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Kyouzaikenkyuu (translated as instructional materials research) is said to be a crucial part of successful Japanese lesson study. Kyouzaikenkyuu is described as the planning portion of the research lesson during lesson study. Kyouzaikenkyuu is also said to be done on a daily basis by Japanese teachers; however, there is very little written about this process in the literature. This study takes an in-depth look into what Japanese junior high mathematics teachers do during their daily kyouzaikenkyuu, and why they do it. Through interviews, observations, and participation in kyouzaikenkyuu, we explain the process and key ideas that many Japanese mathematics teachers go through to prepare their lessons. We document two different approaches to kyouzaikenkyuu. We also found that for some teachers there is a large difference between what they do during kyouzaikenkyuu for a research lesson compared to the kyouzaikenkyuu of a daily lesson. If teachers outside of Japan wish to engage in kyouzaikenkyuu and lesson study, these approaches are a good place to start.

This study aimed to analyze boundaries of the community of teachers’ imple- menting the mathematics textbooks with Lesson Study and Open Approach. For this study, Mathematics textbooks were Japanese mathematics textbooks (Thai version), consisting of mathematics problems, flow of lesson, and students’ mathematical ideas. The participants were 2 expert teachers who use the textbooks in the classroom using Lesson Study and Open Approach since 2013. The data were collected in 2017 school year by using interview andclassroom observation with video recording. The data were analyzed based on Wenger, McDermott, & Snyder (2002)’s framework of community of practice. The results showed that the teachers practiced in 3 boundariesof the community: 1) within school—every week, they use the textbooks to design mathematical problems and anticipating students’ ideas with their school team, then they teach the lesson and observe students’ ideas in the classroom, and they reflect on students’ ideas that occurred in their classroom, 2) across schools—every semester, they form team with teachers who work in different schools of the project to design/observe/reflect a classroom by using the textbooks in school open class activity, and 3) across organization boundaries —every year, they and their school network participated in the activities, the national open class, the workshop for school teachers, the national and international conference, that help them to understand students’ ideas via classroom by using the textbooks and sharing with their school teachers and university experts.

This study was aimed to analyze how students’ mathematical ideas emerged through a flow of lesson in mathematics classroom using Lesson Study and Open Approach. A context of the study was the Open Approach as a teaching approach and the Lesson Study as a way to improve the quality of teaching (Inprasitha, 2015a). The flow of lesson, likewise, is considered to be a tool for accessing to students’ ideas when the students are involved in problem solving and connection between students’ real world and mathematical real world (Inprasitha, 2017b). Ethnographic study was employed as a research methodology in this qualitative study by using a participative research design to form a lesson study team for collaborative designing of lesson plans guided by Thai version of Japanese mathematics textbooks. Research results were shown that the students’ mathematical ideas emerged, through the flow of lesson, when the students’ ideas of a problem solving were mathematized as follows: 1) the mathematical ideas were extended through representations of real world, 2) the mathematical ideas were extended and generalized through semi-concrete aids, and 3) the mathematical ideas were generalized through representations of mathematical world. The processes of mathematization (Isoda & Katagiri, 2012), furthermore, were accomplished when the students’ mathematical ideas become “how to” or tools for learning for the next lessons.

This research aims to analyze how and what teachers learn in community of implementing mathematics textbooks with Lesson Study and Open Approach about addition in number and operations for first grade. The participants were 2 teachers who use the textbook in the classroom using Lesson Study and Open Approach. The mathematics textbooks for this study were Japanese mathematics textbooks (Thai version), and consist of mathematics activities, flow of lesson, and students’ mathematical ideas (Inprasitha, 2015b). The data were collected in October 2015 by interview and classroom observation with video recording. The data were analyzed based on communities of practice (CoP) from Wenger, McDermott, & Snyder (2002), and Shulman & Shulman (2004). The result of this research found that how and what teachers learned in community of implementing mathematics textbooks with Lesson Study and Open Approach, are 2 aspects: 1) teachers learned about the content of mathematics from their sharing on the textbook and students’ ideas together, and 2) teachers learned how to teach the content, through using the textbook for sharing anticipating students’ ideas, observing students’ ideas, and reflecting by using evidence from students’ ideas that appeared in classroom.

