ABSTRACT
This chapter examines the relation between what the teachers intends to teach in mathematics, and what the pupils are likely to learn. It describes the school context and the aims of the didactical sequence. The chapter also describes examples of didactical engineering, where the teaching of specific mathematics topics is considered. Didactical engineering is both a product, resulting from an a-priori analysis, and a process, resulting from an adaptation to the implementation of the product in the dynamic conditions of a classroom. Didactical engineering refers to a research method which is especially useful in dealing with the complexity of the classroom. This method is widespread in French research. The engineering that have presented fits well with the tool-object dialectic. It is organised around a problem that provides meaning to the mathematical conceptions studied. It involves contextualisation, changes of context, reformulation of problems, decontextualisation, and also the personalisation and transmission of procedures and of personal knowledge as well as depersonalisation.
