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27 Background Significant differences in the curricula and approaches to professional learning of teachers in Japan and the United States, together with a lack of experience doing lesson study in the United States, make developing and maturing as a productive lesson study community a challenging process for U.S. teachers. For example, the entire national Course of Study for elementary schools in Japan is contained in a 100- page volume which lays out the hours, goals, and content for all 12 areas of study (including mathematics), allowing for invention and interpretation of best practice. In contrast, U.S. curricula cover many pages of objectives and skills for each con- tent area at each grade level, allowing little interpretation for implementation by teachers. Professional learning activities that are designed to improve instruction are also in stark contrast in the two countries. Lesson study, the primary profes- sional learning model in Japan is a teacher-driven and teacher-directed professional learning model. U.S. teachers experience most professional learning as top-down, outside-expert-directed (Lewis 2002). This chapter is divided into 2 parts. Part 1 is a detailed case description of a group of third-grade teachers in one school district in the United States as they embarked on the process of learning about lesson study and attempting to engage in the process. Part 2 is a research report on the group of teachers using data collected at the beginning and end of the yearlong process. Theoretical Framework Both the lesson study community and the research community benefited from the work of Fernandez et al. (2003), a study of implementation of lesson study in an urban, public school in New Jersey. They found “substantial challenges… must be L. C. Hart et al. (eds.), Lesson Study Research and Practice in Mathematics Education, DOI 10.1007/978-90-481-9941-9_3, © Springer Science+Business Media B.V. 2011 Developing the Habits of Mind for a Successful Lesson Study Community Lynn C. Hart and Jane Carriere L. C. Hart () Georgia State University, Atlanta, GA, USA e-mail: [email protected]

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Page 1: Lesson Study Research and Practice in Mathematics Education || Developing the Habits of Mind for a Successful Lesson Study Community

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Background

Significant differences in the curricula and approaches to professional learning of teachers in Japan and the United States, together with a lack of experience doing lesson study in the United States, make developing and maturing as a productive lesson study community a challenging process for U.S. teachers. For example, the entire national Course of Study for elementary schools in Japan is contained in a 100-page volume which lays out the hours, goals, and content for all 12 areas of study (including mathematics), allowing for invention and interpretation of best practice. In contrast, U.S. curricula cover many pages of objectives and skills for each con-tent area at each grade level, allowing little interpretation for implementation by teachers. Professional learning activities that are designed to improve instruction are also in stark contrast in the two countries. Lesson study, the primary profes-sional learning model in Japan is a teacher-driven and teacher-directed professional learning model. U.S. teachers experience most professional learning as top-down, outside-expert-directed (Lewis 2002). This chapter is divided into 2 parts. Part 1 is a detailed case description of a group of third-grade teachers in one school district in the United States as they embarked on the process of learning about lesson study and attempting to engage in the process. Part 2 is a research report on the group of teachers using data collected at the beginning and end of the yearlong process.

Theoretical Framework

Both the lesson study community and the research community benefited from the work of Fernandez et al. (2003), a study of implementation of lesson study in an urban, public school in New Jersey. They found “substantial challenges… must be

L. C. Hart et al. (eds.), Lesson Study Research and Practice in Mathematics Education, DOI 10.1007/978-90-481-9941-9_3, © Springer Science+Business Media B.V. 2011

Developing the Habits of Mind for a Successful Lesson Study Community

Lynn C. Hart and Jane Carriere

L. C. Hart ()Georgia State University, Atlanta, GA, USAe-mail: [email protected]

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overcome to make this practice [lesson study] purposeful and powerful” (p. 181). In their project, Japanese teachers from a nearby international school collaborated with U.S. teachers, attempting to form a lesson study community. The research team noticed that the Japanese teachers approached lesson study very differently than the U.S. teachers. In their analysis of the data they identified three habits of mind (which they named Critical Lenses) that guided how the Japanese teachers discussed and developed the lessons. They labeled these lenses as the researcher lens, which the teachers used to ask questions about practice and design classroom experiences to explore these questions; the student lens, which the teachers used to understand student thinking and examine all aspects of the lesson through the eyes of the student; and the curriculum developer lens, which the teachers used to orga-nize, sequence, and connect learning experiences. They suggested that these critical lenses were absent in the U.S. teachers and prevented lesson study discussions from moving into rich arenas. Acquiring these lenses will be necessary if lesson study is to become a viable model of professional learning in the United States. In our proj-ect we use the three lenses identified by Fernandez et al. (2003) as a framework to both scaffold teacher thinking and ultimately study teacher change.

