Investigation of the visual reasoning process of the pre-service mathematics teachers

In recent years, the idea that visual reasoning provides a nourishing environment for the learner to understand mathematical concepts has been emphasized by many researchers. To utilize this notion in the field of education, it is expected that teachers should be aware of the importance of visual reasoning as they help students to develop skills regarding it. Therefore, this presented research aims to explore the visual reasoning process of pre-service mathematics teachers to contribute this goal.The research was carried out with three pre-service mathematics teachers. Data were collected in two sessions where teachers were ask to tackle four visual proofs three of which required operative mathematical explanations while the remaining one required pre-service teachers to explain their proofs verbally. To determine the visual reasoning process of these pre-service teachers, the data acquired in this research were analyzed by using grounded theory techniques.The results of the research show that pre-service mathematics teachers encounter several challenges related to perceiving visual proofs and following procedures that they developed and gaining awareness regarding the reached conclusions. In addition, the results revealed that pre-service mathematics teachers have a tendency to prefer algebraic proofs over visual proofs and in some cases they switch between focusing the visual proofs and straying away from them during the solution processes. Nevertheless research results suggest that their solutions on visual proofs are not spontaneous and they create strategies on figures and their solutions.