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ERIC Number: EJ782914
Record Type: Journal
Publication Date: 2008-Jan
Pages: 49
Abstractor: Author
Reference Count: 46
ISSN: ISSN-0737-0008
Mathematical Knowledge for Teaching Fraction Multiplication
Izsak, Andrew
Cognition and Instruction, v26 n1 p95-143 Jan 2008
The present study contrasts mathematical knowledge that two sixth-grade teachers apparently used when teaching fraction multiplication with the Connected Mathematics Project materials. The analysis concentrated on those tasks from the materials that use drawings to represent fractions as length or area quantities. Examining the two teachers' explanations and responses to their students' reasoning over extended sequences of lessons led to a theoretical frame that emphasizes relationships between teachers' unit structures and pedagogical purposes for using drawings. In particular, the present study builds on the distinction made in past research between reasoning with two and with three levels of quantitative units and demonstrates that reasoning with three levels of units is necessary but insufficient if teachers are to use students' reasoning with units as the basis for constructing generalized numeric methods for fraction arithmetic. Teachers need also to assemble three-level unit structures with flexibility supported by drawn versions of the distributive property. (Contains 15 figures and 8 footnotes.)
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:
Publication Type: Journal Articles; Reports - Research
Education Level: Grade 6; Middle Schools
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A