A Theorem and Its Different Proofs: History, Mathematics Education, and the Semiotic-Cultural Perspective

摘要

Several studies claim that integrating the history of mathematics into mathematics education is an important matter. In this article, some theoretical approaches are presented and the importance of the correct cultural contextualization is emphasized. Our purpose is to discuss, from an educational viewpoint, the problem of knowledge development within specific cultural contexts; cultural aspects play a cognitive and epistemological role in the way we think mathematically. More specifically, we provide a comparison of some strategies used by mathematicians in different periods in order to prove that primes are infinitely many. We conclude that historical examples should be understood in their cultural and social context and that the standards of symbolization and rigor depend on this context. In order to emphasize the use of history in education as a real tool for the teacher, we propose an outline of educational opportunities. The perspective presented requires a good level of epistemological skill on the part of teachers; therefore, it should be considered in teacher education.