I have studied "the 6th National Mathematics Curriculum in Korea" (Korea Educational Research Institution, 1992) with a curriculum guideline from the Ministry of Education in Korea. In 1992, when the 5th National Mathematics Curriculum was in effect, the Ministry of Education requested the Korea Educational Research Institution (KERI) to start developing the 6th National Mathematics Curriculum . This is the usual process for the curriculum development in Korea. The 6th mathematics curriculum went into effect in Korea in the spring semester of 1997.
KERI started collecting data for the 6th mathematics curriculum in two major ways. First, the KERI researchers examined the curricular of four foreign countries (Britain, Germany, Japan, and US) as well as the world trend in curriculum development. Second, they examined the effectiveness of the 5th Mathematics Curriculum in the schools. Teacher interviews and national examination scores were used by the KERI researchers to determine the effectiveness of the 5th Mathematics Curriculum. The examination of the curricular from the four countries did not have an impact on the development of the 6th Mathematics Curriculum. I think this fact reflects the general satisfaction of Koreans towared the national mathematics curriculum. This was also evident in my interviews with a mathematics professor from a university in Korea and a highschool graduate from Korea. Therefore, the main focus was on the analysis of the 5th Mathematics Curriculum rather than on other countries' curricular.
KERI states that the 6th Mathematics Curriculum would reflect the reality of the schools, which would address teachers' concerns about the 5th Mathematics Curriculum. But, there is a problem in supporting the KERI's argument, since there was no direct involvement of teachers in the development of the 6th Mathematics Curriculum. So more efforts by KERI are needed to allow an active involvement of teachers in developing the next. This is also what the authors in the Curriculum Development in Mathematics support. But, the 6th Mathematics Curriculum is teacher-centered in many ways. For example, the 6th Mathematics Curriculum is a good guide for teachers planning mathematical contents, instructional methods, and even evaluation methods. Those things are well described in the 6th Mathematics Curriculum. I compared the presentation of mathematics in the 6th Mathematics Curriculum to that of the Standards (NCTM, 1991) in the US or the Common Curriculum (Ontario Ministry of Education, 1995) in Ontario. Therefore, possible confusion among teachers about what to teach, how to teach, and how to evaluate are expected to be reduced to a minimum level . I think this is a strong point of the national curriculum. Of course, it can be criticized for its passive role of teachers as decision makers as well as the non-flexibility of the mathematics curriculum in the schools.
Let me think of the three types of curriculum within the 6th Mathematics Curriculum; the intended curriculum, the taught curriculum, and the learned curriculum. In the process of developing the 6th Mathematics Curriculum, considerations for the intended curriculum were made by KERI and the Ministry of Education. There were also considerations for the taught curriculum by interviews with teachers. Is there an examining process for the learned curriculum? I think that's what is missing in the 6th Mathematics Curriculum. Students were not taken into account in the development of the 6th Mathematics Curriculum.
The national mathematics curriculum in Korea needs to have a balance both from-center-to-peripheral and from-peripheral-to-center. In the Curriculum Development in Mathematics, the authors said the following: " those involved in curriculum design and development will have to take into account the views and needs of all interested parties, but these views will then have to be weighted and mediated" (p. 13). The 6th Mathematics Curriculum did not consider the views and needs of all interested parties. They should have considered of students, parents, school administrators and so on. Some opinions from school administrators and parents were collected by public forums. But, their impact power was minimal. I find a similar problem when I look at KERI researches. They did not represent all interested parties in quality or in quantity. In the KERI research teams, there were only 12 people (2, 2, 8 for the elementary, middle, and high school mathematics curriculum, respectively). In fact, it was unbelievable to me that KERI had such a small number of people deciding the mathematics curriculum for all students in Korea. I think it is critical for KERI to involve teachers in their research teams. Grant, Peterson, and Shojgreen-Downer(1996, p. 234) support this idea: "the real challenges are at the delivery stage". For the 6th Mathematics Curriculum to be teacher-centered in a real sense, the active involvement of teachers both in the process of curriculum development and implementation should have been considered.
There was little influence from the NCTM's Standards (NCTM, 1991) because of some of the social-cultural-philosophical reasons in the Korean educational system. There were several reasons why I expected some influence from the Standards. Several KERI researchers had studied in the United States, and development of the 6th Mathematics Curriculum started in 1992 when the NCTM's Standards began to spread across the world. Probably, in the eyes' of the KERI researchers, the Standards' suggestions would have been too vague and abstract to be given to the teachers of Korea. They have been equipped with specific curriculum guidelines, so it is natural for them to expect the 6th Mathematics Curriculum to have a similar characteristic. For example, there is a sentence in the NCTM's Curriculum and Evaluation Standards for School Mathematics: " the core curriculum is intended to provide a common body of mathematical ideas accessible to all students" (p. 123). To most of the Korean teachers, the meaning of the word core curriculum would be new and difficult to grasp. Many of them would ask what kind of content is included in the core curriculum. I think this example describes the need for gradual change. Grant, Peterson, & Shojgreen-Downer(1996, pp. 509-541) agree in their paper, Learning to Teach Mathematics in the Context of Systemic Reform; They believe that a curriculum change should be a "systemic change". It also should not be the "change without difference" (Roemer, 1991, p. 447). If there had been a movement to change the 6th Mathematics Curriculum drastically, the movement would not have had any support from the members of the mathematics education society in Korea. For example, students, teachers, parents, and educational administrators would have been confused and would have lost their way in learning, teaching, and managing the schools.
Being practical has a deep root in the Korean educational society, and so historically, mathematics has been taught in a practical way. The 6th Mathematics Curriculum is no exception. For example, the 6th Mathematics Curriculum states that students should be able to perform the basic abilities of a good citizen in the 21st century. So, school is a place to practice the social norms; which is consistent with the idea of Goodman's social functionalism(1995). The combination of being practical and social functionalism is reflected in many parts of the educational philosophy of the 6th Mathematics Curriculum. The 6th Mathematics Curriculum wants students to meet the needs of the rapidly changing Korean society and international societies.
