Mary Ellen Schmidt, Ohio State University

Aki Duncan, Discovery School



There is a considerable difference between what goes on in American mathematics classrooms and what goes on in Japanese ones (Jones, 1997). As Reyes & Stantic (1988) stated:


Clearly, we live in a society where racist, sexist, and classist orientations exist in individuals and in institutions. What is not clear is how such ideas are transmitted to and through schools, how the ideas are mediated by the democratic ideals of equality and equality of opportunity, and the extent to which teachers and students accept and resist the ideas. More specifically, we do not yet fully understand how these ideas affect the teaching and learning of mathematics (p. 27).

Culture, a popular catchword, is often used by educational researchers without clarifying what the term means or considering its relevance to mathematics education. Nickerson (1992) recommended coming to some understanding of culture within the classroom before considering how wider aspects of culture impinge on that classroom. This paper will present a Japanese student’s cross-cultural perspective of American education and mathematics education and will provide insight into the classroom culture and the effects of the wider aspects of culture and society in it.

Keiko, a graduate student in an elementary and middle childhood teacher certification and Masters of Education program in a midwestern university, has lived in the midwestern United States for 12 years and is 36 years old. Her American husband and his family are from the Appalachian culture; their two sons attend first grade and fourth grade at an alternative private school which is not associated with any religious group. The school’s philosophy is based on Bruner’s ideas of discovery learning, and is more aligned with the educational environment Keiko desired for her children. Keiko is actively involved in the children’s education both at school and at home.

In the American culture, Keiko is viewed as a ‘super-mom’ and a ‘super-student’ because of her exemplary parenting and outstanding achievements in education. However, Keiko takes responsibility for the family and children as she would in the Japanese culture where her role is to "prepare the child for life, to help provide a bridge between the home and the outside world" (White, 1987, pp. 37-38). In the Japanese culture, the family is the woman’s source of influence and value, and this is embodied in the vertical ties of parent and children rather than in the Western nexus of husband and wife (White, 1987). In Japan, any kind of work requires 100 percent effort and a person who tries to combine different work lives, such as Keiko does, is seen as lacking in a fixed group identity (White, 1987).

While completing her undergraduate degree, a B.Ed in elementary education with areas of concentration in mathematics and social studies, she completed a non-required Honor’s Research project that investigated the effects of language and cultural differences on a Japanese eighth grade student in the mathematics classroom. During the project, Keiko’s mother came to the US to help fulfill the mother role in her family. At other times during her education, however, Keiko gave 100 percent to both roles without any additional family support. Keiko’s cross-cultural perspective of the elementary classroom offers a new perspective about how the wider aspects of culture and society influence students’ learning of mathematics. Indeed, it suggests that these wider aspects have a direct effect on the mathematics learning in the classroom. Reyes and Stantic (1988) said that in mathematics education there is little research documentation of the effects of societal influences on other factors such as school mathematics curricula, teacher attitudes, students attitudes and achievement related behavior, and classroom processes. Moreover, they suggested that documenting these connections is the most difficult and the most necessary direction for further research on differential achievement in mathematics.

Raymond (1997) offered a model describing the relationships between mathematics beliefs (nature of mathematics and mathematics pedagogy) and mathematics teaching practices (mathematical tasks, discourse, environment, and evaluation) which included the factors identified by Reyes and Stantic (1988). In this model, past school experiences (successes in mathematics as a student and past teachers) had a strong influence on the teacher’s mathematics beliefs. These mathematics beliefs and the immediate classroom situation (students’ abilities, attitudes, and behavior; time constraints; the mathematics topic at hand) had a strong influence on the mathematics teaching practices. In turn, teaching practices strongly influenced future teaching practices.

