On July 15–17, 2012, following the 12th International Congress on Mathematical Education in Seoul, Korea, the United States National Commission on Mathematics Instruction and Seoul National University held a joint Korea–U.S. workshop on Mathematics Teaching and Curriculum. The workshop brought together 40 teachers, mathematics educators, mathematicians, education researchers, and other mathematics education specialists from both countries.
Planned by a joint ad hoc committee, the workshop was organized to address questions and issues related to math teaching and curriculum that were generated by each country, including the following: What are the main concerns (or main focus) in the development of the curriculum? What issues have been discussed or debated among curriculum developers, teachers, teacher educators, and scholars regarding the curriculum? How have textbooks been developed for the curriculum? How are curricular tasks designed and what criteria are used? What is the role of learning trajectories in the development of curriculum? This volume summarizes the presentations and discussions at the workshop.
To understand differences in the educational systems of the Republic of Korea1 and the United States, some general information about these nations is useful. According to the World Bank, in 2013 the population of the United States was approximately 316 million, more than six times that of Korea, which had a population of 50 million.2 Although Korea’s population is roughly twice that of Texas, its land area is much smaller—approximately the size of Kentucky or Virginia. The United States spends $10,995 per K–12 student in public education, while Korea spends $6,723, but outpaces U.S. academic performance.3
Korea has gained attention in international assessments of mathematical knowledge. The Trends in International Mathematics and Science Study (TIMSS) is administered to students in grades 4, 8, and 12. Tests and surveys for the Programme for International Student Assessment (PISA) are administered to 15-year-olds. Korea has been a top performer on these assessments for at least a decade. In contrast, the overall U.S. performance has been at or below the international average, although some U.S. states are among the high performers. On the 2012 PISA, for example, the states of Massachusetts and Connecticut had 19 percent and 16 percent of student scores classified as proficiency level 5 or greater. These percentages were above the international average of 13 percent,
1 The Republic of Korea is the official name of “South Korea.” Henceforth, this report refers to it as “Korea.”
and above the U.S. average of 9 percent. The corresponding figure for Korea was 31 percent. A similar pattern occurred for average PISA scores: 514 (Massachusetts), 504 (Connecticut), 481 (United States), and 554 (Korea).4 On the 2011 TIMSS for grade 8, average scores were 561 (Massachusetts), 518 (Connecticut), 509 (United States), and 605 (Korea). The international average was 500. 5
Although Korean performance on international assessments has received much attention in the United States, the structure of Korea’s education system is far less well known. The accounts in this report offer an introduction to this system. They also provide an opportunity to gain a broader and more nuanced understanding of differences in policy, curriculum, and the profession of teaching, and their relationships in the Korean and U.S. education systems.
This wealth of information is grounded in the workshop participants’ different experiences and types of expertise. Some of the Koreans had taught in U.S. schools, worked at U.S. universities, or were familiar with U.S. textbooks, and, in one case, had analyzed them together with one of the U.S. participants. Others, both researchers and teachers, were among the creators of national mathematics curricula, or had worked to embody these national guidelines in instructional materials or professional development offerings (see biographies in Appendix B of this report). Their experiences were reflected in their presentations and in detailed and thoughtful responses to questions from U.S. participants and comments of other Koreans. Among the U.S. participants were a teacher who had taught in two very different school districts; a teacher who now works in a state department of education; researchers who specialize in relationships between educational policy and classroom practice; and mathematicians with long-time interests in elementary mathematics.
This report summarizes a two-day workshop and should not be considered a complete account of the Korean and U.S. educational systems. Because the subject of the workshop was school systems, other educational institutions such as hagwons (private after-school academies) in Korea or test-preparation schools in the United States are not discussed in this report. This is not meant to imply that they may not wield considerable influence on student achievement.6 Likewise, possible effects of college entrance examinations in both countries were raised during discussion, but were not the topic of a presentation.
One fundamental difference between the Korean and U.S. education systems is the distribution of authority. In the United States, many matters related to education are
4 See PISA 2012 Results in Focus and http://nces.ed.gov/surveys/pisa/pisa2012/pisa2012highlights_1.asp.
6 Four of five primary school children receive private education, typically in cram schools known as hagwons. Total private education expenditure for K–12 students in Korea was 20,100 billion won (approximately $20 billion) in 2011.
