Prospective Mathematics Teachers' Ways of Guiding High School Students in GeoGebra-Supported Inquiry Tasks

In this paper, we study how prospective teachers guide students' reasoning in GeoGebra-supported inquiry tasks. Twenty prospective mathematics teachers wrote about how they would react as a teacher in hypothetical situations where high school students present their GeoGebra-supported solutions to the teacher. Before writing their reactions, the prospective teachers investigated the GeoGebra files involved in these situations. We analysed if they tried to draw the students' attention to particular essential aspects, and whether they activated the students to investigate these or revealed the solutions of the potential investigations themselves. We found that the respondents had difficulties in guiding the students to justify their observations, in reacting to trial and error solution methods and in elaborating on unexpected potentially productive ideas. We noticed three levels of the prospective teachers' guidance of students: surface-level guidance, inactivating guidance and activating guidance.