INSTRUMENTAL MEDIATION AND THEOREMS IN GEOMETRY

Luis Moreno-Armella and Marco Antonio Santillan

Cinvestav, Mexico

lmorenoa@data.net.mx

Exploring with computational tools eventually allows students to generate and articulate relationships that are general to the computational environment in which they are working. That means students can develop an ability to state general propositions in the language of the environment. A situated proof is the result of a systematic exploration mediated by a computational environment. It could be used to build a bridge between situated knowledge and some kind of formalization. In our study, whose goal was to explore how students “proved” a mathematical proposition within a computationsl environment, we worked with students, between 15 and 17 years old, trained in dynamic geometry–as it comes in the calculator TI-92. For the development of the activities, teams of two or three students were formed. Each participant was given a notebook to take notes on both individual and team observations and conclusions. One of the activities was organized around the theorem of the central angle inscribed in a circle. The objective was that students constructed the idea of an invariant property. In this, as in other related cases, students became aware of invariants and they could express the relevant ideas but only within the expressive medium made feasible by the calculator. During the oral presentation, we will give full examples as well as references.