An Exploration of the Padovan Sequence in a Mathematics Degree Course

Abstract

The article reports a teaching experience using the Didactic Engineering (DE) methodology applied to the teaching and exploration of the Padovan Sequence. This experiment was conducted in a Mathematics undergraduate class in Ceará-Brazil and has the participation of five students. A questionnaire containing three problem situations was elaborated, from which the resolutions of these teachers information were analyzed. Specifically, it was investigated, from basic concepts related to this sequence, the Binet formula, generating function and construction of the recurrence formula. This fact occurred in the experimentation phase of DE, being complimented, in this phase, with a teaching methodology (Theory of Didactic Situations - TSD). In the other phases, the collected data is discussed, and thus an internal validation of this research is performed. It can be noted that the students had difficulties conjecturing their arguments formulated in the early stages. The teacher then becomes responsible for mediating these discussions, mediating the students to demonstrate and validate these mathematical concepts.