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The objective is to explain the typical rationale design of mathematics education research for a teacher to become a specialist in teaching mathematics. The structure shows (1) learning environments as a natural way to address the teachers in their primary role and an approach for effectively improving mathematics teaching - that is a teaching model based on the theory of didactical situations; (2) illustrating how in a concrete case the model can be brought to life by drawing from processes inherent in mathematics; (3) turning out from a genetic view of mathematics; and (4) dealing with the consequences for teacher education in demanding special mathematical courses for teachers. That is a method by which the students acquire knowledge and skills more than in the past and acquire them self, delivering subject matter to develop their abilities. The main question formulated: What is both scientifically and practically founded teaching method by which the further the development of the student in the desired way? The teachers get two instruments: providing opportunities and stimulating individual growth. The result is that the students with the foundations for a mathematical penetration of all things and phenomena of numerical literacy are in the enlightened educational view of skills. And the student is no longer tuned to passively receiving knowledge but to actively acquiring it. The characteristic of the teaching method is not instruction and receptivity but organization and activity.

rational design, specialist, didactical situation, genetic view of mathematics