In addition, the role of beliefs in teacher change in mathematics education has a long history and is well documented (Cooney and Shealy 1997; Pajares 1992; Richardson 1996). Beliefs about teaching are well established by the time a student enters college. These beliefs, previously identified by Lortie (1975), develop during the apprenticeship of observation that occurs over years as a student. More impor-tantly, we know that the beliefs teachers hold frequently do not support what Ma (1999) refers to as profound, connected understanding of fundamental mathematics teaching. In many instances, a teacher’s beliefs determine the instructional deci-sions that are made in the classroom and limit willingness to engage in alternative pedagogies or behaviors. These beliefs are hard to change. Even in the face of con-flicting evidence, beliefs are often resilient. A goal of professional learning, then, is not only to provide teachers with new frameworks to use as they plan learning experiences, but also to effectively challenge the core beliefs that drive their deci-sion making.

Using these theoretical perspectives, we asked the following research question. Do teachers participating in their initial experiences with lesson study and sup-ported by outside experts (facilitators) develop the lenses needed to be a productive lesson study community?

Overview

In this chapter, we provide a case of third-grade teachers as they develop a les-son study community (Part 1). The process was not easy for teachers raised in our Western educational system, and their struggles and accomplishments make the complexity of their task transparent. In particular, we detail the initial sessions to highlight the multifaceted learning process that was required. In the process, we

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describe our dual role as researchers and facilitators/participants within the group. In Part 2, we share results of analysis of the initial and final research lesson sessions to expose the development of the critical lenses.

Part 1: Becoming a Lesson Study Community

The School System

The school system in this project is a small urban system in the southern Unit-ed States. During the period of the study, the system had six elementary schools. Thirty-eight percent of students were on free or reduced lunch. Fifty-three percent were African-American or other minority, and 47% were Caucasian. For many years, the system had been proactive in educating its teachers on reform mathe-matics as advocated by the National Council of Teachers of Mathematics (2000); however, as is the case in many school systems, attrition diminished the number of teachers who were prepared to teach from a reform perspective. New teachers, both new to the system and new to teaching, continued to bring a traditional way of thinking about the teaching of mathematics. According to the system mathematics coordinator, the curriculum and textbooks supported the philosophy of reform, but a teacher-directed model remained the primary mode of instruction in the classroom. The system sought to initiate a model of professional learning that could facilitate change and be self-sustaining.

Japanese Elementary Lesson Study (JELS)

The system chose to implement lesson study, starting with one grade level. The Japanese Elementary Lesson Study (JELS) Project was supported by a small ex-ternal grant and funds from the school system. The project was facilitated by the mathematics coordinator for the school system and a local university mathematics education faculty member.

The Participants

All third-grade teachers from the school system were invited to participate in JELS. Participation was voluntary and eight of ten teachers opted to participate, represent-ing five of the six elementary schools. There were two African-American females, one Asian male, and five Caucasian females. Teachers ranged from 3 to 30 years teaching experience.

The mathematics coordinator and university faculty consultant acted as facilita-tors/participants for the project. Both were white females and both had extensive

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practice with elementary teachers in developing standards-based learning environ-ments. However, both were also new to the lesson study process and were new learners with the teachers.

Adapting Lesson Study

While preparing for the project, the project facilitators immediately noticed they would need to make adaptations to the lesson study process as it was described in the literature. There were several issues to be considered.

First, teachers would need to study and learn about the lesson study process. Unlike Japanese teachers who experience lesson study as a regular and on-going part of their professional development as early as their preservice program, for the U.S. teachers lesson study was new and not the type of professional learning they normally engaged in. The facilitators also held concerns about the readiness of the participants to engage in meaningful, substantive discussions about content and pedagogy with limited prior experience. To encourage profound, thoughtful discussion, the facilitators planned to be more active members of the lesson study group than described in the literature. They would scaffold the discussion through prompts such as “what if ” and “did you notice” observations. This was supported by Fernandez et al. (2003) when they stated “lesson study…must include room for knowledgeable coaches who can stimulate the thinking of groups so they can rise beyond their own limitations” (p. 182).

