Epistemological, Historical, and Didactic Aspects of University Teaching Faculty Professional Knowledge of Probability

摘要

Educational research has highlighted the need for further research into the knowledge base of university teaching faculty, which needs to go beyond a mere familiarity with mathematical content. What is termed University Teaching Faculty Professional Knowledge would include aspects related to the current teaching of the discipline, such as the perspectives of teachers, the history and difficulties encountered by students, etc. This work addresses the following research topics: professional knowledge of Probability of the teaching staff; Epistemology and History of Probability Theory; and Didactics of Probability Theory. The focus of this study is firstly to address the problem of identifying the constituents of this Professional Knowledge which will be useful to university teaching faculty delivering lessons of Probability Theory in order to design teaching-learning sequences; and secondly, we look into what extent these constituents are taken into account in university teaching. We conduct a phenomenological analysis of Probability Theory, including historical phenomenology, and we study teaching proposals of a group of university teaching faculty of engineering studies by means of a written questionnaire and face-to-face interviews. Our analysis identifies the following aspects which should be part of Professional Expertise: setting out scenarios to introduce concepts; discussing various conceptual formulations of Probability and its historical problems; the implications for Science, Technology and Society for raising the interest level of students; and taking into account students' alternative conceptualizations. The study of the teaching proposals reveals that these constituents are lacking in the Professional Knowledge of the teaching faculty studied, which shows the need for training programs that take account of research-based evidence on the Mathematics Education.