Um cubo em seis pirâmides: aulas de matemática

Abstract

This monograph develops and presents educational products for teaching mathematics in Basic Education, in order to encourage the autonomy of teachers and students into thinking mathematics. We support the idea that teachers can develop their own mathematical problems and transform the classroom into a research environment, promoting learning according to the Theory of Didactic Situations. By using a methodology similar to the Didactic Engineering, we studied the problem of decomposing a cube in six pyramids describing a particular region inside of the cube to avoid the multiplicity of solutions by simmetry and thus. After discretizing the problem, we present a formula that gives the number of solutions to the problem in terms of this discretization. Was also develop geometric constructions that result in planifications of such pyramids, which we use as pieces of a puzzle. We also developed and applied a teaching sequence involving the theorems of Pythagoras and Thales for elementary school. We conclude that the mathematics lessons in Basic Education may be more attractive and productive when teacher and students wish to think mathematics.