Explanation of algebraic reasoning : the Aplusix system

  • J. F. Nicaud
  • M. Saidi
Intelligent Tutoring Systems
Part of the Lecture Notes in Computer Science book series (LNCS, volume 444)


Strategic knowledge is fundamental in order to become adaptive. Though it is crucial in factorization of polynomials and polynomial-equation solving, it is hardly ever taught in school. Aplusix, an ICAI system, tries to deal with this aspect. Aplusix can be either example-driven or reasoning driven. In the first case the problem is solved by the system. However, the student may ask for explanation concerning facts or strategic knowledge. In the second case, the problem is solved by the student. He chooses among the possible transformations and the system performs the necessary computations. The goal of Aplusix is to help the student to discover how to perform the necessary matching operations and to develop efficient strategies. In order to do so, the system shows all the operations performed, including backtracking, when presenting the examples. When solving the equations with the help of the system, the student is relieved of the burden of computation. He can therefore use all his resources on the task of reasoning. This paper describes the problem-solving component of Aplusix and its explanation module.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [Borning & Bundy 81]
    Borning A. & Bundy A.: Using matching in algebraic equation solving. IJCAI7, 1981.Google Scholar
  2. [Bundy 83]
    Bundy A.: The computer modeling of mathematical reasoning. Academic Press, New York, 1983.Google Scholar
  3. [Bundy & Sylver 81]
    Bundy A. & Sylver B.: Homogenization: preparing equations for change of unknown. In proceeding of IJCAI7, 1981, p 551–553.Google Scholar
  4. [Dede 86]
    Dede C.: A revue and synthesis of recent research in intelligent computer-assisted instruction. International Journal of Man-Machine Studies, 24, 1986.Google Scholar
  5. [Faller 83]
    Faller B.: Une application de TANGO au calcul des primitives. Rapport de DEA, LRI, 1983.Google Scholar
  6. [Ferret & Jimenez 87]
    Ferret E., Jimenez C.: A la découverte des méthodes algébriques. Proceeding of EAO87, Cap d'Agde, France, Mars 1987, 389–398.Google Scholar
  7. [Kassel 86]
    Kassel G.: Le système d'explications CQFE: une forme de méta-raisonnement intégrant règles et objets. Thèse d'Université, Paris XI, 1986.Google Scholar
  8. [Nicaud 87]
    Nicaud J.F.: Aplusix: un système expert en résolution pédagogique d'exercices d'algèbre. Thèse d'Université, Paris XI, 1987.Google Scholar
  9. [Nicaud & Vivet 88]
    Nicaud J.F., Vivet M.: Les tuteurs intelligents: réalisations et tendances de recherches. Technique et Science Informatique, vol 7 no 1, 1988, p 22–45.Google Scholar
  10. [Nicaud 89]
    Nicaud J.F.: APLUSIX un système expert pédagogique et un environnement d'apprentissage dans le domaine du raisonnement algébrique. Technique et Science Informatique, vol 8 no2, 1989, p 145–155.Google Scholar
  11. [Pottier 84]
    Pottier L.: Une application de Tango à l'integration formelle, une solution pour le pilotage des sous-problèmes. rapport de DEA, LRI, Paris XI, 1984.Google Scholar
  12. [Resnick 87]
    Resnick L.: Learning in school and out. Educational Researcher, 16 (9), p 13–19.Google Scholar
  13. [Safar 85]
    Safar B.: Explication dans les systèmes experts, Proceeding of les systèmes experts et leurs applications. Avigon, France, May 1985, vol 1, 585–599.Google Scholar
  14. [Saïdi 88]
    Saïdi M.: Système expert d'explication des heuristiques pour Aplusix. Rapport de DEA, Université de Paris XI, 1988.Google Scholar
  15. [Vivet 84]
    Vivet M.: Expertise mathématique et informatique: CAMELIA, un logiciel pour raisonner et calculer. Thèse d'état, Paris VI, 1984.Google Scholar
  16. [Vivet 87]
    Vivet M.: reasoned explanations need reasoning on reasoning and reasoning on the student. IFIP TC3, Frascati R Lewis & P Ercoli eds, North Holland, 1987.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • J. F. Nicaud
    • 1
  • M. Saidi
    • 1
  1. 1.L.R.I. Bât 490 CNRS UA 410Université de PARIS XIORSAY CEDEXFRANCE

Personalised recommendations