Brown & Borko (1992) found that beginning elementary teachers who entered the teaching profession with nontraditional beliefs about how they should teach tended to implement more traditional classroom practices after they were faced with the constraints of actual teaching in the American society. However, Keiko entered the teaching profession with nontraditional beliefs about mathematics and teaching that were developed in the Japanese culture and were reinforced by that society. When she faced the constraints of actual teaching in traditional American classrooms and the classroom management practices used in this society to externally ‘control’ students’ classroom behavior, she experienced cultural conflict.

. Studies concerning teachers’ beliefs about mathematics and mathematics pedagogy, found that teachers’ beliefs are not always consistent with their teaching practices (Kaplan’s study; Peterson, Femmema, Carpenter, & Loef’s study, as cited in Raymond, 1997). However, the inconsistency was deeply rooted in the differences between the cultural and societal expectations in education and mathematics.

While working with Keiko on the research project, we developed a close relationship, the type of nurturing relationship between student and advisor that is expected between a teacher and student in the Japanese culture (White, 1987). We used the term ‘mono-vision’ to define our educational perspective--one eye saw the classroom through Keiko’s cross-cultural view, the other eye saw the classroom through my mathematics educator’s view, and with both of our eyes focused, we more clearly saw the effects of the culture and language on the student’s mathematics learning.

Keiko’s philosophy of education was developed in the Japanese culture and her values influenced her teaching and learning in many ways. Moreover, she learned mathematics thinking and reasoning in Japanese schools. Keiko’s beliefs about mathematics mesh with the goals of NCTM (1989, 1991, &1995) but not with the traditional classroom and ways of teaching mathematics in American schools.

Sugiyama (1993) stated that the higher achievement of Japanese students depends chiefly on the social conditions and the general educational environment in Japan and believes that this, rather than excellent mathematics education, accounts for the higher achievement of Japanese students on international studies. These factors include: the Japanese educational level is higher in general, including mathematics; the situation is caused by the belief that education is the basis of social development of the country and of the prosperity of the individual; the Japanese educational system has no repeaters because effort, rather than ability, determines success; the Japanese educational system has higher quality teachers who are expected to teach higher quality lessons that emphasize the development the students’ ability to solve problems.

During the first two quarters in the graduate level teacher preparation program, Keiko’s value system conflicted with what was emphasized as important in some of the methods courses, in the elementary classrooms she visited and taught in, and in her work in the university Math Lab. By the end of her two week field placement, Keiko concluded that she would not teach in public schools because the cultural and societal differences were too great; they demanded that she give up her identity. Indeed, this was another way to state what she already knew about education in this regional midwestern society -- students from different cultures attend private schools with the exception of the African American students who mainly attend the urban schools; the public schools are homogeneous (Sugiyama, 1993)

The data presented in this paper was gathered primarily from daily e-mail discussions. Other data forms included: videotaped lessons, folders of Keiko’s coursework and reflections, and field observation reports and notes. Pseudonyms were used in the paper; it presents preliminary findings related to the cultural and social values that were in conflict and that are related to mathematics teaching and learning.



Keiko’s beliefs about mathematics and mathematics pedagogy were formed in the Japanese culture and were inconsistent with traditional beliefs about mathematics and the practices of teaching in the American culture. This conflict was apparent to Keiko in the elementary schools and in her work in the university Math Lab.

Many students who use the Math Lab services were taking remedial level mathematics courses focused on middle school and high school mathematics and others were students taking the required courses for the elementary teacher certification program. As lab tutor, Keiko attended the mathematics class so that she could meet the students and encourage them to come to the lab for assistance. However, she was concerned about the teaching in these classes, and she differentiated between teaching for mathematical understanding and teaching procedures. She learned mathematics in Japanese schools and had a understanding of why the procedures ‘worked.’


It was busy in the lab, and my visits to Mrs. M's classes were fun. I see your point, after looking at the textbooks, that they only teach procedures in those classes. But why, though? Those kids are in the classes because they probably have missed something on the way learning math in their previous school experiences, and they don't have the concepts down. Then, they are taught the procedures all over again without any help in understanding the reasons for it??

