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School of Education, Mills College, Oakland, California, USA, and ... began to appear (e.g. Lewis and Tsuchida, 1997, 1998; Stigler and Hiebert, 1999) lesson.

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Facilitating curriculum reforms through lesson study

Facilitating curriculum reforms

Catherine Lewis School of Education, Mills College, Oakland, California, USA, and

Akihiko Takahashi School of Education, DePaul University, Chicago, Illinois, USA

207 Received 22 January 2013 Accepted 4 March 2013

Abstract Purpose – The purpose of this paper is to briefly describe the role of lesson study in implementation of national curriculum reforms in Japan, identifying key features that may be of interest to policy-makers in other countries. Design/methodology/approach – Literature review, observation, and artefact collection were used to study the role of lesson study in educational reform in Japan. Findings – One key characteristic of implementation of national curricular reforms in Japan is that lesson study allows primary and secondary schools, universities, district and prefectural offices, and subjectmatter associations to collaborate in implementation. Some key features of the lesson study-supported system of implementation of curricular reform in Japan includes: the ability of school-based lesson study groups to leverage regional and national subject-matter expertise; school learning routines that enable systematic study, refinement, and dissemination of practice (e.g. kyouzai kenkyuu, public research lessons, grade-level collaboration); and policy structures that support implementation (e.g. grants for designated research schools, a period to try out new standards before they are required by law). Research limitations/implications – While some features of lesson study transfer readily from Japan to other countries (such as the usefulness of curriculum study, live lessons, and interchange with more experienced teachers), comprehensive systems for using lesson study to support curricular reform are yet to develop outside Japan. This paper identifies the policy, cultural, and infrastructural elements of the Japanese system that allow lesson study to effectively support implementation of new curriculum. Originality/value – Successful implementation of curricular reform at the classroom level is a persistent difficulty in many countries. Japan’s system illustrates how the strengths of teacher leadership and research-based content can be joined to support curriculum implementation, through interlocking systems of lesson study. Keywords Japan, Lesson study, CCSS, Standards implementation, Curriculum, Reform, Professional learning Paper type Research Paper

Overview Since the late 1990s, when English-language accounts of Japanese lesson study first began to appear (e.g. Lewis and Tsuchida, 1997, 1998; Stigler and Hiebert, 1999) lesson study has begun to spread around the world (e.g. Doig et al., 2011; Fang et al., 2009; Kullberg, 2010; Lo et al., 2005; http://hrd.apec.org/index.php/Lesson_Study). Some features of lesson study have been readily noticed and embraced by educators around the world, such as careful observation of student learning during live instruction, kyouzai kenkyuu (study of curriculum and content), and accumulation of a body of This work was supported by the Institute for Education Sciences, US Department of Education, under Grant Nos. R305A110491, R305A110500 and R308A960003 and by the National Science Foundation under Grant No. 0207259. Any opinions, findings, conclusions, or recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of the Institute for Education Sciences or the National Science Foundation.

International Journal for Lesson and Learning Studies Vol. 2 No. 3, 2013 pp. 207-217 r Emerald Group Publishing Limited 2046-8253 DOI 10.1108/IJLLS-01-2013-0006

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professional knowledge about teaching (Alston et al., 2011; Hiebert et al., 2002; Morris and Hiebert, 2011; Takahashi et al., 2005). Foreign educators’ interest in lesson study’s mechanisms has even prompted some Japanese lesson study practitioners, like Toshiakira Fujii, to comment that foreign lesson study is sometimes more “authentic” and considered than its Japanese parent. This paper focusses on an aspect of lesson study that, as far as we know, is not widely understood or enacted outside Japan: use of lesson study to implement nation-wide curriculum changes. The paper starts with a description of four different types of lesson study in Japan, followed by a brief case study in which lesson study was used to implement curriculum reform: the introduction of solar energy to the Japanese elementary science curriculum in the 1990s. The case illustrates the synergistic effects of four different types of lesson study in Japan: school-wide, district-level, based at national schools, and association-sponsored (e.g. sponsored by national subject matter associations). Together, these four types of lesson study can promote rapid development and spread of both the knowledge and commitment to implement curricular reforms. The final section of the paper discusses three features of the Japanese educational landscape that support lesson study-based spread of curricular reforms in Japan: “designated research schools” for the curricular reform that allow “rapid prototyping” of the reform; robust professional networks that bring together primary, secondary, and post-secondary educators and allow knowledge to flow across institutional boundaries; and learning routines (including lesson study) that are broadly established at Japanese schools (particularly at primary schools), and that allow systematic study and refinement of reform implementation. Four types of lesson study 1. School-wide lesson study School-wide lesson study is nearly universal in Japanese elementary schools, and fairly common in junior high schools as well (Isoda, 2010; Matoba et al., 2006; Nihon Kyouiku Houhou Gakkai, 2009; Takahashi, in press). While it differs by school and by region, it is common for each grade level or grade band to plan and conduct one or two research lessons per year, focussed on a shared school-wide research theme, and observed and discussed by all the teachers and administrators in the school (Fernandez and Yoshida, 2004; Takahashi, in press). School-wide lesson study often begins with all the teachers at the school considering two questions (Lewis and Hurd, 2011): .

