Abstract:

Teaching Calculus for 1st year higher education students, in particular those enrolled on Engineering studies, has always been a challenge. Large classes, a variety of students’ profiles and a teaching staff with different personalities, are obstacles that we have to face on coordinating a Calculus course.

Teachers believe students prior knowledge on Mathematics is sufficient for them to understand the subjects that are supposed to be taught in these courses. They also think that their students are ready to undertake a complementary autonomous study, as long as they are given the right resources. However, students’ perspectives don’t seem to get along with teachers’ perceptions.

In this article we present a study carried out with 1st year Calculus students enrolled on two different Engineering degrees, taught by the same teacher. Every week there were two different types of classes of two hours each. One was a “classical” class, where the teacher presented the topics, with slides and examples, usually with some discussion. The other took place in a special room with round tables, where students had some tasks to work in groups and the teacher circulated amongst the groups to clarify the doubts that arose. Each table was given three colored cards (green, yellow and red) similar to traffic lights, so that the teacher could help the groups with more difficulties first.

The Moodle platform was used to deliver the resources needed to accomplish a detailed study of the topics taught, including a “study guide”; videos explaining all the course concepts; a textbook I wrote covering all the course syllabus, with examples, solved exercises and suggested exercises with solutions; worksheets.

By the end of the semester the students were asked to answer a survey regarding their experience on this course, focused on the types of classes and resources available for the study of the curricular unit. The different perspectives of the students enrolled in the two engineering degrees, are somewhat unexpected. Although the access grades for the two engineering degrees are not so different, the answers given differ considerably, which is in line with the students' attitude in class and with the final grades in the course unit.

As a (mathematics) teacher, one of my deepest concerns is that students understand what they are doing and why, so, in my textbooks I always try to explain all the procedures, but to my dismay, students claim for detailed answers to exams or worksheets, which they find are the most useful resources to study.
In this paper we will discuss the results of the survey applied by the end of the semester, and make some considerations on the changes required on the teaching methodology to engage more students on their own learning, but also to develop other skills, such as communication, reasoning, self-confidence, and essentially how to break with the paradigm of rote and procedural learning.

Keywords:

Mathematics, Calculus, Rote learning, Procedural learning, Meaningful Learning.