Abstract:

Although computers are being increasingly used in education, in our experience there is still some resistance about allowing the use of Computer Algebra Systems (CAS) in assessment in calculus in higher education. One reason commonly stated by teachers is the fear of generalized exam cheating. However, another cause may be the lack of training and confidence about using these systems by the teachers themselves.

We present a case study about the use of GeoGebra in teaching and assessment in two calculus courses. Starting with a course with a small number of students (more precisely, 84 students), the experience was replicated to a course with high number of students (326 students).

Based on these experiments and also on teacher interviews and student surveys, we propose a reflection about the use of CAS in teaching and assessment in calculus. One important aspect of such reflection is the effect of integrating CAS this way from the beginning of calculus teaching on preparation of students for the actual use of mathematics in their future work.

The choice of GeoGebra was not by chance. Some students had already had previous contact with it, it is a free software, and it provides an exam mode, naturally useful in assessment. We discuss the utility of GeoGebra and its limitations, for algebra and graphics, the use of exam mode and the risk of exam cheating using the methodology we describe.

We present some conclusions of this experiment that, although cannot be generalized, can encourage the implementation of a similar methodology in different contexts. One of the most important results of this experiment was the empowerment of students, with less need to ask teachers about solutions to the proposed problems. Widely mentioned by the students was the easiness of visualizing examples and corresponding graphics and a consequent better understanding of concepts.

Finally, we discuss the importance of using CAS not only in teaching, but also in assessment. Comparing this experiment with previous experiments where these systems were used only in teaching, we noticed a greater involvement of the students during classes for using and learning about CAS, as they know they can take advantage of its features during the exams. This way, we do not need to assess student’s knowledge about using CAS and instead of considering it an additional work to be done, they see it as a way to simplify their lives.

Keywords:

Calculus, assessment, CAS, GeoGebra, higher education.