Lesson Study

The following sections are included:

• FOREWORD
• TABLE OF CONTENTS

Alan Bishop opens the section by providing the readers with the idea of using ‘Lesson Study’ as a means for developing both the theory and practice of mathematics teacher education under the title “Mathematics Education for Knowledge-based Society.” Kaye Stacey shows some analogies of mathematical thinking with schooling, way of learning mathematics, and teaching mathematics. She offers illustrations of how strong mathematical thinking can provide teachers with many possible decisions and actions. Lessons are considered along with students' mathematical understanding via interesting pragmatic examples shown in the paper. In addition, the paper concludes with the teaching of mathematics, drawing on general pedagogy as well as mathematical pedagogical content knowledge to contribute to the solution. David Tall makes some remarkable statements about mathematics classrooms related with Lesson Study in which it serves as the platform for long-term development of individual children. The long-term development depends not only on the experiences of the lesson, but in the prior experiences of the children, and how those prior experiences have been integrated into the children's current knowledge described by the good practices of mathematics classrooms using Lesson Study in Japan according to the Developmental Framework through Embodiment and Symbolism of the three mental worlds. Akihiko Takahashi provides a vivid idea of how Lesson Study can be used as a process for improving mathematics teaching and learning. He reminds us that we need to distinguish between two types of professional development programs; one is to learn new ideas and knowledge, the other is to practice how to incorporate new ideas and procedures in various situations. He then suggests Lesson Study as an ideal phase of the two Professional Developments. TIMSS has had a great impact on many countries. The TIMSS 1999 Video Study has become a potential tool in this APEC project; it has become accessible to more people through the recent availability of all 53 public release videos online (www.timssvideo.com). Frederick K.S. Leung provides the analysis of TIMSS Video Study data for Hong Kong, SAR to see whether there are classroom practices that can be used to explain East Asian students' high achievement in mathematics. He also provides an idea on how conflicting results coming from qualitative and quantitative analyses point to the complexity in interpreting video data on classroom practices and of achievement data in international studies. This also provides us with insight into how cultural aspects come into play in interpreting data. Masami Isoda then discusses the meaning of Lesson Study in the Japanese historical context combined with how theories of mathematics education as a science of teaching have been built by using the subject-based lesson study and school-based lesson study. Obviously, these theories are not meant to prove a scientific proposition but rather to develop classrooms in schools implementing the problem solving approach. Teachers develop their own theory of teaching and improve their practice in Lesson Study cycle. In the last chapter, Maitree Inprasitha describes how to implement Lesson Study to be sustainable in Thailand in which it is integrated with the Open Approach in teachers' professional development. There are some social and cultural aspects influencing the Thai educational system to which the reformers have to be sensitive when they attempt to introduce some innovations. In addition, he shows some empirical data of what has been changing in both teachers and students in Thai school systems that would yield deeper comprehension for those who will use this innovation in their context, especially the schoolteachers who take major roles in the classroom.

The following sections are included:

• WHAT AM I OFFERING IN THIS CHAPTER?
• DEFINITION OF KNOWLEDGE-BASED SOCIETY
• HOW TO CONSIDER EDUCATION IN THIS NEW CONTEXT?
• KINDS OF EDUCATION => KINDS OF MATHEMATICS EDUCATION
• WHERE IS DEVELOPMENT HAPPENING?
• RESPONSES OF MATHEMATICS EDUCATION TO THE GROWTH OF THE KNOWLEDGE-BASED SOCIETY
• WHAT PARTICULAR DEVELOPMENTS SHOULD WE AIM FOR IN FME TO PREPARE OUR STUDENTS FOR THE KNOWLEDGE- BASED SOCIETY?
• FINAL THOUGHTS
• REFERENCES

The following sections are included:

• INTRODUCTION
• IRENE'S LESSON ON THE SPINNERS GAME
• GREG'S LESSONS ON THE SPINNERS GAME
• HELEN'S LESSON ON THE SPINNERS GAME
• CONCLUSION
• A MATHEMATICAL NOTE
• Acknowledgement
• REFERENCES

Lesson Study is a format to build and analyze classroom teaching where teachers and researchers combine to design lessons, predict how the lessons might be expected to develop, then carry out the lessons with a group of observers bringing multiple perspectives on what actually happened during the lesson. This article considers how a lesson, or group of lessons, observed as part of a lesson study may be placed in a long-term framework of learning, focusing on the essential objective of improving the long-term learning of every individual in classroom teaching.

