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Philippe R. Richard Université de Montréal Universitat Autònoma de Barcelona

Contribution of a computer algebra system (CAS) in the solving of problems in geometry with the help of an emerging tutorial system. Philippe R. Richard Université de Montréal Universitat Autònoma de Barcelona. The tutorial system. Technological research project + realization.

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Philippe R. Richard Université de Montréal Universitat Autònoma de Barcelona

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  1. Contribution of a computer algebra system (CAS) in the solving of problems in geometry with the help of an emerging tutorial system Philippe R. Richard Université de Montréal UniversitatAutònoma de Barcelona

  2. The tutorial system Technological research project + realization

  3. About geogebraTUTOR Technological research project + realization

  4. Geometrical competencies Technological research project + realization

  5. Complex problems Technological research project + realization

  6. Student’s interface Technological research project + realization

  7. Possible interface with CAS Technological research project + realization

  8. Some examples a priori Treatment with and without CAS

  9. Examples of treatment • In synthetic geometry (without CAS) • Problem and real solution • Instrumented figural solution • In analytic geometry (without CAS) • With the trace and the worksheet • With a construction and the locus • In analytic geometry (with CAS)

  10. From a modelling problem • On a rectangular ground planned for the installation of a swimming pool, a city decided to divide it in two parts, according to a diagonal, in order to build also a small community centre. If the swimming pool must remain rectangular, where should it be built so that its surface is maximum?

  11. A real solution (15 years old) Synthetic geometry

  12. Paper and pencil with DGS Synthetic geometry

  13. Instrumented figural solution Synthetic geometry

  14. With the trace and the worksheet Analytic geometry

  15. With a construction and the locus Analytic geometry

  16. Traditional modelling solution Analytic geometry

  17. Some technical problems • Is the traditional solution adapted to the use of a CAS? • If the use of a CAS creates a new space for modelling and solving geometrical problems, how we can use it in a classroom? • And, if the use needs to be implemented in an ITS, how can we use it to support the development of geometrical competencies? Analytic geometry

  18. Instrumented solutions with CAS Example of a solving tree, planned to be implemented in an intelligent tutorial system, that uses strongly the computer algebra system Analytic geometry

  19. Analytic geometry

  20. Analytic geometry

  21. To conclude Very briefly

  22. Influence on geometrical competences Technological research project + realization

  23. For the research and development • Other ideas in the integrating equation CAS + DGS + ITS ? Technological research project + realization

  24. Děkuji ! michel.gagnon@polymtl.canicolas.leduc@polymtl.caphilippe.r.richard@umontreal.camichele.tessier-baillargeon@umontreal.ca

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