KERI found that the 5th Mathematics Curriculum was excellent in its implementation in the schools . Therefore, most of the structures from the 5th mathematics curriculum were kept for the 6th Mathematics Curriculum. The 6th mathematics curriculum does not pay attention to the individual student just as the 5th mathematics curriculum did not. Instead, productivity and efficiency are pursued throughout the 6th mathematics curriculum.
I was able to look at an interesting philosophical feature in the 6th mathematics curriculum. The 6th mathematics curriculum explicitly states that students should be able to keep social rules and order. The theory of social reproduction from the critical theory is related to the idea. People seem to believe that mathematics is understood by accurate terminology or symbols representing particular concepts. Then, the students' job is to apply their mathematical understanding to problems. The importance of obtaining the rigorous side of mathematics cannot be ignored in the teaching and learning of mathematics in the 6th Mathematics Curriculum. In the rigorous learning of mathematics, students learn how to keep the rules and this is where the social reproduction begins. It is believed that students will not be able to solve the problems unless they follow defined regulations and order (How different from the idea's of the Standards! The Standards do not say that students should follow every rule when they try to solve a problem). This belief has many reasons, but one of the most important reasons is the political one of North Korea. It is important to Korean people that mathematics education should play a role in keeping the Korean society in a democratic society which is under continuous tension with North Korea.
By stating the importance of respecting the ideas of others, the 6th Mathematics Curriculum is trying to give teachers the power to control their students and classrooms. In a different sense, the students are asked to behave by the 6th Mathematics Curriculum which is a unique feature of the Korean curriculum. Of course, students are expected to respect their peers, but it is striking to see that it is stated explicitly in the 6th Mathematics Curriculum, and not by an implicit agreement among students. I have an interesting thought here. What if a curriculum project in the US handled student displine and teachers' power in the same way as the Korean curriculum does? The first question will be "Is it possible?".
There is a nice statement in the Curriculum Development in Mathematics (p. 183): "The closer one approaches the curriculum to be evaluated, the more aware one becomes of its manifold qualities. " From now on, I will talk about an analogy between curriculum and evaluation which I found from the study of the 6th Mathematics Curriculum. It was evident that no one could separate the issues of assessment from the issues of curriculum. The assessment methods in the 6th mathematics curriculum show some traditional ways of looking at the assessment. The 6th mathematics curriculum says that the evaluation of learning in mathematics should aim at the improvement of teaching and learning in order to actualize the real value of education. Thus, the results of the evaluation should be based on the improvement of individual students and teachers' instructional methods. But, I thought that the improvement in teachers' instruction had more attention throughout the 6th mathematics curriculum than did the improvement in students' learning. I say this because there are many phrases like "focusing teachers' preparation for next classes" or "teachers' obtaining an idea of the levels of achievement from students". This is more evidence that the 6th Mathematics Curriculum is teacher-centered. The 6th Mathematics Curriculum provides teachers with a good guide about assessment-related issues.
It is interesting to see the idea of three types of assessment processes, diagnostic, formative, and summative, for evaluating students' understanding. Every teacher is officially required to have the results from the three assessment methods before and after instruction. The summative evaluation at the end of each semester is used as national data on all students' mathematical achievement. The data is used when the students apply for higher education. In fact, the ministry of education manages all the assessment data from every school. But, it is not a new idea to have diagnostic tests and formative tests. There are some related studies by Lankford, Brown, and Burton in 1970s, (the Psychology of Learning Mathematics , p. 88) foresaw a time when schools might have a diagnostic specialist who would work with children having special difficulty in mathematics. Why does the 6th Mathematics Curriculum want teachers to practice the three assessment processes? The 6th Mathematics Curriculum does not provide reasons for asking teachers to do so. I think the 6th Mathematics Curriculum also has a problem with the diagnostic test. Does the diagnostic test mean the evidence of the prior learning? Or does it mean the students' ability to learn new mathematical content? If it means the former, the issue of measuring students' learning and then applying the information to the classroom should be discussed. If it means the latter, the issue of tracking students according to their ability to learn mathematics would emerge.
Compared to the current issues in assessment, it is interesting to see the domain-specific knowledge as the main focus of the 6th Mathematics Curriculum. The domain-specific knowledge would be easier to measure on the teachers' side, but many suggestions such as ones from the NCTM's Standards should be reflected in the 7th Mathematics Curriculum in Korea. I think this is a change that the 7th Mathematics Curriculum should look for. In addition to that, there should be more voices about problem-solving abilities including communication abilities, reasoning abilities, and the level of mathematical aptitudes in the 7th Mathematics Curriculum since there is little of this in the 6th Mathematics Curriculum.
The 6th Mathematics Curriculum tis clear about selecting the tools of the assessment: "the method or the tool of the evaluation should be something easy to use for most teachers." This is an unique statement which I have not found in any other assessment-related literature. I hope that this statement could not be used as an excuse by mathematics teachers who do not pay attention to their students' various ways of doing mathematics . At any rate, teachers should be able to understand the affective matters of their students and conduct frequent observation of student participation and other various mathematical activities.
Despite all the complex issues related to the 6th Mathematics Curriculum, the best thing for me was to be able to find some strong demands on improved curriculum in the Korean society. I want to believe that the 6th Mathematics Curriculum is the best result of our efforts at this point of time. Otherwise, who would be responsible for practicing a wrong curriculum for all students in Korea? No one would want to be responsible for it. But there should be more effort and consideration for a better mathematics curriculum when KERI starts developing the 7th Mathematics Curriculum. I hope that the criticisms and suggestions in this paper will be under consideration. Finally, I hope that I will be able to participate actively in the curriculum decision process in the future.

