Arbeitsstelle für Semiotik

English version

Faculty 1: History and communication sciences

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The "Zeitschrift für Semiotik"
Abstracts
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"Learning as a Sign Process"

Year:	2000
Volume:	22
Number:	1

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Introduction
Michael Hoffmann
Learning as a sign process

Andre De Tienne
Learning, reasoning, semiose

Michael Hoffmann
The paradox of learning and a semiotic approach to its solution

Falk Seeger
Learning with graphic representations: psychological and semiotic observations

Michael Hoffmann, Marcel Plöger
Mathematics as a process of sign-generalization: a proposal for a teaching unit towards the discovery of incommensurability

Introduction
Learning as a sign process

Michael Hoffmann, University of Bielefeld

Summary. The aim of this introduction is to show which role Peircean semiotic theories can play with regard to two prominent pedagogical and developmental psychological research traditions: on the one hand, the "cultural-historical school" founded by Vygotskij, and on the other hand, Piaget's constructivist approaches. Furthermore, an overview of the articles in this issue is provided.

Learning, reasoning, semiose

Andre De Tienne

Summary. Capturing the elusive essence of learning requires theoretical tools tried and tested through detailed analysis of the general mechanism of representation. Peirce's semiotic logic provides just such an analysis and such tools. This article examines five assertions taken from one of Peirce's most informative works on this matter: that there is an essential relation between learning and the flow of time; that learning is a continuous process; that it is virtually equivalent to reasoning; that is is an interpretation; and finally, that it is representation and, thus, another name for the central category of Thirdness. I propose, among other things, that learning is a process of becoming increasingly sensitive to all kinds of signs, and that this process is accompanied by a progressive comprehension of the general conditional laws, the realization of which shapes future.

The paradox of learning and a semiotic approach to its solution

Michael Hoffmann, University of Bielefeld

Summary. Understanding the process of learning requires an examination of the "paradox of learning" that was first formulated by Plato and then taken up by Jerry Fodor. This paradox raises the following question: how can the advancement from one level of knowledge to the next be explained if, by definition, the new cognitive level contains elements which can neither be deductively derived from the previous level nor be obtained inductively from experience alone? Fodor criticized Piaget's theory for not being able to solve this paradox. This article shows that Piaget's attempt to counter Fodor's objection by developing a concept of possibility is unconvincing because it is too strongly oriented towards the subject of cognition. A possible solution to this problem, however, can be seen in Peirce's concept of "diagrammatic reasoning", which permits an understanding of learning as a process. In this process, the learners construct diagrams, which initially enable them to perceive vague possibilities of their own thinking. This is crucial for making these possibilities an object of reflection. Through subsequent experimentation with these diagrams, relations between their components become evident which are different from the relations the learner used in constructing the diagrams.

Learning with graphic representations: psychological and semiotic observations

Falk Seeger, University of Bielefeld

Summary. This paper discusses certain theoretical aspects of a psycho-semiotic perspective on learning through use of graphical representations. The cultural-historical basis of this perspective is expressed in the belief that conceptional progress is achieved through thorough analysis of the genesis and use of external representations. Comprehending the effects of learning with representations requires a better understanding of the relationship between internal and external representations. Especially important is the idea of qualitative differences between representational systems, which explains why a one-to-one translation or mapping of one system into another is not possible. The consequence for education and the education sciences is that, although it is often considered a classical method of enhancing learning, switching between representational systems while teaching is a problem rather than a solution.

Mathematics as a process of sign-generalization: a proposal for a teaching unit towards the discovery of incommensurability

Michael Hoffmann and Marcel Plöger, University of Bielefeld

Summary. If one wants to understand the value of mathematical education, one must first gain an understanding of the essence of mathematics. This article develops the thesis that mathematics is a process of sign-generalization. It also presents a proposal for a teaching unit that uses a historical example, i.e., the discovery of incommensurability, to illustrate this thesis and render it plausible. In addition, the teaching unit is intended to demonstrate that learning itself can be understood as a process of generalizing representational systems. It follows that the development of mathematical thought can actually serve as a paradigm for cognitive development and learning. More specifically, it becomes clear that both the complementarity of intuitive and formal representations and the creation of new ideal objects and corresponding signs are important for individual and scientific generalization processes. The article closes with a detailed expansion of the teaching unit into three blocks. Preceeding this expansion, however, is information regarding the historical discovery of incommensurability and its philosophical context presented in the form of a critical summary of the current state of research.