In this work we present a study carried out on the implementation of the flipped classroom in a course of Partial Differential Equations (PDEs) of the degree in Mathematics at the University of the Basque Country. We explore how the flipped classroom teaching and learning works in higher education and compare the exam scores and classroom observations with the traditional teaching method used previously in the same subject.

The flipped classroom, also known as the inverted classroom, is a pedagogical model in which the key to its proposal is that the student prepares the theoretical lessons outside the classroom and carries out the practical activities in the classroom. This model has been gaining relevance in recent years due to the need to adapt the learning system to the new generations. However, the PDE course of this study is usually taught in the traditional way, where students primarily listen to lectures and complete exercises on their own outside class time, as are most subjects of the Degree in Mathematics. Therefore, our students are used to the traditional way of learning. Since this course is taught in the final year of the undergraduate degree, the implementation of a new pedagogical model at this point presents its challenges.

One of the major difficulties for implementing the flipped classroom in higher education mathematics is precisely that the students are not used to learning abstract and complex concepts on their own. That is why the PDE course on this study was taught the first half in the traditional way and the second half using inverted classroom. For the second half, after an introductory lesson given by the teacher, the students were invited to learn new PDE solving methods on their own time, by using course notes and slides prepared for the occasion and devote in-class time to problem-solving sessions, interactive discussions and group activities.

We have seen a very positive impact in the exam scores compared to other academic years, where the traditional way of teaching has been applied during the whole course. However, although the engagement level was very high, from the student point of view the perceived understanding was not as desired. Mostly, they felt insecure about the proper understanding of the most complex concepts. Therefore, the implementation of the flipped classroom model in higher level mathematics requires a proper adaptation and a deeper reflection.

Keywords: Higher education, flipped classroom, implementation.