Math Education in Japanese High Schools

Introduction

Before I came to Japan, I had heard much concerning the Japanese educational system. American newspapers and television programs were constantly reporting on  the merits and accomplishments of the young Japanese student. When I first read the brochure concerning the Kanagawa Prefecture Grantee exchange program with my state of Maryland, the part that interested me the most dealt with the opportunity to study first-hand in Japan. I arrived at Narita Airport with high goals and expectations. My mind was excited at the prospect of observing classes, interviewing teachers and actually working with high school students. I anticipated seeing innovative techniques and modern technology integrated in a manner that guaranteed educational success. My dream was to return to my country with a formula that would remedy all the problems and barriers that I had witnessed in American schools. As I look back on this past year, I realize that even with all my education and teaching experience, I was basically rather naive.

In retrospect, it is apparent that I had too much faith in the American reporter. Although a video camera and microphone may at times relay some basic facts, they rarely transmit the  entire truth. The reasons were quite simple. The reporter was not a teacher. When he saw a quiet classroom in Japan with forty-eight students sitting respectfully, he made two inaccurate assumptions. First he reported that the students were learning, and second he concluded that the teacher must be responsible for this optimal educational environment. This was very similar to a story told me concerning the Chicago Police Force. They had heard that the crime rate was very low in Japan, so they sent a delegation to study the methodology of the local police. The logic was that if the rate of crime was low then it must be a result of the efforts of the Japanese police. After only a short time in Japan, it was easy to conclude that the reason the children in this country were literate and the streets were safe were similar. Both had little to do with either the school system or the police force.

It may sound too obvious to say that Japanese society is vastly different from American society. It makes little difference if one is looking at the educational system, police force, big business, recreation or the family. The forces that operate in this country are diametrically opposed to that which we face in America. Many things that occur in Japan are absolutely beautiful regardless of the perspective. From the viewpoint of sociology, everything here has a purpose and is integrated with all other aspects of society. For the individual, life is safe and productive. The primary cause of all these conditions can be traced directly back to the basic philosophy of the Japanese people.

It is impossible to understand the Japanese educational system without addressing the subject of Japanese philosophy. Schools are much more than a place where children are taught the three R’s. It is here the Japanese are taught to be Japanese. The strength of the school system exists at this very basic level. A Japanese child can read, write and compute, yet these things occur not as a direct result of the classroom. They take place because nothing else is acceptable if one is Japanese.

         Philosophy

In order to gain any understanding of Japanese philosophy, it is imperative to appreciate the foundation of American philosophy. Western philosophy has at its very center the rights, values and importance of the individual. These are attributes that we take for granted, yet they affect everything we undertake. Marriages are based upon love. When love vanishes, so does the marriage. The basic principle of business is related to the American dream. Any individual can become wealthy. In American education, the concept is the same. The student is encouraged to raise his hand and ask questions. He is expected to give explanations and reasons for his work. The child is taught to do, try and experiment. It is a virtue if he proves himself capable of standing out and being different.

As American educators, we take the above as universal truth, yet the reality is different in Japan. The first thing a Japanese child learns in school is that he is part of a group. All his efforts and behavior are directed to the success of this group. From the earliest years through secondary school, uniforms are required. Hemlines and hair styles are carefully watched,  Some schools require the students to wear name badges, while many popular magazines and snack foods are prohibited from school grounds. The Japanese student spends more hours in school than his American counterpart, yet much of it is focused upon club activities, whose goal is to promote the group. The teacher is held in great esteem.  This, at times, becomes a barrier to the education process. Prior to the beginning of class, everyone bows in unison to the teacher. This appears very respectful to the outsider, yet it is almost religious in practice. Teachers are thus placed above the students in terms of social order, and this prevents them from being partners in the learning process.

The most direct result of this is that failure is not tolerated. The group is promoted, so the individual is not permitted to fail. Of all the students who enter high school, one hundred percent graduate. This may sound unbelievable to an American educator, yet this contrast exists at the other end of the grading scale also. Nobody fails, yet few receive A’s. Grading is done strictly on a curve, albeit an almost straight curve. Almost all of the students, therefore, receive the same evaluation.

This does not mean there is social promotion. The pressure to perform to the group expectations is extreme. No one can deny that the Japanese student is hard working and diligent. Many hours are spent in and out of school in preparation for tests and exams. Part-time jobs are often forbidden, or at least discouraged. Dating does occur, yet it is nothing as is witnessed in America. There are no such activities as homecoming, proms or even school dances. Instead of being driven or even driving to school, the students use trains, buses and bicycles. They are kept very busy just being students. Problems with drugs, sex and even television usage are minimal.

