# Implementing mathematics teaching that promotes students’ understanding through theory-driven lesson study

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## Abstract

Lesson study (LS) has been practiced in China as an effective way to advance teachers’ professional development for decades. This study explores how LS improves teaching that promotes students’ understanding. A LS group including didacticians (practice-based teaching research specialist and University-based mathematics educators) and mathematics teachers in China explored and documented how teacher participants shifted their attention to students’ learning by incorporating two notions of teaching: learning trajectory (LT) and variation pedagogy (VP). The former describes conjectured routes of children’s thinking and learning with pertinent tasks to move towards the learning goals along the route, while the latter suggests strategies for using systematic tasks progressively. The concepts of LT and VP are used to guide planning, teaching, and debriefing throughout the LS process. Data consist of lesson plans, videotaped lessons, post-lesson discussions, post-lesson quizzes, and teachers’ reflection reports. This study reveals that by building on the learning trajectory and by strategically using variation tasks, the lesson has been improved in terms of students’ understanding, proficiency, and mathematical reasoning. In addition, the LT was refined through the LS. This study displays how theory-driven LS could help teachers improve their teaching and develop the linkage between theory and practice.

## Keywords

Lesson study Learning trajectory Variation pedagogy Theory-driven lesson study## Notes

### Acknowledgments

We thank anonymous reviewers for their invaluable feedback on the revisions of the paper. We appreciate Dr. Dovie Kimmins and Mr. James Willingham from Middle Tennessee State University for their contribution to the improvement of the article. Our thanks go to participating teachers and didacticians for their commitment to the Lesson Study and support of data collection.

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