Designing active Maths for undergraduate STEAM students

This work presents a set of student-centred activities that may help undergraduate students understand mathematics in their first year of a STEAM degree. In particular, the authors refer to the difficulties students meet in making connections between syntactic and semantic dimensions in learning mathematics, especially in Linear Algebra topics. The specific goal of this paper is to present and discuss how it can work in the case of linear transformations. This topic stands in the middle of every Linear Algebra standard course and is pivotal in many recent applications, such as computer graphics. The study describes the teaching-learning experience and reports the results of the first pilot study, which involves about 100 undergraduate Architecture students of Politecnico di Milano. One of the peculiarities of this work is its context since the class is composed of heterogeneous group of students, in terms of knowledge background and attitudes towards mathematics. The main findings of this paper are underlining how a student-centred strategy, based on asynchronous activities and synchronous class discussion, allows misconceptions to emerge and be appropriately addressed.