The following sections are included:

• IMPROVING TEACHING AND LEARNING
• TWO MAJOR TYPES OF PROFESSIONAL DEVELOPMENT PROGRAMS
• LESSON STUDY IN AN IDEAL PHASE TWO PD
• WHAT TEACHERS CAN LEARN THROUGH LESSON STUDY
• CONCLUSION
• REFERENCES

The Third International Mathematics and Science Study (TIMSS) 1999 Video Study aims at describing and comparing eighth-grade mathematics teaching practices among seven countries in order to identify similar or different classroom features. Since East Asian students have consistently performed well in recent international studies of mathematics achievement, this paper intends to analyze the TIMSS Video Study data for the East Asian country of Hong Kong in order to see whether there are classroom practices that can be used to explain students' high achievement in mathematics. The data analysis however yields conflicting results. While a qualitative analysis of the data shows that the quality of mathematics teaching in Hong Kong is high, a quantitative analysis of the same data shows that teaching in Hong Kong is rather traditional and teacher-centred. The conflicting results point to the complexity in interpreting video data on classroom practices and of achievement data in international studies. The results are then interpreted with respect to the underlying cultural values in East Asia, and implications for methodology in analyzing video data, as well as for educational reform in East Asian countries and other countries are discussed.

Lesson Study (jugyokenkyu) is a scientific activity for teachers. It began in the 1870s in Japan and was introduced as a science to reproduce better practice of teaching in the 1880s. From that era, several study topics for Lesson Study (LS) have been shared among related groups and societies. Especially after World War II, Lesson Study topics were shared with regular revisions of the curriculum and the research movement of several societies. As a result of teachers' untiring-efforts to overcome challenges on the topics of LS, several local theories, and especially two general theories of teaching, have been developed. The Problem Solving Approach (PSA), known as a Japanese teaching approach, which is a teaching theory for developing children who learn mathematics by and for themselves. It includes teaching about learning how to learn and the mathematical values. Another theory is the technical terms for teachers for explaining the objective of teaching generally on the curriculum sequence. Those theories are not only used by teachers but also developed by mathematics educators for sharing the curriculum sequence and pedagogical content knowledge (PCK). This paper explains the original Japanese meaning of LS in relation to its origin and theoretical development, and illustrates the LS as reproducible science through demonstrating the effect of LS on PSA for reproducing better practice with some descriptions of PCK.

There have been numerous attempts to introduce new ideas into Thailand for various purposes, but most of them have either failed to materialize or initially accepted, but later proved not to be sustainable. One of the major causes of failure is due to lack of proper preparation for the introduction of such innovations. The Japanese approach to teacher professional development known as “Lesson Study” is an innovation that was introduced around 130 years ago (Shimizu, 2006). Today it has been recognized and adopted for teacher professional development in many countries around the globe. Our team introduced Lesson Study in Thailand in 2002 (Inprasitha et al., 2007) by preparing the necessary surrounding contexts such as teacher education programs, graduate studies, workshops for in-service teachers and a long-term teacher professional development program. This article was aimed to expound on the manner of preparation of the contexts. We began our experiment with the 4th year teacher-education students who were scheduled to do their teaching field work in the 2002 academic year. The following year, all the teacher-education students in Faculty of Education, Khon Kaen University were required to participate in every in-service workshop for teachers sponsored by our Faculty of Education. Then, from 2003-2004, we tried to apply the approach in our usual education workshops for teachers with an additional feature of making a follow-up evaluation in the trainees' schools. In 2006, we had successfully developed a three-year development model (2006-2008) to be implemented in participating schools as a pilot project. The model has gained full support from the National Office of Basic Education Board, the Office of Knowledge Development and Administration, Mathematics Education Graduate Studies and the Center for Research in Mathematics Education of Khon Kaen University, as well as cooperation from abroad. The outcome of our effort to introduce Lesson Study into Thailand helped confirm our belief that the application of Lesson Study in the Thai educational context is possible and can be sustained.