Ideally, what qualities will students have when they graduate from our school?

.

What are the actual qualities of our students now?

By comparing the “ideal” and “actual” qualities of their students, teachers develop a shared lesson study theme that is meaningful to all the teachers. For example, teachers at one Japanese elementary school worried about the solo, passive leisure-time activities of some students (such as video games and TV) and about students’ uncritical willingness to go along with the opinions of students regarded as “smart.” So these teachers chose as their school-wide research theme “For students to value friendship, develop their own perspectives and ways of thinking, and enjoy science” (Mills College Lesson Study Group, 2000). Each grade band applied this research theme to their planning of science research lessons shared with the whole school faculty. So, for example, the upper grades teachers, keen to build students’ own individual

ideas about lifting heavy objects, deposited a 100-kilogram sack of sand in the gymnasium and allowed students to see it and devise their own lifting methods, rather than supplying poles and other materials to build levers, as they previously had in their introduction to the levers unit. Other grade bands applied the research theme to content taught at their level (e.g. the magnets unit in the early grades and weight and motion in the middle grades). In this way, a school-wide research theme elicits and mobilizes teachers’ keenest hopes for students, and connects these hopes to the design and analysis of instruction. Schools pursue topics of particular interest to their teachers and periodically change their theme and content focus to address issues of greatest concern to the teachers, such as newly adopted curricula (Takahashi, in press). One Japanese elementary educator talked about school-wide lesson study as follows: “The students’ actual situation right now is the starting point for your journey and students’ ideal qualities are your destination. Lesson study is the road that links the two” (Yukinobu Okada, comments at Greenwich Japanese School Open House, November 13, 2000). 2. District-level lesson study District-level lesson study (see also Murata and Takahashi, 2002a, b) allows elementary teachers to participate in a lesson study group focussed on a specific subject matter. For example, teachers in one Tokyo district can choose from more than a dozen offerings, including mathematics, art, physical education, Japanese, science, social studies, music, school wide activities, etc. ( JLSIP, 2003). These district-based lesson study groups meet during salaried after-school time once a month and conduct semi-annual research lessons open to all teachers within the school district. These research lessons are held on an afternoon when most students are dismissed early and the research lesson classes stay behind for an extra period. Teachers in this district also participate in school-based lesson study groups, which focus on subject matter and research themes decided each year by each school’s faculty. So the district-level lesson study enables sustained work in each subject area by teachers from different schools who have a particular interest in that subject area and who typically develop considerable expertise over years of studying it; the work of district-based lesson study naturally flows back into elementary schools through the teachers’ regular participation in school-based lesson study at their school sites. 3. National school-based lesson study Japan has 73 national elementary schools, most of which are affiliated with national universities, and many of which train student teachers. Each prefecture (state) in Japan has at least one national elementary school, and teachers at these schools take as their mission not just teaching their students, but also improving the current curriculum and instructional methods. As one national elementary school teacher commented, “When I taught in a regular elementary school, we teachers talked a lot about how to teach the science curriculum; here, we talk a lot about what Japan’s science curriculum should be.” National schools differ in how they select students (typically some combination of examination and lottery) and in faculty tenure (some have rotating faculty who stay for only a set number of years, whereas others have career tenure for teachers). Common to all national elementary schools is that they recruit teachers who wish to build and spread improvements to instruction and curriculum (Lewis and Tsuchida 1997, 1998; Shimizu, 2002). In many different ways, these teachers act as conduits between research

