-focusing on building connection between research and practice...

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How to conduct lesson study

-Focusing on building connection between research and practice

Rongjin Huang, Middle Tennessee State University, USA

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Research program: three phases

Qualitative QUANTATIVE AND MIXED METHODS

DESIGN-BASED RESEARCH

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Phase 3: Design-based studies

Theory-informed Lesson studies

Teachers’ Knowledge, e.g. of • Content• Student thinking• Curriculum and standards

Teachers’ Beliefs, e.g.• Expectations for student

achievement• Pedagogical commitments

Routines and Norms of Professional Learning, e.g.

• Study content with colleagues

• Inquiry stance in observing and discussing student learning

• Share challenges and learnings

Instructional Tools and Routines, e.g.,

• Discussion tools• Tasks

Instructionand

Student Learning

Study

Plan

Teach

Reflect

Intervening Changes OutcomesLesson Study Cycle

Lewis et al. (2009)

Clivaz (2018)

Lewis et al., (2018) Dudley et al., (2018 )

Research paradigm (I): Action research-oriented

Key features No explicit guiding theory;No repeated teaching;No knowledgeable others;

Research purposes: Address authentic problems; Develop practical knowledge

Research paradigm (II): Design research-oriented

Key featuresExplicit guiding theories;Iterative process ;Knowledgeable others;

Research purposes: Addressing authentic problems; Developing practical and theoretical knowledge

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Why Chinese Lesson study

Lewis (2016)

Similarities: – The same structure;– Nation and system wide;– Job-embedded;– Long history

Differences:– Content-focused: Perfecting a

lesson;– Various types (report lesson to

demo lesson);– Multiple iterations – Knowledgeable involvement

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Understanding Chinese LS

Lesson study is a research methodology:

building connection between research and practices

What is the gap between research and practice

研究者抱怨很多理论概念、模型、建议都是与实

践相关的，完全有可能帮助改进实践，但实践领

域对这些理论知识却知之甚少(Heid et al., 2006)。

实践者抱怨研究太过抽象，过于理论化的内容离

他们的实践背景太遥远(Silver & Lunsford, 2017)。

• Silver和Lunsford (2017)指出3个方面：– 第一是对于教育实践的关联性很低，研究者为了研究而做研究，很少有研究者会揭示对儿童和成人的数学学习能够产生真正影响的东西;

– 第二是对于支持实施和传播教育研究的基金和设施的匮乏，这意味着很多研究发现仅仅是为研究者这个小的群体书写和阅读的，难以在实践者中间得到传播。

– 第三是研究者和实践者之间在目标、价值和需求上的不匹配，教师的工作强调规范性、个体性、特殊性和实验性，而研究者的工作强调分析性、智力性、普遍性和理论性(Labaree, 2003)。

What strategies for narrowing the gap 1. Silver (2003)主张，由于研究者与实践者处

于不同的角色领域，因此他们需要跨越领域的界限进行合作研究，这样双方都能互利共赢。

2. Kieran, Krainer和Shaughnessy (2013)主张，应该发展研究者和实践者之间双向互通的关系，实践者应该被视为实施研究的核心利益相关者；

3. 最近，Cai等人(2017b, c, d)构想了一副数学教育群体的未来美丽图景。

Silver和Lunsford (2017)使用5个隐喻来概念化研究与实践之间的分离：

– 管道(pipeline)、– 翻译(translation)、– 渗透(osmosis)、– 跨越边界(border crossing)、– Pasterur象限(Pasterur Quadrant)。

结合这些隐喻的内涵，可能有助于发现解决这一分离的有效方法。

在学术界，缩小研究和实践之间分离的三条重要途径是

– 设计研究(design research)、– 行动研究(action research)和– 对话式的教师与研究者的合作(dialogic teacher-

researcher collaboration)。设计研究包括设计、实施、分析和再设计的循环(Brown, 1992; Cobb, Jackson, & Sharpe, 2017; Design-based Research Collective, 2003)，目的是创造有效的学习环境和发展学习的理论，尤其注重发展对学习过程和支持学习过程的方法层面的研究(Cobb et al., 2016)

– 关于对话式的教师-研究者的合作，Kieran, Krainer和Shaughnessy (2013)的研究发现，实践者是研究

的核心利益相关者，并且实践知识和学术知识可以同时得到发展。

– 课例研究作为一种典型的合作性研究，它为研究者和实践者一起合作来改进实践、实施研究和发展理论提供了一个自然的平台。Silver和Lunford (2017)强调了研究和实践之间关系的理想特征：识别和理解真实的问题；使用已有的理论和实践知识解决这些问题；得到专家的反馈（研究者和实践者）；在实践中检验解决方案；得到进一步改进的反馈。

What are the unique features of theory‐informed LS

Stigler和Hiebert (2016)认为课例研究也可以被视为一种研究方法——一种可能特别适合于改

进我们教学知识和教学质量的研究方法。他们进一步指出课例研究不仅是真正的研究，而且其中蕴含的方法论作为一种发展有关改进教学知识的方式具有重要的价值，因为它通过将课程作为分析单元来维护研究的生态效度，一个单元小到足以被研究，但却也大到足以代表课堂教学系统中的关键组成部分

