Mathematics Curriculum, Teacher Professionalism, and Supporting Policies in Korea and the United States: Summary of a Workshop (2015)

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MATHEMATICS CURRICULUM IN KOREA

One of the differences between the United States and Korea is the way in which curriculum change is initiated and implemented. For example, the Korean national curriculum framework describes goals to be achieved in each subject curriculum. “Fostering the creative human,” a core objective of the current framework, has two components: character building and the development of creativity. Thus, the creators of the mathematics curriculum faced the question of how to interpret creativity and character building in mathematics instruction. Workshop presenters described how textbooks and teacher’s guides have been designed to support the achievement of these and other goals specific to the mathematics curriculum, in particular, learning of fractions. These presentations were followed by a reflection from Do Han Kim, president of the Korean Mathematical Society, giving his perspective on the role of mathematical societies and the problems of Korean education.

After the presentations and over the course of the workshop, U.S. participants commented on aspects that were notable to them. Among other things, they mentioned achievement gaps and pilot schools, and the idea of creativity for all students. They asked questions about the meaning of character building (), leading to more extensive discussion. An edited version of this discussion appears at the end of this chapter.

Textbooks as Mediators of the National Curriculum

Oh Nam Kwon of Seoul National University discussed how a new subject curriculum is created, how it is related to the national curriculum framework, and how it influences what happens in the classroom.

In Korea, the authority of the textbook seems to be quite different than in the United States. It can almost be compared to the Bible, said Kwon. Textbooks and teacher’s guides are an important mediator between the national mathematics curriculum and what happens in the classroom. Instruction is textbook based rather than curriculum based. Because of this, it is important to develop high-quality textbooks and curriculum materials that are tightly coupled with changes in the national curriculum.

The national curriculum framework describes overarching goals and grade-level structure, and gives instructions for implementation. These are elaborated in the mathematics curriculum, which gives detailed specifications for:

• Learning goals by school level;
• Grade-level content objectives;
• Benchmarks;

• Instructional methods; and
• Assessment.

Guidelines for writing textbooks, teacher’s manuals, and student workbooks are then written to be consistent with these specifications.

The 2011 Mathematics Curriculum Revision

Hee-Chan Lew of the Korea National University of Education discussed events that informed the revision of the mathematics curriculum and key accompanying policies.

The current curriculum focuses on creativity and personality. Society requires that students become not only more creative and competent but also more rational and sensible, so that they can comply with the rules and orders of the greater society. The previous curriculum included competencies that are believed to be fostered by engaging in mathematical processes such as mathematical reasoning, problem solving, and communication.

But, Lew said, speaking as a writer of the national mathematics curriculum, we have recognized another important factor in mathematics education: mathematical attitude. Korea has performed well on the two international assessments: the Trends in International Mathematics and Science Study (TIMSS) and the Programme for International Student Assessment (PISA). On the mathematics PISA, for example, Korea was ranked second in 2003, third in 2006, and fourth in 2009. But Korean students’ attitudes toward mathematics were among the worst in the world, according to surveys that accompanied the assessments. Moreover, analysis of scores for the 2003 and 2006 PISA showed an achievement gap according to school location: Urban students scored much higher than rural students. In urban areas, Korea was among the best in the world. But the more rural the area, the lower the scores; in villages and small towns, achievement was below the international average for PISA countries.¹

Why so different? Korea is a small country. Teachers, curriculum, textbooks, and school facilities are almost the same across the country. Lew believes that differences in educational outcomes may come from differences in mathematical attitudes of students and parents.²

For Lew, these findings are part of the background for the curriculum revision. In his view, key points of the revision and key accompanying policies are:

• Contextual learning from which students grasp concepts and make connections to everyday life;

• Manipulative activities through which students may attain an intuitive idea of what they are learning and enhance their creativity;

• Reasoning to justify mathematical results based on students’ knowledge and experience;

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¹ Much of the Korean population is concentrated in metropolitan areas, with about 20 percent in Seoul. Lower-income Koreans tend to live in rural areas rather than cities.

² There is a socioeconomic gap between urban and rural regions. Pahlke, Hyde, and Mertz analyzed Korean grade 8 results from TIMSS 2003 and 2007. They found that the father’s education and family possessions, as well as the economic disadvantage of the school, were all significant predictors of mathematics and science performance.

