The physical and digital game “Trilha do Resto” in understanding the Divisibility Criteria from the perspective of undergraduate Mathematics students

Abstract

The objective of this study is to investigate how undergraduate Mathematics students formalize the Divisibility Rules for Natural numbers by 2, 3, 5, 7, 9 and 11, with the mediation of a playful resource. To do this, we are based on a qualitative research approach. Regarding the instruments for data collection, a questionnaire with open and closed questions was used, as well as observation of the students' actions during the experience of the mini-course entitled “The physical and digital game 'Rest Trail ' and the institutionalization of the concept of multiples and divisors of a natural number”. This mini-course took place at a Federal Public University and was divided into two distinct moments: in the first moment we addressed the digital game and in the second moment the physical game, as well as the process of institutionalizing the divisibility rules. To analyze the results, the concept of multiples and divisors of a natural number was formalization and we delved deeper into the definition of the divisibility rules by 2, 3, 5, 7 and 9. The results demonstrated that the students, when reflecting on the Divisibility Rules from a playful resource, associated them with the way it is presented in Basic Education, not linking it to the way it is treated in the context of Number Theory in Higher Education. Furthermore, they were also able to reflect on the need to diversify methodological approaches in Basic Education and on the use of play in teaching Mathematics.