Linear quantity models in US and Chinese elementary mathematics classrooms

ABSTRACT

Linear quantity models such as pre-tapes, tape diagrams, and number line diagrams have drawn increasing attention in mathematics education around the world. However, we still know relatively little about how teachers actually use these models in the classroom. This study explores how exemplary US and Chinese elementary teachers use linear quantity models during mathematics instruction. Based on an examination of 64 videotaped lessons on inverse relations, we identified 110 “diagram episodes.” An analysis of these episodes reveals that linear quantity models, especially tape diagrams, were used more frequently in US classrooms than in Chinese classrooms. However, Chinese lessons used these models for the sole purpose of modeling the underlying quantitative relationships, whereas US lessons mainly used them to aid in computation. In addition, while US teachers rarely involved students in discussion of linear quantity models, Chinese teachers spent significant time engaging students in co-constructing, comparing, and explaining these models.

KEYWORDS:

• Linear quantity model
• tape diagram
• number line diagram
• elementary mathematics
• US and Chinese classrooms

Acknowledgment

This work is supported by the National Science Foundation at Temple University (DRL-1350068). Any opinions, findings, and conclusions in this study are those of the authors and do not necessarily reflect the views of the funding agency. Thanks also go to Aki Murata for two rounds of feedback on the initial manuscripts. We are also grateful to the editor and four anonymous reviewers’ insightful feedback as well as Tim Fukawa-Connelly and Eli Barnett’s input for the manuscript revision.

Notes

1. To solve division problems, Chinese students are taught to use multiplication rhythm (乘法口诀)。This is a common mathematical practice generation by generation.

Additional information

Funding

This work was supported by the National Science Foundation [1350068].