Developing a theory of mathematical growth.

Autor/in	Tall, David O.
Titel	Developing a theory of mathematical growth.
Quelle	In: ZDM : mathematics education, 39 (2007) 1-2, S. 145-154 PDF als Volltext Link als defekt meldenVerfügbarkeit
Sprache	englisch
Dokumenttyp	online; gedruckt; Zeitschriftenaufsatz
ISSN	1863-9690; 1863-9704
DOI	10.1007/s11858-006-0010-3
Schlagwörter	Entwicklungspsychologie; Kognitive Entwicklung; Mathematisches Denken; Modell; Theorie
Abstract	In this paper I formulate a basic theoretical framework for the ways in which mathematical thinking grows as the child develops and matures into an adult. There is an essential need to focus on important phenomena, to name them and reflect on them to build rich concepts that are both powerful in use and yet simple to connect to other concepts. The child begins with human perception and action, linking them together in a coherent way. Symbols are introduced to denote mathematical processes (such as addition) that can be compressed as mathematical concepts (such as sum) to give symbols that operate flexibly as process and concept (procept). Knowledge becomes more sophisticated through building on experiences met before, focussing on relationships between properties, leading eventually to the advanced mathematics of concept definition and deduction. This gives a theoretical framework in which three modes of operation develop and grow in sophistication from conceptual-embodiment using thought experiments, to proceptual-symbolism using computation and symbol manipulation, then on to axiomatic-formalism based on concept definitions and formal proof.
Erfasst von	FIZ Karlsruhe - Leibniz-Institut für Informationsinfrastruktur
Update	2010/1