Keiko related what she observed in a 5th grade classroom to the teacher’s knowledge and understanding of mathematics and then to what she knew about the college level students taking the Mathematics for Elementary Teachers courses. She began by talking about the 5th grade teacher and said:


For math, she uses the manuals exclusively, but when she teaches Language Arts, her lessons are great. I could see she was enjoying teaching the subject, too. I guess it is safe to say that math is not her strong subject area. I was helping a few math students in the lab earlier this afternoon who are taking math 105 this quarter, also, but it was amazing how little they understand the material. I can see when those students finish the program and go out to teach, they might be tempted to rely on manuals. Even though they might be exposed with how exciting math learning is/should be while they are in the (education) program, once they are out in the schools and when they feel the time-crunch, it is easy for them to spend more time preparing for other subject areas which they are interested in and put off math until the last minute. And meanwhile, the students suffer, don't they?

In an elementary classroom, she observed that teaching mathematics was often avoided and was concerned about the message that gave the students. As a primary subject, Keiko thought that it should not only be taught daily, but also be taught when the children were ready to do their best thinking.


You know, as many days as I have been in the classroom, so far I have not seen one math lesson there. I am beginning to wonder if she ever teaches it! My co-op definitely likes to replace her "math period" with other busy work period. I'm afraid this is giving the kids an impression that math is not a desirable or important subject in the relationship to the others. It will be interesting when I take it over; we'll see how the kids react to the change. I plan to move math to the morning, whenever possible, as the kids' are ready to work the best then.

Keiko observed how little the mathematics methods courses in the education program affect the teaching practices in the classroom. Several teachers she worked with were graduates of the same teacher preparation program she was in, yet, in the classroom the philosophy of education and the pedagogical practices in mathematics were not evident. Indeed, some of the teachers advised her to ‘play the game’ at the university, and you can join the real world of teaching in the schools after you graduate. This advice disturbed Keiko greatly, because most of what she learned about teaching at the university in the mathematics methods course was consistent with her cultural view.

The teaching differences between Japanese and traditional American teaching in mathematics are well documented in the literature. In traditional American classrooms, mathematics is a unrelated collection of facts, rules, and skills, while in nontraditional classrooms, mathematics is dynamic, problem driven, and continually expanding. The nontraditional view of mathematics is aligned with the beliefs Keiko had about the nature of mathematics and mathematics pedagogy, and inconsistent with the traditional view that is prevalent in this society.

Keiko questioned how some professors ‘helped’ students learn in the university setting. For example, she talked about how a professor ‘gave her the right answers’ and wondered how that helped her learning. Keiko believed that as a student it was her responsibility to solve problems and that the professor was there to provide guidance rather than answers. Again this is consistent with the roles of student and teacher in the Japanese culture but is not always the case in the American culture. She said:


When I went to see Dr. P to go over my lesson plan Wednesday afternoon, I was surprised when she started editing my plan. She had a pencil in her hand and wrote what I should say word for word.

Reflection is a part of Keiko’s life; she desired strongly to understand the events of her life. She remembered that when she was in school, there was a time period at the end of each day when students reflected about the day’s events, and she noticed this type of reflection was not a part of the task-oriented American classroom life. Moreover, she recognized individual differences. She said:


But at the same time, I know some Japanese adults who just cannot reflect at all, so there is certainly an individual difference there. Through reflecting and thinking about what happened, you can learn to recognize that there are variety of reasons for a thing to go well/not to go well. It's not "you" only who is responsible for the outcome, usually.

In a message she shared another discovery that helped her understand more about the conflict she was experiencing related to general pedagogy and its implication for her as a teacher. She said:


As I was working on a paper, I came across a book on my shelf. As I read through it, it made a lot of sense to me, now, that I understand those educational terms. It talks about why Japanese teachers teach the way they do, and the Japanese students learn the way they learn. What I found interesting was that it gave me insight as to why I disagreed with so many things Dr. P said in the pedagogy classes. My experience in schools has been so different that now it is understandable why I couldn't agree with what she said proven effective in American classrooms.

