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ERIC Number: EJ1020159
Record Type: Journal
Publication Date: 2013-Sep
Pages: 8
Abstractor: ERIC
ISSN: ISSN-1073-5836
Developing Multiplicative Thinking from Additive Reasoning
Tobias, Jennifer M.; Andreasen, Janet B.
Teaching Children Mathematics, v20 n2 p102-109 Sep 2013
As students progress through elementary school, they encounter mathematics concepts that shift from additive to multiplicative situations (NCTM 2000). When they encounter fraction problems that require multiplicative thinking, they tend to incorrectly extend additive properties from whole numbers (Post et al. 1985). As a result, topics such as fraction equivalence are difficult for students to understand even after formal instruction (Kamii and Clark 1995; Ni 2001). Fraction equivalence is "generally viewed as the ability to call the same number by different names, the ability to ignore or imagine partition lines, and/or a manifestation of flexible thought" (Kamii and Clark 1995). When generating equivalent fractions, students typically multiply or divide the numerator and denominator by the same factor. By building on additive strategies, such as unit and composite unit relationships, teachers can give students a foundation for developing an understanding of these multiplicative strategies on their own. In this article, authors use the context of restaurants to teach a lesson in equivalent fractions.
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:; Web site:
Publication Type: Journal Articles; Reports - Descriptive
Education Level: Elementary Education
Audience: Teachers
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A