The most obvious result of this group dynamic relates to shyness. One cannot be in Japan for more than a day and fail to realize that shyness is almost a universal characteristic. This behavior is encouraged as a direct consequence of this philosophy. The opposite of shyness is boldness, and this attribute would obviously be in contrast to group norms. In the classroom students do not raise their hands to ask questions, but if they are called upon to answer a question, their response is given in such a low voice that it is impossible to hear. Oral reports and class discussions are almost nonexistent. When a girl, and sometimes even a boy, smiles, her hand is placed over her mouth to hide her face. This behavior can even be witnessed on television by TV journalists. Shyness has become a national virtue.

A relatively new problem occurring in Japan today relates to “returnees”, who are students that have left Japan and studied in other countries because of their parents’ employment for two years or more. Upon their return to their native school, they do not seem to fit in and have trouble adjusting to the more traditional life style of Japan. They had learned to become aggressive and outgoing, and they no longer want to be a member of the old group. American society can be very addictive, and these students face a severe case of culture shock in relation to their attitudes towards school, teachers and peers.

It is impossible to understand anything about Japan without first fully appreciating the importance of the group. Their economic success can also be directly related to this attitude. Individual sacrifice for the good of the group is not a noble deed. It is expected! This philosophy is taught, encouraged and expected at all levels of Japanese education.

         Observation Summary

 I would first like to thank the many teachers, who were students in my classes here at K.I.A., and invited me to visit their schools. I also appreciate the efforts of Mr. Takimura who arranged a meeting with Mr. Shibuya, the Superintendent of Schools for Kanagawa. Through their help, I was able to visit several schools and observe many classes. I further appreciate the time and energy that the teachers in the schools gave me. Without their interest and honesty, it would have been a very fruitless year. It was stimulating discussing our respective educational programs together. The most noticeable fact concerning schools in Kanagawa concerns class size, with an average of forty-seven students. The teachers mentioned that this presented a problem, and there is a move to have it lowered. The classes were generally orderly. I never witnessed any truly bad behavior, yet I never saw any really actively involved classes. Students not paying attention, talking with friends or doing other work did occur. I never witnessed or heard a teacher correct the behavior of a child, even when it was obvious that such action was needed. However, my presence may have prevented this.

Scheduling is similar to a modified block format. For the academic portion of their day, the students remain together. They stay in their homeroom class for the majority of the day, and the teachers travel to their assigned rooms for instruction. The students even eat lunch together in this classroom since there is no cafeteria. Sometimes their homeroom teacher will be present and eat with them, yet for the majority of the time, they are left alone. They are given a considerable amount of freedom at this time, and they seem to handle it well. They are also responsible for the general maintenance of this room, such as sweeping the floors and cleaning the boards, since there are no custodians in the school. There is a short homeroom period at the beginning and end of each day, plus an extended homeroom for one period on one day of the week. There are no guidance counselors in the schools, and the homeroom teachers seem to fulfill part of this responsibility. This appears to be a major weakness of the system, since the position of the Japanese teacher does not lend itself to confidant or “friend” as with the American system, and the teachers have very little training in this field.

The most striking observation related to the observed classes deals with the uniformity of technique. Each class had a rather slow start, and none of the teachers had heard about the advantages of a warm-up drill. However, when the class officially began with the “kiotsuke”, an announcement of the start of class, the students generally began to work quickly. All the lessons could be described as teacher dominated, where the teacher either presented theory or worked out problems. An average of no more than three questions would be asked during each period. I never saw a student explain the solution for a problem or say more than a few words to the teacher during class. If a student was asked a question, his response was directed in a voice only audible to the teacher.

Whether a child mastered the topic or not was rarely checked by the teacher. The students would occasionally work on as few as three problems during class time. Sometimes students did put their work on the board, but they never explained it, and occasionally a teacher would circulate around the room looking at the students’ work.

There was a visible discrepancy in the sexual make-up of the upper level classes. In the third year courses, there were usually only about six to eight girls per class. When I questioned some teachers concerning this, their comments reflected those that could have been made in America many years ago. I also only saw two female math teachers in all the schools that I visited, and out of almost one hundred high schools in Kanagawa, there are only two female principals. When I mentioned this to a male principal, he just laughed at the idea of a female principal. There are three public all-girl schools in Kanagawa.

