This study examines the links that the ‘Collège’and ‘Lycée’, as institutes of mathematical learning, make between a numerical calculation and the calculator. The main question is the place and role of decimal approximation in this practical and theoretical linking of the mathematical and the technical.
The framework of anthropological theory allows the study to show first of all how the praxis of decimilisation combines the use of instruments and elements of theory in the carrying out of calculations. The work uses the example of trigonometrical calculations. The historical evolution in France of a successive choice of means of putting mathematical theory into practice (like the use of tables and algebraic calculations) shows that with the techniques and instruments used in institutions, the use of decimal approximation comes up against the constraints which tend to avoid the main theoretical requirements of numerical approximation. In other words the educational institution struggles in connecting the calculating tool and the decimal approximation. In our research work connecting is definite as intervention of controls which integrate mathematical knowledge on the precision of decimal results produced with an instrument. A more detailed analysis in ‘collèges’and ‘lycées’today of the ecology and economy of techniques tied in with the use of calculators explains the reasons for the difficulty in reconciling the instrument method with the mathematical method.
The study then undertakes to work, at the ‘lycée’level, at a calculator-approximation link, making it part of the teaching of Calculus. It relies on the theory of didactical situations where in several sessions the two fundamental problems of numerical approximation are encountered. The construction of a trigonometrical table serves as a way in to this educational feat of engineering.