Second, there would need to be adaptations to the Everyday Mathematics (EM) curriculum used in the system. The EM curriculum is relatively scripted and lessons are sequential and developmental. General objectives of a lesson could be used as a starting point, but it was anticipated that it would be necessary to revise the lesson to assure that student thinking was exposed and could be observed. We anticipated that it would be necessary for the group to develop single research lessons that could be inserted into the EM sequence. The teachers could identify concepts from EM they felt were difficult to teach and difficult to learn and develop introductory research lessons for those concepts.

Third, no common planning time was available that would allow the participat-ing teachers to meet during the school day throughout the year. After school, con-flicts prohibited using out-of-school time to meet. In-school time was necessary and substitutes were required. In order to schedule substitutes, full day sessions would be needed (a day to plan the lesson; a second day to teach/observe, debrief, and revise the lesson; and a third day to teach the revised lesson and reflect).

Finally, there existed a wide range of mathematical backgrounds of the partici-pating teachers in the project. To engage in substantive discussions, substantive mathematics needed to be explored. The facilitators would develop a mathematics lesson for the teachers to explore the concept before they planned a research lesson for third graders. The exploratory lesson would immerse the teachers in the concept before they began the planning process.

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Summer Sessions

The first of three summer professional learning days was held in June. On that day, teachers began to learn about lesson study. A video of a research lesson Can you lift 100 kilograms? (Lewis 2000) was used to introduce the process. After discussing the video, the group developed group norms for how they would work together. They developed a common vision of good teaching. They developed a list of long-term goals for students. Finally, they identified four troublesome topics specific to their grade level that they would address from EM: addition/subtraction word prob-lems, the language of probability, comparing and ordering decimals, and naming parts of the whole in fractions. In preparation for the two professional learning days in August, the teachers were asked to read Lesson study: A Handbook of Teacher-led Instructional Change (Lewis 2002).

In August, the teachers met two days to discuss the book, develop a research theme, and plan the first of four research lessons for the year. This was daunting, slow work as the teachers were not accustomed to professional activities in which they were expected to not only share the authority, but to take the lead. They were not accustomed to considering or discussing what they thought were the important, over-arching learning goals for third-grade students.

Planning the Initial Research Lesson

Planning the research lesson consumed the remainder of the day and all of the next. The process began with one of the facilitators initiating a discussion on the mathemat-ics that would be the center of the research lesson, i.e., thinking models for addition and subtraction word problems (join, separate, part/part/whole, and comparison), by using a “tell me what you know” approach. The teachers brainstormed their un-derstandings of the eleven different forms the problems could take, discussing the relative difficulty of each type. After the discussion, the teachers examined existing EM curricula and materials, shared ideas from their own classrooms, looked at other resources, and collaboratively worked on developing a lesson. This too was difficult. The teacher participants had never formally shared pedagogical knowledge, negotiat-ed teaching strategies, and discussed student learning and outcomes with colleagues. As teachers presented ideas that were not well received, group norms had to be revis-ited. How will we deal with differing opinions? How will we decide which strategy to use? Ultimately, the teachers agreed on a plan in which the students would solve one problem for each type of thinking model ( join, separate, part/part/whole, and com-parison). Students would discuss similarities and differences across the problems.

The group wrote the following four problems:

• There were 16 students in Mr. Bob’s third-grade class. After winter break, he got three new students. How many students are in the class now? [ join]

• Mr. Bob had 16 students in his third-grade class. Three students moved away. How many students are in the class now? [separate]

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• Of the 16 students in Mr. Bob’s class, seven are boys. How many girls are in the class? [ part/part/whole]

• There are seven boys and nine girls in Mr. Bob’s third-grade class. Of all the students in the class, how many more girls are there than boys? [comparison]

Teachers chose to use the same basic scenario and similar, simple numbers for the problems so the students would not get lost in the computation or the context. They wanted the students to focus on the differences in the thinking involved in the four problems types.

Students would be divided into small groups with chart paper divided into four sections. The four problems would be posted at different tables. Students would rotate from table to table with their chart paper and record their work in the appro-priate section of the chart paper. Colored counting chips would be available at each table. When the rotations were complete the four charts would be posted side-by-side on the board and discussed, across all solutions for each problem number and then across the four problem types. The teacher was to focus the discussion on what was similar about the problems and what was different.

