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E-book Connecting Mathematics and Mathematics Education : Collected Papers on Mathematics Education as a Design Science
he objective of this introductory chapter is to explain the common rationalebehind the papers of this volume. The structure is as follows.The first section shows that learning environments are a natural way to addressteachers in their main role, teaching, and that therefore this approach is promisingfor improving mathematics teaching in an effective way. The section ends with ateaching model based on Guy Brousseau’s theory of didactical situations.The second section illustrates how in a concrete case the general terms in thisteaching model can be brought to life by drawing from processesinherentin math-ematics.The general principles behind this special case are explained in the third section.It will turn out that they arise from a genetic view of mathematics.The fourth section deals with the consequences for teacher education that resultin demanding special mathematical courses for teachers. This led him to the following question: “How to teach teachers so as to be useful forteaching mathematics so as to be useful?”The main professional task of a teacher is to prepare, conduct, analyze lessonsand mark papers, and the success of teaching crucially depends on getting studentsactively involved, not by applying extrinsic means of motivation but by applyingintrinsic ones.
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