Ernst von Glasersfeld

Radical constructivism : a way of knowing and learning

Growing up Constructivist - Languages and Thoughtful People Unpopular Philosophical Ideas - A History in Quotations Piagets Constructivist Theory of Knowing The Construction of Concepts Reflection and Abstraction Constructing Agents - The Self and Others On Language, Meaning and Communication The Cybernetic Connection Units, Plurality, and Number To Encourage Students Conceptual Constructing.

Cognition, Construction of Knowledge, and Teaching

The existence of objective knowledge and the possibility of communicating it by means of language have traditionally been taken for granted by educators. Recent developments in the philosophy of science and the historical study of scientific accomplishments have deprived these presuppositions of their former plausibility. Sooner or later, this must have an effect on the teaching of science. In this paper I am presenting a brief outline of an alternative theory of knowing that takes into account the thinking organism’s cognitive isolation from ‘reality’. This orientation was proposed by Vico at the beginning of the 18th century, disregarded for two hundred years, and then propounded independently by Piaget as a developmentaly grounded constructivist epistemology. The paper focuses specifically on the adaptive function of cognition, Piaget’s scheme theory, the process of communication, and the subjective perspective on social interaction. In the concluding section it then suggests some of the consequences the shift of epistemological presuppositions might have for the practice of teaching.

