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Glossaries, index

Friday September 16, 2010   

 The first glossaries of the Theory of Situations were written by researchers and thesis-writers at the COREM at the end of the 80's. In 1995, for a volume he was writing at the time with Marie Claude Chevalier, Joel Brian produced another which I co-signed without doing much to it.

The first text presented here in French owes its publication to Bernard Sarrazy and dates from 1996. In 2003, Ginger Warfield translated it into English. [This glossary available here.]

Consult or download the Glossary published in January 2010 (in original French)

I am hoping that together we can improve the entries, make them more precise and perhaps augment them in order to improve them yet more. This page will also present an index of the terms of the theories of situations (mathematical and didactical) and their translation into English.

See an index of the TSD http://www-didactique.imag.fr/Brousseau/Dico.html

Reflections ... on the glossaries, on the use of paradoxes, and on polemics -- on the glossaries.

The drafting of a Glossary poses some difficult problems when the notions presented emerge from a complex process of observations and reflections that is still going on, and their publication risks leaving the author stuck in points of view that may be transitory. A new concept that requires two hours to explain cannot always be reduced to a summary. This explains my reluctance to intervene on these extracts of my courses. But no more should the choice of some happy expressions that an auditor has found to be a clarification be neglected.

I rediscovered my response, a little embarrassed, to a letter (which I unfortuntely can't find) from a reader who was interested in the first glossaries -- relative to the theory of mathematical situations as of 70-80 -- but who had strong objections to the notions of contract and didactical situation.   

- on the use of paradoxes
The use of paradoxes is delicate. A paradox is something that seems contradictory from a certain point of view, but reveals itself in another.

It is a didactical procedure that clearly marks the necessity of a change of point of view. Unfortunately, it is only intelligible if the person it is destined for is willing to admit, or at least consider, the second point of view.

For example, Zeno's paradox is based on the one hand on the impossibility of conceiving, in a primitive mathematics, that the sumof an infinite number of terms can be finite and on the other on the knowledge of the obvious fact that Achilles is going to catch up with the tortoises that are running away from him. Proposed to someone who didn't know that Achilles could successfully pursue the tortoises but who knew the mathematics, the paradox would be reduced to a false proof.

Thus, for omeone who does not accept its resolution the paradox can have the air of a provocation, closer to polemics than to scientific proof. For him, what claims to be a paraox remains a contradiction. A lover of polemics could then turn it back against its author: "Do you take me for an imbecile? What you just said is trivially false!" [which I would translate to "What I want to understand of what you said is trivially false!"]

The paradoxes that I advanced to justify abandoning the theories in use in our societies, concerning the organization of school learning, were comforting to those who were convinced that it needed doing. But they also incited the defenders of "traditions" to declare that our works led to pronmoting a "pedagogy of the void". However, a look at our accounts of our experiments in teaching all of the major mathematical subjects required for schoolswould have shown them that that void was in fact full of mathematics, that the students were really learning, and that Achilles would indeed catch his tortoises...

 - on polemics
I hope that my proposals will not revive the polemics. I flee from them. Polemics are pleasant, but they are a caricature of a debate. A type of grotesque comedy where rhetoric plays the role of art and of reason. Al lthat counts is the instant impact to hoodwind the spectator.

J’espère que mes propos ne raviveront pas les polémiques. Je les fuis. La polémique est plaisante mais c’est une caricature de débat. Un genre de comique grotesque où la rhétorique se joue de l’art et de la raison. Seul l’impact instantané compte pour embobiner le spectateur. En alternant, comme au petit bonheur, des arguments véritables et des inférences vraies, douteuses ou franchement fautives, des déclarations erronées et des faits établis, des allusions fumeuses, des questions insolubles et finalement de vrais mensonges, on fait un discours impossible à décortiquer par la raison et donc à réfuter… Tout est subordonné à un but dérisoire et vaniteux: paraître « dominer » son adversaire devant un aréopage rigolard.   

Je ne suis curieux que des faits, et pas du bruit qu’ils font… Je veux instruire le procès des idées ou des croyances – et aucune n’est sacrée à mes yeux, surtout pas les miennes -. Je ne veux pas faire le procès de ceux qui les adoptent, bonnes ou mauvaises. Je me borne donc [1] à envisager les conditions qui favorisent leur adoption sans jamais impliquer personnellement les personnes qui les adoptent. C’est la règle d’or de l’enseignement des mathématiques : ne pas attendre de subterfuges et de pressions sur les personnes ce qui peut et doit venir de l’activité mathématique elle-même.   

Alors voici des glossaires à l’amélioration desquels je vous invite à exercer vos talents.      GB Août 2010.  

Consulter ou télécharger le Glossaire mis à jour en Janvier 2010


 [1] D’accord chers polémistes, je suis borné ! C’est un avantage sur ceux qui ne se connaissent pas de bornes.