Symbolizing, Modeling and Tool Use in Mathematics Education

ISBN-13: 9781402010323 / Angielski / Twarda / 2002 / 308 str.

Koeno Gravenmeijer; K. P. Gravemeijer; R. Lehrer

Opis

The almost universal rejection of the notion of symbols as carriers of meaning' has created the need to find an alternative for the use of models as embodiments of mathematical concepts. By taking its point of departure as a concern for the way students actually use tools and symbols, and for what these signify for them, this book explores the option of building on symbolizing, modelling and tool use as personally meaningful activities of students. This theme is approached from different angles and different perspectives. One dimension is that of setting, varying from the study of informal, spontaneous activity of students, to an explicit focus on instructional design, and goals and effects of instruction. Another dimension is the theoretical framework of the researcher, varying from constructivism, to activity theory, cognitive-psychology and instructional-design theory. This book will appeal to a wide audience, varying from researchers, instructional designers, educators, and graduate students.

Spis treści

Introduction and overview; K. Gravemeijer, et al. Preamble: from models to modelling; K. Gravemeijer. Section I: Emergent Modeling. Introduction to Section I: Informal representations and their improvements; B.van Oers. The mathematization of young childern's language; B.van Oers. Symbolizing space into being; R. Lehrer, C. Pritchard. Mathematical representations as systems of notations-in-use; L. Meira. Student's criteria for representational adequacy; A. diSessa. Transitions in emergent modeling; N. Presmeg. Section II: The Role of Models, Symbols and Tools in Instructional Design. Introduction to Section II: the role of models, symbols and tools in instructional design; K. Gravemeijer. Emergent models as an instructional design heuristic; K. Gravemeijer, M. Stephan. Modeling, symbolizing, and tool use in statistical data analysis; P. Cobb. Didactic objects and didactic models in radical constructivism; P.W. Thompson. Taking into account different views: three brief comments on papers by Gravemeijer and Stephan, Cobb and Thompson; C. Selter. Section III: Models, Situated Practices, and Generalization. Introduction to Section II: models, situated practices, and generalization; L. Verschaffel. On guessing the essential thing; R. Nemirovsky. Everyday knowledge and mathematical modeling of school word problems; L. Verschaffel, et al. On the development of human representational competence from an evolutionary point of view: from episodic to virtual culture; J. Kaput, D. Shaffer. Modeling reasoning; D. Carraher, A. Schliemann. Index.