This section introduces various perspectives on lesson study and professional development. Shizumi Shimizu and Kimiho Chino provide the history of Lesson Study in developing good practices in Japan. This chapter traces the roots of Jugyo-Kenkyu (translated as “Lesson Study”) in Japan. They then explore pre-service education for teachers and in-service professional development for teachers in the post-World War II era. Finally, examples of actual lessons are used to examine issues regarding jyugyokenkyu in Japan today. Catherine Lewis provides ideas from the history of lesson study in the U.S. that may be useful to educators seeking to implement lesson study outside Japan. A lesson study team including Ban Har Yeap, Peggy Foo and Poh Suan Soh examines the impact of Lesson Study on the professional development of secondary mathematics teachers who are participants in their research. This chapter offers empirical data useful to school leaders and/or policy makers considering the implementation of lesson study in Singapore schools in accordance with Singapore's mathematics education focusing on mathematical problemsolving at the heart of its curriculum. It also provides insight on how to implement the innovation in other countries. Kazuyoshi Okubo and Hiroko Tsuji report on the effort to raise teachers' abilities based on concrete practice examples (adding and subtracting fractions in the sixth grade), about the study method used, and describe the kind of practices and “good practice” for Teaching and Learning Mathematics through Lesson Study. Maitree Inprasitha describes how the openended approach integrated with lesson study in Thailand has been used innovatively to improve mathematical teacher education after the long history of Thai teacher education programs. The empirical data used to support mathematical teacher education development fit with classic questions raised in several teacher education programs: What are the essential characteristics of a professional program for teachers? What should be the distinctive features of the treatment of subject matter in each type of program? Soledad A. Ulep states in the chapter on in-service teacher education in mathematics through Lesson Study, “Learners learn most effectively from experiences that are engaging, meaningful, challenging, and relevant, and from teachers who facilitate construction of knowledge from such experiences.”

The following sections are included:

• INTRODUCTION
• ROOTS OF JYUGYO IN JAPAN
• POST-WORLD WAR II PRE-SERVICE AND IN-SERVICE EDUCATION FOR TEACHERS
• LESSON EXAMPLES FROM JAPAN: CURRENT SITUATION AND FUTURE TASKS
• CONCLUSION
• NOTE
• REFERENCES

The following sections are included:

• INTRODUCTION
• FOCUS ON THE BENEFITS OF LESSON STUDY FOR TEACHERS
• HOW DO TEACHERS LEARN IN LESSON STUDY?
• EXPECT CHANGE TO TAKE TIME, AND LOOK FOR IT IN THE RIGHT PLACES
• CONCLUSION
• REFERENCES
• APPENDIX

The quality of teachers has been identified as one of the critical success factors of high-performing education systems. The main purpose of this study is to investigate how lesson study can deepen the professional development of teachers in Singapore. The findings will be derived from a case study in a secondary school. The findings will be discussed in terms of knowledge of subject matter, instruction and other impacts such as teachers’ perceptions of collegiality among colleagues. Implications from these findings can help school leaders and/or policy makers consider the choice and implementation of lesson study as an effective ground up, teacherdriven professional development platform to raise the collective expertise of teachers in the long run.

