Ebook: Intelligent Learning Environments: The Case of Geometry
- Tags: Artificial Intelligence (incl. Robotics), Combinatorics, Algorithms, Geometry
- Series: NATO ASI Series 117
- Year: 1996
- Publisher: Springer-Verlag Berlin Heidelberg
- Edition: 1
- Language: English
- pdf
This book is a thoroughly revised result, updated to mid-1995, of the NATO Advanced Research Workshop on "Intelligent Learning Environments: the case of geometry", held in Grenoble, France, November 13-16, 1989. The main aim of the workshop was to foster exchanges among researchers who were concerned with the design of intelligent learning environments for geometry. The problem of student modelling was chosen as a central theme of the workshop, insofar as geometry cannot be reduced to procedural knowledge and because the significance of its complexity makes it of interest for intelligent tutoring system (ITS) development. The workshop centred around the following themes: modelling the knowledge domain, modelling student knowledge, design ing "didactic interaction", and learner control. This book contains revised versions of the papers presented at the workshop. All of the chapters that follow have been written by participants at the workshop. Each formed the basis for a scheduled presentation and discussion. Many are suggestive of research directions that will be carried out in the future. There are four main issues running through the papers presented in this book: • knowledge about geometry is not knowledge about the real world, and materialization of geometrical objects implies a reification of geometry which is amplified in the case of its implementation in a computer, since objects can be manipulated directly and relations are the results of actions (Laborde, Schumann). This aspect is well exemplified by research projects focusing on the design of geometric microworlds (Guin, Laborde).
Content:
Front Matter....Pages I-VIII
A Model of Case-Based Reasoning for Solving Problems of Geometry in a Tutoring System....Pages 1-16
Modelling Children’s Informal Arithmetic Strategies....Pages 17-35
Cognitive Interpretation of Micro world Operations....Pages 36-45
Calculus Revisited....Pages 46-62
Computer Aided Proofs in School Geometry....Pages 63-81
A Cognitive Analysis of Geometry Proof Focused on Intelligent Tutoring Systems....Pages 82-93
Modelling Geometrical Knowledge: The Case of the Student....Pages 94-112
Intelligent Microworlds and Learning Environments....Pages 113-132
A Constructivist Model for Redesigning AI Tutors in Mathematics....Pages 133-156
The Influence of Interactive Tools in Geometry Learning....Pages 157-187
Socratic Tutoring with Software: An Example and a Prospectus....Pages 188-202
Students’ Constructions and Proofs in a Computer Environment — Problems and Potentials of a Modelling Experience....Pages 203-217
Some Hyperbolic Geometry with CABRI-G?om?tre....Pages 218-230
Micro-Robots as a Source of Motivation for Geometry....Pages 231-245
Complex Factors of Generalization Within a Computerized Microworld: The Case of Geometry....Pages 246-261
Back Matter....Pages 263-276
Content:
Front Matter....Pages I-VIII
A Model of Case-Based Reasoning for Solving Problems of Geometry in a Tutoring System....Pages 1-16
Modelling Children’s Informal Arithmetic Strategies....Pages 17-35
Cognitive Interpretation of Micro world Operations....Pages 36-45
Calculus Revisited....Pages 46-62
Computer Aided Proofs in School Geometry....Pages 63-81
A Cognitive Analysis of Geometry Proof Focused on Intelligent Tutoring Systems....Pages 82-93
Modelling Geometrical Knowledge: The Case of the Student....Pages 94-112
Intelligent Microworlds and Learning Environments....Pages 113-132
A Constructivist Model for Redesigning AI Tutors in Mathematics....Pages 133-156
The Influence of Interactive Tools in Geometry Learning....Pages 157-187
Socratic Tutoring with Software: An Example and a Prospectus....Pages 188-202
Students’ Constructions and Proofs in a Computer Environment — Problems and Potentials of a Modelling Experience....Pages 203-217
Some Hyperbolic Geometry with CABRI-G?om?tre....Pages 218-230
Micro-Robots as a Source of Motivation for Geometry....Pages 231-245
Complex Factors of Generalization Within a Computerized Microworld: The Case of Geometry....Pages 246-261
Back Matter....Pages 263-276
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