This research aims to examine how the third-grade preservice mathematics teachers learn plane equations in the learning environments created via the GeoGebra dynamic software. In this way, we tried to find out the role of the software in their learning process. Case study method was used and six groups participated in the research, each including two participants with low, intermediate and high levels of success, who were selected by the researchers. The data were collected semi-structured interviews, observation, worksheet and models created by the preservice teachers on the GeoGebra screen and they were analysed in accordance with qualitative data analysis methods. As a result of the research, it was confirmed that the preservice teachers were able to observe the planes and orthogonal vectors much better on the 3D screen of the software. It was also seen that the preservice teachers, who tried to form the equation of a plane parallel to a line passing through two points, were able to shift the points via the dynamic feature of the software and to observe that mixed scalar product of the line directional vector and the vectors on the plane is always zero. Equations of planes were mathematically generalised with the formed structures. It was seen that they had some difficulty as the toolbars did not include the command of vector product but most of them were able to solve the problem through the definition.