As recommended in the lesson study literature, the teachers agreed that ob-servers would not interact with students. There was, however, discussion about whether observers would stay at a table or rotate with a student group. Pros and cons for both (understanding how all the children thought about one problem vs. how one set of children thought about all the problems) were discussed. In the end, the group opted to stay at one table in order to observe all students’ thinking on one problem.

Once completed, a typed version of the lesson plan was created. The plan in-cluded teacher actions and strategies, anticipated student responses and thinking, and points for the observers to notice.

Organizing the Debriefing of the Research Lesson

The possibility of a public discussion about the lesson (the debriefing as a group) created some angst amongst the teachers. The facilitators reminded the teachers that the reflection was not a review of “how well the teacher had done” rather it was an assessment of how well the lesson exposed student thinking and how well it reached the objectives. It was agreed that once the group reconvened after the lesson, the teacher who taught would begin by sharing his or her observations and thoughts. The observing teachers would then share the data they had collected while observing the children. The facilitators would summarize the discussion, not-ing themes and issues that emerged, and the lesson would be revised based on observations shared during the debriefing. Planning for the first research lesson was completed on the last day of the summer meetings. Peg, a third-year teacher, volunteered to teach the first lesson. Subsequent lessons would be taught by the other teachers.

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School-Year Sessions

The teaching of that initial lesson occurred three weeks after the school year began. Three additional cycles occurred over the year and followed the same process. The teachers would meet for one day to plan the lesson on the concept identified during the previous summer. On the next day, the lesson would be taught, debriefed, and revised. On the third day, the revised lesson would be taught to another group of third graders.

Teaching the Initial Lesson

The first 45-minute lesson was implemented during the third week of school. Peg, the teacher for this initial lesson, explained the purpose of the observers to the stu-dents, went over the problems with the students, put the children in groups, and set them to work. The observers watched the students and made notes.

Debriefing the Initial Lesson

After teaching the lesson, Peg began the debriefing. She expressed overall satisfac-tion with how the lesson proceeded, but acknowledged she was “more nervous than she expected to be” with observers in the room. She expressed concern that the les-son had not been as successful as she hoped because some groups had not put their problems in order on the chart paper, making it impossible to line them up when placed on the board. She felt that the goal of comparing and contrasting the problem types was not reached because the children could not see the relationships visually. After she was done, each teacher shared his or her observations of individual stu-dents and groups, and what they had observed about the students. During that time, the facilitators took notes. After all teachers shared, the facilitators raised questions to stimulate development of the lenses that would encourage rich discussion about the mathematics and student learning. For example, from this initial lesson they asked:

• What do you think about the difficulty level of the problems? [Student lens]• Do you think the order in which the problems were solved/presented impacted

student understanding? [Curriculum developer lens]• Did you notice dominant students in the groups? Do you think that impacted the

learning? What could we do to limit that in future group work? [Researcher lens]

As experienced observers of classroom interactions, the facilitators were accus-tomed to carefully watching and listening to students, noticing themes, and raising questions about what they observed. The questions they raised emerged from the discussion, but were not ideas that the teachers addressed directly in the discus-sion. The questions were designed to move the teachers beyond the limits of their

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observations. Finally, before closing the debriefing, the facilitator asked if anyone wanted to make a comment or reflect on the process of lesson study. Teachers com-mented on how difficult it was to watch the students and not interact with them, i.e., to remain quiet. At the end, Peg made a statement that promoted the development of the culture of lesson study within the group. She said, “A couple of times during the discussion today I was getting defensive about what was being said, but I realized that everyone was taking responsibility for the lesson and it wasn’t about me it was about the lesson. It was hard, but I think I understand better about the process and what we are trying to do.”

A complete description of the three subsequent lessons is not included in this chapter. The remaining three lessons followed the same format as described above. It is, however, necessary to visualize the problems in the last research lesson in or-der to interpret the research findings discussed in Part 2. The final lesson required the students to name the fractional parts of a square region (see Fig. 1). The students were asked to label the fractional part of the whole that each section represented. No parts were shaded.

