The richness of patterns. Applications to mathematics education in Italy

Abstract: We present an overview of features of patterns and their applications in mathematics education for the learning of relevant contents such as division, infinity, space, isometries and groups. In this paper we emphasize the conceptual richness of patterns to be used in several domains and in mathematics education. Patterns are often used on primary school copybooks as aesthetic ornaments. The aesthetic dimension of patterns is the starting point of friezes. Patterns are used as a compositional tool in American minimal music, as proved by the score of Clapping music by Steve Reich. The regularity of patterns conceals a conceptual richness: in fact they can often be found in many items used to test mathematical-logical skills, for example in the determination of IQ. Teachers favour activities with patterns in order to improve the coordination of eyes and hands movements, or simply, to engage smarter boys while their schoolfellows end the work. The act of copying a pattern and repeat it on the copybook, in itself, requires a long sequence of elementary acts: observation, ordering, copying, and repeating,... Patterns present interesting mathematical issues about geometry, arithmetic and logic. Our research group worked and will work on the utilisation of patterns as tools for learning - teaching and research.