In this article we present a case study concerning a simple but efficient technical and logistic concept for the realization of blended teaching of mathematics and its applications in theoretical mechanics that was conceived, tested and implemented at the Department of Civil, Environmental and Mechanical Engineering (DICAM) of the University of Trento, Italy, during the COVID-19 pandemic. The concept foresees traditional blackboard lectures with a reduced number of students physically present in the lecture hall, while the same lectures are simultaneously made available to the remaining students, who cannot be present, via high-quality low-bandwidth online streaming. The case study presented in this paper was implemented in a single University Department and was carried out with a total of n=1011 students and n=68 professors participating in the study. Based on our first key assumption that traditional blackboard lectures, including the gestures and the facial expressions of the professor, are even nowadays still a very efficient and highly appreciated means of teaching mathematics at the university, this paper deliberately does not want to propose a novel pedagogical concept of how to teach mathematics at the undergraduate level, but rather presents a technical concept of how to preserve the quality of traditional blackboard lectures even during the COVID-19 pandemic and how to make them available to the students at home via online streaming with adequate audio and video quality even at low internet bandwidth. The second key assumption of this paper is that the teaching of mathematics is a dynamic creative process that requires the physical presence of students in the lecture hall as audience so that the professor can instantaneously fine-tune the evolution of the lecture according to his/her perception of the level of attention and the facial expressions of the students. The third key assumption of this paper is that students need to have the possibility to interact with each other personally, especially in the first years at the university. We report on the necessary hardware, software and logistics, as well as on the perception of the proposed blended lectures by undergraduate students from civil and environmental engineering at the University of Trento, Italy, compared to traditional lectures and also compared to the pure online lectures that were needed as emergency measure at the beginning of the COVID-19 pandemic. The evaluation of the concept was carried out with the aid of quantitative internet bandwidth measurements, direct comparison of transmitted video signals and a careful analysis of ex ante and ex post online questionnaires sent to students and professors.
Chess, visual memory and geometric transformations
