Cognitive Science and Genetic Epistemology: A Case Study of Understanding

1. Introduction.- Knowledge, Representation, and Operational Structure: Toward a Confluence.- Between Representation and Operational Structure.- On Computational and Operational Structures.- I. Understanding Seriation Algorithms.- 2. The Basic Algorithm-Experimental Approach.- Method.- Analysis of the Task: Space, Time, and Length.- Space.- Time.- Length.- The Transformations Performed by the Algorithm.- Hierarchy of Protocols.- Uncoordinated Couples.- The Ascending Row.- Inhibition of Composition.- The Longest to the Right.- Progress in Representation.- 3. Procedure Representations.- Representing the Execution Space.- Understanding the Effects of the Procedure.- Execution and Simulation.- Temporal Indexation.- From Partial Results to General Conclusions.- Equivalence of the Part and the Whole.- Representativity.- Continuation.- Reformulation.- An Idiosyncratic Confusion.- Summary.- 4. Simulation and Understanding.- Formalizing Mental Simulation.- Discussion of the Notation.- The Cursor.- Rules and Meanings.- Selective Individualization-Optional Quantification.- Summary.- 5. The Extraction Algorithm beneath the Basic Algorithm.- Description of the Extraction Algorithm.- The Components.- The Transfer Operations.- The Psychological Reality of the Underlying Structure: Transfer between Problem Isomorphs.- Transfer Experiment.- Method.- Results.- Discussion.- Transfer to a More Complex Variant: The Triplets Algorithm.- Summary.- II. The Structural Approach.- 6. Seriation Strategies and Anticipatory Schemata.- Anticipatory Schemata.- Strategies of Seriation.- Piaget's Classification.- Detailed Classification.- Absence of Anticipatory Scheme.- Inadequate Construction Scheme.- Anticipatory Scheme and Procedural Scheme.- Method of Final Positions.- Method of the Extremum.- Insertion.- 7. Experiments with Children.- Experiment 1: Weight.- Method.- Classification of Behavior According to Piaget.- Experiment 1b: Control with Weight.- Method.- Results.- Experiment 2: Lengths.- Method.- Results.- Experiment 2b.- Method.- Classification.- Results.- Comparison of Experiments 2 and 2b.- Experiment 3: Questions/Lengths.- Method.- Results.- Experiment 3b: Length/Screen.- Experiment 4: Questions/Position.- Method.- Results.- 8. General Discussion.- Main Components.- Implementation Aspects.- The Role of Spatial Structure.- Anticipatory Schemes.- Logico-Mathematical Operational Structure.- Procedures and Operational Structures.- References.