Keiko can think and speak fluently in both Japanese and English. We found that there were some differences in translating mathematical ideas between English and Japanese that were not easily noticed. For example, while teaching second grade mathematics, a question arose about 2 dimensional shapes, and Keiko discovered a difference between the languages.


Rectangles must have four right angles. I guess I was thinking about quadrilaterals, and also thought that in Japanese there is not such a word as "rectangles"---there is a term for quadrilaterals, though, to generally include all four-sided figures. Isn't it interesting? So, culture and language DO matter when it comes to learning mathematics.

After discussing this difference, we pondered why in the American culture, primary students are taught the general word triangle to name all 3 sided shapes, and yet, more specific names, such as square and rectangle, are taught for 4 sided shapes, rather than the general word quadrilateral.

This society’s ideas of competition and perfectionism were ones that Keiko often reflected about and discussed while trying to understand her place in the cohort group. Her locus of control is internal, and her confidence, creativity, humor, and openness, come from this feeling of personal control. However, as she struggled to understand competition and perfectionism, she observed that when the locus of control is external, a negative sense of competitiveness, helplessness, unwillingness to be open to new ideas, fear, etc. were developed as personal traits in her peers. Keiko shared a discussion she had about one peer in the cohort (Jeanette) with a field advisor (Katie).


I told Katie that I am a perfectionist, too, but my way is so much different from Jeanette's. I said that Jeanette's perfectionism depends heavily on others' approval. She is always so concerned about how others perceive her, and she can get pretty annoyed when things do not go her way. I think her perfectionism comes from her uncertainty of herself. She has to do everything better than the others because, otherwise, she thinks that others will not recognize her. My perfectionism comes from my confidence. I know I can do it well, whatever I do, and I try my best to go up to (live up to) my own expectation (of myself) because I am confident about my capability. Perfectionism comes with some negative sense in this culture, while it does not in Japan. If you consider perfectionism in Jeanette's terms, I think it is pretty negative.

Keiko also talked about sensitivity, a character trait that has a positive meaning in the Japanese culture, but she found it had an opposite meaning in this culture. Indeed, it was a character trait she fostered in herself and in her children.


I always thought the word "sensitive" was positive, but when he said to me, "you are too sensitive about everything!", it shocked me. That was a culture shock---I thought the more sensitive the better.

She related these ideas about character to the relationships adults have with children in the classroom environment and power struggle that she observed between the teachers and students. This power struggle, often under the guise of classroom management or discipline, was in conflict with the mores of Japanese culture. In Japan, the teacher is a respected member of the classroom community, where hard work and fun were one in the same thing. Moreover, teachers and students develop close bonds since they stay together as a community of learners for the first six years of school. Power was not an issue in the classroom because the societal and cultural expectation of education were different.


I was thinking that the message I want to send to the kids most is "you don't have to be overwhelming/strong & big physically/pushy/verbally abusive/etc. to be respected. I want them to know that quiet and sweet person can be just as strong or stronger, mentally, than those people who try to exhibit their strength on the surfaces. What I am trying to do here might be to change the cultural norm, and I know it will not be done easily.

During the first week of full time field placement teaching, Keiko was enthusiastic about teaching second grade, especially, teaching mathematics.


I interviewed the kids about shapes using tangrams today. You know they really amazed me. I feel that I can just teach Geometry all year like this---they should be able to understand "infinite planes" by the end of the year. It's such a joy to work with them. Those surprises (students’ thinking) I encounter in the classroom are what makes teaching so interesting! I feel that I want to do more and more when they give me their new ideas. It's just soooo wonderful:-).

However, at the end of the first week Keiko explained her feelings about teaching in the public school. She was overwhelmed by the realisation of the differences between the culture and society:


One of the major roles schools play in each culture is to teach children their own societal values so that they fit in the culture. In a homogeneous community setting such as this, it seems that this role becomes even more important. Teachers, schools, and parents have the same value system so that children are socialised in the dominant culture. Because the cultural belief is so rigid and not accepting of differences, every child is forced to fit in. I am from a different culture, and I will not be very effective in that role.

