ISBN:
9780387242705
Language:
English
Pages:
Online-Ressource (VII, 389 p, digital)
Series Statement:
SpringerLink
Series Statement:
Bücher
Parallel Title:
Buchausg. u.d.T. Activity and sign
Keywords:
Science History
;
Mathematics
;
Education
;
Education
;
Science History
;
Mathematics
;
Aufsatzsammlung
;
Mathematikunterricht
Abstract:
"The advancement of a scientific discipline depends not only on the ""big heroes"" of a discipline, but also on a community's ability to reflect on what has been done in the past and what should be done in the future. This volume combines perspectives on both. It celebrates the merits of Michael Otte as one of the most important founding fathers of mathematics education by bringing together all the new and fascinating perspectives created through his career as a bridge builder in the field of interdisciplinary research and cooperation. The perspectives elaborated here are for the greatest part motivated by the impressing variety of Otte's thoughts, however, the idea is not to look back, but to find out where the research agenda might lead us in the future. This volume provides new sources of knowledge based on Michael Otte's fundamental insight that understanding the problems of mathematics education - how to teach, how to learn, how to communicate, how to do, and how to represent mathematics - depends on means, mainly philosophical and semiotic, that have to be created first of all, and to be reflected from the perspectives of a multitude of diverse disciplines."
Description / Table of Contents:
Grounding Mathematics Education; Mathematics, Sign and Activity; Agency and Creativity in the Semiotics of Learning Mathematics; The Semiotic Approach to Mathematical Evidence and Generalization; Signs as Means for Discoveries; Diagrammatic Thinking; Notes on a Semiotically Inspired Theory of Teaching and Learning; Semiotic Mediation in the Primary School; Do Mathematical Symbols Serve to Describe or Construct "Reality"?; Metaphor and Metonymy in Processes of Semiosis in Mathematics Education; On Practical and Theoretical Thinking and Other False Dichotomies in Mathematics Education
Description / Table of Contents:
The Semiotics of the SchemaTowards a Normal Science of Mathematics Education?; The Study of the Didactical Conditions of School Learning in Mathematics; The Formal, The Social and the Subjective; Reflective Learning; Thinking and Knowing About Knowledge; The Cognitive Unconscious; Hilbert, Weyl, and the Philosophy of Mathematics; Mathematical Metaphors in Natorp's Neo-Kantian Epistemology and Philosophy of Science; Newton's Program of Mathematizing Nature; Did Hermann and Robert Graßmann Contribute to the Emergence of Formal Axiomatics?; A Case Study in Generalisation
Description / Table of Contents:
Some German Contributions to Mathematics Research in BrazilData Structures and Virtual Worlds; Variables, in Particular Random Variables; Deduction, Perception, and Modeling; Models of Data, Theoretical Models, and Ontology; Some Sober Conceptions of Mathematical Truth; Can There Be an Alternative Mathematics, Really?; An Interview with Michael Otte
Description / Table of Contents:
Grounding Mathematics Education : Michael Otte's contribution / Michael Hoffmann, Johannes Lenhard and Falk SeegerMathematics, Sign and Activity / Michael Otte -- A. Sign Processes -- Agency and Creativity in the Semiotics of Learning Mathematics / Paul Ernest -- The Semiotic Approach to Mathematical Evidence and Generalization / Susanna Marietti -- Signs as Means for Discoveries : Peirce and His Concepts of "Diagrammatic Reasoning," "Theorematic Deduction," "Hypostatic Abstraction", and "Theoric Transformation" / Michael Hoffmann -- Diagrammatic Thinking : Affordances and Constraints / Willibald Dorfler -- Notes on a Semiotically Inspired Theory of Teaching and Learning / Falk Seeger -- B. Sign Processes in the Mathematics Classroom -- Semiotic Mediation in the Primary School : Durer's Glass / Maria G. Bartolini Bussi, Maria Alessandra Mariotti and Franca Ferri -- Do Mathematical Symbols Serve to Describe or Construct "Reality"? : Epistemological Problems in Teaching Mathematics in the Field of Elementary Algebra / Heinz Steinbring -- Metaphor and Metonymy in Processes of Semiosis in Mathematics Education / Norma Presmeg -- On Practical and Theoretical Thinking and Other False Dichotomies in Mathematics Education / Anna Sierpinska -- The Semiotics of the Schema : Kant, Piaget, and the Calculator / Luis Radford -- C. Mathematics Education as a Science -- Towards a Normal Science of Mathematics Education? / Kenneth Ruthven -- The Study of the Didactical Conditions of School Learning in Mathematics / Guy Brousseau -- The Formal, the Social and the Subjective : Variations on a Theme of Michael Otte / Roland Fischer -- D. Crossing Boundaries -- Reflective learning : Problems and Questions Concerning a Current Contextualization of the Vygotskian Approach / Bernd Fichtner -- Thinking and Knowing about knowledge : A Plea for and Critical Remarks on Psychological Research Programs on Epistemological Beliefs / Rainer Bromme -- The Cognitive Unconscious : Recalling the History of the Concept and the Problem / Thomas Mies -- E. History of Mathematics and Mathematics Education -- Hilbert, Weyl, and the Philosophy of Mathematics / Hans Niels Jahnke -- Mathematical Metaphors in Natorp's Neo-Kantian Epistemology and Philosophy of Science / Thomas Mormann -- Newton's Program of Mathematizing Nature / Karl-Norbert Ihmig -- Did Hermann and Robert Grassmann Contribute to the Emergence of a Formal Axiomatics? / Mircea Radu -- A Case Study in Generalization : The Notion of Multiphcation / Gert Schubring -- Some German Contributions to Mathematics Research in Brazil / Circe Mary Silva da Silva Dynnikov -- F. Making Philosophy of Mathematics Relevant -- ata Structures and Virtual Worlds : On the Inventiveness of Mathematics / Andreas Dress -- Variables, in Particular Random Variables / Hermann Dinges -- Deduction, Perception and Modeling : The Two Peirces on the Essence of Mathematics / Johannes Lenhard -- Models of Data, Theoretical Models and Ontology : A Structuralist Perspective / C. Ulises Moulines -- Some Sober Conceptions of Mathematical Truth / Marco Panza -- Can There Be an Alternative Mathematics, Really? / Jean Paul van Bendegem -- G. Coda -- An Interview with Michael Otte / Roland Fischer.
Note:
Includes bibliographical references and index
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