Philippe R. Richard Université de Montréal • Canad á Josep M. Fortuny

Desarrollo de recubrimientos curriculares y gestión de itinerarios adaptados al

aprendizaje instrumentado con el

geogebraTUTOR

Philippe R. Richard

Université de Montréal • Canadá

Josep M. Fortuny

Universitat Autònoma de Barcelona • España

Pedro Cobo

IES Font i Quer • España

What geogebraTUTOR does?

Interface and system

Interface of the student

Tutor agent helps student to solve the problemTutor agent helps student to solve the problem

Interface of the teacher

Problems’ filesProblems’ files Strategies’ filesStrategies’ files Messages’ filesMessages’ files

Setting up local and global solving processSetting up local and global solving process

What geogebraTUTOR hides?

Spaces, tags, trees and forests

Basic space of the problem

Contains all cognitive and heuristic statesContains all cognitive and heuristic states

Discursive messages

Messages are based on a set of possible inferencesMessages are based on a set of possible inferences

Tags and «ID card»

The system retains tags from the solving processThe system retains tags from the solving process

Characterization of each problem uses a set of tagsCharacterization of each problem uses a set of tags

Trees and forests

Each sub-problem is a cognitive messageEach sub-problem is a cognitive message

Trees and forests

(...)

Set of root problems– itinerary of learningSet of root problems– itinerary of learning1

System generates trees using tags of «ID cards»System generates trees using tags of «ID cards»

2

Restructuring trees using retained tags in solvingRestructuring trees using retained tags in solving3

Forests fit to the learning process of each studentForests fit to the learning process of each student 4

Theory and research

Foundations of geogebraTUTOR

Context

New curriculum paradigm in mathematics learning (from objectives to competencies).

Importance of social debate in the building of mathematical knowledge.

Pedagogical agents with an artificial tutorial system can convey argumentative strategies to improve mathematical competencies and knowledge.

Hyperspace of four reference axis

Theoretical background

EpistemologicalDialectical of proofs and refutations (Lakatos, 1984)

SemioticRegisters, models of representation (Duval, 1995; Richard, 2004)

SituationalTheory of didactical situations (Brousseau, 1998)

InstrumentalCognitive approach of the contemporary instruments (Rabardel, 1995)

Future of geogebraTUTOR in research

Four objectives in research projects (due very soon)

Instructional modelTo analyze the didactic effectiveness of the tutorial system

Interpretation

and theorization

To interpret and theorize on the representational, epistemological, didactic and instrumental characteristics of the system «student-milieu»

Evaluation

and controlTo evaluate the constancy of the system «student-milieu» in interaction

Implication in

vocational trainingTo test the empathy in problem solving and the effects of tutoring actions

Any questions?

To have inside information outside

To know more about evolution

Richard & Fortuny (2007). Amélioration des compétences argumentatives à l’aide d’un système tutoriel en classe de mathématique au secondaire. Annales de didactique et de sciences cognitives, 12, 83-116. Strasbourg: Université Louis Pasteur.

Cobo, Fortuny, Puertas & Richard (2007). AgentGeom: a multiagent system for pedagogical support in a geometric proof problem. International Journal of Computers for Mathematical Learning, 12, 57-79. Springer Science+Business Media.

Proceedings of World Conference E-Learn 2004, 2005, 2007, ED-Media 2005, 2006 and SITE 2007.

¡Gracias!

philippe.r.richard@umontreal.caJosepMaria.Fortuny@uab.cat

pcobo@xtec.cat