See http://monitor.icef.com/2014/01/high-performance-high-pressure-in-south-koreas-education-system and http://kostat.go.kr/portal/english/news/1/8/index.board?bmode=read&aSeq=254474.
under the jurisdiction of the states rather than that of the federal government.7 There are 50 states and each has its own department of education.
Korea’s educational administration system is centralized. Its offices are the central government’s Ministry of Education, Science, and Technology (MEST), 16 provincial education offices, and 182 county and city offices of education. About 75 percent of the budget for local education offices is provided by the central government, which also underwrites private school deficits (Kim et al., 2008, p. 43). Public and private school teachers have comparable salaries and pensions (Kim, 2009, pp. 31, 42–43). Consistent with this, a workshop presenter noted that schools across the country are similar in teacher quality, facilities, and other resources.
Since the local autonomy law of 1991, local educational autonomy has been promoted. MEST has delegated much of its budget planning, personnel management, and administrative decisions to local authorities.
MEST funds several educational research institutes. Among them is the Korea Institute for Curriculum and Evaluation (KICE), which conducts basic and policy research on teaching and learning. KICE also develops and disseminates methods and materials for primary and secondary education. These include the assessments administered to all students in grades 6, 9, and 11, and college entrance examinations. Together with ordinary citizens, experts from schools, universities, and institutes like KICE participate in revising the national curricula (Huh, 2007, pp. 59–61).
Chapter 2 focuses on changes in the Korean national curriculum—in particular, the new goals of creativity and character building—and how these changes have been implemented in mathematics textbooks, teacher’s manuals, and instructional guidelines. In Korea, the national curriculum framework for all subjects is developed first. Subject curricula are then written in alignment with the framework. These include objectives and content for each grade and guidelines on instruction and evaluation. Curriculum revision is a “complicated, time-consuming process” involving a multiyear plan for textbook revision and the provision of manuals and training for teachers (Huh, 2007, pp. 56–58). Implementation is left to the joint efforts of schools and provincial and local offices of education.
Since 1953, Korea has had seven national curricula.8 In the past, curriculum changes tended to be wholesale, but since the seventh curriculum, changes have been incremental.9 This history and the framework–subject curriculum structure are reflected in nomenclature. The Korean workshop participants referred to the current mathematics curriculum as “the 2011 revised mathematics curriculum” (referencing the year of its
7 The Tenth Amendment of the U.S. Constitution states, “The powers not delegated to the United States by the Constitution, nor prohibited by it to the states, are reserved to the states respectively, or to the people.”
9 See Education in Korea, p. 6.
release) or “the 2009 revision” (referencing the year of the associated curriculum framework). See Table 1-1.
TABLE 1-1 Release Dates for National Curricula in Korea, as of July 2012
SOURCE: Bae et al., 2011; pp. 128–129; Park, 1997.
Chapter 3 discusses curriculum changes in the United States. In the United States, determination of curriculum guidelines and textbook criteria is distributed between state governments and school districts. Each state has a department of education, which sets performance standards. In many states, public schools receive a substantial part of their funding from taxes on property within their district. This variability in funding is part of the nationwide variability in schools and teachers.10 Often, but not always, states, rather than districts, also set curriculum guidelines and textbook adoption criteria. Textbooks are created, for the most part, by commercial publishers. Development of research-based textbooks and other curriculum materials for mathematics is typically supported by private funders or the National Science Foundation. Timelines for initial development depend on funding guidelines (Schoenfeld, 1999, p. 11) as do subsequent evaluation and revision (Clements, 2007, p. 59).
The U.S. federal government and its Department of Education (DoED) have more limited policy roles than in Korea. The DoED’s Institute of Education Sciences conducts the National Assessment of Educational Progress, which periodically tests a sample of students in grades 4, 8, and 12. Since 2001, the No Child Left Behind Act (NCLB) has made state receipt of federal school funding contingent on annual testing of every public school student in grades 3 through 8 and high school. In general, these tests have been created separately for each state.
10 See, for example, Honegger, 2010. Table 7 shows amounts of federal, state, and local funding for various districts. Table 2 gives total spending per pupil per state.
In 2010, the Common Core State Standards for Mathematics and for English Language Arts and Literacy in History/Social Studies, Science, and Technical Subjects were launched. By the end of 2010, 41 states and the District of Columbia adopted the Common Core State Standards.11 The development of the Partnership for Assessment of Readiness for College and Careers and Smarter Balanced Assessment Consortium as consortial assessments was supported, through a competitive grant process, by the United States Department of Education. These consortia worked with educators from around the country to develop tests aligned with the Common Core State Standards. Presentations and comments from U.S. participants mentioned issues related to teacher training and assessment, and the development of textbooks and related teacher manuals as possible obstacles to successful implementation of the Common Core State Standards.