The following sections are included:

• INTRODUCTION
• MATHEMATICS EDUCATION FOR ENHANCING STUDENTS' CREATIVITY: INSTRUCTION ON PROBLEM SOLVING
• CONCRETIZATION OF INSTRUCTION BY PROBLEM SOLVING METHODS

During the 1970s and 1980s, the open-ended approach emerged as a method to reform mathematics teaching in Japanese classrooms and has spread around the world. In the 1990s, other countries learned about lesson study, a Japanese style of professional development, through the videotape study component of Third International Mathematics and Science Study. During this same time the educational reform movement in Thailand began focusing on reforming students' learning processes and calling for innovative teacher education programs. This paper describes how in this era the open-ended approach integrated with lesson study has become an innovation to improve mathematical teacher education in Thailand.

The following sections are included:

• COLLABORATIVE LESSON RESEARCH AND DEVELOPMENT (CLRD): A MEANS FOR IMPROVING CLASSROOM TEACHING AND LEARNING
• WHAT IN-SERVICE TEACHERS LEARNED THROUGH CLRD
• CONCLUDING REMARKS
• REFERENCES

This section introduces how Lesson Study has been implemented around the world. The first chapter by Maitree Inprasitha is Transforming Education through Lesson Study: Thailand's Decade-Long Journey. It provides some exemplars of how Lesson Study and the Open-ended Approach were adapted in the Thai cultural and social context from the early stage of incubation of the idea and then experimentation in some schools. Innovations have been integrated into the Mathematics Education program. In the last year of the program, the mathematics student teacher interns conduct practice in the project schools, which provides platforms for school teachers, student teacher interns, researchers, and experts to cooperate to improve student learning in accordance with the Lesson Study and Open Approach as an adaptive approach. Marsigit describes Mathematics Teachers' Professional Development through Lesson Study in Indonesia, which took place from 1999 to 2005 through cooperation between the Government of Indonesia, JICA and three universities; UPI Bandung, UNY Yogyakarta and UM Malang carried out a project called IMSTEP-JICA. The current Lesson Study activities are conducted under the auspices of Strengthening In-Service Teacher Training of Mathematics and Science Education (SISTTEM) at the junior secondary level (established under the cooperation between JICA and MONE). In Chile, Grecia Gálvez reported that in November, 2005, the implementation of a Project of Improvement for the Teaching of Mathematics with Technical Assistance of Japan was started in Chile. This project was included in an Agreement executed between the Governments of Chile and Japan, in connection with the pertinent Agencies of International Cooperation, JICA of Japan, and AGCI of Chile. This project was completed over three years, aimed at university academicians preparing teachers of Primary Education. Chap Sam Lim and Chin Mon Chiew from Malaysia describe an attempt to use Lesson Study to promote good practices through a collaborative culture in mathematics teaching. It begins with cogent arguments for the need to promote good practices and collaborative culture in Malaysian mathematics teaching, followed by a brief description of the Lesson Study projects in Malaysia. In Vietnam, Tran Vui showed the research focusing on Lesson Study as a means to innovation. The results from this lesson study showed that good teaching practices are powerful models for changing the quality of mathematics education. The project developed a video tape recorder (VTR) of good lesson as a product of lesson study to use for teacher education. Christine Kim Eng Lee and Yanping Fang from Singapore conducted research lessons in collaboration with a government local primary school in the early stage of a 2-year (2006— 2007) intervention project funded by the Center of Research in Pedagogy and Practice (CRPP), National Institute of Education (NIE), Singapore. During the 2-year learning by doing pilot intervention, six research lessons and their revisions on three mathematics topics were taught (division for grades 2 and 3; fraction for grades 3 and 5; and area & perimeter for grade 4). In the Philippines, Soledad A. Ulep described an innovation which the University of the Philippines National Institute for Science and Mathematics Education Development (UP NISMED) has been trying to promote in its training program: teaching through problem solving. An example of this training program was a five-day workshop, which was conducted on 24—28 April 2006 upon the request of the Office of the Mayor of Pasig City in Metro for in-service mathematics teachers from a cluster of 10 schools. Lesson Study originated in Japan, therefore the Japanese are presumed be the best practitioners of the innovation. Takeshi Miyakawa has provided some examples according to the principles of good lessons analysis. These principles are not only for the Japanese but they can allow practitioners from different countries to better understand what kind of lessons are called good lessons that become integral to Japanese practitioners' daily practice. This would also provide other Lesson Study practitioners ways to develop their good lessons. Finally, Patsy Wang-Iverson and Marian Palumbo present a school's first attempt at using Lesson Study in the U.S.; they partnered with the schoolteachers to launch the Lesson Study team. The team members discussed collaboratively how to develop students' mathematical thinking during the lesson study process; the teachers identified current characteristics of the students they encountered in their classes and how they hope their students would develop. This approach could serve as a basis for developing lessons focused on helping students to learn and think in mathematics.