In this chapter, we analyse three fundamental practices of Japanese mathematics teachers to better understand the set of community values that influence their work as teachers. The three fundamental practices are: writing detailed lesson plans, kyozaikenkyu (a planning practice), and emphasizing student mathematical reasoning in instruction. An analysis of these community practices resulted in eight potential values of the Japanese mathematics teacher community. These values help the field better understand why Japanese teachers engage in the work of teaching the way that they do.

Japanese lesson study was introduced to the West in the late 1990s. Certain widely disseminated publications and classroom videos, and also reports on international surveys of students achievement, led many to consider that Japanese mathematics teaching is highly creative and effective, with lesson study as a main explanatory factor. As a result, substantial efforts have been deployed in many countries to engage mathematics teachers in lesson study. In this paper, we argue that lesson study is but one element of a comprehensive Japanese “infrastructure” for developing teacher knowledge, both personal and shared, and that the functions and workings of any particular element in this infrastructure cannot be fully understood when viewed in isolation. In this paper, we offer a systemic (institutional) analysis of how these “infrastructure” elements interact in crucial ways. Specifically we study two episodes where a teacher’s “practice research” is clearly motivated and supported by other infrastructural conditions, such as the possibility to present the outcomes at a regional teacher conference, and in a publication. Moreover, a central prerequisite for the creative part of “lesson planning” is a much more limited activity: the patient study and discussion of mathematical tasks and materials. This activity is also crucially supported by elements of the infrastructure.

According to Japanese mathematics educators, Lesson Study is not only a professional development activity for teachers but also a part of a feedback mechanism to inform curricular revisions. The learning from Lesson Study informs the revision of the National Course of Study (NCOS), which takes place about every 10 years. Lesson Study also informs the revision of commercially produced textbook series, which are revised much more frequently than the NCOS. In an earlier study, Watanabe (Transformation of Japanese elementary mathematics textbooks: 1958–2012. In: Li Y, Silver EA, Li S (eds), Transforming mathematics instruction: multiple approaches and practices, 199–216. Springer, Cham, 2014) examined how Japanese elementary mathematics textbooks have changed over the years as Japanese mathematics teachers transformed mathematics teaching from teacher-centered instruction to what Stigler and Hiebert (Teaching Gap: Best Ideas from the World’s Teachers for Improving Education in the Classroom. The Free Press, New York, 1999) called structured problem-solving style instruction. That study revealed that Japanese textbooks indeed changed over the years to reflect more closely the structured problem-solving style lessons. However, the previous study could not attribute those changes to Lesson Study. In this follow-up study, we examined Lesson Study artifacts from the 1980s to see how Lesson Study might have affected the changes in Japanese textbooks. Although we cannot definitively conclude that Lesson Study led to specific changes in textbooks, there are some evidences that suggest its influence. We speculate that certain features of the Japanese education system may contribute to making such influences possible.

Problem solving has been a major theme in Japanese mathematics curricula for nearly 50 years. Numerous teacher reference books and lesson plans using problem solving have been published since the 1960s. Government-authorized mathematics textbooks for elementary grades, published by six private companies, have had more and more problem solving over the years. As a result, almost every chapter in Japanese mathematics textbooks for elementary grades begins with problem solving as a way to introduce students to new concepts and to introduce new procedures. But a large wave of teacher retirement in recent years has left newly hired teachers without the collegial support they need to develop the expertise to teach through problem solving. In order to overcome this challenge, the latest edition of a major mathematics textbook series in Japan includes more resources to help teachers teach through problem solving and to help students learn through problem solving. The book contains more alternative approaches to a problem, provides diagrams meant to help students solve problems independently, and includes pages that teach students how to take notes effectively. By comparing the latest two editions of this textbook series, the author will highlight how the text has increased its support of problem solving, and will relate the changes to recent trends of Japanese mathematics textbook designs.