References

Goodman, J. (1995). Change without Difference: School Restructuring in Historical Perspective,

Harvard Educational Review, 65 (1), pp. 1-28.

Howson, G., Keitel, C. & Kilpatrick, J. (1981). Curriculum Development in Mathematics. New

York, NY: Cambridge University Press.

Korea Educational Research Institute. (1992).The Studies on the 6th National Mathematics

Curriculum. Seoul, Korea.

National Council of Teachers of Mathematics. (1989). Curriculum and Evaluation Standards for

School Mathematics. Reston, VA.

Resnick, L & Ford, W.W. (1981). The Psychology of Mathematics for Instruction. Hillsdale,

New Jersey: Lawrence Erlbaum Associates.

Roemer, M. (1991). What we talk about when we talk about school reform. Harvard Educational

Review, 61, pp. 434-448.

Grant, S., Perterson, P., and Shojgren-Downer, A. (1996). Learning to Teach Mathematics in the

Context of Systemic Reform. American Educational Research Journal, 33 (2), pp. 509-541.

Ontario Ministry of Education. (1995). The Common Curriculum:Policies and Outcomes. Grades

1-9. Toronto: Queens' Printer.

Ontario Ministry of Education. (1995). The Common Curriculum:Provincial Standards.

Mathematics. Grades 1-9. Toronto: Queens' Printer.

Weiler, K. (1988). Critical Educational Theory, Women Teaching for Change: Gender, Class &

Power. New York, Bergin & Garvey.