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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

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

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Desarrollo de recubrimientos curriculares y gestión de itinerarios adaptados al aprendizaje instrumentado con el geogebraTUTOR. Philippe R. Richard Université de Montréal • Canad á Josep M. Fortuny Universitat Autònoma de Barcelona • España Pedro Cobo IES Font i Quer • España. - PowerPoint PPT Presentation

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Page 1: 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

Page 2: Philippe R. Richard Université de Montréal  •  Canad á Josep M. Fortuny

What geogebraTUTOR does?

Interface and system

Page 3: Philippe R. Richard Université de Montréal  •  Canad á Josep M. Fortuny

Interface of the student

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

Page 4: Philippe R. Richard Université de Montréal  •  Canad á Josep M. Fortuny

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

Page 5: Philippe R. Richard Université de Montréal  •  Canad á Josep M. Fortuny

What geogebraTUTOR hides?

Spaces, tags, trees and forests

Page 6: Philippe R. Richard Université de Montréal  •  Canad á Josep M. Fortuny

Basic space of the problem

Contains all cognitive and heuristic statesContains all cognitive and heuristic states

Page 7: Philippe R. Richard Université de Montréal  •  Canad á Josep M. Fortuny

Discursive messages

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

Page 8: Philippe R. Richard Université de Montréal  •  Canad á Josep M. Fortuny

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

Page 9: Philippe R. Richard Université de Montréal  •  Canad á Josep M. Fortuny

Trees and forests

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

Page 10: Philippe R. Richard Université de Montréal  •  Canad á Josep M. Fortuny

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

Page 11: Philippe R. Richard Université de Montréal  •  Canad á Josep M. Fortuny

Theory and research

Foundations of geogebraTUTOR

Page 12: Philippe R. Richard Université de Montréal  •  Canad á Josep M. Fortuny

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.

Page 13: Philippe R. Richard Université de Montréal  •  Canad á Josep M. Fortuny

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)

Page 14: Philippe R. Richard Université de Montréal  •  Canad á Josep M. Fortuny

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

Page 15: Philippe R. Richard Université de Montréal  •  Canad á Josep M. Fortuny

Any questions?

To have inside information outside

Page 16: Philippe R. Richard Université de Montréal  •  Canad á Josep M. Fortuny

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.

Page 17: Philippe R. Richard Université de Montréal  •  Canad á Josep M. Fortuny

¡Gracias!

[email protected]@uab.cat

[email protected]