs in these activities could be observed on the program and that these activities were remarkable, dynamic, practical and suitable for sensitive measurements. It was observed that the participants explained the effects of the activities performed in GeoGebra dynamic geometry software on cognitive skills such as establishing relationships, keeping in mind, making sense, visualizing, concretizing, and on the ability to prove on affective skills such as learning with pleasure, learning with fun. As a result, it is recommended to develop students' nonverbal proof skills with GeoGebra dynamic geometry software in mathematics education. Keywords: Mathematical Proof, Proofs Withouts Words, Visualization, Dynamic Geometry Software, GeoGebra