The ambiguous relationships, both epistemological and pedagogical, between mathematics and exp?rimental science ; the place of the sciences in the selection of ?lites and in promoting social utility ; the relationship of science to technology : these are some of the questions raised by this Round Table. But it also discusses the connexions between thought, truth and the world ; the relative places of science and art in the culture ; rationality and order ; the role of irritation. These are all considerations bearing closely on the teaching of science, its content, aims and methods.

The teaching of sciences is dogmatic, inept, practically ineffective, epistemologically erroneous : the 1978 report on the topic was highly critical. A number of ideas which were innovative at the time are now commonplace ; methodological advances, an emphasis on process, student participation. A. Giordan revisits these developments of the last two decades, showing the limitations of this pedagogical "revolution" and pointing out the new problems that scientific progress now poses for society and for education policy.

Should the teaching of science be concerned with its practical applications ? Over the last twenty years a new discipline has been included in college curricula : technology. J-L Martinand argues that it should have four different aims : to act as a tangible support in the orientation process ; to provide the necessary knowledge for understanding technology as a basic component of modern society, to guarantee mastery of computing, and to develop a pedagogy to support these developments.

The teaching of mathematics provokes contradictory reactions. Mathematics is a ``nightmare'' for students who otherwise take on board its educational importance and role in selection. The author demonstrates that mathematics can be seen from two points of view, that of pure rationality and that of formal structure. Charged with cultural arbitrariness, symbolic violence and being an instrument of selection, mathematics does not escape sociological critique. The justification for teaching it rests nevertheless on the institutional authority of the discipline as well as its epistemological credentials. Is it possible to carry on teaching maths ? If so, given what conditions ? P.Trabal distinguishes three possible positions a teacher might adopt and suggests that the issue is not only about pedagogy but also about the status and social function of science.

Curriculum subjects often become 'out-of-date' and programmes are abandoned along with programmes in neighbouring disciplines so as to leave room for new types of content. The result is that the overall coherence of the curriculum becomes jeopardised. Mathematics has not escaped this process and the rationale for teaching it has suffered. How can it retain its coherence ? By a public redefinition of its aims. G. Sensevy picks out four types of justification, to do with : its modelling fonctions, its role in understanding the world and in critical discussion of proofs, and its contribution to education for democracy.

Science analyses phenomena in their smallest detail, categorising and classifying them, but as this abstract conceptualisation proceeds 'real' knowledge disappears. ``The young people who come to us have learnt everything but know nothing'', C. Flahault wrote in 1901, adding that one of his brilliant botany students had admitted not being able to tell one tree from another ! Pedagogy should take a different course. It should be based on concrete observations of the most simple phenomena and on the questions that these raise, leading both to laboratory work and to field trips.