If I were forced to evaluate the quality of instruction according to standards I learned as a department head in Maryland, most of the teachers would have received ratings of satisfactory or below. I only saw one teacher that actively encouraged, challenged and taught “her” students. The teachers were hard-working and dedicated. They only teach about 17 hours a week, but they have school for five and a half days a week. They all have school responsibilities outside the classroom, and there is no teacher union, They discuss and complain about their schools in much the same way as their American counterparts.

The climate in the schools very closely resembled that of a good American public high school. Students could be seen playing in the halls, yet never in a dangerous or distracting manner. Violence in the high schools is very rare, yet teachers did say that it is becoming a problem in the junior high school. The students were extremely friendly and curious about American teenagers, their lifestyle and schools. The students also appeared more naive than American students did.

         Entrance Examinations

Perhaps the most striking difference between the Japanese and American systems of education relates to the   influence that examinations have on the life of the students. There are two types of exams that control and regulate what occurs in Japanese high schools. The first are the exams that are required in order to initially enter high school. All junior high school students in Kanagawa must take an entrance exam, and each high school sets its own passing score. The schools are ranked in order determined by the number of seniors from the previous year’s graduation class who passed the college entrance examination. This ranking is called “hensachi”, and it is published in the local newspapers. In order for students to be admitted to a particular high school, they must apply and be accepted. A high school education is not a right, but a privilege. It should be noted that high schools begin with the tenth grade, and that between five and ten percent of junior high students are unable to continue their education. Besides the exam score, junior high grades are also considered as entrance criteria. The grading procedure is well- defined at the junior high level where classroom grades must fit a lower weighted curve. Only a few A’s are allowed in each class. The competition for exemplary young students is, therefore, very intense.

The other type of exam that has an effect on the Japanese high school is the college entrance examination. The only criterion for entering colleges (two year) or universities (four year) is this exam. Students’ grades, extra-curricular activities and teacher recommendations are not even considered. The post-secondary schools do not examine a collection of the students’ work history, as is done in American colleges. Grading in the high school, therefore, can be a little more flexible, since it is not that important. However, the pressure that the students experience in relation to these exams is tremendous. This pressure is best described by the expression “jukenjigoku” which translates roughly to “examination hell”.

         Curriculum

There are four basic characteristics of the curriculum for mathematics in the Japanese high schools. The first relates to its parameters or the forces that control it. As mentioned earlier, the college entrance examinations are of extreme importance in the evaluation and ranking of secondary schools. They dictate the fundamental principle for curriculum development, which states that if it will not be tested on the exam, then it will not be taught in the schools. The entire academic curriculum is targeted for these examinations. This is not necessarily bad in relation to mathematics, but with regard to other subjects, it is devastating.

A prime example would be the English curriculum. One of the primary tests for college entrance is English syntax and grammar, and the test format is a written objective exam.  The six years that the Japanese students study English, they are taught primarily grammar with very little time on developing listening and speaking skills. As there is no oral portion of the exam, the average student has no working knowledge of English as a language. English is taught in much the same way that Latin was taught in American schools many years ago.

The next aspect of curriculum control relates to the goals and objectives of the mathematics program. The purpose of the curriculum is to produce technically literate students that will be a valuable asset in the work place. It must be mentioned that by this standard, the secondary math program is a success. The problem centers on the fact that this objective is all-inclusive. There is no place in the classroom for focus on areas such as problem solving, creative thinking and independent discovery. In the math classroom, the student is never given the time to discover a concept for himself. All theory is routinely presented by means of a lecture and then simply committed to memory. The math teachers are aware of this problem, and they feel compelled to teach on a strict timetable which offers no room for students to think and contribute in the class.

The third characteristic of the math curriculum is its simplicity. There are only four math courses offered for the three years a student is in high school. The first is basic Math I which includes such topics as: simplifying algebraic expressions, radicals, imaginary numbers, factoring, inequalities, absolute value, functions, quadratic equations, linear equations, circles and elementary trigonometry. The second course is Algebra and Geometry which includes vectors, matrices, topics in trig, conic sections and vectors in 3-space. The third course is Basic Analysis which offers the following: comprehensive trig, logs, series, limits, graphing theory and elementary calculus. The final course is Calculus, which includes the basic components of two-dimensional calculus.