Part 2: The Research Project

Data Collection and Analysis

The previous detailed description of a novice lesson study community provides the context in which to understand the findings of this study. There were three subse-quent lesson study cycles during the school year that followed the same sequence as the first. For the purposes of the research, we analyzed the planning and debriefing sessions for the first lesson and the last lesson.

Research Question

In order to answer our research question on whether the teachers developed the critical lenses (Fernandez et al. 2003) necessary to be a productive lesson study community, a qualitative methodology was employed using enumerative analysis

Fig. 1 Student problems for last lesson study

Problem 1 Problem 2 Problem 3 Problem 4

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(Lincoln and Guba 1985) in which previously defined units or categories are sub-jected to systematic counting or identification. The first and last lesson study cycles were videotaped and supported through field notes. The videos were transcribed. Using the group as the unit of analysis, the transcriptions were coded for evidence of a researcher lens (R), a curriculum developer lens (C), or a student lens (S). Since prompting from the facilitators was used to encourage development of the lenses, only discussion prior to facilitator comments was coded. Both the frequency and nature/quality of the comments were noted.

For the student lens, coding was made for any comment about students: what they did, what they said, or what they appeared to understand. Any comment about how the lesson was constructed or ordered was coded as curriculum developer lens. For the researcher lens, we looked for initiation of questions that could be answered through experimentation similar to action research.

Results

Results from analysis of the video data show that over the course of the year the teachers developed a qualitatively richer student lens and curriculum developer lens. While comments about students were found at both the beginning and the end of the year, the substance of the comments was quite different. Teacher comments coded as the student lens from the initial lesson were primarily about how students behaved:

The children were so cooperative.My group was very calm and respectful.I did notice they played with their name tags.Only Molly Emma played with the manipulatives in my group.

and what the students did during the lesson:They responded well.They listened attentively to responses of the other children.My boys spoke more than my girls.My group shared the jobs equally.Megan drew a picture to answer the questions. Jason was definitely in charge and Moses was happy to let him be in charge.

Only one comment stood out that suggested some deeper thoughts about student understanding. One teacher said:

I don’t think they noticed the differences in the word problems. Only one boy said “all these are about Mr. Bob.”

In the final lesson on fractional parts of a square region, teachers commented on what students appeared to understand about the mathematics:

It was interesting because in [problem] number two, India, if she would have, if Steve would have let her say exactly what she thought right when she saw it—which was [point-ing to the diagram] “this is one-fourth, one-fourth, one-fourth” which when she looked at

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that large space, she actually saw that. But then Steven said, “there’s no line here” and then India said “OK,” when he did that, she looked at the diagram, and she goes [pointing to the diagram] “so this is one-fourth, one-fourth, one-fourth.” She saw it right off the bat….Briana…she’s the one who when they were doing these examples just drew that, one-third, one-third, one-third, and so she used her diagonals.And, yeah, at the beginning when you were getting information from them, I thought it was great they said equal a lot, they said one-third because three makes a whole so that made me think—I don’t know how, that child obviously knew denominator, but I don’t know how.

and what was confusing the students:

I still don’t know if they know really what the denominator represents, though, or they’re not there yet. I mean I think they know they can divide things up, but I don’t think they know what that denominator really is and are able to connect that to what they’re writing to what the figure is and, and what you’re representing with the figure.It’s hard for them to jump from the one in the numerator to anything beyond one in the numerator.I have down the word denominator in big letters because I really think that the concept of denominator is just hard. It seemed like my groups could divide anything into one-eighth, one-sixth….I think that was the big challenge of this—when they see that larger region—that in their minds they put those ones together and make it two-fourths instead of one-fourth and one-fourth.

As the quotes suggest, the teachers began to look at problems through the student’s eye, acknowledging what learners were unfamiliar with or struggling with, e.g., “not having parts shaded-in” and “unequal fractional regions.” They discussed how the way a problem was presented would impact student thinking. They began to un-pack the mathematics in a problem and ponder about how students would approach the different parts.

Changes in the comments coded as the curriculum developer lens also changed qualitatively over the year. Initial comments focused more on how the organization of a lesson or materials aided in management issues so the students would stay on task or not get confused.

I think your giving an overview of the lesson was helpful.I think turning over the bags helped so kids wouldn’t play.I am not sure about the manipulatives. They just played with them.

