Sometimes mathematics is different - studies on mathematical practices in electrical engineering

Abstract

The six studies collected in this thesis deal with praxeological analyses of mathematical practices in a Signal Transmission module of an electrical engineering study programme. The research framework is the Anthropological Theory of the Didactic (ATD). Our analyses concern the introduction of the Dirac delta impulse in textbooks on signals and systems, the lecturer’s sample solution to an exercise on the envelope demodulator, and the lecturer’s sample solution and the students’ solutions to an exercise on amplitude modulation. Three research foci are developed in the collected studies. The first focus is The subject-specific reconstruction of mathematical practices (Hochmuth & Peters, 2021; Peters & Hochmuth, 2021). We analyse two exercises and the corresponding sample solutions given by the lecturer and students’ solutions. Based on methodological developments we were able to reconstruct aspects of two different mathematical discourses as well as how they interact within the analysed practices. We also propose a graphical representation of the results of our analyses. The second focus is The epistemological and philosophical relationship between mathematics and electrical engineering (Hochmuth & Peters, 2020, 2022). Our aim is to gain a better understanding of the mathematical practices involved in the introduction of the Dirac delta impulse in a textbook on signals and systems. We realised that certain mathematical steps could be better understood from an engineering point of view if historical-philosophical studies of the relationship between physics and mathematics were also taken into account. Here, we are not referring to the philosophical positions of students or lecturers. We are referring to philosophical studies that focus on the societal aspects that play a role in the historical concrete formation of practices. The case of the Dirac impulse is well suited to illustrate the fruitfulness of such studies for subject-specific analyses. Finally, the third focus is Revisiting the relationship between mathematics and electrical engineering, on how ideas for the development of teaching can be derived from the other two perspectives (Peters, 2022; Peters & Hochmuth, 2022). Looking back at our previous studies, we show how our research findings allow for a conceptualisation of the relationship between mathematics and engineering that differs from the standard application and modelling approaches. We also focus on the phenomenon of disconnectedness of the mathematical practices in mathematics service courses and engineering courses.Based on our analyses of engineering mathematical practices, we develop the idea of modifying exercises from a mathematics service course. The key feature of this approach is that it is an alternative to the usual approaches that propose the use of engineering application examples or the use of modelling tasks.