• Reform of textbooks and the classroom environment: emphasis on “storytelling” as a strategy for teaching science, technology, engineering, and mathematics; and

• Emphasis on the professionalism of mathematics teachers, for example, sending 1,000 teachers to the 12th International Congress on Mathematical Education.

In the mathematics curriculum, content has been decreased and more emphasis has been placed on modeling.³ Lew believes that the reduction will significantly ease students’ study load, and give more time for creative activities and fostering positive attitudes toward mathematics.

The goal of this reform is that, with only few exceptions, all students should be able to gain the mathematical confidence and competence required for private and public activities, and the mathematical skills necessary for their careers. They should also recognize the social and cultural importance of mathematics.

Mathematics Curriculum Design

JeoungSuk Pang of the Korea National University of Education described important aspects of recent curriculum frameworks reflected in the design of mathematics curricula. Pang and other workshop attendees participated personally in the national curriculum revisions. She identified four key aspects:

• Objectives (why to teach/learn)
• Content (what to teach/learn)
• Progression (when to teach/learn)
• Instruction (how to teach/learn)

The basic objectives that have remained in national mathematics curricula are the following:

• Acquisition of mathematical knowledge and skills
• Enhancement of mathematical thinking ability
• Cultivation of problem-solving ability and attitude

In the 2007 revision of the mathematics curriculum, more objectives were added:

• Mathematical communication
• Positive attitude

Mathematical communication was included because it may deepen mathematical thinking and because Korean students are perceived as passive and silent. Although positive attitude is affective and the curriculum places more importance on cognitive abilities than affective aspects, Pang said, these could not be ignored after the release of the TIMSS and PISA findings about Korean students’ attitudes toward mathematics.

New objectives of the 2011 revision were as follows:

• Mathematical creativity
• Character building

Mathematical creativity is especially emphasized for national competitiveness. In the Korean mathematics curriculum, it is construed as having three subabilities: (1) problem solving, (2) communicating, and (3) reasoning. Because of the characteristics of mathematics as a discipline, character building was not previously emphasized in mathematics instruction. But school violence has been a serious social issue recently, and it could no longer be ignored.⁴

Pang said with respect to content, since the fourth curriculum (1981), the general tendency in official curriculum documents has been to reduce it. But in practice, curriculum designers have only shifted content across grade levels. For example, in the seventh curriculum (1997), the intent was to reduce the content by 30 percent, but mathematics curriculum designers did not comply with this policy. Optional topics for advanced students and material intended for underachieving students were taught to all students because there is a strong belief that all content in the textbook should be covered in mathematics lessons. The result is a heavy study load for students and a high teaching load for teachers. Since 2012, this tendency has more serious consequences because the number of schooldays per week has been reduced from five and a half to five. Without any change in the curriculum, this would leave no room for mathematical processes.

Pang said that the writers of the 2011 mathematics curriculum tried to delete optional topics and topics that were mentioned only once or isolated from others. The remaining topics were reorganized in five grade bands: elementary (1–2, 3–4, 5–6); middle (7–9), and high school (10–12). For instance, numbers were dealt with more effectively. Four-digit numbers, for example, were put in the first grade band, rather than being distributed over three grades: numbers up to 100 in grade 1, up to 1,000 in grade 2, and up to 10,000 in grade 3. So, said Pang, they think of teaching fewer topics in greater depth, instead of teaching more topics in a cursory manner.

With regard to progression—when to teach—greater flexibility as to when specific mathematical topics are to be taught has been gradually introduced. In 1997, the mathematics curriculum specified grade levels and even the semester level. Similar topics were separated inefficiently. In 2011, however, schools were given greater flexibility in organizing topics within grade bands.

Concerning when to teach, two other aspects were considered: (1) the difficulty of a given topic and (2) relationships among related topics. For example, relationships among quadrilaterals were moved from grade 4 to middle school. Formerly, the different concepts of fractions were spread over grades 2 to 5. That range will contract to the second grade band (grades 3 and 4).

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⁴ School violence in Korea includes bullying and fistfights, but not guns (which are illegal in Korea). See the Ministry of Education, Science, and Technology’s 2014 Report on School Violence: Survey and Analysis.

In mathematics curriculum documents, four instructional objectives have been consistently emphasized:

1. Meaningful questions
2. Mathematical concepts and principles
3. Problem-solving ability
4. Students’ positive disposition

Comments were added to the 2011 mathematics curriculum about methods to enhance communication, thinking and reasoning abilities, and students’ creativity and character building.

