Tool, Object, Setting, Window: Elements for Analysing and Constructing Didactical Situations in Mathematics

  • Régine Douady
Part of the Mathematics Education Library book series (MELI, volume 10)


The classroom is a living place where complicated interactions take place between the teacher and the pupils. What is at stake is a certain mathematical knowledge. The pupils arrive in class in a certain state of knowledge and must reach another expected state of knowledge, under the teacher’s direction. Various factors act upon these relations — of a scientific, social, cultural, hierarchical, or personal order — often in contradictory ways. One of the functions of teacher training is to provide teachers with the means of recognizing those factors which they can influence, considering the constraints to which they are subject. Another point is to determine how they can manage these elements in order to obtain a desired result in the pupils’ learning.


Mathematical Knowledge Algebraic Setting Imaginary Number Geometrical Setting Numerical Setting 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Artigue, M. and Douady, R.: 1986, ‘La didactique des mathématiques en France, émergence d’un champ scientifique’, Revue Française de Pédagogie 76, 69–88.CrossRefGoogle Scholar
  2. Artigue, M. and Robinet, J.: 1982, ‘Conceptions du cercle chez des élèves de l’école élémentaire (7–9 ans)’, Recherches en Didactique des Mathématiques 3.1, 5–64.Google Scholar
  3. Bachelard, G.: 1977, La formation de l’esprit scientifique,Vrin, Paris, 10e éd.Google Scholar
  4. Bishop, A.J.: 1980, ‘Classroom conditions for learning Mathematics’, Proceedings of PME 4, Berkeley, California.Google Scholar
  5. Boero, P.: 1989, ‘Mathematical Literacy for all, Experiences and Problems’, plenary lecture, Proceedings of PME 13, Paris, 52–76.Google Scholar
  6. Brousseau, G.: 1986, Fondements et méthodes de la didactique des mathématiques’, Recherches en Didactique des Mathématiques 7.2, 33–115.Google Scholar
  7. Douady, R. 1985, ‘The Interplay between Different Settings; Tool-Object Dialectic, Proceedings of PME 9, Noordwijkerhout, Vol. 2, 33–52.Google Scholar
  8. Douady, R.: and Perrin, M.J.: 1989, ‘Un processus d’apprentissage du concept d’aire de surface plane’, Educational Studies in Mathematics 20, 387–424.Google Scholar
  9. Hoyles, C. and Noss, R.: 1988, ‘Children Working in a Structure Logo Environment: From Doing to Understanding’, Recherches en Didactique des Mathématiques 8, 1/2 131–174.Google Scholar
  10. Joshua, M.A. and Joshua, S.: 1988/1989, ‘Les fonctions didactiques de l’expérimental dans l’enseignement scientifique’, Recherches en Didactique des Mathématiques, première partie, 83, 231–266, deuxième partie, 9.1 5–30.Google Scholar
  11. Perret-Clermont, A.N.: 1979, La construction de l’intelligence dans l’interaction sociale. Peter Lang, Berne.Google Scholar
  12. Piaget, J.: 1975, L’équilibration des structures cognitives, PUF, Paris.Google Scholar
  13. Robert, A. and Tenaud, I.: 1989, ‘Une expérience d’enseignement de la géométrie en Terminale C’, (section scientifique, élèves de 17–18 ans), Recherches en Didactique des Mathématiques 9.131–70.Google Scholar
  14. Schoenfeld, A.: 1985, Mathematical Problem Solving, Academic Press, Orlando.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1991

Authors and Affiliations

  • Régine Douady

There are no affiliations available

Personalised recommendations