Construction of arithmetical meanings and strategies

I: On the Construction of the Counting Scheme.- Childrens Counting.- The Counting Types.- Perceptual Unit Items.- Figural Unit Items.- Motor Unit Items.- Verbal Unit Items.- Abstract Unit Items.- Ontogenetic Analysis.- Stages.- Adaptation.- Counting as a Scheme.- The First Part of the Counting Scheme.- The Third Part of the Counting Scheme.- Other Sources of Numerosity.- Perceptual Mechanisms.- Spatial Patterns.- Meaning Theory.- Reflection and Abstraction.- II: The Construction of Motor Unit Items: Brenda, Tarus, and James.- 1. Brenda.- The Perceptual Period.- The Motor Period.- Discussion of Brendas Case Study.- The Perceptual Period.- The Motor Period.- 2. Tarus.- The Perceptual Period.- The Motor Period.- Discusion of Taruss Case Study.- The Perceptual Period.- The Motor Period.- 3. James.- The Perceptual Period.- The Motor Period.- Discussion of Jamess Case Study.- The Perceptual Period.- The Motor Period.- Perspectives on the Three Case Studies.- Period Criterion.- The Incorporation and Invariant Sequence Criteria.- The Reorganization Criterion.- III: The Construction of Verbal Unit Items: Brenda, Tarus, and James.- 1. Brenda.- Discussion of Brendas Case Study.- 2. Tarus.- Discussion of Taruss Case Study.- 3. James.- Discussion of Jamess Case Study.- Perspectives on the Case Studies.- The Verbal Period as a Subperiod in the Figurative Stage.- Counting-on.- IV: The Construction of Abstract Unit Items: Tyrone, Scenetra, and Jason.- 4. Tyrone.- The Motor Period.- The Abstract Period.- Discussion of Tryones Case Study.- 5. Scenetra.- The Motor Period.- The Verbal Period.- The Abstract Period.- Discussion of Scenetras Case Study.- 6. Jason.- The Motor Period.- Creating Verbal Unit Items.- The Abstract Period.- Discussion of Jasons Case Study.- Perspectives on the Case Studies.- Stages.- Incorportation Criterion.- Transition to the Abstract Period.- The Reorganization of Counting.- V: Lexical and Syntactical Meanings: Brenda, Tarus, and James.- 1. Brenda.- The Perceptual Period.- The Motor Period.- The Verbal Period.- Discussion of Brendas Case Study.- The Perceptual Stage.- The Figurative Stage.- 2. Tarus.- The Perceptual Period.- The Motor Period.- The Verbal Period.- Discussion of Taruss Case Study.- The Perceptual Stage.- The Figurative Stage.- 3. James.- The Perceptual Period.- The Motor Period.- The Verbal Period.- Discussion of Jamess Case Study.- The Perceptual Stage.- The Figurative Stage.- Perspectives on the Case Studies.- The Perceptual Stage.- Finger Patterns.- The Figurative Stage.- Mobile Finger Patterns.- Sophisticated Finger Patterns.- Spatio-Auditory Patterns.- Dual Meanings of Number Words.- Counting as the Meaning of Number Words.- Summary of the Types of Preconcepts and Concepts.- Meanings of Ten.- Ten as an Enactive Concept.- Ten as a Countable Figural Unit.- Ten as a Countable Motor Unit.- Adding Schemes.- The Perceptual Stage.- The Figurative Stage.- Comments on Prenumerical Children.- VI: Lexical and Syntactical Meanings: Tyrone, Scenetra, and Jason.- Systems of Integration.- Integrations.- Sequential Integration Operations.- Progressive Integration Operations.- Part-Whole Operations.- 4. Tyrone.- The Emergence of the Integration Operation.- The Period of Sequential Integration Operations.- The Period of Progressive Integration Operations.- The Period of Part-Whole Operations.- Discussion of Tyrones Case Study.- The Emergence of the Integration Operation.- The Period of Sequential Integration Operations.- The Period of Progressive Integration Operations.- The Period of Part-Whole Operations.- Unit Types of the Unit of Ten.- 5. Scenetra.- Recognition and Re-Presentation of Patterns.- The Emergence of the Integration Operation.- The Period of Sequential Integration operations.- The Period of Progressive Integreation Operations.- Discussion of Scenetras Case Study.- The Emergence of the Integratoin Operation.- The Period of Sequential Integration Operations.- The Period of Progressive Integration Operations.- Unit Types of the Unit of Ten.- 6. Jason.- Recognition and Re-Presentation of Patterns.- The Emergence of The Integration Operation.- The Period of Sequential Integration Operations.- The Period of Progressive integration Operations.- The Period of Part-Whole Operations.- Discussion of Jasons Case Study.- The Emergence of the Integration Operation.- The Period of Sequential Integration Operations.- The Period of Progressive Integration Operations.- The Period of Part-Whole Operations.- Unit Types of the Unit of Ten.- Perspectives on the Case Studies.- The Emergence of the Integration Operation.- Numerical Patterns.- Number Sequences.- Stages in the Construction of the Numerical Counting Scheme.- Piagets Invariant Sequence and Incorporation Criteria.- The Reorganization Criterion.- Units of One.- The Unit of One in Sequential Integration Operations.- The Unit of One in Progressive Integration Operations.- The Unit of One in Part-Whole Operations.- Units of Ten.- The Stage of Sequential Integration Operations.- The Stage of Progressive Integration Operations.- The Stage of Part-Whole Operations.- Other Perspectives.- VII: Strategies for Finding Sums and Differences: Brenda, Tarus, and James.- Brenda.- Independent Solutions.- Number Word Coordinations.- Tarus.- Independent Solutions.- Number Word Coordinations.- James.- Independent Solutions.- Number Word Coordinations.- Perspectives on the Case Studies.- Number Facts.- VIII: Strategies for Finding Sums and Differences: Tyrone, Scenetra, and Jason.- Sequential Integration Operations.- Jason.- Tyrone.- Scenetra.- Discussion: Sequential Integration Operations.- Progressive Integration Operations.- Jason.- Tyrone.- Scenetra.- Discussion: Progressive Integration Operations.- Part-Whole Operations.- Jason.- Tyrone.- Perspective on the Case Studies.- Arithmetical Context.- Thinking Strategies and Integration Operations.- Thinking Strategies and the Basic Facts.- Thinking Strategies and the Construction of Part-Whole Operations.- Goals for Teaching Thinking Strategies.- IX: Modifications of the Counting Scheme.- Predicting Modifications of the Counting Scheme.- Mathematical Learning.- The Perceptual Stage.- Temporary Modifications.- Procedural Accommodations.- Engendering Accommodations.- Isolated Procedural Accommodations.- The Figurative Stage.- Procedural Accommodations.- Temporary Modifications.- Retrospective Accommodations.- Re-presentation and Review of Prior Activity.- The Figurative Stage: Tyrone, Scenetra, and Jason.- Procedural Engendering Accommodations.- Temporary Modifications.- Metamorphic Accommodations.- Stages in the Construction of Part-Whole Operations.- Sequential Integration Operations.- Procedural Accommodations.- Engendering Accommodations.- Progressive Integration Operations.- Internal Reorganizations.- Part-Whole Operations.- Phylogenetic Perspectives.- Zones of Potential Development in Retrospect.- Figurative Stage.- Sequential Integration Operations.- Progressive Integration Operations.- Part-Whole Operations.- Final Comments.- References.

Radical Constructivism in Mathematics Education.

