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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.

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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.

Author information

Authors and Affiliations

  1. Middle Tennessee State University, Murfreesboro, USA

    Rongjin Huang

  2. Hangzhou Normal University, Hangzhou, China

    Zikun Gong

  3. Dominican University, River Forest, USA

    Xue Han

Authors
  1. Rongjin Huang
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  2. Zikun Gong
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  3. Xue Han
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Corresponding author

Correspondence to Rongjin Huang.

Appendices

Appendix 1: Post-lesson assessment

Greetings, class! To understand your learning situation in the class, we designed this questionnaire. Please carefully answer each question according to the instructions given. Just write down what you think. We will not grade your work and compare you answers with others. Thank you for your cooperation.

First, you need to compute arithmetic expressions. Then, justify your computations using as many as methods as possible such as verbal explanation, visual diagrams, or arithmetic expressions. The more details the better.

  1. 1.

    How many glasses of 1/5-L are there in 3 L of milk?

  2. 2.

    How many glasses of 2/3-L are there in 1 L of milk?

  3. 3.

    How many glasses of 2/3-L are there in 3 L of milk?

  4. 4.

    How many glasses of 1/5-L are there in 1/3 L of milk?

  5. 5.

    How many glasses of 2/3-L are there in 4/5 L of milk?

Appendix 2

Learning trajectory and associated tasks in research lesson 1

Learning trajectory

Mathematics task

First teaching

Second teaching

1. Connecting to previous knowledge (divisions with whole numbers) (e.g., 1 ÷ 5 = 1 × 1/5)

T1: There is a 5-L bucket of water. Five friends share the bucket equally, how much does each friend get?

T1: A 1-kilogram rectangle cake is shared between five friends, how much does each friend get?

2. A fraction divided by a whole number (when the numerator is the multiplier of divisor) (e.g., 4/5 ÷ 2)

T2: 4/5 of a rectangle paper is cut into two equal parts, how much does each parts have?

T2: A 4/5-kg of cake is shared between two friends, how much does each friend get?

3. A unit fraction divided by a whole number (e.g., 1/5 ÷ 2)

Not available

T3: A 1/5-kg cake is shared between 2 friends, how much does each friend get?

3. A fraction divided by a whole number (when the numerator is not a multiplier of divisor) (e.g., 4/5 ÷ 3)

T3: 4/5 of a rectangle paper is cut into three equal parts, how much does each parts have?

T4: A 4/5-kg cake is shared between 3 friends, how much does each friend get?

Practice: A 3/10-kg cake is shared between 8 friends, how much does each friend get?

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Huang, R., Gong, Z. & Han, X. Implementing mathematics teaching that promotes students’ understanding through theory-driven lesson study. ZDM Mathematics Education 48, 425–439 (2016). https://doi.org/10.1007/s11858-015-0743-y

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