This paper is the first part of a study on the teaching of decimal numbers.
The author analyses in detail different ways of teaching decimal numbers that have been used in France for the last twenty years. He notes that the changes brought by the Educational Reform of 1970 did not really affect school results in this domain. This is due to the fact that the pedagogical and didactical theories used to justify the reform had many deficiencies, especially in dealing with teaching situations. Using Piaget,s and Bachelard’s works, the author criticizes these theories (giving precise examples) for not modelling the teacher’s task, for erroneous views of learning processes and above all for their lack of epistemological basis.
The next part will be devoted to a didactical experiment relying upon a mathematical, historical and epistemological analysis of different conceptions of rational and decimal numbers. It will describe the main characteristics of the situations and processes enabling pupils to acquire these conceptions.
In order to attest the value of this theoretical approach the author has repeated (over ten times) the same didactical process, so as to make obvious the part of different order variables and the part of didactical decisions on the evolution of the process. This process has been chosen in order to offer a real alternative to the predominant conception on decimal numbers studied in the first part and not for its optimal educational properties.
This attempt in « experimental epistemology » enables us to look for new criteria in evaluating teaching processes.