The conceptual basics of pre-service mathematics teacher education can briefly be characterized with the following three perspectives.
Many people regard mathematics as a firmly-established system of definite terms, rules and procedures which can be derived from each other and are tailor-made for certain classes of tasks. In this view, learning mathematics is understood as repeating and reproducing predefined knowledge elements and instructions. The IEEM, however, promotes a different understanding of mathematics. Mathematics is not a finished product but forming in the process of searching for coherences, abnormalities and appropriate interpretations of mathematical relations. In other words: mathematics is the science of patterns.
Many adults regard learners as ignoramuses to whom the necessary knowledge has to be imparted. Utterances and actions not complying with the adults’ expectations are seen as faulty and immediately needing correction. The IEEM, on the other hand, propagates a perception focusing on the learners with their knowledge and their understanding: What could they have thought? What do they already know? What are the sensible backgrounds of an approach which adults consider to be wrong?
From a resource-oriented perspective, the different nature of students’ thinking is not seen as the student’s deficit but as an authentic form of expression, hence, as the difference between children and adults.
Occasionally, mathematics classrooms are still seen as a place where subject matter – the completely organized building of mathematics – is proportioned in small bits which are imparted in small and equal steps. In such classrooms, students are objects of indoctrination. The orientation towards the learning subjects, their background knowledge and abilities, on the other hand, is absolutely necessary. But it should not be equated with subject centering. Good mathematical teaching benefits from a productive duality of openness and structure. It is built on individually different competences and conceptions. At the same time, it is target-oriented and conceptionally profound.