Pang gave more detailed explanations of the four objectives from the 2011 mathematics curriculum:

1. Students acknowledge that communication is crucial in learning and using mathematics by their actions of clarifying and reflecting on their thinking through representing and discussing mathematics.

2. To enhance mathematical thinking and reasoning ability, students infer mathematical facts with induction or analogy, and justify or prove them.

3. To nurture mathematical creativity, mathematical tasks are used to produce different ideas, stimulating students’ divergent thinking. (In the past, creativity has been associated mainly with gifted students, said Pang, but it is relevant to all students. Also, there is a difference between mathematical creativity and general creativity.)

4. To nurture character building, students respect different solution methods and opinions posed by their peers.

So, what are the emergent challenges? Pang listed five:

1. A thorough review of curriculum via systematic research, considering two questions: What are the essential topics? How can educators assess the efficacy of curricular changes?

2. How can teachers promote mathematical processes in their students?

3. Use of differentiated instruction is another challenge. Since the seventh national curriculum, Korea has tried to use differentiated instruction, but has met with much resistance from students and insufficient numbers of teachers for implementation.⁵ So, the national curriculum left decisions about implementation to individual schools.

4. How can teachers change students’ negative dispositions about mathematics, considering the learner’s perspective and the prevailing pressure of the high-stakes college examination in Korea?⁶

5. Although important, an effective curriculum does not suffice if other elements of the educational system are not in place. The challenge is to connect an effective mathematics

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⁵ A workshop participant said that the attempt to use differentiated instruction was implemented by splitting one or two classes of students into smaller groups according to student level, each with one teacher. For example, two classes were temporarily split into three levels, each with its own classroom.

⁶ According to the Korea Institute for Curriculum and Evaluation’s Education in Korea, “Since entering a good university is a matter of high importance in Korea, the evaluation content and method of CSAT [College Scholastic Ability Test] have great influence on the content and method of education in elementary, middle and high schools.”

curriculum to high-quality instructional materials, efficient classroom teaching by well-educated teachers, and students’ performance.

Creating Elementary Textbooks for the 2011 Curriculum

Man Goo Park of the Seoul National University of Education described how the 2011 revision of the mathematics curriculum has been reflected in elementary textbooks. His institution specializes in the education of preservice elementary teachers, and he is an experienced member of an elementary textbook writing team. He noted that, so far, Korea has had only one elementary mathematics textbook series, but the Ministry of Education, Science, and Technology (MEST) has changed its textbook adoption policy to allow the existence of more than one elementary textbook series.

Under the new policy, MEST provides stronger guidelines for textbook writers, including the number and size of pages. This constrains the approaches that can be used in textbooks. Mathematics textbook writers have to think about how to cover the content of the curriculum within those constraints.

There was concern that some textbooks were not being tested in real classrooms. The 12 experimental schools in which textbook material has been piloted before publication generated many problems with the textbooks for the writers to solve, but it is not easy to revise textbooks within the time lines.

Another constraint for textbook writers is how to implement the new instructional approaches, like storytelling, in mathematics textbooks. The spirit of introducing storytelling is wonderful, said Park. But it is not easy to integrate mathematical concepts into storytelling.

Another concern is how detailed the textbook content should be. Is it better to have less or more? Similarly, there needs to be a balance between classroom centeredness and student centeredness.

Park showed an example from his first-grade textbook, which is still under development. The section presented was about the concept of rhombus, used real-world situations, and has been much revised. The textbook illustrates a carjack lifting a very heavy car and a rack for drying clothes. Students are asked to think about the rhombuses within the carjack and clothes rack. At the end, there is an application section asking students to think about designing clothing or jewelry. (Park showed an illustration of a sweater, ring, and chain-link fence, all with a rhombus pattern.) It asks students to look around them, find examples of tools that use rhombus shapes, and talk about the features of those tools and how they are used.

Reflecting Curriculum Goals in Instruction

Rae Young Kim of Ewha Womans University spoke about how curriculum objectives have changed since the 1980s, how those changes have been reflected in instructional materials and methods, and issues arising from the process.

Curriculum trends in the United States and Korea were similar until the 1980s.⁷ In 1992, as Korea became aware of international comparison studies, its sixth curriculum started to deviate from that of the United States. Kim focused on how changes in the four most recent Korean curricula (the sixth and seventh curricula, and 2007 and 2009 revisions) were reflected in textbooks.

