El estudio de los frisos como estrategia didáctica para la enseñanza y aprendizaje de los conceptos de divisibilidad y la factorización de números enteros positivos

Abstract

El presente trabajo aborda una estrategia didáctica para la enseñanza y aprendizaje de los conceptos de divisibilidad y la factorización, mediante el estudio de frisos de números enteros positivos, con el fin de que los estudiantes de grado Sexto del Colegio Distrital Bravo Páez, puedan observar, determinar y registrar propiedades que se presentan en el conjunto de los números enteros positivos.

Abstract This paper deals with a teaching strategy for teaching and learning of the concepts of factorization and divisibility, through the study of positive intergers numbers friezes, so the students from the sixth grade of Bravo Paez School in Bogot´a, will be able to see, to say, and to register properties arising in the set of positive integers by using its divisors. For that purpose, it starts with a historical review which gives some results that have been found with the help of hidden symmetries in various types of mathematical objects, the presence of Leonardo’s groups in the architecture and groups of friezes in the urban area of a city in Spain and the archaeological findings of the Quimbaya culture. Then it is given some concepts regarding the theory of groups and dynamic geometry. Further, some investigations reported by J.H Conway and H.S.M Coxeter in [11] are described as well. Also refers to the concepts related to friezes of positive integers numbers and the analysis of the distribution of primes in the Ulam spiral. Finally, proposes an educational activity in which students propose their arguments using the “Argumentative Toulmin model”.