Abstract

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 21st-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. The cognitive view in educational psychology is considered one of the traditional perspectives for psychologists, who recognize that students may have different but identifiable conceptions of learning. The work aimed to compare initial conceptions of statistical modeling processes and levels of statistical reasoning in engineering students. The research had a qualitative approach with a multiple-case design. As a source of data collection, a questionnaire was designed and applied to 38 students taking the subject Probability and Statistics. The results and data analysis showed that none of the participants went through all the phases of statistical modeling, evidencing a low ability to establish relationships in the data and interconnect statistical concepts. Consequently, the students failed to reach the maximum level of statistical reasoning. The participants also identified difficulties in establishing coherent interpretations when making representations of statistical models such as frequency tables, graphs and measures of central tendency. Therefore, there is a need to continue developing research that provides theoretical foundations for the characterization of the modeling and statistical reasoning processes to improve the learning of statistics and probability in university students.