Does Mathematical Learning Occur in Going from Concrete to Abstract or in Going from Abstract to Concrete?

Autor/inn/en	Roth, Wolff-Michael; Hwang, SungWon
Titel	Does Mathematical Learning Occur in Going from Concrete to Abstract or in Going from Abstract to Concrete?
Quelle	In: Journal of Mathematical Behavior, 25 (2006) 4, S.334-344 (11 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0732-3123
DOI	10.1016/j.jmathb.2006.11.006
Schlagwörter	Mathematical Logic; Mathematical Concepts; Mathematics Instruction; Abstract Reasoning; Concept Formation; Logical Thinking; Thinking Skills + Suchen Sie Ihr Suchwort? Mathematical logics; Mathematische Logik; Mathematics lessons; Mathematikunterricht; Abstraktes Denken; Denken; Concept learning; Begriffsbildung; Denkfähigkeit
Abstract	The notions of "abstract "and "concrete" are central to the conceptualization of mathematical knowing and learning. It is generally accepted that development goes from concrete toward the abstract; but dialectical theorists maintain just the opposite: development consists of an ascension from the abstract to the concrete. In this article, we reformulate the relationship of abstract and concrete consistent with a dialectical materialist approach to conscious human activity, as it was developed in the line of cultural-historical psychology. Our reformulation of development in and through interpretation shows that rather than being a movement from concrete to abstract or from abstract to concrete, development occurs in a double ascension that simultaneously moves in both direction: it is a passage of one in the other. In the proposed approach, the theoretical contradictions of earlier approaches to the issue of abstract have been eliminated. (Contains 1 figure.) (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10