Effective learning in mathematics

Effective Learning is seen in the contemporary context as having the following important features: knowledge base in society is increasing rapidly; the “sage on stage” approach is no longer an option; and there is a wider range of processes to generate knowledge. Moreover, employment prospects relate more to the ability to enhance and transfer learning. This research was conducted at University of Aveiro, with a class of 40 mathematics students from first academic year/semester. The course followed an Inquiry-based learning (IBL) approach with both formal and informal assessment as learning progresses along the learning continuum, encouraging teamwork, researching, and improving learning through portfolios. Moreover, to improve mathematical knowledge and skills, collaborative work habits were encouraged as well as using computational tools to study and investigate in mathematics. In this paper, we describe the methodology and present results of the assessment of skills, students’ attitudes, and knowledge as a qualitative study. This was a first IBL experience in the mathematics department, with appropriate conditions, namely a room with several blackboards and round tables, in opposition to the classic teacher centered environment, and with online platforms like MS Teams, allowing effective interaction of students and peer learning. The construction of portfolios, a rare occurrence in mathematics higher education, made it possible to follow students’ evolution from the beginning to the end of the semester, proving to be a fundamental tool for effective learning. About 95% of students appreciated this practice. Compared to other analogous courses, the results of skills and knowledge assessment were positive. A questionnaire and interviews at the end of the semester were applied to collect data about student’s evaluation of the course. Results showed that this methodology increases motivation and improves students' working skills, engaging them in individual and collaborative learning of mathematical topics that are the core of the course, and improving their scientific writing skills while, at the same time, developing critical thinking. The data we collected also show students' preference for this methodology when compared to traditional methods widely used in mathematics teaching.publishe