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.
สารบัญ
Grounding Mathematics Education.- Sign Processes.- 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.- Mathematics, Sign and Activity.- Sign Processes in the Mathematics Classroom.- 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.- The Semiotics of the Schema.- Mathematics Education as a Science.- Towards a Normal Science of Mathematics Education?.- The Study of the Didactical Conditions of School Learning in Mathematics.- The Formal, The Social and the Subjective.- Crossing Boundaries.- Reflective Learning.- Thinking and Knowing About Knowledge.- The Cognitive Unconscious.- History of Mathematics and Mathematics Education.- 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.- Some German Contributions to Mathematics Research in Brazil.- Making Philosophy of Mathematics Relevant.- Data 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?.- Coda.- An Interview with Michael Otte.
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