Key changes in overarching curriculum goals have been more emphasis on problem solving and increased movement toward student-centered instruction. Recently, there has been a focus on strengthening mathematical communication.

Since the sixth curriculum, problem solving has been emphasized, and this emphasis has been reflected in the improvement of the instructional method and assessment. The seventh mathematics curriculum added an emphasis on strengthening mathematical reasoning and mathematics in daily life. It initiated emphasis on student-centered curriculum and suggested differentiated curriculum tailored to students’ level of ability and lessons that fit students’ ability. Consistency in instruction, textbooks, and assessment were emphasized.

Content changes included selection and arrangement of content as well as changes in approaches to the content. One change in approach has been increased emphasis on problem solving. For example, more tasks that ask students to create their own problems.

Other changes have been pedagogical. Since the seventh curriculum, there has been a movement toward student-centered learning. There has been a focus on individualized instruction (e.g., differentiation based on student level), and concern about motivation and inculcating positive attitudes toward mathematics. Other changes involve the use of technology in instruction and changes in assessments.

In the 2007 revision, the emphasis was on mathematical communication and positive attitudes. Before 2007, curricula described the same objectives for all grades. In 2007, the objectives differed by school level: elementary, middle, and high school. Attention to students’ aptitude and their way of thinking was mentioned. At this point, the 2009 curriculum had been published, but textbooks for it had not yet been developed.

To move toward student-centered learning (a focus of 2007), emphasis on algorithms in elementary textbooks was shifted to let students choose computation methods, and to promote more variety in solution approaches and group collaboration (textbook instructions include “Let’s do it together” and “Do it yourself”). Between the seventh curriculum and the 2007 revision, there was increased emphasis on communication via classroom discussion. To promote mathematical communication skills, the 2007 textbook does not stop with asking elementary students to solve problems but also asks for explanations of how they solved the problems, orally (“Try to explain”) as well as summarizing in writing (“Try to write”). For example, a textbook

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⁷ According to Education in Korea, immediately after Korea’s liberation from Japan in 1945, the United States Army Military Government in Korea stipulated education policy. Later curricula followed U.S. trends. For example, the main focus of the third mathematics curriculum (1973–1981) was “new math” and the fourth (1982–1988) was “back to basics” (Pang, 2014; Park, 1997).

problem says: “Here is the work of Young and A-Ram for the same problem. Try to explain their methods.” It shows (–2/3 × 1/4) ÷ –5/6, followed by two different computations.

Changes in Content

Jee Hyun Park, a teacher at Seoul Finance High School, described issues of selection and arrangement of content raised by curriculum changes. She gave two examples.

The first example concerned vertical consistency in the case of fractions. As noted earlier, in the 2011 curriculum, concepts of fractions contracted to the second grade band (grades 3–4). Formerly, these were distributed and introduced between grades 2 and 6:

• Grade 2, division of a single-unit whole.
• Grade 3, parts of a multiunit whole.
• Grade 4, proper, improper, and mixed fractions.
• Grade 5, addition, subtraction, and multiplication of fractions.
• Grade 6, division of fractions.

In later curricula, content was reduced or removed to optimize learning. For example, between the seventh curriculum and the 2007 revision, the binary system and correlation were removed, proofs that involved the application of similarity were reduced, and direct and inverse proportion was shifted to upper grades.

A second example of change was in conceptual focus—how concepts were construed. For example, in the sixth curriculum, functions were interpreted as correspondences between two variables, in the seventh they were approached via proportional relations, and in the 2007 revision, as relations among variables.

Changes in Pedagogy

Jung Sook Park, a teacher at Taenung High School, described pedagogical changes made in response to national curriculum changes.

To illustrate changes for individualized instruction, Park contrasted pages of a textbook for the seventh curriculum with a student workbook for the 2007 revision. The latter showed a row of three colored dots above each problem to indicate the difficulty level of each problem and allow students to choose problems according to their abilities.

To promote positive attitudes toward mathematics, 2007 revision textbooks included cartoons to stimulate interest, used puzzles to practice terminology, employed approaches using empirical experiments, and inserted photos of students to give a sense of realism.

The use of technology changed. In the 2007 revision, computers were used as illustrative tools in instruction as well as in homework assignments. E-books were developed alongside paper textbooks.

Assessments changed. The seventh curriculum textbooks only give problems. The 2007 revision textbooks include performance assessments, asking students to make up their own problems or to analyze data. For example, after an illustration using a spreadsheet to manipulate data in a frequency table, a textbook directs, “Collect data from everyday life. Using a computer program, represent your data as a frequency table and in various graphical forms. Then analyze the data.”

