An approach to teach Calculus/Mathematical Analysis (for engineering students) using computers and active learning – its conception, development of materials and evaluation

Dissertação para obtenção do Grau de Doutor em Ciências da Educação

This thesis reports a new approach to the teaching of Mathematical Analysis 1/ Calculus (AM1) to students of engineering, applying results of research on the use of computers and active learning with the aim of enhancing understanding. The main goal of the new approach is to reduce the known problem of failure and superficial understanding in introductory college mathematics in Portugal (and other countries). This researcher created the approach named ActivMathComp where: - Students are active and collaborate with colleagues during classes; - Computer is embedded as a communication, interaction and computational tool; - Students use interactive digital learning documents; - Students explore concepts in order to develop a deep understanding of them; - Students contact with mathematical applications; - Students have frequent short quizzes with immediate feedback on a Learning Management System; - The teacher/student relationship is grounded on trust, on mutual understanding and on students’ involvement on their own learning. The interactive digital documents were created assuming principles such as the zone of proximal development and multiple representations. Towards its comparison with the traditional approach, the ActivMathComp was implemented in a group of 16 AM1 students at the Civil Engineering Undergraduate Program of the Instituto Superior de Engenharia de Lisboa. The participants freely chose to enrol in the group and were required to bring their own laptop to classes. Took place a quasi-experiment where all the other seven classes following AM1 were taken as a comparison group. The participating students got significantly higher grades than the other students and had a higher success rate. Data gathered from questionnaires and tests were screened to identify possible bias. The participating students evaluated ActivMathComp as highly positive in nearly all aspects.