课例研究包括如下5个重要特征。1. 确定真实的、有意义的研究问题：基于文献综述(主要来自

于专家)和实践问题(主要来自于教师)来设定课例研究的目的是非常关键的；

2. 教师是核心利益相关者当研究者积极参与课例研究时：教师通过积极参与课例研究的整个过程来学习。

3. 通过跨越边境(border crossing)拓展学习：通过致力于边界对象(boundary objects)的工作，课例研究为研究者和教师进行拓展性学习提供了理想的环境(Huang & Han, 2015; Sztajn, Wilson, Edgington, & Myers, 2014)。

4. 发展有关教学与学习关系的知识：Nuthall (2004)认为，关于教学与学习关系的研究需要考虑几个方面，包括对学生所学内容和完成情况的深度评价、对学生个人体验和课堂活动的连续性追踪数据。他进一步强调，最重要的标准是需要有个体学生体验的连续性观察数据。

5. 传播共享的教学产品：Morris和Hiebert (2011)提出了一种通过创建共享的教学产品来改进教学的新方法，并认为课例研究是开发这种可共享的教学产品的强有力手段。

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案例1: 理论指导下的课例研究

Huang, Gong, & Han (2016):Han, Gong, & Huang (2017);Han & Huang (2018).

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Theory-driven Lesson study cycle

Planning: -Identify learning goals -Select variation problems -Anticipate students’ responses

Assessment and reflection -Evidence of student learning -Effect of instruction regarding student learning

Instruction: -Elicit student thinking -Monitor, and conduct whole class discussion-Build connections of multiple representations

LTs and TV

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Teaching for understanding

2 12 1

4 ?

2 12 1

4 5

2 4 52 10

Why? Mental computation ? Drawing a diagram ?

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Learning trajectory

Mathematical tasks

First teaching Second teaching

1. 1 divided by a unit fraction (e.g. 1÷⅕)

T1: How many ⅕-liter glasses are there in 2 liters of milk?

T1a: How many ⅕-liter glasses are there in 1-liter of milk?T1b: How many ¼ -liter glasses are there in 1 liter of milk?T1c: How many ⅓-liter glasses are there in 1 liter of milk?T1d: How many ⅙-liter glasses are there in 1 liter of milk.

2. 1 divided by a fraction (e.g., 1÷⅖).

T2: How many ⅖-liter glasses are there in 1 liter of milk?

T2a: How many ⅖-liter glasses are there in 1 liter of milk?T2b: How many 2/7-liter glasses are there in 1 liter of milk? T2c: How many ¾-liter glasses are there in 1 liter of milk. T2d: How many ⅗-liter glasses are there in 1 liter of milk.

3. A whole number divided by a fraction (e.g., 3÷⅖)

T3: How many ⅖-liter glasses are there in 3 liters of milk?

T3a: How many ⅖-liter glasses are there in 2 liters of milk?T3b: How many ⅖-liter glasses are there in 3 liters of milk?T3c: How many ⅖-liter glasses are there in 4 liters of milk?T3d: How many ⅖-liter glasses are there in 100 liters of milk?

4. A fraction divided by a fraction (e.g., ¾ ÷⅖)

T4: How many⅓-liter glasses are there in ½ liters of milk?

T4a: How many ⅖-liter glasses are there in ¾ liters of milk?T4b: How many ⅖-liter glasses are there in ⅝ liters of milk?T4c: How many ¾- liter glasses are there in ⅘ liters of milk?

Mathematics tasks and LT for LS2

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Increase of means in overall performance (mean difference=.85), visual representation (mean difference=.18) and proportional reasoning (mean difference=.81) from the first teaching (26 students) to the second teaching (28 students) A t-test further detects that the changes of mean in overall performance (t=2.57, p=.0) and proportional reasoning (t=2.2, p=.04) are statistically significant, but not in visual representation (t=45, p=.65).

Student learning

0

1

2

3

4

5

6

Performance visual representation proportional resoning

1st

2nd

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案例 2: 加或减？

卡车1 载7匹马，卡车2 载4匹马，卡车1 载比卡车2 多多少匹马？

4+3=7 7， 6，5，4，3 7-4=3

卡车1 载7匹马，比卡车2 多载4匹马，卡车2载多少匹马？

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基于学习路径的变式教学

• Huang, Zhang et al. (2018). Developing students’ ability to solve word problems through learning trajectory-based and variation task-informed instruction.

ZDM: https://doi.org/10.1007/s11858-018-0983-8

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Learning trajectory of solving comparisonLevel 1 Solve problems with unknown difference set;Level 2 Solve problems with unknown big or small setsusing consistent language;Level 3 Solve problems with unknown big or small setsusing inconsistent language.To lay a strong foundation for this learning trajectory, weidentified four sub-levels within each level:

1a Physically acting out the comparison subtractionmodel within a daily context;1b Using manipulatives to model comparison subtractionconcretely;1c Drawing diagrams to represent the relationship visually;and1d Creating mathematical equations.