Students must complete at least two years of math, and there appears to be some grouping of students according to ability within the various courses. Two things are obvious concerning the course offerings. First, there are no such subjects as business math, consumer math or general math. These topics must be mastered in the lower grades, or the student does not proceed to high school. Part of the math philosophy in Japan is almost revolutionary in terms of American education. Japanese teachers and parents believe that all children can learn math. It is not accepted as an excuse that the student is “not good in math”.  It should also be noted that most students state that they do not enjoy math, yet they are competent in it.

The final observation concerning the course offerings relates to what cannot be observed. There is no such thing as a Gifted and Talented program. The reasons for this are twofold. First there would be no purpose for it in terms of college admission since colleges do not consider high school transcripts. The most important reason, however, relates to the philosophy of the group. The foundation of a G/T program correlates to the importance of the individual. In a society where the group is all-supreme, the individual and programs associated with him are non-existent. There are, therefore, no such courses as college level courses or independent study. There are also no Computer Science courses offered; however, I did hear that a couple of schools in Tokyo were preparing to add a programming course to the curriculum. Another course that is absent is Plane Geometry with its emphasis on proofs. Facts are taught concerning the content of this subject, but there is no time allowed for something considered so unimportant as thinking through a problem, arriving at a solution and justifying your results by writing a proof.

         Cram Schools

Cram schools are not part of the formal structure of the Japanese school system, yet they have become an indispensable component. In order to understand the importance of these tutor centers, it is necessary to understand the most basic and radical difference concerning Japanese philosophy in education. Very simply stated, in Japan it is the responsibility of the student to learn. This may initially sound trivial or obvious, yet the opposite is true in American education, where it is the responsibility of the teacher to teach. In America, if a student does not learn factoring, it is the teacher’s fault. Grades have to be justified with the accuracy and diligence of an accountant. Deficiencies must be sent home, or the child cannot fail. Teachers are constantly being questioned concerning student progress by parents and administrators, and must always be on the defensive. The first thing that a teacher learns is not to teach, but to document.

In a Japanese high school, the material is presented with little time set aside for practice and mastery. The students are then tested, and if they fail, the fault is theirs. The student or family would never think to blame the teacher, and the result is that most of the students are forced to receive extra help after school. Obviously this does occur in America, but never on the same scale as in Japan. The family of the average Japanese college-bound student spends approximately $20,000 on this extra instruction by the time the child graduates from high school.  It is important to note that this is not necessary remedial work, since it is considered impossible to pass the college entrance examinations without this help. The first type of cram school is the “juku”. These are rather informal, and occur more commonly at the elementary and junior high level. The students usually go to the home of a teacher or a rented office on the average of two nights a week for two or three hours. During any vacation periods, they may go five nights a week for three hours with added time required for homework. The informal curriculum will closely follow the student’s actual course work, since grades are considered in junior high for acceptance in high school. Each juku class will have about five to ten students, and the tuition depends on the qualifications of the teacher.

At the senior high level, in addition to the jukus, the students will probably attend a more formal auxiliary school called a “yobiko”. These schools offer classes after school during the school year, in addition to scheduling special formal courses during the spring, winter and summer vacations. The curriculum is very structured and is entirely directed toward the college entrance examination. If the student upon graduation fails the college entrance exam, they may attend these schools full time in order to qualify for the following year. The tuition for the yobiko is equivalent to that of a regular college.

Two things are important to realize in relation to these cram schools. The first is that almost everybody attends them. Passing both the high school and college entrance examinations is almost impossible without this extra preparation. The second aspect is that these institutions form the backbone of the public education system in Japan. Jukus and yobikos are private in nature, and it is here where the students receive the individual attention that is required to master the course work presented in public schools.

Japanese students spend many hours studying and preparing for school, however one point cannot be over stressed. Their approach to mathematics is to simply learn the various algorithms necessary to solve a given set of problems. Both formulas and techniques are memorized. The time required for this is extensive, and the pressure to perform is great. Schools devote little time to the activities which would be enjoyable to students and foster their interest and curiosity in mathematics such as math contests and games.

         Teacher Training

The training that a perspective teacher receives in a Japanese college is very similar to that which is offered in an American institution. They must take a required number of education courses and participate in a student teaching experience. Their student teaching session only lasts two weeks in either a junior or senior high school as compared with the ten weeks divided between the two levels that American trainees receive. This time difference, however, is not that important in terms of actual teacher preparation. Upon graduation, the new teacher must take a teacher examination in order to be certified. This exam is comprehensive and tests the new teachers in many fields, which include their subject area and educational theory. This examination is considerably more rigorous than the National Teacher Exam which is offered in the United States, the function of which is just to test for literacy.

