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Solving Probabilistic Problems with Technologies in Middle and High School: The French Case

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Broadening the Scope of Research on Mathematical Problem Solving

Part of the book series: Research in Mathematics Education ((RME))

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Abstract

The place of probability in the teaching of mathematics is currently growing and makes greater use of technology. Like in many other domains, calculators and computers have become very useful and necessary tools in that domain, and indeed, they are widely used in teaching. This chapter is a survey of how these tools are used to solve probability problems in French middle and high school. These tools are perhaps neither as transparent nor as easy to use as may first appear and may pose didactical problems. After describing the current French context (didactical frameworks, curricula and official resources), a study of the problems most commonly given in classrooms, and the associated tasks to be performed by students, is undertaken through an analysis of official documents and textbooks, two of the resources most used by teachers.

Random generators set up in computers and calculators allow the performing of a great number of tries of random experiments in a quite short time. This can foster the introduction of a new approach to the notion of probability. In many cases, to solve some problems, students first have to elaborate – even if it is most often implicit – a model of the situation and then to simulate it using software in order to get an idea of the solution and, possibly, a way towards the proof. By so doing they have to move through several probabilistic and statistical paradigms, mostly with no explicit clue to help them identify the suitable one(s), which may result in their mixing up statistical and probabilistic notions.

The French curricula introduce inferential statistics at the end of high school; here, as well, technology has changed how estimation problems can be solved. Another curricular question is the introduction of continuous probability distributions, especially normal law. This question is tackled by textbooks through problematic situations, concrete or general, but in this intended processes software is in most cases underused (when not ill-used).

Although concerned with the French situation, some elements may, of course, apply to other countries in which the same problems are given to students.

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Notes

  1. 1.

    My translation.

  2. 2.

    See Brousseau (1997) and Warfield (2006).

  3. 3.

    See Chevallard (1999), and Chevallard (2002).

  4. 4.

    See Vergnaud (1990).

  5. 5.

    My translation.

  6. 6.

    My translation.

  7. 7.

    My translation.

  8. 8.

    My translation.

  9. 9.

    My translation.

  10. 10.

    My translation.

  11. 11.

    My translation.

  12. 12.

    My translation.

  13. 13.

    My translation.

  14. 14.

    My translation.

  15. 15.

    My translation.

  16. 16.

    Although in fact, when simulating a random experiment, what one actually does is testing the quality of the generator.

  17. 17.

    My translation.

  18. 18.

    This implies that a model of the experiment is available, that is, a probability can be assigned to each issue.

  19. 19.

    The origin of this problem is the entry ‘Croix ou Pile’ in the Encyclopédie (1751–1772) supervised by Jean le Rond d’Alembert and Denis Diderot.

  20. 20.

    The students were in fact given the original text, in which d’Alembert gives both the solution given ‘by all authors’ (3/4) and his own solution (2/3).

  21. 21.

    My translation.

  22. 22.

    My translation.

  23. 23.

    Deledicq, A. (dir.) Mathématiques classe de Seconde. Collection Indice. Bordas, Paris 2000, 138.

  24. 24.

    My translation.

  25. 25.

    Beltramone et al., 2015

  26. 26.

    My translation.

  27. 27.

    Malaval et al. (2011), p. 399.

  28. 28.

    Barra, R. et al. Mathématiques classe de Première. Collection Transmath. Nathan, Paris 2011, 303.

  29. 29.

    This division into five parts is mine; it is intended to make the following discussion easier.

  30. 30.

    My translation.

  31. 31.

    ‘When the number of experimentations grows up the relative frequency gets nearer the probability’.

  32. 32.

    In this case, the ‘pedagogical artefact’ consisting of colouring the dice is no use.

  33. 33.

    My translation.

  34. 34.

    My translation.

  35. 35.

    After Beltramone et al. (2015).

  36. 36.

    The use of a logical function is not necessary; it just entrusts the conclusion to the device.

  37. 37.

    My translation.

  38. 38.

    My translation.

  39. 39.

    My translation.

  40. 40.

    My translation.

  41. 41.

    In particular, for the area condition GeoGebra can display the area under the curve of a function.

  42. 42.

    Le Yaouanq (2012), p. 399.

  43. 43.

    We may notice that the big size of the sample results in a histogram very close to the theoretical curve and consequently makes the analogy easier to conceive and accept.

  44. 44.

    My translation.

  45. 45.

    Le Yaouanq (2012), p. 400.

  46. 46.

    My translation.

  47. 47.

    My translation.

  48. 48.

    My translation.

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Authors and Affiliations

  1. Bernard Parzysz, Université d’Orléans, Orléans, France

    Bernard Parzysz

  2. Laboratoire de Didactique André Revuz, Université Paris-Diderot, Paris, France

    Bernard Parzysz

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  1. Bernard Parzysz
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Correspondence to Bernard Parzysz .

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Editors and Affiliations

  1. Universidade do Algarve and UIDEF Instituto de Educação, Universidade de Lisboa, Lisbon, Portugal

    Nélia Amado

  2. Universidade do Algarve and UIDEF Instituto de Educação, Universidade de Lisboa, Lisbon, Portugal

    Susana Carreira

  3. School of Education, University of Southampton, Southampton, UK

    Keith Jones

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Parzysz, B. (2018). Solving Probabilistic Problems with Technologies in Middle and High School: The French Case. In: Amado, N., Carreira, S., Jones, K. (eds) Broadening the Scope of Research on Mathematical Problem Solving. Research in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-319-99861-9_3

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  • DOI: https://doi.org/10.1007/978-3-319-99861-9_3

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