O design e o uso de um micromundo musical para explorar relações multiplicativas

Abstract

The aim of this work was to design and evaluate a musical microworld, created to enable users to explore concepts related to multiplication. Inspired by the constructionist perspective of Papert, the study evolved from the conjecture that by engaging in the construction of a musical rhythm, learners could interact with various aspects of the multiplicative field. To investigate this conjecture, a teaching experiment of two phases was conceived. The analyses in both these phases were based on the distinction made in the research of Confrey between the world of counting and the world of splitting. In the design phase, attention was given to the aspects of the microworld that might permit learners to construct conceptions that go beyond a vision of multiplication as repeated addition. The experimentation phase involved two groups of six students of the 5th Grade of a school within the public education system in the city of São Paulo. Using as their bases the interactions of students during the construction of their own rhythmic compositions, the analyses explored the different ways through which the learners made use of tools of the microworld and, in particular, the ways they chose to represent and express ideas related to notions such as ratio and proportion. The results suggest that, with the support of these tools, the learners gradually came to associate their musical activities with mathematical properties and concepts. They also showed how, during the experiment, the learners were enabled to explore the relations half and double within a perspective coherent with the world of splitting, as well as to use a diverse set of representations of these two relations