Opportunities to Learn: Inverse Relations in U.S. and Chinese Textbooks

ABSTRACT

This study, focusing on inverse relations, examines how representative U.S. and Chinese elementary textbooks may provide opportunities to learn fundamental mathematical ideas. Findings from this study indicate that both of the U.S. textbook series (grades K-6) in comparison to the Chinese textbook samples (grades 1–6), presented more instances of inverse relations, while also containing more unique types of problems; yet, the Chinese textbooks provided more opportunities supporting meaningful and explicit learning. In particular, before presenting corresponding practice problems, Chinese textbooks contextualized worked examples of inverse relations in real-world situations to aid in sense making of computational or checking procedures. The Chinese worked examples also differed in representation uses especially through concreteness fading. Finally, the Chinese textbooks spaced learning over time, systematically stressing structural relations including the inverse quantities relationships. These findings shed light on ways to support students’ meaningful and explicit learning of fundamental mathematical ideas in elementary school.

Acknowledgments

The author is grateful to the editor and the five anonymous reviewers for their constructive feedback. Thanks also go to Xiaobao Li and Kelley Marshal for reliability checking and to Ryan Hassler for editorial assistance.

Additional information

Funding

This study is partially supported by the National Science Foundation CAREER program under Grant No. DRL-1350068 at Temple University. Any opinions, findings, and conclusions in this study are those of the author and do not necessarily reflect the views of the National Science Foundation.