Mathematics and Education

A slow blog

Interpreting Standards from Other Nations: Considerations of National Context

leave a comment »

Over the past decade, comparisons of U.S. standards for mathematics have been made with “standards” from other countries, e.g., national curriculum standards, syllabuses, or courses of study. Some of these comparisons overlook important details, resulting in conclusions whose accuracy could be improved considerably without much additional effort. This post gives a brief overview of two differences in national context that affect interpretation of documents from other countries, in particular, China, Hong Kong, Japan, Korea, Singapore, and Taiwan. (Further details are in an appendix at the end of this post.) The two posts that follow (here and here) discuss comparisons that have been made by (respectively) the mathematicians James Milgram and Jonathan Goodman.

My background. My Ph.D. is in mathematics, but I have spent considerable time with education researchers and have published some articles in education research. (More information is here.) I’ve been interested in East Asian mathematics education for a long time, and have followed related research, beginning with the work of Stevenson and Stigler in the 1980s which was summarized in The Learning Gap. I’ve worked (off and on) with Liping Ma since 1996. (Ma began her career as an elementary teacher in China, and subsequently studied elementary teachers’ knowledge of mathematics in China and the U.S. Two articles that discuss the impact of her book Knowing and Teaching Elementary Mathematics are here (short, no pay wall) and here (long, free abstract).) I also have a long-time interest in the Japanese practice of lesson study together with the national mathematics curriculum that supports it, and have consulted for related projects in the U.S. As a result, I have had unusual opportunities to discuss details of Chinese and Japanese mathematics education with experts for almost two decades and contact with people familiar with mathematics education in Hong Kong, Korea, and Singapore, even though I’ve spent little time in Asian countries. I’m also very familiar with the Common Core State Standards and am the editor for the Progressions for the CCSS. 

Differences in Testing

The standards documents listed in the table are posted at Mathematics Standards in APEC Economies. The page lengths shown in the table illustrate one easily measured difference in these documents, which also vary in writing style and type of objectives. As indicated by the titles, all but the CCSS have curriculum as a major focus, describing what is taught at each grade. In contrast, the CCSS focus on what students know and are able to do at each grade. To summarize, the CCSS are performance standards, but the documents from other countries are curriculum standards that sometimes include performance standards.

This difference is associated with the differences in the frequency of high-stakes testing shown in the rightmost column. The United States tests students far more often. Although frequent testing may seem to have begun with the No Child Left Behind Act of 2001, it grew from a long tradition of using standardized tests for monitoring the educational system and measuring student progress  (OTA, 1992, chap. 4).

Country, date

Standards or guidelines document title

Page count

Pre-college high-stakes tests

China, 2001 Mathematics Curriculum Standards 
[grades 1–9] 


Grade 10 entrance
Hong Kong, 2000 Mathematics Curriculum Guide [grades 1–9]


Japan, 2008 Course of Study [grades 1–9]


Grade 9 entrance
Korea The National Curriculum: Mathematics 
[grades 1–10; grades 1–9 are compulsory]


Grade 9 entrance
Singapore, 2006 Mathematics Syllabus Primary [grades 1–6]Secondary Mathematics Syllabuses 
[O, N(A), or N(T) courses, grades 7–10; additional mathematics, grades 9–10]



Primary School Leaving ExamO or N level, grade 10
Taiwan [no date or title given, grades 1–9]


Senior high school entrance
United States, 2010 Common Core State Standards for Mathematics [grades K–12]


No Child Left Behind: grades 3–8, high school

Notes. University entrance exams are not included in this table. Although Singapore has published syllabuses in 2013, the 2006 syllabuses are listed here because they were used for comparisons in 2010.
* Hong Kong uses results from pre-secondary standardized attainment tests to allow school test results to be scaled and used in determining students’ choices of secondary schools. Currently, these tests are optional (Education Bureau, 2013 May).

To have scores be legally defensible, tests were (and are) subject to psychometric constraints such as validity and reliability. Testable goals common to groups of states or school districts were generally limited to basic skills (Feuer & Fulton, 1994, p. 38) as suggested by the names of commonly used tests, e.g., Iowa Test of Basic Skills.

In the NCLB era, this situation changed. States could no longer share tests because different state standards required different state tests. But, creating psychometrically acceptable test items is expensive. After the enactment of NCLB, one group of states—New Hampshire, Rhode Island, and Vermont—decreased their individual costs by forming the New England Common Assessment Program.

But many states did not form consortia, creating another problem: the test industry did not have the capacity to create all the different state tests, particularly given that portions of these tests were released after use. A symptom of this lack of capacity was poorly constructed items and mistakes in scoring. Another symptom was less publicized: tests that weren’t fully aligned with state standards and focused on low-level skills (Toch, 2006, p. 6).

