Philippe R. Richard Université de Montréal Universitat Autònoma de Barcelona
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Transcript of Philippe R. Richard Université de Montréal Universitat Autònoma de Barcelona
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Contribution of a computer algebra system (CAS) in the solving of problems in geometry with the help of an emerging tutorial system
Philippe R. RichardUniversité de Montréal
Universitat Autònoma de Barcelona
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The tutorial system
Technological research project + realization
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About geogebraTUTOR
Technological research project + realization
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Geometrical competencies
Technological research project + realization
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Complex problems
Technological research project + realization
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Student’s interface
Technological research project + realization
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Possible interface with CAS
Technological research project + realization
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Some examples a priori
Treatment with and without CAS
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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)
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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?
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A real solution
(15 years old)
Synthetic geometry
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Paper and pencil with DGS
Synthetic geometry
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Instrumented figural solution
Synthetic geometry
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With the trace and the worksheet
Analytic geometry
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With a construction and the locus
Analytic geometry
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Traditional modelling solution
Analytic geometry
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Some technical problems
1. Is the traditional solution adapted to the use of a CAS?
2. If the use of a CAS creates a new space for modelling and solving geometrical problems, how we can use it in a classroom?
3. 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
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Instrumented solutions with CASExample of a solving tree, planned to be implemented in an intelligent tutorial system, that uses strongly the computer algebra system
Analytic geometry
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Analytic geometry
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Analytic geometry
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To conclude
Very briefly
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Influence on geometrical competences
Technological research project + realization
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For the research and development
• Other ideas in the integrating equationCAS + DGS + ITS ?
Technological research project + realization