CAVALIERI'S PRINCIPLE THROUGH PROBLEM SOLVING: AN EXPERIMENT WITH TEACHER TRAINING

Abstract

This paper presents an experiment report about a set of activities developed to approach Cavalieri’s principle using the Teaching-Learning-Assessment methodology through Problem Solving. This practice, which was applied to undergraduate students from a mathematics licentiate degree program, proposes the use of concrete materials and dynamic applications in GeoGebra 3D. The research was an exploratory qualitative study, whose experimentation allowed for the identification of the potentialities and caveats of the learning objects employed and their influence on the teaching and learning of Mathematics. With the application of the activities, we noticed the importance of the concrete material for visualization and its use combined with dynamic applications that enable simulating many situations. On the other hand, the students’ lack of experience in working with result approximation in experimental problems caught our attention, clearly pointing the need for more activities with similar situations. Furthermore, it was noticeable that the students were not familiar with Cavalieri’s principle, using the equations with no reflection about their origins. When formalizing, we discussed how that result applies when calculating volumes for many solids, stressing its importance in the training of teachers and showing the possibility of using it in Primary School as well.