Some U.S. readers may interpret documents from other countries through the lens of U.S. testing tradition and recent history, viewing objectives as inevitably being performance objectives. And, they may interpret each performance objective of the CCSS as inevitably translated into a single item that is part of a low-quality test.

Details that don’t appear in official documents

Terse official documents that focus on curriculum do not always include details about intentions for student performance and teaching. However, there are other sources of information: research studies and curriculum materials.

There is a wide variety of research studies, including analyses of textbooks. Some large-scale examples are studies of classrooms, parents, and children described in The Learning Gap; analyses of textbooks conducted as part of the TIMSS by William Schmidt and his colleagues; and ethnographic studies of teachers and teaching conducted by Harold Stevenson and Roberta Nerison-Low. Such studies routinely involve researchers from the countries studied, helping to minimize misinterpretation of country documents and practices.

Aside from standards and course of study documents, other curriculum materials are sometimes available in English. For Japan, these include the teacher’s guides for the course of study, a series of textbooks, and some excerpts from teacher’s manuals. For Singapore, these include a series of textbooks and teacher’s manuals. In both of these countries, textbook development is closely monitored by the Ministry of Education and the pace of curriculum change is slow (see details and references in the appendix at the end of this post). This makes textbooks and teacher’s manuals from these countries more accurate reflections of intended objectives than is sometimes the case in the U.S.


Education policy is complicated, and cross-national comparisons of education policy are even more complicated. This post is not meant to be a comprehensive account of either, but to make the following points:

  • In their official documents, not all countries communicate the kind of detailed expectations for student performance that U.S. readers are accustomed to seeing in standards documents.
  • Details of curriculum and expectations for student performance may occur in teacher’s guides, textbooks, and teacher’s manuals; and in findings of empirical research.

The two posts that follow comment on two comparisons of the CCSS with standards and course of study documents from other countries, adding relevant details from textbooks, teacher’s manuals, and other sources.


Standards, Course of Study, and National Policy Documents

Note that curriculum documents for several countries (including China, Japan, and Singapore) may be downloaded here:

Hong Kong

Education Bureau Hong Kong. (2000). Mathematics key learning area curriculum guide (primary 1–secondary 3), [The “2002” refers to the expected implementation date.]

Education Bureau Hong Kong. (2013 May 21). Education Bureau Circular Memorandum No. 52/2013,


Korea Institute of Curriculum and Evaluation. Education in Korea,

Korea Institute of Curriculum and Evaluation, The national curriculum: Mathematics [grades 1–10],


Ministry of Education, Culture, Sports, Science and Technology. (2010). Junior high school teaching guide for the Japanese Course of Study: Mathematics (Grade 7–9) (Masami Isoda, trans.). CRICED, University of Tsukuba. Available at

Takahashi, A., Watanabe, T. & Yoshida, M. (2008). English translation of the Japanese mathematics curricula in the course of study, grades 1–9. Available at [translation of 2008 course of study]


Curriculum Planning and Development Division, Ministry of Education Singapore. (2006). Mathematics syllabus primary,

Curriculum Planning and Development Division, Ministry of Education Singapore. (2006). Secondary mathematics syllabuses,

Ministry of Education Singapore. (n.d.). The Singapore education journey,


Ministry of Education Taiwan. (2007). Compulsory education,

Ministry of Education Taiwan [no date, no title],

United States

National Governors Association Center for Best Practices and Council of Chief State School Officers. (2010). Common Core State Standards for Mathematics,

U.S. Department of Education. (2007). Standards and assessments peer review guidance: Information and examples for meeting requirements of the No Child Left Behind Act of 2001,

Education Research

Feuer, Michael J., & Fulton, Kathleen. (1994). Educational testing abroad and lessons for the United States. Educational Measurement: Issues and Practice, 13, 31–39.

Stevenson, H., & Stigler, J. (1992). The learning gap. New York: Simon & Schuster.

Toch, T. (2006). Margins of error: Testing in the age of No Child Left Behind. Educator Sector.

U.S. Congress, Office of Technology Assessment (OTA). (1992). Testing in American schools: Asking the right questions, OTA-SET-519. Washington, DC: U.S. Government Printing Office.

Appendix: Details of national context 

Length of compulsory education. In China, Japan, Korea, Singapore, and Taiwan, compulsory education is less than 12 years. However, in these countries some students continue their mathematical studies beyond compulsory courses. This further study may require an entrance examination, a type of high-stakes examination that is unusual in the United States before college.