From the sixth curriculum on, the vision has been student centered, with the use of real-life contexts to try to encourage creative problem solving. The trend is emphasis on mathematical reasoning and classroom communication.

Textbook Development, Approval, and Implementation

Mi-Kyung Ju of Hanyang University described the process for textbook development, approval, and implementation. One focus in textbook development is mathematical personality traits, including creative problem solving and various forms of mathematical communication. A second focus is character building.

In 2009, the national curriculum framework was released, and in 2011 the mathematics curriculum was released. In 2012, Korea was developing textbooks for the mathematics curriculum. There are three types of textbook adoption processes:

• Type A. MEST is the author.
• Type B. A publisher develops the textbook and is its author. The textbook is approved by MEST.
• Type C. A publisher develops the textbook, and is its author. The district approves the textbook.

The trend has been that type C has increased, and types A and B have decreased. In the recent past, all elementary textbook adoptions were of type A. Middle and high school adoptions were of types B and C.

Table 2-1 describes the time line for textbook development, approval, and adoption. Textbooks were to be implemented incrementally, by grade band. Textbooks for the first grade bands at each level, that is, for grades 1–2 and 7–9 were to be developed first. The plan was for textbooks for these grade bands to be submitted for approval in August 2012, the results were to be announced in October 2012, and implementation was to occur in spring 2013. Table 2-1 shows the time lines for later grade bands. Textbooks for the last grade band will be implemented in classrooms in 2015.

TABLE 2-1 Time Lines for Textbook Development (D), Approval (A), and Implementation (I)

MEST formed a committee for textbook policy that solicited opinions from teachers, policy makers, and mathematics education experts. Three recommendations were prominent:

• More autonomy and variety needed to be allowed in textbook development.
• Textbooks should reflect academic and social shifts promptly.
• Textbooks should be accessible (i.e., “student-friendly,” readable), interesting, and familiar to students. Material should be developed to promote students’ interest in mathematics.

In response to the recommendations, all textbook adoptions for the 2009 curriculum were of type C. Specific guidelines were removed, such as textbook size, color, paper quality, and length. The approval criteria were changed to allow more autonomy and variety.

A system that allows selection and reorganization of content to meet current needs was recommended, so that textbooks reflect academic and social shifts promptly. Also, more teachers should participate as textbook authors, since they are the ones that can see needs and shifts in the classroom. Textbooks should be changed and approved on a flexible, rather than a fixed, schedule.

Ju concluded by listing authors’ responses to the recommendation that textbooks should be easy, interesting, and familiar to students:

• Use of real-world problems to introduce and develop mathematical concepts and principles.
• Development of aligned materials for teaching and learning of mathematics.
• Development of mathematics textbooks based on storytelling, to provide students opportunities to be absorbed in doing mathematics via activities and projects.

Reflection on Korean Education

Dohan Kim, the president of the Korean Mathematical Society, made some brief remarks about Korean education.

He noted that when the seventh curriculum was introduced, both the mathematics and mathematics education communities were very shocked. The seventh curriculum benchmarked Japan’s Yutori curriculum and reduced the content of school mathematics by one-third. Japan had lower student achievement with the Yutori curriculum, but soon acknowledged its failure. In Korea, however, the mathematical community as a whole was not aware of this failure for a long time.

In response to this event, the Korean Federation of Mathematical Communities formed to address policy as a united professional organization. The federation’s members include the Korean Mathematical Society, Korean Society of Mathematical Education, Korean Society for Industrial and Applied Mathematics, and Korean Women in Mathematical Sciences.

Kim said that in the past, when there was a curriculum reform or other change, government representatives did not listen to mathematicians, saying “How can you, the representative of one organization, represent all communities?” But nowadays, the federation brings experts in the field to meet government representatives and they listen to the federation’s suggestions most of the time.

Kim described what are, in his view, the problems of Korean education. It is very competitive. Parents let their children learn ahead of the school curriculum. Some teach their children calculus before they enter high school. Politicians use education to score political points, but opportunity for experts to express their opinions has lessened.

He hopes that experts in mathematics education express their opinions via professional organizations and journals, and that Korea improves education for advanced students as well as for those who fall behind.

