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ERIC Number: EJ784186
Record Type: Journal
Publication Date: 2007-Dec
Pages: 40
Abstractor: Author
Reference Count: 59
ISBN: N/A
ISSN: ISSN-0737-0008
The Influence of Reasoning with Emergent Quantities on Students' Generalizations
Ellis, Amy B.
Cognition and Instruction, v25 n4 p439-478 Dec 2007
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.)
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
Publication Type: Journal Articles; Reports - Evaluative
Education Level: Grade 8; Middle Schools
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A