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and practice. Since they are based at universities and typically have a university professor as the school principal, teachers at these schools have ready access to research and ideas from Japanese universities (and to the ideas that flow into universities from foreign countries). One or more times a year, they open up their practice in large public research lessons (koukai kenkyuu jugyou), sometimes attracting thousands of educators from across Japan (such public research lessons may be projected to a large audience using a video projector and microphones.). National school teachers write articles and books based on their own classroom experiences, and are invited all over Japan to comment on research lessons. They host teachers-in-residence at their schools, from periods ranging from a few days to a year. National schools are at the cutting edge of experimentation with new approaches and curriculum. As one national school teacher said of the periodic revisions in the national Course of Study, “When a revision occurs, we’re already thinking about the next revision that will be made ten years down the road; our job is to create the next set of changes.” 4. Association-sponsored lesson study Independent associations also sponsor lesson study. These range from small circles of teachers (e.g. circles of teachers interested in local history or local use of wholelanguage approaches) to large national associations of teachers interested in a particular discipline (mathematics, history, physical education, music, etc.) or particular issue (interdisciplinary teaching, moral development, school as learning community, local civic engagement, etc.). Japan has a variety of national subject-matter organizations which, on first glance, seem similar to their US counterparts-voluntary membership organizations for pre-primary through university educators interested in the teaching of a particular subject matter, such as mathematics, science, language arts, physical education, music, social studies and history, and so forth. One big difference between the US and Japanese versions of the organizations, however, is the central role played by lesson study in the Japanese associations. Public research lessons focussed on a shared research theme are often the central feature of annual meetings. The first author was surprised, when attending the annual meeting of a national science education association that the meeting occurred not in a hotel, but primarily in elementary and secondary schools around a city. Only after observing and discussing public research lessons across the city, all of them designed around the shared conference theme, did the attendees all come together for a plenary session in a hotel. So the central focus of the conference was observing and discussing live research lessons designed to bring to life in classrooms the research theme chosen by the association members. Likewise, attendees at the Annual Meeting of the Japan Council of Mathematics Educators had the opportunity to observe 39 different mathematics lessons planned around the shared theme of “Creation of mathematics education that nurtures the desire to learn.” The lessons were taught during summer vacation, and students at a national school were asked to come to school for a part-day during their summer vacation. The case of solar energy In the 1990s, the addition of solar energy to the Japanese elementary science curriculum created ripples of activity across Japan, as teachers and researchers began to conduct lesson study cycles centered on teaching solar energy. Japanese elementary teachers are generalists who teach all subjects. So solar energy posed the considerable challenge of building the content and pedagogical knowledge of elementary teachers

across Japan, most of whom do not have a specialized background in science. The national Course of Study specified just the basic learning objectives related to solar energy, not the teaching methods. Through the four types of lesson study described in the preceding section, and the synergistic interactions among them, Japanese educators rapidly developed and spread a body of knowledge about solar energy and it’s teaching. National schools had been researching solar energy teaching prior to its addition to the Course of Study, and were in a position to conduct large public research lessons, where they shared not only their teaching, but lesson plans and records of student learning over time. Commentators on these lessons were often university-based science researchers, some of whom had been part of the lesson planning team over time, working with them to study available research and curriculum materials (some of it from the USA and Europe) during the kyouzai kenkyuu phase of lesson study. Likewise, science associations and district-based lesson study groups took up solar energy and brought to life in research lessons their ideas about teaching it. Finally, ordinary elementary schools conducted research lessons on solar energy. Dozens of ordinary elementary schools throughout Japan applied to become “designated research schools” on solar energy. Designated research schools, as described in more detail in the next section, apply for small grants to study a curriculum change and bring it to life in public research lessons. Other elementary schools chose to focus on solar energy within their regular, ongoing school-wide lesson study. As Akihiko Takahashi (in press) has documented, Japanese elementary schools have a well-structured process to use school-wide lesson study to make sense of and enact changes in the national Course of Study, drawing on knowledgeable outsiders and knowledge developed in other settings. The lesson study on solar energy conducted in the various different settings shared many commonalities. Research lessons, embedded in ongoing study of practice, provided the evidence to progressively refine teaching materials and approaches based on student responses. Public research lessons were held only after substantial study of within-school research lessons (typically for a year or so). Groups did not work in isolation, but were linked to each other through networks of school-based and universitiesbased science educators. The tens of thousands of educators, researchers, and policymakers who attended public research lessons on solar energy could see and discuss live instruction designed to enact the solar energy standards, question the teachers about the rationale for their design choices, scrutinize the entire unit plan and records of student learning across the unit, and offer their own ideas and critiques. Over the first year or two of public lessons, knowledge about how to teach about solar energy spread rapidly. Shared knowledge developed about the practical aspects of teaching – for example, which solar toys were inexpensive and made important ideas visible – as well as about the kinds of student thinking to expect, how to handle it, and the subject matter itself. For example, a teacher observing a public research lesson asked about the scientific significance of student strategies, including moving a solar cell closer to a light source, adding a second light source, and using a magnifying class to “concentrate” light: I want to know whether the three conditions the children described – “to put the solar cell closer to the light source,” “to make the light stronger” and to “gather the light” – would all be considered the same thing by scientists. They don’t seem the same to me. But I want to ask the teachers who know science whether scientists would regard them as the same thing.