The international education community has taken an interest in lesson study, the Japanese approach to school education. Lesson study first came to the attention of educators outside of Japan primarily through the publication of The Teaching Gap (Stigler and Hiebert in The teaching gap: Best ideas from the world’s teachers for improving education in the classroom. The Free Press, New York, 1999) and the TIMSS video study, which showed the typical structure of Japanese mathematics instruction in the classroom. However, while there has been tremendous international interest in using lesson study as a model for professional development, there has been less of a focus on applying the method of Japanese mathematics instruction, which is teaching mathematics through problem solving. This paper discusses the interplay between lesson study and teaching mathematics through problem solving and outlines suggestions for educators seeking to improve both teaching and lesson study outside Japan.

Japanese mathematics education is characterized by structured problem solving (Stigler and Hiebert in The teaching gap. Free Press, New York, 1999). Lesson study, where a group of teachers develops a lesson together, refines it furthermore. This learning opportunity has spread to various levels of the educational system during the last one hundred years, forming the lesson study practice and of today and becoming a part of our educational culture. This chapter addresses the culture, which Japanese mathematics education has nurtured from three perspectives such as history, community, and institution. These perspectives are discussed with a basis on Bishop in Mathematical enculturation: A cultural perspective on mathematics education. Kluwer, Dordrecht (1989). Besides these, a fourth perspective, developmental assistance, is also employed to compare the perspectives of Japan with those of developing countries.

Several national and international surveys have showed that a very low percentage of Japanese high school students believe mathematics to be useful in daily life. To rectify this issue, problem-based learning (PBL) was introduced into the Japanese mathematics curriculum. However, it is doubtful whether this change will bring about the intended result. Therefore, we propose to integrate entrepreneurship education into PBL in order to develop an attitude of risk taking by using mathematical ways of viewing and thinking. In this study, we developed a framework for gaming instructional material. Moreover, we conducted a trial lesson to evaluate its effects.

This study examines the difficulty level of mathematics textbooks in junior secondary schools in China, the USA, South Korea, Singapore, and Japan. The analysis uses a novel framework which focuses on content breadth, content depth, difficulty level of worked examples, and difficulty level of exercises. Based on the analysis of five selected topics—numbers and calculation, equations, triangles, solids, and statistics—China has the most difficult textbooks, followed by South Korea and Singapore. The US difficulty levels are quite similar to those in Japan, which has the easiest textbooks. In addition, the selected Chinese mathematics textbook seems to value “shapes and geometry” most significantly among the five nations, whereas the selected US textbook seems to emphasize “numbers and calculation.” Furthermore, it is found that the selected Japanese mathematics textbook series involves the least amount of mathematics, and also shows a lack of statistics.

Mathematics education community in Japan has continuously and extensively developed 'mathematical thinking' as an educational value. In this paper, the historical review was conducted on mathematical thinking in terms of its evaluation and educational method, textbook change, and research on treatment of diversified mathematical thinking. This approach can provide methodologically an important perspective to grasp, clarify and make relative the values in mathematics education in different times of each culture. Values here mean those attitudes which lay at the back of the intention, judgment, and selection of teaching-learning activity exhibited by primary teachers. As a result of this research, it is learnt that the theme in mathematics education research does reflect values held by the primary mathematics teachers. They, in turn, have held central ideas and value utilizing children's diversified mathematical thinking, letting them subjectively and extensively construct mathematical ideas in the lesson. The major characteristics of Japanese Mathematics education is the open-ended approach, which has been developed as an evaluation and educational method of mathematical thinking. This is available as translated version of 'The Open-Ended Approach: A New Proposal for Teaching Mathematics' (The original version (Shimada) is in Japanese published in 1977).