Levels of schooling. U.S. school districts have a 5-3-4 system or a 6-2-4 system. Elementary grades are grades 1–5 or 1–6. “Middle school” thus refers to grades 6–8 or 7–8. “High school” refers to grades 9–12.

Other countries use different systems. For example, Japan has a 6-3-3 system, with the names of the different levels often translated as “primary,” “lower secondary,” and “upper secondary.” Upper secondary students have the choice of several course sequences (Yoshikawa, 2008, p. 14).

Singapore has a (mostly) 6-4-2 system with four secondary grades and two preuniversity grades. Secondary students have the choice of three mathematics course sequences, with the option of additional mathematics starting in grade 9. About 60% of secondary students take additional mathematics. About 90% of preuniversity students take mathematics (Soh, 2008, pp. 30–31).

Frequency of high-stakes testing. In Singapore, students take high-stakes standardized tests twice: once at the end of elementary school and once at the end of secondary. (See The Singapore Education Journey at the Singapore Ministry of Education or Soh, 2008.) Similarly, the only mention of “test” or “examination” at the Japanese Ministry of Education web page describing the school system is: “Students must normally take entrance examinations to enter upper secondary school [grades 9–12].” Japan does give a National Assessment of Academic Ability at grades 6 and 9 but this is not high stakes and is more akin to the U.S. National Assessment of Educational Progress. For similar reasons, Korea administers the National Assessment of Educational Achievement at grades 6, 9, and 11. In Hong Kong, the Pre-secondary Attainment Test plays a different role because it is one of several factors used to determine the student’s choice of secondary school. (See page 4 of the leaflet to parents and note also the Education Bureau’s May 2013 Memorandum.)

In the United States, the No Child Left (NCLB) Act requires at least seven standardized tests: at the ends of grades 3 to 8 and at least once in grades 10–12. (See p. 1 of the U.S. Department of Education’s Standards and Assessments Peer Review Guidance.)

Stability of expectations. In the United States, education policy is often described in terms of “pendulum swings.” In some other countries, expectations change very slowly. For example, Singapore’s 2012 syllabuses say: “While there is a need to constantly review what students learn, the changes in content will not be the key lever. In fact, little has been changed in the content as this has stabilised over the years. Instead more focus has now been given to the skills and competencies that will make a better 21st-century learner” (see Primary Mathematics Teaching and Learning Syllabus, p. 6; Secondary Mathematics Syllabus, p. 6; Additional Mathematics Syllabus, p. 8). Compared with the U.S., there is often little new information to be communicated. This is illustrated in documents such as Singapore’s Changes in 2007 Syllabus (Primary 1 – Primary 4) which details differences between the 2001 and 2007 syllabuses in its two pages.  

Textbook development and approval process. Some countries have a multi-year textbook development and approval process that involves several interactions between the Ministry of Education and a textbook publisher. For example, the textbook development process is four years long in Japan (Yoshikawa, 2008, p. 16). Lewis and Tsuchida (1997) give examples of changes in elementary science textbooks that have occurred during this process. Korea has three different types of textbook development processes, each with several stages at which outcomes are reviewed by the Ministry of Education (Pang, 2008).

In contrast, federal or state monitoring of textbook development is not an official part of the textbook approval process in the United States. Instead, textbooks are developed, then approved (or not) by state or local boards. Reflecting this, the state approval process in California is six months long. (See Instructional Materials Adoption Process, 2012.)

References for appendix

Lewis, C., & Tsuchida, I. (1997). Planned educational change in Japan: The case of elementary science instruction. Journal of Education Policy, 12(5), 313–331,

Lewis, C., & Tsuchida, I. (1998). A lesson is like a swiftly flowing river. American Educator, 14–17, 50–52,

Pang, J. (2008). Design and implementation of Korean mathematics textbooks. In Z. Usiskin & E. Willmore (Eds.), Mathematics curriculum in Pacific Rim countries—China, Japan, Korea, and Singapore (pp. 95–125). Charlotte, NC: Information Age Publishing.

Soh, C. K. (2008). An overview of mathematics education in Singapore. In Z. Usiskin & E. Willmore (Eds.), Mathematics curriculum in Pacific Rim countries—China, Japan, Korea, and Singapore (pp. 23–36). Charlotte, NC: Information Age Publishing.

Yoshikawa, S. (2008). Education ministry perspectives on mathematics curriculum in Japan. In Z. Usiskin & E. Willmore (Eds.), Mathematics curriculum in Pacific Rim countries—China, Japan, Korea, and Singapore (pp. 9–22). Charlotte, NC: Information Age Publishing.


Written by CK

August 3, 2013 at 1:42 pm

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )


Connecting to %s