# Developing students’ ability to solve word problems through learning trajectory-based and variation task-informed instruction

## Abstract

Solving word problems is challenging in elementary schools, both for the teacher in teaching students to solve word problems and for the student in learning to solve them. This paper examines how the ideas of learning trajectory and variation pedagogy could be integrated as an instructional principle for teaching this content in the context of solving additive comparison problems. Based on research literature, a learning trajectory for solving additive comparison problems was identified. Informed by variation pedagogy and using a lesson study approach, a research team explored how to teach solving comparison word problems based on this learning trajectory. Data included lesson plans, videotaped research lessons, students’ pre- and post-tests, and students’ interviews. A fine-grained analysis of the data demonstrated that the lessons unfolded through exploration of a series of deliberate tasks along the learning trajectory, focusing on the structure of comparison problems and targeted at objects of learning. Purposefully constructed patterns of variation and invariance provided students with necessary conditions to discern and experience the objects of learning. Students were actively engaged in making sense of comparison problems and articulating their thinking using multiple representations. While the post-test and interview data show students’ understanding of key aspects of solving additive comparison problems to be at various levels, students’ gains in overall performance from pre- to post-test were statistically significant. Implications for teaching comparison word problems are discussed.

## Keywords

Additive comparison word problems Lesson study Variation theory Learning trajectory## Notes

### Acknowledgements

We extend our thanks for the strong support from the participating school, Qiaotou no. 2 Elementary School of Yongjia County, City of Wenzhou, and especially to teaching research specialist Ms. Yuxiao Nan and mathematics teacher Jing Huang for their intellectual contribution to improving the design and teaching of the comparison word problem lessons.

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