By the last lesson, comments focused more on how the organization of the lesson supported or hindered student understanding and development of the concept being taught.

I wonder about shading, if there was something…the idea that a lot of their history is with shading and the way they’ve learned to identify parts is by what’s shaded. We had no shaded parts and they had to just label from that.And I’m thinking [problem] number two, how we could have done that one, adjusted it so it made more sense or if there was something we could have worked up to do number two, shading the one-fourth.I guess it was two things, though, I mean if we just wanted them—not shading it was trying to get them to not be familiar because they’re use to shaded, but also we’re giving them a large region, so maybe one or the other would have been good to do for number two.

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…in the large group discussion could you, when you’re talking about the thirds on the figure, could you shade, you know, two of those thirds, and say “OK, well what part of the circle is that?” So then that maybe they could take that piece of the discussion and transfer it to the problem.

Not only did the teachers point out specific ideas that were difficult (e.g., the use of unequal regions and the lack of any shading), but they made suggestions for how the lesson should or could be changed to scaffold understanding.

No evidence was found of the researcher lens in the first cycle. The teachers did not question their practice. In the final session, the teachers asked, “I wonder…” questions where they pondered how something was presented or understood. For example, the quote from above where the teacher wonders about the lack of shading of the diagrams:

I wonder about shading, if there was something…the idea that a lot of their history is with shading and the way they’ve learned to identify parts is by what’s shaded. We had no shaded parts and they had to just label from that.

We would expect that if the group of teachers held a rich researcher lens, the discus-sion would move on to suggesting activities or experiments to test their hypothesis. This did not happen.

Discussion

In Part 1 of this chapter we provide a case study of the development and implemen-tation of a novice lesson study community by a group of third-grade teachers. The detailed description of each piece of the process provides a context within which to understand the significant change in the group. Adaptation of the lesson study model was necessary to meet the particular circumstances of the school system, but was done so without removing the essential pieces of the model (See Chap. 1 by Murata, this volume). This detailed account also exposes the cultural and educa-tional differences of U.S. teachers. The teachers were not comfortable with taking the lead in planning lessons. They were not comfortable with being observed. They became defensive when their ideas were challenged. In addition, limited-to-no ex-perience of observing other teachers’ teaching and analyzing student thinking mini-mized the depth of initial discussions. However, as Fernandez et al. (2003) suggest, adaptations to the lesson study process are necessary for U.S. teachers to “move beyond the popularized view that currently exists in the U.S. of lesson study as a completely teacher-led and teacher-run activity” (p. 183). As this study confirms, the knowledgeable others (facilitators) can support lesson study communities in developing the critical lenses necessary to “push their lesson study practice into rich arenas” (p. 182). There is room for the active support of external facilitators who are knowledgeable about the lesson study process and who embrace the values of lesson study: A culture of self-criticism, openness to the ideas of others, and willing-ness to embrace mistakes.

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The U.S. teachers in this study showed gains in developing two of the three criti-cal lenses needed to create and reflect on mathematical lessons that dramatically move student learning forward. And, while their initial discussions demonstrated a stance that aligned with many standards-based instructional practices, the change in the richness of their discussions from the beginning to the end of the year suggests that merely holding beliefs that support standards-based learning environments does not guarantee the profound knowledge of planning, teaching, or learning that aligns with those beliefs.

The results from this chapter address only one small part of what we need to learn about lesson study as a useful model of professional learning. Clearly, there is still much to be learned. How do we develop the culture of lesson study with U.S. teachers? What role should the outside expert (facilitator) play in the lesson study process? How much should he or she intervene? What resources are needed to support U.S. teachers in developing the deep content knowledge and pedagogical knowledge needed in a lesson study approach to professional learning? How will participation in lesson study impact student learning? Research in this arena is still in its infancy. These questions are just a few that need to be explored as we study the lesson study model of professional learning and attempt to implement it in new arenas.

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Fernandez, C., Cannon, J., & Chokshi, S. (2003). A US–Japan lesson study collaboration reveals critical lenses for examining practice. Teaching and Teacher Education, 19, 171–185.

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Lewis, C. (2002). Lesson study: A handbook of teacher-led instructional change. Philadelphia: Research for Better Schools.

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