Over the course of the workshop, several U.S. participants commented on the different policy arrangements in the two countries and their effects. For example, one participant noted the effect of having politically appointed education officials:
The fundamental contrast between the two countries is that Korea has a ministry of education … staffed by mathematics educators, teacher professionals, and others who are relatively stable in their positions. They don’t change with each election, and they’re professionals who devote themselves to educational problems.
A Korean presenter mentioned that textbooks were piloted in designated schools and discussion touched on this practice. This also occurs in the United States for textbooks developed by education researchers, and, to a lesser extent, by commercial publishers. From a U.S. standpoint, it is perhaps more notable that Korea piloted policy changes such as new methods of school and teacher evaluation in designated schools before adoption.12 Also, the evaluation methods themselves are quite different from those in the United States.
Several of the U.S. participants took note of a presenter’s remark that for Korean teachers the authority of the textbook seems to be like that of the Bible. In contrast, one participant said, “U.S. teachers … teach whatever they want to teach, with great latitude.”
Development of Instructional Materials
Chapter 4 describes the development of instructional materials for mathematics in Korea, including the organization of content. In the United States, the Common Core State Standards drew on research-based learning progressions. A learning progression consists of:
11 How the content and organization of the new mathematics standards differs from that of previous standards was not discussed at the workshop.
12 This was only briefly mentioned during the workshop. Pilots for the teacher evaluation program began in 48 schools in 2005. By 2009, pilots had expanded to 1,570 schools (Kim, 2009, pp. 73–76).
- A set of mathematical goals;
- A clearly marked developmental path; and
- A coherent set of instructional tasks or activities.
A related Korean term is GaeNyumdo (, roughly “concept map”). Part of the presentation on instructional materials described how GaeNyumdo are used in developing curricular materials and the instruction that accompanies them. This was followed by discussion that raised the question “Are teachers given the conceptual framework that led to the development of the tasks?” According to several of the teacher participants, teachers in Korea are familiar with the GaeNyumdo used by curriculum developers. This led to a discussion of teacher’s manuals and how they might support teachers’ understanding (“speaking to the teacher”) versus providing a script for teachers to follow.
A U.S. mathematician was struck by who was involved in developing instructional tasks—a team of mathematicians, mathematics educators, and mathematics teachers—and said that he would love for that to be routine in the United States. “We are expecting children to understand the concepts behind the math, but there might be teachers who don’t understand them,” said a U.S. teacher. Textbooks and manuals that support teachers’ understanding can allow “teachers to grow with kids.”
Teachers, Professional Learning, and the Organization of Teaching
Research on teacher knowledge suggests the importance of retaining teachers while giving them opportunities to learn. The structure of the education system appears to be an important factor in developing teacher expertise and specialized mathematical knowledge for teaching. In some education systems, teachers can acquire and increase this knowledge over the course of their careers.13
In Korea, teacher attrition is very low. Prospective teachers face stiff competition for admission to teacher preparation programs and in employment tests. New public school teachers who pass employment tests are initially hired as “second-rank teachers” by provincial offices, then complete “qualification training” before teaching. After further training and satisfactory evaluations, they can be promoted to first-rank teacher, master teacher, school inspector, research officer, or principal (Kim et al., 2008). Master teachers have a 40 percent reduction in teaching time, allowing them to help other teachers or carry out innovations in schools. Public school teachers rotate within their districts approximately every five years. Because many areas of Korea are densely populated, teachers often need not travel far to reach a different school.
13 Ma (1999) compared samples of U.S. and Chinese elementary teachers, finding that many more Chinese teachers had specialized mathematical knowledge for teaching. More profound forms of this knowledge occurred among Chinese teachers with an average of 18 years of teaching experience, but not among the experienced U.S. teachers in the sample. Specialized teacher knowledge of mathematics is hypothesized as a necessary condition (Ma, 1999, 2013).
