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Context: One of the most relevant tasks of mathematics education is the teaching professional development (TPD) of mathematics teachers. In higher education, it is evident that the type of teaching in mathematics courses for engineering has not been transformed despite the changes that the curriculum has undergone. Objective: To show the design stage of a teaching experiment in relation to professional development programmes for higher education mathematics teachers who teach engineering careers, created under the principles that guide such effective improvements. Design: Through a qualitative approach, we chose the design-based research to design a TPD programme for university teachers who teach mathematics in an Engineering College, whose training is aimed at teachers of basic sciences and mathematics for engineering, attending to the changes required by the 21 st -century teaching. Environment and participants: With the eight principles of effective TPD programmes and the ALaCT process, cycles of reflection are planned to train university teachers. Data collection and analysis: A teaching experiment for effective TPD is designed. This design considers situations created by the experts and those presented by the participating teachers. Results: The situations that the participants face will allow them to have a series of problems for their teaching, with their justifications in the field of mathematics didactics. Conclusions: The different stages of the ALaCT reflection cycle allow the experts to install the reflection in the teachers participating in the experiment. One of the main difficulties was counting on the process of teaching and learning linear algebra problems brought by the participants.