Designing Maths Interactive Lessons

In this article, we report a set of student-centred lessons that may inspire higher education teachers to structure interactive lessons for first-year Maths courses in Science, Technology, Engineering, Arts and Maths (STEAM) programs. In particular, we want to address difficulties first year students often meet when making connections between syntactic and semantic dimensions in learning mathematical concepts, especially in Linear Algebra topics. The specific goal of this paper is to present and discuss how a teacher can make it work in the particular, but relevant, case of a linear transformation. This topic is a pivotal subject in every Linear Algebra standard course and has many recent applications, such as computer graphics. We describe the teaching-learning experience and the results of the first pilot study, which has involved circa 100 undergraduate Architecture students from Politecnico di Milano. The group of students is heterogeneous, both in terms of knowledge background and attitudes towards Maths, which makes the lesson design challenging. The main findings of this article, together with a previous one on the planned activities, underline how a student-centred strategy, based on asynchronous activities and synchronous class discussion, allows misconceptions to emerge and be addressed immediately.