Resumen

This article presents the genesis and the main elements that compose the cycle of the dialogic learning. The development of the concept of self-controlled and sustainable learning is based on a personal encounter between two teachers of entirely different subjects: Mathematics and German. Two examples show how uncomplicated teaching mathematics in the classroom can be, once the teacher has gained the courage to trust in the capabilities of the children. The three German textbooks “Ich-Du-Wir” (“I-You-We”) for mother tongue and mathematics in the first six years of elementary school provide support.