The Influence of Reasoning with Emergent Quantities on Students' Generalizations

Autor/in	Ellis, Amy B.
Titel	The Influence of Reasoning with Emergent Quantities on Students' Generalizations
Quelle	In: Cognition and Instruction, 25 (2007) 4, S.439-478 (40 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0737-0008
Schlagwörter	Algebra; Teaching Methods; Mathematics Instruction; Mathematical Concepts; Student Attitudes; Thinking Skills; Generalization; Models; Middle School Students; Grade 8; Interviews; Observation; Grade 7 + Suchen Sie Ihr Suchwort? Teaching method; Lehrmethode; Unterrichtsmethode; Mathematics lessons; Mathematikunterricht; Schülerverhalten; Denkfähigkeit; Analogiemodell; Middle school; Middle schools; Student; Students; Mittelschule; Mittelstufenschule; Schüler; Schülerin; School year 08; 8. Schuljahr; Schuljahr 08; Interviewing; Interviewtechnik; Beobachtung; School year 07; 7. Schuljahr; Schuljahr 07
Abstract	This paper reports the mathematical generalizations of two groups of algebra students, one which focused primarily on quantitative relationships, and one which focused primarily on number patterns disconnected from quantities. Results indicate that instruction encouraging a focus on number patterns supported generalizations about patterns, procedures, and rules, while instruction encouraging a focus on quantities supported generalizations about relationships, connections between situations, and dynamic phenomena, such as the nature of constant speed. An examination of the similarities and differences in students' generalizations revealed that the type of quantitative reasoning in which students engaged ultimately proved more important in influencing their generalizing than a mere focus on quantities versus numbers. In order to develop powerful, global generalizations about relationships, students had to construct ratios as emergent quantities relating two initial quantities. The role of emergent-ratio quantities is discussed as it relates to pedagogical practices that can support students' abilities to correctly generalize. (Contains 14 figures.) (Author).
Anmerkungen	Lawrence Erlbaum. Available from: Taylor & Francis, Ltd. 325 Chestnut Street Suite 800, Philadelphia, PA 19106. Tel: 800-354-1420; Fax: 215-625-2940; Web site: http://www.tandf.co.uk/journals/default.html
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10