On the same day, the field supervisor gave advice during the final seminar that summarized the cultural conflict she observed and experienced in the classroom. The field supervisor said:


‘The most important thing for a classroom teacher to have is a strong control over students.’

At the end of the second week, Keiko recognised the ‘big dragon’--conflict between cultures.


As strongly as I feel about my philosophy, I am so sick of the way they are treating the kids at school out there, and I feel powerless because I cannot do anything about it. It bothers me greatly that the kids are not respected as "kids" at all. And teachers' role in it is so significant that I really do not want to have any part of it. So, in Autumn quarter, I was upset because I felt that I was fighting against "the cohort", but now I gave up because I know I am fighting against "the culture", and I know I cannot do much about it at all.

The first week of full-time field placement teaching was exciting for Keiko, but during the second week, cultural differences about how to deal with immediate classroom situations caused Keiko to reconsider her desire to obtain teaching certification for public education. She felt that she would have to give up her identity to fit in the classroom and school culture, and to meet the societal expectations of public schools.



Clearly, Keiko was in cultural conflict and the causes of her conflict were embedded in the differences between the cultures and the societal values fostered in the educational system. Although she was knowledgeable about mathematics, could teach mathematics effectively for understanding, and loved teaching and her students, she decided that she would not continue in the certification program and teach in public schools. She believed that: the classroom was a community of learners, with the teacher at the center of the learning; the responsibility for learning rested with the student; the role of the teacher was to challenge and nurture the students growth; the interactions between students and teacher were based on a loving relationship rather than a power struggle; and, hard work and fun were one and the same thing. Instead, she will teach mathematics in a private school where the philosophy and goals of education are more compatible with her beliefs.

White (1987) said that the children in Japanese classrooms are good as well as happy because no one taught them that there is any contradiction between the two. As early as in 1919, John Dewey observed the absence of overt discipline in Japanese classrooms.


They have a great deal of freedom there, and instead of the children imitating and showing no individuality -- which seems to be the proper thing to say -- I never saw so much variety and so little similarity in drawings and other handwork, to say nothing of its quality being much better than the average of ours. The children were under no visible discipline, but were good as well as happy; they paid no attention to visitors … I expected to see them all rise and bow. (White, 1987, p. 122)


Reform in mathematics curriculum, teaching, and assessment have been espoused since the National Council of Teachers of Mathematics Standards documents (NCTM, 1989, 1991, & 1995) were written, however, the philosophy and spirit of the reform has had limited influence reforming mathematics teaching and learning. American students were ‘at-risk’ in mathematics when they were compared to Japanese students in the Third International Mathematics and Science Study (TIMMS) report. Although American students’ scores were in the average range in elementary years, middle grade students and high school students scored poorly. The report has generated much concern about the teaching and learning mathematics in American middle grade and high schools, through its comparisons between the curriculum and mathematics pedagogy in the two countries. Indeed, the traditional mathematics teaching and learning in the elementary grades is a factor affecting students future poor school performance in middle and high school mathematics. However, this is not the case in the Japanese schools where the emphasis in elementary mathematics is on developing mathematical thinking by exploring, developing, and understanding concepts, or discovering multiple solutions to the same problems.

In both cultures, the teachers’ beliefs about mathematics are formed during their personnel experiences in mathematics learning, and these beliefs are reinforced by societal expectations. Moreover, American teacher preparation programs have little effect on reforming teaching practices in the classroom because they are in opposition to the cultural norms in the classroom and in the broader society. Indeed, many of the teachers are as ‘at-risk’ in mathematics as their students are. How can all students learn mathematics when culture and societal norms conflict with the desired outcomes of the reform? To answer this question, consideration need to be given to the effects of the culture and societal expectations on students performance in mathematics.



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