The development of teaching and the teaching profession is an issue countries around the world have been struggling to solve for many centuries. Lesson study, a Japanese way of professional development of teachers, dates back nearly 140 years, in 1872 the Meiji government invited foreign teachers to teach Japanese teachers about “whole class instruction” (Isoda, 2007). Ironically, in 1999, Stigler and Hiebert brought back to the U.S. the same idea on how to present whole class instruction, “If you want to improve education, get teachers together to study the processes of teaching and learning in classrooms, and then devise ways to improve them” (Stigler, 2004 cited in Fernandez & Yoshida, 2004). Although the education reform movement around the world calls for effective reform tools or even ideas like Japanese lesson study, transferring those tools/ideas to other socio-cultural setting in other countries is not easy and always complicated. Thus, education reform movements sometimes support but sometimes hinder movement of society. Taking Japan as a case study, Japan has undergone the movement of society from agricultural to industrialized, to information, and now knowledge-based society during the two centuries since the late 18th century to the present. Not visible to outside people, an evolution in the approach to school has taken place in Japan, which supports the movement of society, which has not occurred in most developing countries, including Thailand. Thailand has looked to Japan for ideas and has been implementing Lesson Study since 2000 but with a unique approach to adaptation. Thailand's experience with Lesson Study has been shared with APEC member economies over the last six years and has been deemed “quite a success” in improvement of teaching and learning of mathematics.

From 1999 to 2005, under a cooperation between the Government of Indonesia (GOI) and JICA-Japan, three universities, UPI Bandung, UNY Yogyakarta and UM Malang, carried out a project called IMSTEP-JICA [JICA Technical Cooperation Project for Development of Science and Mathematics Teaching for Primary and Secondary Education in Indonesia] for pursuing good practices of mathematics and sciences teaching by developing and strengthening teacher education. The project resulted in pilot lesson study activities for secondary mathematics teaching in three cluster sites of West Java, Central Java, and East Java. The results of the studies indicated significant improvements of the practice of secondary mathematics teaching and learning processes in teaching methodology, teacher competencies, students' achievement, alternative evaluation, teaching learning resource and syllabi. However, some misconceptions remained as obstacles to effective implementation of lesson study.

The current lesson study activities are conducted under the auspices of SISTTEM (Strengthening In-Service Teacher Training of Mathematics and Science Education) at the junior secondary level. The overall goal of SISTTEM is to develop the model of in-service teacher training primarily through MGMP [Teachers Club] activities using lesson study to continue teacher professional development in the target province and to improve the level of student learning in mathematics and science in the target districts.