The real difference that Japanese teachers experience in terms of training occurs after their employment begins. It is at this point that all training ceases. Teachers are never observed by administrative personnel or subject area coordinators. The latter position does not even exist. They are, therefore, never given the opportunity to receive any support or suggestions which could improve their teaching techniques. Very few teachers or administrators ever continue their education or pursue an advanced degree in order to update their content material and witness new techniques in education. No funding is available for postgraduate courses, and no time is allocated for sabbatical leaves. The teachers I interviewed marveled at the opportunities that American teachers had to continue their education.

The consequences of the failure to in any way review or update the training of the educational staff are twofold. First, teachers who are never observed by any educational specialist are in effect never evaluated. I asked one principal what he would do if he had an incompetent teacher on his staff. His reply was that he has never had one. I wanted to inquire how he knew this if he has never observed anybody, yet proper protocol prohibited this.

The second impact is that teachers obviously become complacent in their behavior and attitude toward their profession. After only observing a few classes, I found myself becoming bored and frustrated in what I witnessed, and I could only imagine what the students were feeling. The vast majority of the teacher presentations and techniques were totally uniform and uninspiring. I observed teachers that were obviously intelligent and competent in their field, yet only considered teaching as the process of “presenting” information to their students.

An interesting area concerning training relates to administrative personnel. As mentioned earlier, advanced degrees are almost non-existent, so principals must be named from a pool of educators who for the last twenty years have experienced little formal education. I asked a group of teachers and their assistant principal to explain the selection process, and they all just laughed. They said the question was very difficult, and no one was sure of the details. It appears that principals are simply selected by the use of only political criteria.

         Conclusion

There are two main questions that have formed the thrust of this study from the very beginning. What is it about the Japanese education system that produces the highest level of math literacy in the industrialized world, and how can American education profit from it? The answer to the first question is filled with contradictions. The teachers are qualified and diligent, yet they do nothing that could be rated as extraordinary. The students devote many hours in and out of school studying, although none are involved in anything that could be labeled as creative or independent. Even though the schools are safe and orderly, the classes are large, and there are is no qualified staff to handle any personal problems that may develop with students. The students excel on standardized tests, but are too shy and embarrassed to speak out and express their views. The administrators manage a well-run school, yet their appointment is purely political. The question still remains; what is the strength of this system that is filled with paradox?

Within Japanese society the basic social unit, the family, is strong. Most families include only two children, and divorce is relatively rare. The fathers do work long hours, still the children are constantly being supervised and nurtured. PTA meetings are not considered a chore, and teachers report that they see almost one hundred percent of the parents of their students each year. In elementary schools, the teachers are required to make a home visit to each of the families of the students they teach, and junior high teachers must visit each of their homeroom families. Japanese television is not as exciting or entertaining as that in America, which may be a blessing. After school, when the children are not busy studying at jukus, playing at various sports, practicing the piano, or attending club activities and martial arts classes, they can often be found simply reading.

Education is considered an important family priority, and additional tuition spent on tutors is viewed as a necessity. Mathematics textbooks, which cost less than five dollars, must even be purchased by the student. School is considered a child’s first and only responsibility, and from a class of approximately fifty students, there are rarely more than one or two absentees. Teaching is also considered the teacher’s primary responsibility, and the average teacher rarely misses more than one or two days from school a year. The teaching profession is held in esteem, and any assistance that a teacher gives a child is greatly appreciated. Education is considered the ultimate responsibility of the family, and schools are instruments that aid in this objective. It is apparent that none of the above are conditions that are visible in America.

What does all of this mean for education in America today? First and foremost, education must again become the responsibility of the family. Parents must be informed, encouraged and even forced to visit schools and take an active part in their children’s education. Even in a good American high school, teachers are fortunate if they see thirty percent of the parents of their students. Teachers and parents must form a working partnership based upon mutual trust and responsibility. Education is not just something that occurs during the daytime in a big modern air-conditioned building. Japanese schools are not equipped with air conditioning or even central heating, and schools are never closed because of inclement weather. There are lessons to be learned here for the future of American education, and they do not relate to any mystical Eastern techniques that would entice students to new cognitive heights