By Eugène Chouraqui, Carlo Inghilterra (auth.), Jean-Marie Laborde (eds.)

ISBN-10: 3642609279

ISBN-13: 9783642609275

ISBN-10: 3642646085

ISBN-13: 9783642646089

This ebook is a completely revised end result, up-to-date to mid-1995, of the NATO complex examine Workshop on "Intelligent studying Environments: the case of geometry", held in Grenoble, France, November 13-16, 1989. the most objective of the workshop was once to foster exchanges between researchers who have been all in favour of the layout of clever studying environments for geometry. the matter of scholar modelling used to be selected as a valuable subject matter of the workshop, insofar as geometry can't be diminished to procedural wisdom and as the value of its complexity makes it of curiosity for clever tutoring process (ITS) improvement. The workshop targeted round the following issues: modelling the data area, modelling scholar wisdom, layout ing "didactic interaction", and learner regulate. This ebook includes revised models of the papers offered on the workshop. the entire chapters that persist with were written through contributors on the workshop. each one shaped the root for a scheduled presentation and dialogue. Many are suggestive of analysis instructions that may be performed sooner or later. There are 4 major concerns working in the course of the papers provided during this booklet: • wisdom approximately geometry isn't wisdom in regards to the genuine global, and materialization of geometrical gadgets implies a reification of geometry that is amplified in terms of its implementation in a working laptop or computer, for the reason that items might be manipulated without delay and family are the result of activities (Laborde, Schumann). This element is easily exemplified by way of examine initiatives concentrating on the layout of geometric microworlds (Guin, Laborde).

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**Example text**

It thus turned out that the global aspects of the model are stable, even though the local ones need not be. But since all interpretations were based on these global aspects, local instability was irrelevant. For obvious reasons, it is very important that the cognitive interpretations of a model are not sensitive to small perturbations in the data and thus to the kind of arbitrary decisions that have been exemplified above. In the case of the model for transfer, this stability has been achieved by means of the fact that the Transfer and Quality Indices were computed on the basis of many microworld operations, typically about twenty.

At this stage, more than one rule could match the memory items. To select one of the possible rules, production systems have conflict resolution strategies. The implementation uses the simple conflict resolution strategy, rule ordering, that is, it selects the first of the list of possible rules. In addition, a rule may match more than one memory item. To overcome this problem, the implementation chooses the item that was added last (most recent item) to the memory. (The last action triggers the next action).

Cognitive Theory, vol. 2. Hillsdale, NJ: Erlbaum. Gelman, R. R. (1978). The Child's Understanding of Number. : Harvard University Press. Hennessy, S. (1986). The role of conceptual knowledge in the acquisition of arithmetic algorithms. PhD thesis. University College, London. Modelling Children's Infonnal Arithmetic Strategies 33 Hennessy. , Evertsz, R. : 1989. An intelligent tutoring system approach to teaching primary mathematics. Educational Studies in Mathematics, 20, 273-292. , O'Shea, T.

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