The following sections are included:

• LINKS BETWEEN JAPAN AND CHILE IN RELATION TO MATHEMATICS EDUCATION
• PRIMARY SCHOOL AND MATHEMATICS EDUCATION IN CHILE
• LESSON STUDY AND LEM COMMUNAL WORKSHOPS OF MATHS
• A DIDACTIC UNIT FOR THE LEARNING OF FRACTIONS
• PLAN OF THE THIRD LESSON
• POSSIBLE ISSUES FOR DISCUSSION AND REFLECTION WITH TEACHER-READERS USING THE VIDEO
• CONCLUSION
• REFERENCES

The following sections are included:

• INTRODUCTION
• THE NEED TO PROMOTE GOOD PRACTICE AND A COLLABORATIVE CULTURE IN MATHEMATICS TEACHING
• LESSON STUDY PROJECTS IN MALAYSIA
• AN EXEMPLAR LESSON
• SUGGESTIONS FOR ADOPTION/ADAPTATION OF THE LESSON PLAN
• LESSON STUDY FOR TEACHER PROFESSIONAL DEVELOPMENT
• CONCLUSION
• AFTERTHOUGHT
• REFERENCES
• APPENDIX 1
• APPENDIX 2

In Vietnam, the reform mathematics curriculum requires more than mastery of basic mathematical skills and knowledge of algorithms in solving a class of specific problems. The teaching of mathematics is changing. We are seeking innovative approaches in teaching and learning mathematics. The teacher ought to think of teaching in terms of several principal hands-on activities, problematic real life situations, and open-ended questions. The innovation of teaching is to help students construct their own knowledge in an active way, and to enhance their thinking through solving non-routine problems while working cooperatively with classmates. Through these approaches, students' talents and competencies can be developed. There are several possibilities for innovation of mathematics education in an economy. Lesson study, which originated from Japan, is currently a central focus in the U.S. and other economies for the professional development of teachers and the improvement of student learning…

The following sections are included:

• Context of the Long Division Case
• LESSON STUDY PROCESS AND AN INNOVATIVE APPROACH IN THE CLASSROOM
  • Lesson Study Process as Innovative Teacher Professional Development for the School and the Teacher Team
  • Lesson Study Process and an Innovative Approach in a Third Grade Mathematics Classroom
• Acknowledgments
• REFERENCES
• APPENDIX 1
• APPENDIX 2

The following sections are included:

• INTRODUCING LESSON STUDY ON MATHEMATICS IN THE PHILIPPINES
• LESSON STUDY: THE KEY PROCESS FOR LINKING TEACHER TRAINING AND CLASSROOM TEACHING
• CONCLUSIONS
• REFERENCES
• APPENDIX

The following sections are included:

• INTRODUCTION
• JAPANESE LESSONS AND TEACHERS
• TDS AS A TOOL TO ANALYSE A LESSON
• ANALYSIS OF THE TASKS
• ANALYSIS OF THE VIDEOTAPED LESSON
• DISCUSSION AND CONCLUSION
• Acknowledgements
• REFERENCES
• APPENDIX

Developing U.S. students' mathematical thinking frequently is an elusive goal. The reasons are varied. Some of them include: 1. teachers' own lack of understanding of mathematics caused in part by an absence of a coherent mathematics curriculum (Schmidt et al., 2002); 2. insufficient or no professional development focused on the scope and sequence of mathematics within and across the grades; 3. inadequate knowledge and concrete examples of what mathematical thinking entails for both students and teachers; 4. lack of clear and explicit examples for how to connect students' procedural knowledge with conceptual understanding through mathematical thinking.

To focus APEC (Asia-Pacific Economic Cooperation) member economy specialists' attention on the importance of and approaches to the development of mathematical thinking of both students and teachers, the 2-7 December 2006 APEC lesson study conference in Tokyo/Sapporo, Japan, offered various keynote presentations (Katagiri, March, 2007, Lin, March, 2007, Stacey, March, 2007, Tall, March 2007). The speakers shared their perspectives on approaches to developing mathematical thinking, thus setting the stage for observation and discussion of four lessons, discussion of specialists' papers on mathematical thinking, and preparation for work following the conference. Prior to the end of the conference, the APEC member economy specialists were charged with the task of returning to their country and conducting a lesson study cycle that helped teachers work with their students to develop mathematical thinking skills while working on a specific mathematical concept.

The following section is included:

• CONTRIBUTORS