A workshop presenter mentioned that Korean teachers have a strong desire to learn and to increase their capacity as teaching professionals, describing how this desire is supported by MEST policies and MEST-funded activities. MEST funding is distributed by district offices to teacher research groups for the development of curriculum materials or innovative instructional methods and materials. Teacher research groups also provide professional development for other teachers.14
The Korean Society of Teachers of Mathematics (KSTM) is the first and largest teacher-created organization in Korea. It began in 1994 and is now one of three teacher organizations that are government-approved professional development providers. KSTM publishes a journal and also runs common interest groups, including a group for “lesson analysis.” Chapter 5 describes the organization of teacher preparation and professional development in Korea, including an educational researcher’s description of government-supported teacher research groups and mandated activities, followed by the KSTM founder’s description of teacher-initiated activities.
Workshop discussion touched on a new strategy employed during the 2009 curriculum revision. MEST gave approximately $5,000 to 1,000 groups of 5 teachers to develop the national subject curricula. Following the curriculum revision, these groups were engaged in teacher training.
In the United States, there is a wide range of teacher preparation programs. Among sources of variance are selectivity in admissions and program requirements (see literature review and findings of Schmidt, Houang, and Cogan, 2012). A well-publicized statistic is “half of beginning teachers leave teaching within five years.” This was publicized by the 2003 report No Dream Denied, which documented considerable turnover among U.S. teachers. In the workshop, this turnover was illustrated by a presentation from a teacher who was ready to quit teaching, but “fell in love with teaching again” when she moved to another district in another state. Her experience also illustrates research findings that suggest that school organization is a major factor in retaining teachers.15 School organization is also a factor in supporting the existence of professional learning communities, an infrastructure or a way of working together that results in continuous school improvement (Hord, 1997). In addition to the account of a teacher who almost left teaching, Chapter 6 gives an overview of the landscape of professional learning communities in the United States.
In discussing these presentations, a U.S. participant noted that professional learning communities have existed for decades, but in isolated pockets. “We can create pockets of things done well, but it’s very hard to do it at scale,” said another. “There is no system for helping teachers, principals, and schools improve.”
14 Research groups and individual teachers may be recognized as winners of competitions sponsored by offices of education. Teaching competitions are reported on national television news. Three-time winners receive the title of “treasured teacher.”
15 Information about teacher preparation programs is summarized in the 2010 National Research Council report Preparing Teachers: Building Evidence for Sound Policy. Studies of attrition and turnover have been conducted by Richard Ingersoll and his colleagues. See, for example, the summary in Chapter 2 of The Mathematical Education of Teachers II.
One participant returned to the theme that U.S. classrooms tend to be places of isolation for teachers, saying “there’s a history of teachers closing their doors, closing the world out, and doing things on their own.” Another commented: “Now, the Common Core provides us an avenue to open up those doors.” In contrast, one of the Korean teachers said, “We have quite well-established teacher communities…. Even with our busy schedules, we try to get together in our school or with nearby schools.”
The discussion also touched on the consequences of student test results. In the United States, NCLB is “the continuation of a steady trend toward greater test-based accountability that has been going on for decades,” according to the National Research Council report Incentives and Test-Based Accountability in Education (2011). A current example is “widespread interest in using student test scores as a way of rating and rewarding teachers and principals,” which has been manifested in discussions of “value-added” measures.
Workshop discussion mentioned differences in Korean and U.S. systems for evaluation of teachers and methods of improving teacher quality. In 2010, after 10 years of piloting, the Korean government began using a new system for evaluating public school teachers. Findings from evaluations are used to create customized teacher training (Kim, 2009, pp. 73–76). Some details of evaluation and accountability were mentioned by Korean workshop participants. Schools keep a detailed, year-long log of educational activities. Monitoring committees who visit each school examine this log carefully, together with the principal. If a school is judged as providing a good quality education, it gets some extra funding. If a school has many low-achieving students, then the government provides support in the form of assistant teachers. Teachers themselves help to monitor teaching quality via observation and feedback on each other’s lessons as required by regulations.
At the workshop, the comments of Korean teachers reflected a culture of teaching professionalism, in which teachers initiate their own study groups, conduct professional development, produce research and teaching materials, and collaborate with mathematicians and education researchers to produce curricular tasks. This suggests a type of teacher professionalism that seems rare in the United States. A Korean teacher said the workshop caused her to reflect on why she and teachers engage in these activities so much, wondering if it was due to cultural expectations for teachers, rather than a desire for self-improvement.
Like this teacher, readers will bring their own knowledge and experience to the accounts in the report, finding other aspects of interest. As often occurs, contrasts between nations provide a mirror, not a blueprint for improvement. They are an opportunity for reflecting on why each country does things the way it does, provoking closer examination of policy and practice.