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Teachers were also able to ask about the basic purpose of teaching about solar energy. One elementary educator asked after a public research lesson: I haven’t taught fourth graders for a while, so I have no idea how and why solar batteries were added to the curriculum. I’m only guessing that including solar batteries reflects adults’ hope that children will become [y] interested in solar energy and thereby help Japan. Science education specialists might be concerned about children using the proper vocabulary or setting up certain experimental conditions, but if the goal of including solar batteries in the curriculum is to get children interested in the fact that electric current can be changed by light, then Mr Hori’s lesson fulfilled that. So I’d really like to know the reason why solar batteries were included as a new curriculum material for fourth graders.

As these quotes suggest, the lesson study and public research lessons occurring across Japan allowed school-based and university-based educators to develop and share the many intertwined types of knowledge needed to enact the solar energy standards well – knowledge of instructional materials, teaching methods, student thinking, content, and larger purpose. At least three features of the Japanese educational landscape, discussed next, support such curriculum enactment. Supports for implementation of curriculum reform through lesson study 1. “Designated research schools” and related policy supports Even before a curriculum change is enacted in the Course of Study, schools can apply to ) for the curricular change. These schools be “designated research schools” ( receive modest grants and their educators study the curricular reform and bring it to life in public research lessons, often by working with outside researchers or educators who are particularly knowledgeable. The grant usually lasts for a period of two years or so, and the modest funds (perhaps around $US 5,000-10,000) are sufficient to pay an honorarium to an outside educator with expertise related to the reform, and to host public research lessons and print-related materials (lesson plans, records of practice, and reflections on what was learned). Schools may apply to be designated research schools because a principal and/or group of teachers are particularly interested in a reform, or may be “volunteered” by principals or district officials who like to see their schools take on this work as a way to build local capacity. Many districts, cities, and prefectures, as well as the nation as a whole, have programs of small grants for designated research schools, and sometimes local educational authorities encourage all schools, in turn, to step up to the plate to apply as a designated research school – much as all teachers are encouraged to open their instruction to colleagues in research lessons if they have not done so in recent years. Several features of Japanese educational policy support the “designated research school” system. Perhaps most obvious is the national Course of Study, which ensures that teachers all over Japan are focussed on the same standards. Changes in the Course of Study are relatively infrequent-major changes occur about once a decade – so that educators are not bombarded with multiple, quickly changing priorities. The proposed changes are typically researched for a substantial amount of time in national school classrooms before the Course of Study is actually changed, and the curriculum changes are announced substantially in advance of being required, so that the designated research schools and other lesson study venues have a chance to build knowledge and share it in public lessons. For example, the 1989 Guidelines for Daily Life Studies confirm that “it took about 20 years of consideration until the new subject area, Daily Life Studies, was established” (Monbushou (Ministry of Education Science Culture),

1989, p. 1). The long-term perspective on change was underlined by a national educational bureaucrat who said: We change the Course of Study about every ten years. But the truth is that ten years is too short a time to change classroom education. If we greatly changed the Course of Study every ten years, teachers would be turning their heads this way and that so often that their necks would break. So we make major changes in the Course of Study only every twenty years or so, and in between it’s just fine tuning.