There is No More Safety in Numbers: A New Conception of Mathematics Teaching.- Mathematical Discussions.- Notations and Representations as Mediators of Constructive Processes.- Making Math Mean.- Treatment of Refutations: Aspects of the Complexity of a Constructivist Approach to Mathematics Learning.- Learning to Listen: A Students Understanding of Powers of Ten.- Understanding Students Beliefs About Probability.- A Constructivist Approach to Second Grade Mathematics.- The Constructivist Teaching Experiment: Illustrations and Implications.- Didactic Constructivism.- Two Layers of Constructivist Curricular Interaction.

An Exposition of Constructivism: Why Some Like it Radical

When the Neapolitan philosopher Giambattista Vico published his treatise on the construction of knowledge,† it triggered quite a controversy in the Giornale de’Letterati d’Italia, one of the most prestigious scholarly journals at the time. This was in the years 1710–1712. The first reviewer, who remained anonymous, had carefully read the treatise and was obviously shocked by the implications it had for traditional epistemology—all the more so because, as he conceded, the arguments showed great learning and were presented with elegance. He was therefore impelled to question Vico’s position, and he very politely suggested that one thing was lacking in the treatise: the proof that what it asserted was true.

THE RADICAL CONSTRUCTIVIST VIEW OF SCIENCE

From the constructivist perspective, science cannot transcend thedomain of experience. Scientific theories are seen as models that helpto order and manage that domain. As the experiential field expands,models are replaced by others based on novel conceptual constructs. Thepaper suggests the substitution of ‘viability’ or ‘functional fit’ forthe notions of Truth and objective representation of anexperiencer-independent reality. This by-passes the scepticsincontrovertible arguments against certain real-world knowledge andproposes the Piagetian conception of cognition as the function thatgenerates ways and means for dealing with the world of experience.From the constructivist perspective, science cannot transcend thedomain of experience. Scientific theories are seen as models that helpto order and manage that domain. As the experiential field expands,models are replaced by others based on novel conceptual constructs. Thepaper suggests the substitution of ‘viability’ or ‘functional fit’ forthe notions of Truth and objective representation of anexperiencer-independent reality. This by-passes the scepticsincontrovertible arguments against certain real-world knowledge andproposes the Piagetian conception of cognition as the function thatgenerates ways and means for dealing with the world of experience.

The reluctance to change a way of thinking

The theory of Radical Constructivism is restated with emphasis on its two basic principles: 1) that knowledge is built up through subjective activity, and 2) that the function of cognition is adaptive and focused on the organisation of the experiential world. The work of Piaget is used both to illuminate an innovation in constructivistic theory that was misinterpreted, and to provide a language for analysing such misinterpretations. The most frequent misinterpretations and objections to Radical Constructivism are outlined and refuted. These include the issues of solipsism, instrumentation, the relativity of problems and solutions, and the constructivist analysis of language and communication.

Radical constructivism and teaching

Learning will be defined as a conceptual activity and teaching distinguished from training. The role of language in these processes will be examined. The author maintains that there can be no understanding without reflection. Reflection is induced by verbalization and can therefore be encouraged by fostering conversation. Ceccato’s notion of ‘operational awareness’ will be shown to be relevant to teaching and compatible with Piaget’s theoretical model.

On the concept of interpretation

Abstract Whenever a piece of language is interpreted, the process involves building up a conceptual structure. Though the structure may be a novel composition, the elements of which it is composed are always elements derived from the interpreters own experience. One persons interpretation of a certain item can, therefore, be at best considered compatible with anothers. While a particular interpretation may be inconsistent or incompatible with the given text, any claim that there can be only one “correct” interpretation seems unwarranted in the light of a constructivist theory of knowledge.

chapter 2 – Linguistic Communication: Theory and Definition

Publisher Summary nThis chapter provides an overview of theory and definition in context to the linguistic communication. The sum of language as a communicatory system can be concluded into three indispensable characteristics. (1) There must be a set, or lexicon, of artificial signs. (2) These signs can be and are used as symbols; in other words, they are used on the conceptual level and without reference to a particular perceptual or behavioral instance of the item they signify. (3) There must be a grammar, that is, a set of conventional rules that govern the formation of sign combinations that have semantic content in addition to the meanings of the individual signs. The artificiality of signs and, thus, their communicatory status may be established only after prolonged observation in the wild. In the laboratory, it is a foregone conclusion that the signs are artificial as they are manmade and, as such, not a part of the subjects original behavioral repertoire. The use of signs as symbols by free-living organisms could be established only after a minute examination of their sign repertoire and the activities preceding and following the occurrence of specific signs. In the experimental situation, on the other hand, how the signs are being used can be discovered by certain questions, that is, by means of the very system of communication to which the subject is being introduced. The question of conformity to grammatical rules of sign combination is a good deal easier to decide.