This article presents an instructional model (inclusively responsive instruction) that takes advantage of student diversity in order to differentiate student learning while maintaining high expectations. In the history of U.S. education, diversity and academic rigor were often considered at odds, and educators tried to emphasize one at the expense of the other. This article uses a detailed set of examples from Japanese mathematics education to illustrate how diverse ideas, as important resources, can drive classroom instruction. Teaching and learning supports are described that are essential to helping all teachers balance group and individual learning in classrooms. Current U.S. instructional approaches and the model of inclusively responsive instruction are compared in terms of balancing diversity and academic expectations.

This study aims to capture similarities and differences in teachers’ questioning in German and Japanese mathematics classrooms, specifically focusing on the stage of introducing new mathematical content. The author analyzed consecutive mathematics classes taught by experienced teachers in Germany and Japan, who were recruited based on their locally defined “teaching competence” in the Learner’s Perspective Study. The results revealed that even questions that required students to recall previously learned content or provide the results of a calculation, which were regarded as lower cognitive questions in previous studies, played key roles at the stage of introducing new mathematical content in both German and Japanese classrooms. Further, distinctive patterns in the sequences of teachers’ questioning were identified. These differences suggest what is valued as quality mathematics teaching in each educational system.

Improving the quality of teaching and learning of primary mathematics has always been a major concern of mathematics educators. TIMSS is a collaborative research project sponsored by the International Association for the Evaluatioan of Educational Achievement (IEA). It is the largest and most ambitious study of comparative educational achievement tests in mathematics and science ever undertaken. Every effort was made to help ensure that the tests represented the curricula of the participating countries and that the items did not exhibit any bias towards or against particular countries, including modifying specifications of the items by subject matter specialists within the participating countries, and conducting thorough statistical item analysis of data collected in the pilot testing. This article briefly summarizes develompment of Indonesian, Malaysian and Japanese mathematics education. It concludes with description of a method for teaching mathematics in those countries.

This paper outlines mathematical education before the Meiji Restoration, and how it changed as a result. The Meiji Restoration in 1868 completely changed the social structure of Japan. In the Edo period (1600–1868) Japan was divided into domains (han) governed by local lords (daimyo). Tokugawa Shogunate supervised local lords and governed Japan indirectly. In the Edo period there were no wars for more than two centuries and many people participated in cultural activities. Japanese mathematics developed in its own way under the influence of old Chinese mathematics. Japan also had a good education system so that the literacy rate was quite high. Each domain had its own school for samurai but mainly education was provided privately. Private schools for elementary education were called terakoya, in which mainly reading and writing and often arithmetic by the soroban (Japanese abacus) were taught. In the Edo period the soroban (abacus) was the only tool for computation and Arabic numerals were not used. The Meiji government was eager to establish a modern centralized state in which education played a key role. In 1872 the Ministry of Education declared the Education Order, whereby in elementary schools only western mathematics should be taught and the soroban should not be used. But almost all teachers only knew Japanese traditional mathematics “wasan” so they insisted on using the soroban. This was the starting point of a long dispute on the soroban in elementary education in Japan. Two Japanese mathematicians, KIKUCHI Dairoku and FUJISAWA Rikitaro, played a central role in the modernization of mathematical education in Japan. KIKUCHI studied mathematics in England and brought back English synthetic geometry to Japan. FUJISAWA was a student of KIKUCHI at the Imperial University and studied mathematics in Germany. He was the first Japanese mathematician to make a contribution to original research in the modern sense. He published a book on mathematical education in elementary school, which built the foundation of mathematical education in Japan.