2. Robust networks of expert subject-matter educators Robust networks that include both school-based and university-based subject matter educators grow out of the collaborations within and between national subject matter associations, designated research schools, and school-wide and district-based lesson study efforts. Looked at from a US perspective, these networks of educators are remarkably strong and enduring. It is not uncommon for these relationships among educators to go on for many decades, with opportunities for each side to observe lessons in the other’s setting. Mr H, an elementary teacher specializing in science who taught at a national elementary school, typically received about 75 invitations per year to serve as final commentator on research lessons throughout Japan or to give demonstration lessons at various schools. Public research lessons typically include outside commentators (often from universities or national lab schools), who, because they may comment at research lessons across Japan, serve as a conduit for information across sites (Watanabe and Wang-Iverson, 2005). Mr H often consulted for a year or more in advance of the research lesson with the schools that invited him to comment, providing feedback at critical junctures as they conducted kyouzai kenkyuu, lesson planning, and actual research lessons. Often he was invited into the school by a colleague who had originally seen him teach a public research lesson at his national lab school, or as part of the annual meeting of a national subject-matter association. Several aspects of these networks are noteworthy. First, these networks are firmly rooted in observation and discussion of shared research lessons, even if some of the participants have “only” taught at the university level. So, for example, university-based commentators on the solar energy lessons talked about inquiry science teaching and about the scientific content of solar energy using specific examples from the public research lesson participants had seen. The onus lies on the outside expert to connect the jointly viewed research lesson to larger subject-matter and pedagogical issues not on classroom teachers to connect a professor’s theoretical lecture with classroom practice. Second, school-based educators ultimately exercise control over which universitybased experts thrive. For example, school-based educators decide who is invited to their school as a commentator, whose research lesson they want to travel and see, and whose lesson study-based books they want to buy. University-based commentators who are unhelpful (or offensive) are not likely to be invited back. On the other hand, commentators who receive many invitations gain cachet, and I have often seen university-based educators introduced with a preface such as “he received invitations to 50 schools last year.” Because large public research lessons provide opportunities to hear various commentators, it is possible to see different models of commentary and learn what participants find useful. We have not found in the USA anything quite comparable to the networks of commentators in Japan, who are able to carefully observe a live research lesson and figure out what comments will help teachers deepen

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their content and pedagogical knowledge as well as their desire to take the next step in improving their own instruction. One reason for the lack of such commentators in the USA may be the lack of a shared curriculum, which makes it more difficult for educators to build shared knowledge about the teaching of particular topics. Whatever the reason, many US projects use mathematics educators originally trained in Japan as commentators.

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3. Broadly established school-based learning routines. While not every teacher may be intrinsically interested in, say, solar energy, all teachers are likely to be strongly invested in the school-wide research theme they helped to forge at their school. School-wide lesson study and other school-based learning routines thus allow elementary teachers to connect curriculum reforms from outside the school to their own aspirations for their own students. A strong system of organizational learning routines, feeding into school-wide lesson study, allows teachers to do the challenging work of instructional change. For example, in the school-based effort to implement changes in the mathematics curriculum documented by Takahashi (in press), the school organized a Research Steering Committee (RSC) that included teachers from each grade level and the teacher responsible for supporting other teachers’ mathematics instruction. This RSC performed key roles in the school-wide lesson study effort, such as inviting an experienced teacher from outside the school to do a demonstration lesson, developing four points to observe during the demonstration lesson, proposing a change in the research theme based on teachers’ reflections on the first year’s activities, and summarizing and connecting the work done by the different grade-band lesson study teams. Committees such as the RSC, as well as school and district administrators who work with them on matters of scheduling, personnel allocation, etc., thus provide important support for school-based learning routines such as lesson study. In addition, other basic organizational routines for teacher learning in Japanese schools no doubt support effective use of lesson study to enact curricular changes. For example, regular grade-level curriculum meetings and daily check-ins in the teacher’s room (where teachers at the same grade level have adjoining desks) enable very frequent consultation on how students are responding to the curriculum, what concepts they missed on the unit tests, and so forth (Akita, 2004; Okano and Tsuchiya, 1999; Tsuneyoshi, 2001) School-wide events (arts festival, sports day, school trips, etc.) build substantial collaborative skill, bonds between teachers and provide leadership opportunities for all teachers, so that teachers are quite accustomed to working together and to reciprocal leadership. Hansei (self-critical reflection, e.g. What went well? What would we do differently next time?) is a typical learning routine that is found in a host of different school activities, providing another likely undergirding of school-based lesson study (Lewis, 1995; Tsuneyoshi, 2001). Final thoughts Four challenges were posed regarding the use of lesson study to facilitate curriculum implementation, namely, to identify: (1) the extent of change required by a curriculum reform, and how lesson study helps teachers do the learning needed to implement a major curriculum reform; (2) how the tension between teacher “ownership” and mandated curriculum is handled in the lesson study effort; (3) how public research lessons are used; and (4) what is the role of government-sponsored vs grassroots-initiated lesson study.

