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

This e-book is a completely revised end result, up-to-date to mid-1995, of the NATO complicated 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 excited by the layout of clever studying environments for geometry. the matter of pupil modelling used to be selected as a imperative subject of the workshop, insofar as geometry can't be lowered to procedural wisdom and as the value of its complexity makes it of curiosity for clever tutoring process (ITS) improvement. The workshop focused round the following topics: modelling the information area, modelling scholar wisdom, layout ing "didactic interaction", and learner keep watch over. This ebook comprises revised types of the papers offered on the workshop. all the chapters that persist with were written through individuals on the workshop. each one shaped the root for a scheduled presentation and dialogue. Many are suggestive of analysis instructions that may be conducted sooner or later. There are 4 major concerns operating during the papers awarded during this publication: • wisdom approximately geometry isn't wisdom concerning the actual international, and materialization of geometrical items implies a reification of geometry that is amplified on the subject of its implementation in a working laptop or computer, due to the fact gadgets might be manipulated at once and relatives are the result of activities (Laborde, Schumann). This element is definitely exemplified by way of learn tasks targeting the layout of geometric microworlds (Guin, Laborde).

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1983). A developmental theory of number understanding. P. ), The Development of Mathematical Thinking. London: Academic Press. Young, R. : 1982, Errors in children's subtraction, Cognitive Science 5, 153-177. Appendix Details of subjects and results of study on commutativity stages, generalization to subtraction and 3-tenn addition. ability is one of high, medium or low (determined by the teacher). subtraction column: G for generalization, SFL smaller from larger, 0 zero, NP not possible, - for those not tested.

2. 3. 4. 5. 6. 7. 8. 9. AAK DR S1M JMS AAN KD MC YPR AS 11. 12. 13. 14. 15. 16. 17. 18. 19. AK AN MSN VS RDP AAN RDD 10. 9 H H H H H H H H H H H H M H H M M M M comm. stage subtraction grouping II III II i ii G NP G NP NP 6 4 6 6 6 II i Iii 0 IV IV IV NP NP 0 G 0 G 0 NP iv 0 III IV IV iii III iv 1 4 1 1 2 2 1 1 1 6 1 6 34 R. Devi et al. 20. 2l. 22. 23. 24. 25. 26. 27. 28. 29. 30. 3l. 32. 33. 34. 35. 36. 37. 38. 39. 40. 4l. 42. 43. 44. 45. 46. 47. 48. 49. 50. 5l. 52. 53. 54. 55. 56. 57. 58. 59. 60.

Cognition and Instruction, 1(1), 109-116. Baroody, AJ. E. (1984) The development of the commutativity principle and economical addition strategies. Cognition and Instruction, 1 (3),321 - 339. , Devi, R. (1988). GADL: A Graphical Interface for Mental Arithmetic Algorithms. CITE Report No. 49, The Open University. Gelman, R. (1977). How young children reason about small numbers. In N. J. Castellan et al. ), Cognitive Theory, vol. 2. Hillsdale, NJ: Erlbaum. Gelman, R. R. (1978). The Child's Understanding of Number.