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

Děkuji !

michel.gagnon@polymtl.canicolas.leduc@polymtl.ca

philippe.r.richard@umontreal.camichele.tessier-baillargeon@umontreal.ca