As the foregoing comments suggest, Japanese educators have successfully used lesson study to facilitate major curriculum changes, such as the addition of solar energy to the elementary science curriculum, the shift from “teaching as telling” to “teaching for understanding” in elementary science, and the incorporation of “teaching through problem-solving” and substantial increases of contents in mathematics (Lewis and Tsuchida, 1997; Stigler and Hiebert, 1999; Lewis, 2010; Takahashi, in press). They have done this by using four different types of lesson study: school-wide, district-level, based at national schools, and organization-sponsored (e.g. sponsored by national subject matter associations). Each supplies unique contributions, such as the cuttingedge research that flows in through national schools and national associations, the commitment and local knowledge of students that is supplied through school-wide lesson study, and the conduit between national and local efforts provided by districtbased lesson study. Public research lessons are integral to curriculum implementation, and occur under many different kinds of sponsorship (school, district, national school, association). Public research lessons allow educators to see, question and use other educators’ ideas about implementation of the curriculum reform. In all, three features of the Japanese educational landscape provide crucial support for lesson study used to facilitate curriculum implementation: the system of designated research schools, the robust networks that bring together university-based and schoolbased educators, and the established learning routines at Japanese schools (such as reflection, grade-level collaboration, and teachers’ leadership of school initiatives). In fact, the multiple forms of lesson study in Japan, and the synergistic relationships between government-sponsored inputs (such as national funding for designated research schools) and teacher-initiated inputs (such as choosing to focus school-wide lesson study on an upcoming curriculum change) greatly blur the dichotomies that are often clear in the US (grassroots vs government-sponsored; teacher ownership vs curriculum mandate). A post-script to the solar energy story underlines the intimate intertwining of national and individual initiative. Solar energy originally came to the attention of national policy-makers in Japan through research lessons designed and conducted by elementary teachers, many of them teaching in ordinary elementary schools. In the midst of an energy crisis, these teachers felt that Japanese elementary students should be learning about solar energy, not just conventional batteries (as then required in the Course of Study), so they developed and taught lessons using solar cells. These lessons caught on through networks of science educators, and caught the attention of the national Ministry of Education, eventually resulting in the addition of solar energy to the elementary curriculum. So the addition of solar energy was grassroots-initiated before it became a policy mandate, after which it again became a teacher-initiated implementation process. To educators in other countries, the Japanese system poses a challenge to use lesson study in ways that similarly help us join the strengths of individual teachers’ initiative, research-based knowledge, and national policy. References Akita, K. (2004), “The Japanese model of cooperative learning: teachers professional development”, paper presented at the International Association for the Study of Cooperative Education, Singapore, June 22-24. Alston, A.S., Pedrick, L., Morris, K.P. and Basu, R. (2011), “Lesson study as a tool for developing teachers’ close attention to students’ mathematical thinking”, in Hart, L. C., Alston, A. and Murata, A. (Eds), Lesson Study Research and Practice in Mathematics Education, Springer, Dordrecht, Heidelberg, London, and New York, NY, pp. 135-151.

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Okano, K. and Tsuchiya, M. (1999), Education in Contemporary Japan: Inequality and Diversity, Cambridge University Press, New York, NY. Shimizu, Y. (2002), “Sharing a new approach to teaching mathematics with the teachers from outside the school: The role of lesson study at ‘Fuzoku’ schools”, paper presented at the USJapan Cross Cultural Seminar on the Professionalization of Teachers Through Lesson Study, Park City, UT, June 30-July 20. Stigler, J.W. and Hiebert, J. (1999), The Teaching Gap: Best Ideas From the World’s Teachers for Improving Education in the Classroom, Summit Books, New York, NY. Takahashi, A. (in press), “Supporting the effective implementation of a new mathematics curriculum: a case study of school-based lesson study at a Japanese public elementary school”, in Li, Y. and Lappan, G. (Eds), Mathematics Curriculum in School Education, Springer, New York, NY. Takahashi, A., Watanabe, T., Yoshida, M. and Wang-Iverson, P. (2005), “Improving content and pedagogical knowledge through kyozaikenkyu”, in Wang-Iverson, P. and Yoshida, M. (Eds), Building Our Understanding of Lesson Study, Research for Better Schools, Philadelphia, PA, pp. 77-84. Tsuneyoshi, R. (2001), The Japanese Model of Schooling: Comparisons with the United States, Vol. 27, RoutledgeFarmer, New York, NY. Watanabe, T. and Wang-Iverson, P. (2005), “The role of knowledgeable others”, in Wang-Iverson, P. and Yoshida, M. (Eds), Building Our Understanding of Lesson Study, Research for Better Schools, Philadelphia, PA, pp. 85-92. Corresponding author Catherine Lewis can be contacted at: [email protected]

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