Abstract:

The students' ability to understand calculus has been a cause for ongoing concern from teachers. They are often enclosed in a structured way of thinking, which represents an obstacle to understand those concepts. That is a consequence of a historical mathematical formalism that rejected other forms of semiotic representation (example: visual) as a demonstration and analysis tool.

In the context of Basic Sciences Department of our University, the teaching of abstract concepts and their application in Engineering have always been an important pedagogical challenge. Fortunately, new virtual teaching forms and computational mathematic advances generated possibilities to develop new working styles and implement alternative teaching-learning methodologies.

This paper deals with an adjustment of the teaching methodology for Mathematical Analysis I (MA-I) course, from a competence-based and interactive perspective among different disciplinary areas, in order to appropriate abstract concepts and relate them with meaningful and motivational activities. This pedagogical proposal, applied on the teaching of calculus with the introduction of thermodynamic concepts, allows to rethought and strengthen the interaction among different disciplinary areas, articulating with elements of physics, chemistry, probability and statistics (Joule experiment, behavior analysis of macro/microscopic physical systems, etc.). To carry it out, didactical strategies based in computer assisted learning (CAL) are articulated with intensive laboratory activities, without neglecting the rigorousness of the theoretical foundation.

An extracurricular workshop with this didactical proposal carried out with MA-I students is presented. It consisted of three modules, starting with an epistemological analysis of historical becoming of entropy concept and its interdisciplinary “incursion”. Then, from the ideal gases properties as a guide, function and limit concepts were developed, and evoking the Carnot cycle, the integral calculus’ was introduced. At the end of the workshop, students expressed their thoughts and suggestions about that experience.

This methodological proposal allowed valuating an innovative form of co-working teaching, promoting a theory-practical-technological integration.

Keywords:

Computational mathematics, competencies, thermodynamics, calculus, teaching strategies.