A Comparative Analysis of the Distributive Property in U.S. and Chinese Elementary Mathematics Textbooks

This study examines presentations of the distributive property (DP) in two widely used U.S. elementary text series and one main Chinese text series along three dimensions: problem contexts, typical problem types within each problem context, and variability in using the DP. In general, the two U.S. t...

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Bibliographic Details
Published in:Cognition and instruction 2010-01, Vol.28 (2), p.146-180
Main Authors: Ding, Meixia, Li, Xiaobao
Format: Article
Language:English
Subjects:
Algebra
Arithmetic
China
Comparative Analysis
Computation
Cultural Differences
Curricula
Distributivity
Elementary education
Elementary School Mathematics
Foreign Countries
Fractions
Fundamental Concepts
Learning
Mathematical Concepts
Mathematical problems
Mathematics
Mathematics Education
Numbers
Studies
Textbooks
United States
Whole numbers
Word problems
Word Problems (Mathematics)
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Summary:This study examines presentations of the distributive property (DP) in two widely used U.S. elementary text series and one main Chinese text series along three dimensions: problem contexts, typical problem types within each problem context, and variability in using the DP. In general, the two U.S. texts were found to resemble each other but to differ considerably from the Chinese text series. Both U.S. texts are computation-dominated, presenting various strategies centering on "breaking apart a factor to perform multiplication." These strategies limit the use of the DP mainly with whole numbers and in a regular direction. The underlying principle of these strategies is seldom made explicit. In contrast, the Chinese text approaches focus on the underlying principle and are well aligned with cognitive research suggestions. Multiple-step word problems with particular structures are used in a systematic and hierarchic manner across grades to help students learn and transfer the DP. The Chinese texts also tend to ask students to "compute in convenient ways" involving various numbers (e.g., whole numbers, decimals, fractions, and percents) and using the DP in both regular and opposite directions. The introduction of repeated variables is a timely application of the DP, which provides an entry to algebra (e.g., expressions and equations with repeated variables). The Chinese approaches (e.g., contextual interferences, spaced practice, and encoding variability) suggest alternative insights into developing U.S. students' understanding of the DP and readying them for algebra.
ISSN:0737-0008
1532-690X
DOI:10.1080/07370001003638553