In this paper, we describe an activity carried out with mathematics teachers of high school. The general objectives are: on the one hand, to include a stage of programming in the process of solving problems, emphasising the importance of discrete mathematics and logic to the training of all students. On the other hand, opening possibilities of introducing basic knowledge of programming into schools, an issue with high impact in higher education in computing. Finally, to introduce a functional language -MateFun- as a tool for achieving the said goals. The activity is organised in two parts: in the first one teachers are taught to program solutions to problems taken from their courses in MateFun; in the second part, the teachers choose a subject and design didactic instances of teaching it to their students using MateFun. In this way, the learning of programming is naturally presented to students as part of the mathematics course, integrating theoretical and empirical foundations of the concepts.