Abstract:

Engineering students in the first year of mathematics find solids of revolution in the syllabus of integral calculus subjects in R. A solid of revolution is created by rotating a planar region around a line. The integration can be used to find the area, volume and arc length. However, visualizing and defined the planar areas and the solids of revolution is often difficult for students, or even for teachers to explain. Some teaching experiences indicate that most students have difficulty to solving problems with integrals. In this context, the need arose to find alternative forms of teaching/learning that allow the student to visualize these solids. Thus, STEM (Science, technology, engineering and mathematics) education was integrated to teach solids of revolution. Information technologies such as Geogebra, the graphing calculator and Computer Algebra System (CAS) were used, providing an opportunity for students to improve their knowledge and competencies in an intuitive and visual way. With Geogebra it was possible to create a dynamic geometry environment, where real objects were modelled by adjusted one or more functions, allowed an excellent resource for the study of solids of revolution. With a graphing calculator and CAS (Computer Algebra System), students can calculate and visualize the volume of solids of revolution represented in Geogebra.

This paper describes the study carried out with students of the first year of the Electrotechnical Engineering degree, at the Coimbra Institute of Engineering, in Mathematical course unit. The study was developed in the first semester of the academic year 2019/2020, as a way to improve students’ knowledge in applications of integral calculus to areas, volumes and arc lengths. The combination of teaching mathematics with the use of information technologies provides the ideal context in which students can build the studied models. The involvement of students in modelling a real object can stimulate creativity, facilitating the formation of connections between the knowledge acquired in various study disciplines. With CAS and Geogebra students use simultaneously a computer algebra system and an interactive geometric system, thus increasing their cognitive skills in the best way. Based on the results obtained, it is possible to state that GeoGebra, graphing calculator and CAS are effective assistance tools in understanding the mathematical specificities related to the concept of Differential and Integral Calculus applied to calculate the area, volume and arc lengths of the solids of revolution. With this study, it was concluded that STEM activities enrich teaching and learning practices, transmitting the syllabus in a more targeted and precise manner, improving motivation and stimulation of knowledge in mathematics. When using mathematical modelling as pedagogical alternatives, students are involved in the elaboration and resolution of problems that, in general, originate outside of mathematics. In the future, more projects will be developed covering even more topics and program content to take advantage of STEM learning mathematics in several different ways.

Keywords:

STEM, teaching strategies, significant learning, information technology, mathematics, Engineering.