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研究发现

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• the paired t-test (2-tailed) showed a significant increase from pre-to post-test

• students averaged 66% of the total score (18.22 out of 28). • students achieved 65% correctness (2.45 out of total score 4) on

item 7 which is the most difficult (e.g., Verschaffel et al.1992) • a surprise that the lowest score was on item 5, which is about

finding the difference given two numbers because this was greatly emphasized in the two lessons.

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China vs. U.S.

Chinese approach US approachSimilarities Setting clear learning goals Setting clear learning goals

Implementing high cognitive demand tasks Implementing high cognitive demand tasks

Use of multiple tools and representations Use of multiple tools and representations

Using student misconceptions as learning resources

Using student misconceptions as learning resources

Differences Explicit attention to the structure of the quantitative relationship

Attention to multiple strategies leading to a solution

Funneling questions dominant Focusing questions dominantBidirectional relationship among representations

Unidirectional relationships among representations

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Case 3: Using students’ errors as learning resources

Barlow et al. (2018). Inspection-Worthy Mistakes: Which? And Why? Teaching Children Mathematics, 24 (6), 384-393

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• Teachers were introduced to the motto, “Mistakes are expected, inspected, and respected” (Seeley 2016, p. 26).

• Inspecting mistakes opens a space for enhancing students’ conceptual understandings (Boaler 2015; Borasi1996).

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Types of errors

• Procedural errors • Inappropriate solution process • Misconceptions

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The Sharing Chocolate problem:Two groups of friends are sharing chocolate bars. Each group wants to share the chocolate bars fairly so that every person gets the same amount and no chocolate remains. In the first group of friends, four students receive three chocolate bars. How much chocolate did each person get in the first group.

Peach Tarts Problem: Ms. Stangle wants to make peach tarts for her friends. She needs two-thirds of a peach for each tart, and she has 10 peaches. What is the greatest number of tarts that she can make with 10 peaches?

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1. To fi nd perimeter, students often mistakenly count the “border tiles” (in red in fi g. 5b). Whether students report the perimeter to be fourteen (a literal count of the border tiles) or eighteen (double‐counting the corners), counting the squares represents a misconception regarding perimeter. That is, the students do not recognize perimeter as a measurement of length that should be found by counting the units of length (i.e., the sides of the squares) that make up the perimeter of the rectangle.2. In determining area, students will state that the area is represented by the “inside squares” and then limit the area to the enclosed blue squares (see fig. 5b). This misconception regarding what constitutes the area of a fi gure is likely related to viewing the border tiles as representing the perimeter. Why

This book brings together and builds on the current research efforts on adaptation, conceptualization, and theorization of Lesson Study (LS). It synthesizes and illustrates major perspectives for theorizing LS and enriches the conceptualization of LS by interpreting the activity as it is used in Japan and China from historical and cultural perspectives. Presenting the practices and theories of LS with practicing teachers and prospective teachers in more than 10 countries, it enables the reader to take a comparative perspective. Finally, the book presents and discusses studies on key aspects of LS such as lesson planning, post-lesson discussion, guiding theories, connection between research and practice, and upscaling.Lesson Study, which has originated in Asia as a powerful effective professional development model, has spread globally. Although the positive effects of lesson study on teacher learning, student learning, and curriculum reforms have been widely documented, conceptualization of and research on LS have just begun to emerge. This book, including 38 chapters contributed by 90 scholars from 21 countries, presents a truly international collaboration on research on and adaptation of LS, and significantly advances the development of knowledge about this process.

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走向未来：理想的数学教育

Cai and his editorial team: Journal for Research in Mathematics Education (2017-2018) 探讨国际数学教育难题：

教育研究如何同实践紧密结合

对实践工作的大面积提高产生积极影响。

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Shift

Boundary objects Teachers as Key stakeholders

Teachers as consumers

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理想学习共同体

• 研究者和实践者公共解决来自教师实践的重要问题，确定学习目标，通过课堂教育实际提供学习机会，反复实践改进；

• 通过网状研究者和实践者合作团体建立一个：可持续，查询，共享的在线专业知识库 ( Useful findings and artifacts that are continuously refined over time, indexed by specific learning goals and subgoals, and that assist teachers and researchers in implementing learning opportunities in their classrooms” (Cai et al., 2017d, p. 469).

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A vision of LS: Design research

Low High Theoretical implication

Action research oriented

Design research oriented

I II

III IV

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中国智慧：课例研究(Improvement science

• Problem-specific and user-centered

• Focus on variation in performance

• See the system produce the current outcome

• Measurable changes• Disciplined inquiry to drive

improvement • Accelerate learning through

networked communities

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建立基于科学研究方法中国教研体系和知识库

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结束语

• 我们有好的教学实践;• 有效的教师教育体系和好教师；

• 需要加强研究建立中国特色的教育理论；

• 基于中国智慧，杨长避短，为国际数学教育做贡献。

Thanks!Email: [email protected]

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