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ERIC Number: EJ1048269
Record Type: Journal
Publication Date: 2015-Jan
Pages: 22
Abstractor: As Provided
Reference Count: 54
ISBN: N/A
ISSN: ISSN-0021-8251
Two Perspectives on Proportional Relationships: Extending Complementary Origins of Multiplication in Terms of Quantities
Beckmann, Sybilla; Izsák, Andrew
Journal for Research in Mathematics Education, v46 n1 p17-38 Jan 2015
In this article, we present a mathematical analysis that distinguishes two distinct quantitative perspectives on ratios and proportional relationships: variable number of fixed quantities and fixed numbers of variable parts. This parallels the distinction between measurement and partitive meanings for division and between two meanings for multiplication--one rooted in counting equal-sized groups, the other in scaling the size of the groups. We argue that (a) the distinction in perspectives is independent from other distinctions in the literature on proportional relationships, including the within measure space versus between measure space ratio distinction; (b) the psychological roots for multiplication suggest the accessibility of the two perspectives to learners; and (c) the fixed numbers of variable parts perspective, though largely overlooked in past research, may provide an important foundation for central topics that build on proportional relationships. We also suggest directions for future empirical research.
National Council of Teachers of Mathematics. 1906 Association Drive, Reston, VA 20191-1502. Tel: 800-235-7566; Tel: 703-620-3702; Fax: 703-476-2970; e-mail: orders@nctm.org; Web site: http://www.nctm.org/publications/
Publication Type: Journal Articles; Reports - Research
Education Level: Elementary Education; Secondary Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A