Comments

Workshop participants offered a wide range of comments on a variety of topics, including the following:

Similarities between the countries

• Both countries are trying to reduce content and cover subjects more deeply.
• Both countries emphasize differentiation and try to meet the needs of individual students.
• Both countries are moving toward e-books, and are increasing the use of online textbooks.

Attitudes toward textbooks

• Korean teachers cover all the material in the textbooks, while in the United States, teachers act as independent contractors and teach whatever they want to teach with great latitude.
• MEST wants the textbook to be one of many teaching-learning materials, lessening its status.

Character building (Korea)

• In the national curriculum framework in Korea, the objective of “character building” had its origins in the school subject of ethics. The meaning of the English term “character building” includes honesty, keeping one’s word, being considerate of others, and cooperating with others. Character building does not belong in the textbook, but in instruction and should be embedded in the curriculum. Ways of accomplishing this are still in the exploration and research stage.
• One example of embedding character building is the storytelling lesson structure that was developed, which is intended to stimulate imaginative ability. It is called “creating story structure.” Students tell stories that fit given mathematical content. They then collect information from the outside world and make their own stories. Making a mathematical decision about whether data and information in the newspaper really speak the truth mathematically is one possible approach.
• In elementary school, there are two instructional methods for character building: One is indirect, involving why we do math, mathematics as a human activity, and the pursuit of precision and accuracy. The second method is to use cooperative work during mathematics instruction to illustrate diverse ways one can think and to ask students to suggest two or three methods, consider which shows better thinking and whether it can help them solve other problems.
• From an elementary school perspective, the context is selected to develop character, such as helping out in nursing homes, where teachers can talk about character naturally. The other is using properties of mathematics itself, such as the properties of the identities 1 and 0, such as: x × 1 = x, x × 0 = 0. In relation with others, there are personality types, such as self-absorbed or absorbed in others.
• Since teachers teach all subjects at elementary schools, a teacher can use interdisciplinary teaching, combining math and social sciences. But in secondary school, it is not easy because math teachers teach only math courses. It is impossible

• to realize this goal unless a curriculum combining math and art, math and science, and so forth, is created and appropriately assessed.

• Giving Korean students some open exploration did not result in any noticeable drops in academic performance. Classroom teachers notice that students find math more interesting with this approach.
• Giving Korean students the opportunity to name figures, such as the example of the isosceles triangles is very nice, but that kind of work is advancing their creativity more than character building. Character building may be related to what people like Paul Cobb⁸ and his colleagues call “sociomathematical norms”; that is, how do children behave when they do mathematics in a classroom? How is a student treated if he or she makes a mistake? That makes a great deal of difference in the student’s feeling about participating in mathematics in the classroom. When you want to cultivate a culture of reasoning and proving—of justifying mathematical claims—you want to treat the classroom as a kind of intellectual community. Listening critically to the ideas of others. That is a mathematical process but it also very deeply involves human behavior and interaction. That is where you see character building integrated with mathematical work.

Student authorship (United States)

• In the United States, the closest thing to character building is “developing students’ authorship or their own voice,” finding out they can do mathematics and that it is a sensible pursuit. U.S. teachers have sometimes gone overboard in that direction, and everything and anything that students say is praised and carried forward.
• In the United States, it is challenging to maintain accountability to the discipline along with student authorship. It is called “the tension between authorship and accountability.”

Teachers’ reactions to curriculum revisions

• The time line for going from curriculum revision to development of materials and to implementation is very fast compared to that typical in the United States. Every time a new curriculum is implemented or changes are made in Korea, there is professional development among teachers and the district sends material helpful for teaching. Districts also provide lots of teacher training focused on how to assess via teacher activity, with references, and examples of assessment.
• In Korea too, there is a constant battle between the teacher-centered, or academic, approach and the student-friendly approach. Korea is strongly influenced by mathematicians. Another factor dominating Korea is the college entrance exam. Korean teachers ask themselves, “How can I help my students achieve higher scores in college exams in order to go to the best college?”
• The 2009 revision in Korea was called the “Creativity–Character Building Curriculum” (CCBC). Previously, the finished curriculum and curriculum materials were delivered to the districts. For the 2009 revision, the Korea Foundation for the Advancement of Science and Creativity recruited 1,000 groups, each consisting of four or five teachers, and provided support for these groups for materials

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⁸ Yackel, Erna, and Paul Cobb. 1996. “Sociomathematical Norms, Argumentation, and Autonomy in Mathematics.” Journal for Research in Mathematics Education 27 (4):458–477.