Individual mathematics teachers may value different aspects of teaching and learning mathematics, but at the same time their value systems are under the influence of socially shared values. This paper describes such values in Japanese mathematics education from a historical and normative perspective. After the introduction of Western mathematics into the modern school system in the Meiji period (1868–1912), the people of Japan struggled to adapt and absorb it onto the foundation of Japanese tradition. In the subsequent development of Japanese mathematics education, the integration of both practical and theoretical aspects have been issues, alongside changes in educational focus and in society at large, which are symbolically represented by the enrolment rates at all of elementary, secondary, and tertiary education levels. Mathematics education in Japan has also been subject to international influences, such as the reform movement and the modernization movement, at critical junctures in its development. Key concepts such as mathematical ideas, mathematical thinking, and mathematical activities are traces of such historical efforts by the Japanese mathematics education community, and represent their socially shared values.

Previous research gives evidence that Japanese mathematics teachers “may have a more detailed and widely shared theory about how to teach effectively” when compared to their U.S. counterparts (Jacobs & Morita, 2002). This study explores the conceptions and cultural scripts of a group of Japanese mathematics teachers by analyzing the conversations between cooperating teachers and student teachers. It describes 6 principles of high-quality instruction that arose in at least half the conversations we analyzed. Each of these principles is examined in detail. Finally, some advantages of having a strong, shared conception of high-quality instruction and focusing on widely applicable instructional principles are presented.

The entrance examination for Japan′s university lays a great emphasis on multiple-choice questions, so most of high school students are said to be taught in a way that memorizing the formulae mechanically is the shorter route to high score in test than ever. The best cure for rote memorizing and formulism is to stimulate the intellectual curiosity of undergraduate students newly entering universities. We must make classes more appealing to the freshmen if we are to draw out and cultivate their intellectual curiosity. In Shinshu University, every affiliated faculty assists the Center of Development of Higher Education Programs by sending professors to give the Liberal Arts Lectures from special field of their own. This paper presents the very constructive trial to draw out the intellectual curiosity of the science course students in Shinshu University. Discussions are made on the role of Lecture “Mathematics and Wasan Culture” in stimulating student′s interest. Wasan, the traditional Japanese Mathematics made amazing development as very advanced mathematics equivalent to Western Mathematics. It was widely applied to several technical areas such as map manufacture, astronomical observation and reclamation construction in the era of Edo Period. Especially, an analytical technique in search of a center of gravity of an object is explained by many old Wasan mathematicians. In this lecture, the author used Wasan Problems as the teaching materials. As one of means to improve the analyzing sense of science phenomena, the students learn the old technique used by Wasanka who did not know any formulae of Western Mathematics.

In this paper, I summarize the influence of mathematical problem solving on mathematics education in Japan. During the 1980–1990s, many studies had been conducted under the title of problem solving, and, therefore, even until now, the curriculum, textbook, evaluation and teaching have been changing. Considering these, it is possible to identify several influences. They include that mathematical problem solving helped to (1) enable the deepening and widening of our knowledge of the students’ processes of thinking and learning mathematics, (2) stimulate our efforts to develop materials and effective ways of organizing lessons with problem solving, and (3) provide a powerful means of assessing students’ thinking and attitude. Before 1980, we had a history of both research and practice, based on the importance of mathematical thinking. This culture of mathematical thinking in Japanese mathematics education is the foundation of these influences.

The Third International Mathematics and Science Study (TIMSS) reports that the mathematics teaching in Japan is distinctly different from that found in the United States. They attribute part of that difference to the professional development practice of Lesson Study. However, is the pre-service preparation of Japanese mathematics teachers also different? In an effort to understand the Japanese secondary mathematics student teaching process better, the author spent two weeks in Japan at three different universities and their affiliated junior high schools observing student teachers as they interacted with their cooperating teachers. This article is a description of that process as seen through the eyes of an American mathematics teacher educator. The author found that the main focus of student teaching at the observed junior high schools is on the preparation, teaching and reflection on the lesson itself.

