Introducing eigenspaces: semiotic analysis and didactic engineering

This paper reports part of the author’s PhD research, that focuses on eigentheory teaching and learning processes. We describe how the results of a pilot study, based on multimodal semiotic analysis, together with a broader epistemological, didactical and ecological analysis of the mathematical knowledge at stake and the learning context have informed the conception and a priori analysis of activities and methodologies designed within the didactic engineering methodology. These activities have been designed by the author and the teacher of a linear algebra course, with a high number of class attendees, offered in a mechanical engineering degree program in a public University in Italy. We report the multimodal analysis of a fragment of students’ activity during the course implementation, to validate the hypotheses guiding their design.