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334-370). New York: Macmillan. Steen, L. A. ). (1990). On the shoulders of giants: New approaches to numeracy. Washington, DC: National Academy Press. DIDACTICAL ENGINEERING AS A FRAMEWORK FOR THE CONCEPTION OF TEACHING PRODUCTS Michèle Artigue Paris / Reims 1. INTRODUCTION In French research on didactics of mathematics, the issue of preparing mathematics for students, which is the topic of this chapter, is located at a crossroads between two not independent but nonetheless distinct theoretical fields: the theory of didactical transposition, developed since the beginning of the 1980s by Y.
However, it must also be recognized that, at present, the application of this approach at the level of production engineering is not easy, and, moreover, stimulates, through the questions it raises, the theoretical development of research. Artigue and Perrin (1991) have attempted to analyze these difficulties in the construction of engineerings for classes mainly containing learning-disabled students. Working with such classes functioned like a magnifying glass through which the drastical changes of nature accompanying the transmission become particularly visible.
For example, most students are convinced that there must be a recipe that permits the exact algebraic integration of any type of differential equation (as they never encounter any others), and that the only aim of research is to complete the existing recipe book. If one considers the current evolution of the field, of the growing importance of numerical and qualitative aspects, such teaching is, despite its long stability, inevitably threatened with becoming obsolete. The aim of the work undertaken was to construct a teaching object that was epistemologically more satisfying, mainly by: 1.