Mathematical understanding in problem solving with GeoGebra: a case study in initial teacher education

The initial training of mathematics teachers in Spain can start in the final year of the mathematics degree when the students, and future teachers, select courses related to teaching the discipline. At that time, since over the next two years they will probably be certified to enter the profession, it is worth asking oneself what mathematical knowledge they should have and what is needed to teach at the secondary education level. This paper describes one case study in which a group of final-year students solves a task containing aspects of mathematical understanding that are present in solving problems using GeoGebra. This was done using a solution protocol intended to emphasize the different possibilities offered by GeoGebra, presenting three approaches for the solution: dynamic, numeric and algebraic. We noticed that the use of technology is key to bringing out some of aspect and to demonstrating an understanding of mathematics for teaching.