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
The tutorial system
Technological research project + realization
About geogebraTUTOR
Technological research project + realization
Geometrical competencies
Technological research project + realization
Complex problems
Technological research project + realization
Student’s interface
Technological research project + realization
Possible interface with CAS
Technological research project + realization
Some examples a priori
Treatment with and without CAS
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)
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?
A real solution
(15 years old)
Synthetic geometry
Paper and pencil with DGS
Synthetic geometry
Instrumented figural solution
Synthetic geometry
With the trace and the worksheet
Analytic geometry
With a construction and the locus
Analytic geometry
Traditional modelling solution
Analytic geometry
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
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
Analytic geometry
Analytic geometry
To conclude
Very briefly
Influence on geometrical competences
Technological research project + realization
For the research and development
• Other ideas in the integrating equationCAS + DGS + ITS ?
Technological research project + realization
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