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ERIC Number: EJ780691
Record Type: Journal
Publication Date: 2007-Jul
Pages: 27
Abstractor: Author
ISBN: N/A
ISSN: ISSN-1098-6065
EISSN: N/A
Pattern Generalization with Graphs and Words: A Cross-Sectional and Longitudinal Analysis of Middle School Students' Representational Fluency
Nathan, Mitchell J.; Kim, Sunae
Mathematical Thinking and Learning: An International Journal, v9 n3 p193-219 Jul 2007
Cross-sectional and longitudinal data from students as they advance through the middle school years (grades 6-8) reveal insights into the development of students' pattern generalization abilities. As expected, students show a preference for lower-level tasks such as "reading the data," over more distant predictions and generation of abstractions. Performance data also indicate a "verbal advantage" that shows greater success when working with words than graphs, a replication of earlier findings comparing words to symbolic equations. Surprisingly, students show a marked advantage with patterns presented in a continuous format (line graphs and verbal rules) as compared to those presented as collections of discrete instances (point-wise graphs and lists of exemplars). Student pattern-generalization performance also was higher when words and graphs were combined. Analyses of student performance patterns and strategy use contribute to an emerging developmental model of representational fluency. The model contributes to research on the development of representational fluency and can inform instructional practices and curriculum design in the area of algebraic development. Results also underscore the impact that perceptual aspects of representations have on students' reasoning, as suggested by an Embodied Cognition view. (Contains 8 figures and 1 table.)
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 - Research
Education Level: Middle Schools
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A