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

Abstract

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.

ACKNOWLEDGMENTS

We are grateful to the editor and reviewers for their constructive comments on an earlier version of this article. Thanks also go to Becky Kromminga, Kelsey Campfield, and Melinda diSessa for helpful assistance.

Notes

The meaning of multiplication is represented differently in Chinese texts. Thus, the total length of 18 knots with each 3/5 meter long is represented as 3/5 × 18 rather than 18 × 3/5 (as is common in the United States). This type of thinking is consistent across word problems in Chinese texts.

The Chinese text uses “a” triangles, which is clear among Chinese characters. For clarity, we changed “a” to “n” in this article.