Japanese education has been the subject of considerable research and educational commentary in the United States over the last 20 years. Since the early 1990s, there has been increased interest in Japanese methods for teaching mathematics, and the Third International Mathematics and Science Study has accelerated American interest in Japanese methods. Observational studies, teacher and student surveys, and analyses of classroom videotapes have provided a rich picture of how the Japanese teach the whole class. However, little has been written about how academically low-achieving math students fare in Japanese schools. This article briefly summarizes Japanese methods for teaching mathematics and describes how the educational system addresses academic diversity. It concludes with a description of a method for teaching mathematics that some Japanese mathematics educators feel has promise for students with learning disabilities.

Quality of teaching is a major factor in students’ mathematics learning. Stigler and Hiebert (1999) showed that mathematics teaching in Japanese schools is significantly different from what is typically observed in US classrooms. However, Japanese mathematics educators claim that Japanese mathematics teaching has transformed significantly over the last 50 years. Although teaching is influenced by a variety of factors, textbooks play a significant role in what mathematics is taught and how it is taught. In other words, textbooks may significantly influence students’ opportunities to learn. Thus, six editions of a Japanese elementary school mathematics series since 1958 were analyzed to identify any change that might indicate the transformation of mathematics instruction in Japan. The analysis revealed that the features included in the series have changed over the years to support more explicitly the problem-solving-based mathematics instruction described by Stigler and Hiebert (1999).

Historically, we can find cross-curricular activities (“life unit study”) after World War II in Japan. When we consider the arguments of “life unit study”, the following three approaches will serve as reference: the approach orientated to the independent aspect, the approach orientated to the societal aspect, the approach orientated to the scientific aspect. By reflecting the critique of “life unit study”, it is suggested that a balanced approach should be carried out. In other words, teachers had better focus on one aspect according to the aim of classroom teaching, and balance three approaches on the whole.

Connection making is one of the major standards proposed by the National Council of Teachers of Mathematics, however, unlike problem solving, it has no long history of being designated as a goal of mathematics teaching. An examination of classroom observations of mathematics lessons taught in Japan reveal that connection making appears to be an implicit if not explicit standard for Japanese mathematics education. As a perspective from which to re-examine and re-assess our own practice, this paper describes several episodes of connection making as they occurred in Japanese elementary school classrooms. By reflecting upon the methods used in these classrooms, other approaches to connection making are suggested and explored.

This study was designed to determine the perceptions of five concerned groups about the outcomes for the elementary school mathematics curriculum in Japan. The outcomes and a Likert-type scale were submitted to the following concerned groups: (a) elementary school mathematics teachers; (b) elementary school principals; (c) mathematics educators; (d) professors of education; and (e) scientists, mathematicians, and engineers. The list of outcomes contained 71 statements of outcomes expected to result from the study of mathematics. These were based on the four major headings of (a) general skills; (b) attitude, interests, and appreciations; (c) knowledge; and (d) intellectual abilities and skills. The ordinal ranks were determined by mean ratings of each outcome for each group. Nine outcomes were ranked by all concerned groups in the first quartile. Twenty-three other outcomes were ranked by one or more concerned groups in the first quartile. The correlation of perceptions between each pair of the c...

This brief report compared the lesson on addition and subtraction of signed whole numbers in three seventh-grade Japanese mathematics textbooks with the corresponding lesson in four U.S. mathematics textbooks. The results indicated that Japanese books contained many more worked-out examples and relevant illustrations than did the U.S. books, whereas the U.S. books contained roughly as many exercises and many more irrelevant illustrations than did the Japanese books. The Japanese books devoted 81% of their space to explaining the solution procedure for worked-out examples compared to 36% in U.S. books; in contrast, the U.S. books devoted more space to unsolved exercises (45%) and interest-grabbing illustrations that are irrelevant to the lesson (19%) than did the Japanese books (19% and 0%, respectively). Finally, one of the four U.S. books and all three Japanese books used meaningful instructional methods emphasizing (a) multiple representations of how to solve worked-out examples using words, symbols, and pictures and (b) inductive organization of material beginning with familiar situations and ending with formal statements of the solution rule. The results are consistent with classroom observations showing that Japanese mathematics instruction tends to emphasize the process of problem solving more effectively than does U.S. mathematics instruction ( Stevenson and Stigler, 1992 ).

