In this paper, the characteristics of an initial training program for secondary school physics and chemistry teachers are presented. This program is based on the resolution of professional problems, in order to develop preservice teachers' competencies for integrating inquiry-based science education (IBSE) into their future teaching. With this goal in mind, the methodology of problem solving as an investigation was introduced, and preservice teachers had to solve a sequence of open-ended problems using this IBSE-type methodology. The article describes how they solved the practical problem "What might happen when two substances are placed in contact with each other?" with a specific focus on the roles of both the students and the professor. Moreover, the paper provides guidelines for implementing the problem, which is compatible with the curricular content of secondary education. Finally, an analysis of preservice teachers' written reports about the problem suggests that the procedures which they found more difficult were those involved in the stages of "design of resolution strategies" and "analysis of results".