A comparison between strategies applied by mathematicians and mathematics teachers to solve a problem

This study analyses the results obtained from comparing the paths shown by expert mathematicians on the one hand and mathematics teachers on the other, when addressing a hypothetical problem that requires the construction of a mathematical model. The research was conducted with a qualitative approach, applying a case study which involved a group of mathematics teachers and three experts from different mathematical areas. The results show that the process of constructing a mathematical model differs between these two groups mainly by the type of cognitive processes developed. It was observed that the modelling routes depended on the graphical representations used by the individuals to address the problem. The mental model related to the situation plays an important role in the externalisations of the participants.