This report deals with U.S.-Japan cross-national mathematics achievement results and problem solving and creativity of U.S. and Japanese students. It addresses U.S. misconceptions about Japanese mathematics education and responds to “explanations” for low U.S. mathematics achievement. Various factors accounting for superior Japanese achievement are presented and discussed, including social, cultural, and mathematical education factors such as the “open approach” to teaching. U.S.-Japan cross-national research results on students’ problem solving behaviors are also reported. The paper concludes with some observations concerning what can be learned from the Japanese.

Japan has been a member country of IEA since the organization was first established and has participated in all of its mathematics studies: the first in 1964 (FIMS), the second in 1981 (SIMS), the third in 1995 (TIMSS), and most recently in 1999 (TIMSS-R). In addition, Japan has participated in several IEA studies of science education and computer education. Both the results and the methodology of the IEA studies (Robitaille et al., 1993; Robitaille & Garden, 1996) have had a strong impact on Japanese education. In this paper, the impact of the TIMSS results on the Japanese mathematics education are interpreted and discussed. Readers may find it helpful to read more on this topic in the chapter by Miyake and Nagasaki on Japan in The Impact of TIMSS on the Teaching and Learning of Mathematics and Science (Robitaille, Beaton, & Plomp, 2000). LEARNING FROM THE FORMER IEA STUDIES OF MATHEMATICS Mathematics education has a long history in Japan (JSME, 2000). In recent years, lEA’s international mathematics studies have impacted on mathematics education in Japan in a number of ways. Japanese mathematics educators have paid particular attention to students' outcomes in the affective domain and to background information as well as achievement in the cognitive domain. FIMS revealed that higher-achieving Japanese students tended to think of mathematics as stable knowledge to be memorized (NIER, 1967). In response to this, national courses of study developed during the 1970s and 1980s stressed the developmental aspects of mathematics, now more commonly known as “mathematical ways of thinking.” SIMS revealed that Japanese students did not like mathematics and that they thought of mathematics as being irrelevant to society. It further revealed that calculators were not used in mathematics classrooms (NIER, 1981; NIER, 1982; NIER, 1983; NIER, 1991). The national courses of study developed in the 1990s therefore

Wasan, Japanese arithmetic, is an amazing mathematical system. Most people think that there is only one kind of mathematics, just as some philosophies will have us believe that there is only one truth. In fact the Japanese have their own special system which is unique to their culture. We used to believe that modern mathematics was the only type, but we now know that there are different varieties, each with its own value.

Much research has been conducted comparing education in the United States with education in Asian nations, such as Japan, but just how much of this research has been of real use to teachers in the United States? We believe that despite the significant amount of impressive research that has been done analyzing Japanese teaching practices, the manner in which these important findings have been reported to teachers has been largely ineffective. This is unfortunate, because one of the unique strengths of crossnational research is that it provides intact working models of successful practices. Japan is particularly important in this respect because, in many ways, it represents one of the most successful models of constructivist mathematics teaching in the world. We believe that this information is not pursued by U.S. teachers for two general reasons. First, research studies frequently couch results in terms of U.S. deficits. Although we believe these results to be accurate and important, it is difficult for teachers in the United States to compare themselves to teachers in Japan when much of the research that is available makes the persistent lament that U.S. teachers and their students are underachievers. Second, we believe that although important differences exist between Japanese and U.S. school systems (e.g., length of the school year, total time spent on mathematics), the truth is that teachers in both nations have a great deal to learn from each other in terms of the successful practices they use. An unfortunate consequence of the focus on test scores is that school system differences have been mistakenly conflated with teaching practices. This has led to the propagation of several myths about Japanese practices that U.S. teachers tend to cite as evidence of the unsuitability of Japanese practices for U.S. classrooms. We believe that U.S. teachers should separate differences in school systems from differences in teaching practices that could be beneficial to teachers in both nations.

The theme of the International Commission on Mathematical Instruction study ‘What Is Research in Mathematics Education, and What Are Its Results?’ has also been of increasing concern among Japanese mathematics educators. One reason is a gap in interests between researchers and mathematics teachers. Mathematics teachers tend to expect direct and specific prescriptions to solve the problems they experience in their classrooms, whereas researchers tend to address problems raised in research communities that are not always directly related to teachers’ concerns.

This article describes a novel assessment method used to examine Japanese and American teachers’ ideas about what constitutes effective mathematics pedagogy. Forty American and 40 Japanese teachers independently evaluated either an American or Japanese mathematics lesson captured on videotape. Their comments were classified into over 1600 idea units, which were then sorted into a hierarchy of categories derived from the data. Next, the authors hypothesized underlying ideal instructional scripts that could explain the patterns of responses. Whereas the U.S. teachers were supportive of both traditional and nontraditional elementary school mathematics instruction and had different scripts for the two lessons, the Japanese teachers had only one ideal lesson script that was closely tied to typical Japanese mathematics instruction. The findings suggest that U.S. teachers may have more culturally sanctioned options for teaching mathematics; however, Japanese teachers may have a more detailed and widely shared theory about how to teach effectively.

In the last few years, numerous articles extolling the virtues of the Japanese educational system have appeared both in academic publications and in the popular press (e.g., Cogan 1984; Morimoto 1982; Shimahara 1985). Although the United States and Japan together lead the industrial world in percentage of young people entering high school (both over 95%), Japanese mean scores on international tests of mathematics and science are consistently higher than those of any other country including the United States (Rohlen 1983). Because of such remarkable results, many Americans are quite interested in knowing more about education in Japan. A six-month-long visit to Indiana University by Toshiaki Yabe, a Japanese elementary school mathematics specialist, provided a unique opportunity for Indiana educators to learn more about Japanese mathematics education and for both sides to benefit from a mutual exchange of ideas. In this article we have collaborated to give a brief overview of Japanese education, followed by some more specific ideas about important considerations in the teaching of mathematics in the elementary grades.

Ever since the results of the International Achievement Tests in Mathematics were announced, much interest has been expressed in the outstanding performance made by the Japanese students.1 The test results displayed an accomplishment that at age thirteen, and overall, was far su perior to the other countries involved. Many analyses have been made of the subject matter involved in the questions, of the type of questions, of the teachers of the students, and of the curricula of each of the countries, to either sustain or disprove popularly expressed superiority of Japanese mathematics education. This article merely reviews the existing structure of Japanese education and points to some unique features of Japanese culture that may offer a partial explanation. It is not intended in any sense to suggest that the Japanese program or its culture— which is evidently satisfying to their own people—is one that would be satisfactory for others. It is merely one of many cultures which we should corne to under stand as the world grows closer knit in its forward progress.

In December 1979 Izaak Wirszup, Professor of Mathematics at the University of Chicago, submitted a memorandum to the U.S. National Science Foundation outlining recent changes in science and mathematics education programs of the Soviet Union. Based on his extensive studies of Soviet technical and educational literature, Wirszup concluded that graduates of Soviet secondary schools now receive so much more mathematical and scientific training than U.S. students that the gap poses a formidable challenge to American national security. Wirszup’s report soon circulated widely; it was noted by science journalists, and led to major news stories in many cities. These ominous reports of foreign progress in education exacerbated the continuing public criticism of U.S. education, re-awakened memories of earlier studies showing superb performance of Japanese mathematics students but only modest achievement of U.S. young people, and sent many American mathematics educators to the Fourth International Congress on Mathematics Education with a mixture of curiosity and concern about our national effort in mathematics teaching.