Mathematics international curricula

Summary: Comparisons of mathematics curricula worldwide help facilitate growth and development.

A long history exists of comparisons between undergraduate mathematics curricula in other countries and the United States, and in recent decades, similar comparisons are being made at the primary and secondary levels. A recent movement in mathematics education has shifted the focus of how mathematics at all grade levels is taught. This movement was in large part spurred by the results of international testing. Since 1995, the Trends in International Mathematics and Science Study (TIMSS) has collected data on student achievement for fourth-, eighth-, and twelfth-grade students around the world.

The TIMSS was designed to allow for international comparisons, and has motivated educators to examine more closely those countries that consistently show success in educating students. Another international assessment, the Programme for International Student Assessment (PISA), focuses on measuring the mathematical literacy of 15-year-olds. The results of the PISA reflected those of the TIMSS, prompting educators in less successful nations to explore how some countries, such as Singapore, Japan, and Korea, educate students in mathematics. One area that has been explored as a result of the TIMSS and PISA is that of curricula. Liping Ma’s 1999 book Knowing and Teaching Elementary Mathematics, which compared teaching methods in the United States and China, has also spurred numerous discussions about curricula and teaching methods, including teacher education and preparedness of teachers for presenting mathematical concepts at all levels.

It is important, first of all, that a distinction be made between curriculum and instructional programs. “Curriculum” is generally defined as a set of standards or objectives that guides what is taught at a particular age or grade level. “Instructional programs,” on the other hand, are resources that are available to teach the curriculum, such as textbooks. On the international stage, a variety of instructional programs exist and are in use, but mathematics curricula across nations remain surprisingly similar.

An analysis of 16 countries’ curricula conducted by Graham Ruddock demonstrated that different nations used the same basic mathematical principles as a foundation for building mathematics curricula: number, algebra, geometry, measures, probability, and statistics. While some of the principles may be combined together into a single topic (for example, probability and statistics), these basic principles existed in the curricula of all nations that were studied. However, Ruddock pointed out that it is important to realize that just because nations use the same label, it does not mean that the content included in the principles is consistent across nations, nor does it mean that each nation explores each of the principles with equal rigor.

Nations also generally agree which principles of mathematics should be taught in the lower grades. Number is the primary focus for younger students, with a shift in focus toward algebra as students move into the middle grades. Nations vary widely in their mathematics curricula for upper grades, because of the nature of the different educational systems. For example, Japan uses an integrated approach to mathematics through the upper grades, where all principles are taught in varying degrees at all grade levels, while the United States utilizes a traditional division of mathematics topics (for example, algebra, geometry, calculus as separate courses).

Recent Pedagogical Changes

Interestingly, most nations at the beginning of the twenty-first century incorporate what is known as a “spiral curriculum,” which is designed so that students revisit topics that were previously learned. This form of curriculum represents a shift in thinking in mathematics education that occurred during the 1990s. The purpose of the spiral curriculum is to assist students in making connections between mathematical ideas as well as ensure that students retain the knowledge that has been previously taught. A well-designed spiral curriculum is designed to encourage students to view mathematics as an integrated whole, rather than as discrete, unrelated topics.

An additional pedagogical shift has come as mathematics educators consider the value of conceptual understanding versus procedural understanding. Curricula in various nations have been adapted to include a stronger focus on the conceptual understanding of mathematics, rather than rote memorization and mastery of basic math skills. For example, curricula in Japan, Korea, and Singapore, all of which have consistently performed well on the TIMSS and PISA, have shifted from the learning of basic skills through rote memorization to an emphasis on problem solving and critical thinking. Curricula in other nations have followed this example.

National Mathematics Curricula

Some nations, such as England, France, Italy, and Japan, have required national mathematics curricula. Other nations, such as the United States, Australia, Canada, and Germany, view education as a local responsibility; therefore, a national mathematics curriculum does not exist. However, organizations such as the National Council of Teachers of Mathematics have developed national standards as suggested guidelines for what mathematics should be taught at different grade levels.

The greatest difference between nations regarding curricula is that of implementation. Curricula implementation varies widely among different nations, with some nations, like Hungary and Spain, placing a focus on local implementation while Japan has national guidelines for how teachers are to implement the curricula into their classrooms. From this variety of approaches comes the question of intended versus enacted curriculum. In other words, are teachers implementing the mathematics curriculum as it was designed? While the intended curricula across nations appear to have some strong similarities, especially at the lower grades, the enacted curricula may be quite different, thus resulting in substantial differences in student learning.

In recent years, the Singapore mathematics curriculum has garnered a great deal of attention because of the impressive performance of Singapore students on the TIMSS. The Singapore curriculum focuses on developing concept mastery through an in-depth exploration of a few mathematical topics each year. Also emphasized are the use of visual strategies in problem solving and establishing connections between mathematical topics. The Singapore mathematics curriculum has undergone a variety of changes since it was first developed in 1981, with the latest version including the introduction of calculators at a younger age and a reduction in emphasis on mental mathematics. Several countries, including the United States and Canada, have begun to implement curricula that mirror the Singapore mathematics curricula in the hopes of acquiring similar levels of student achievement on national and international assessments.

The International Baccalaureate (IB) Programme has also gained in popularity in recent years. The IB is designed to be a broad-based international curriculum, and is offered at three different levels: the Primary Years Programme (PYP), the Middle Years Programme (MYP), and the Diploma Programme (DP). While the IB does not focus specifically on mathematics, all three levels include mathematics as an integral part of the IB experience, as “mathematics is a universal language with diverse applications.” Mathematics in the IB is viewed as a key connection to students’ understanding of culture and history, and as a primary method of developing students’ logic and critical thinking skills.

Since World War II, a growing number of foreign-educated students in mathematics and other related fields have chosen to attend graduate school or seek postdoctoral positions at American universities, with the largest growth occurring in the 1990s. For example, studies show that in 2002, nearly one-third of all graduate students enrolled at U.S. universities came from abroad. Many reasons are cited for this effect, including the quality of research universities, the availability of funding, and the existence of desirable job opportunities. A phenomenon colloquially known as “brain drain” reflects the significant migration of students with mathematical and technical skills away from their native countries, diminishing these countries’ ability to compete in the global marketplace. In response, countries are beginning to expand their efforts to retain these students. For example, China has reorganized some current universities and built new ones, as well as engaged in significant curriculum reform. This reform includes new partnerships, such as a new Danish-Chinese University Centre for collaborative technology research, which was formalized in 2010.

Bibliography

Committee on Policy Implications of International Graduate Students and Postdoctoral Scholars in the United States. “Policy Implications of International Graduate Students and Postdoctoral Scholars in the United States.” Washington, DC: The National Academies Press, 2005.

International Baccalaureate. “Academic Programmes.” http://www.ibo.org/general/what.cfm.

Ma, Liping. Knowing and Teaching Elementary Mathematics. Mahwah, NJ: Lawrence Erlbaum Associates, 1999.

Mansfield, C. S., N. A. Pateman, and N. Bednarz. Mathematics for Tomorrow’s Young Children: International Perspectives on Curriculum. Berlin: Springer, 2010.

National Center for Education Statistics. “Program for International Student Assessment (PISA).” http://nces.ed.gov/surveys/pisa.

National Center for Education Statistics. “Trends in International Mathematics and Science Study (TIMSS).” http://nces.ed.gov/timss.

Ruddock, G. “Mathematics in the School Curriculum: an International Perspective.” http://inca.org.uk/pdf/maths‗no‗intro‗98.pdf.

“The Singapore Math Story.” http://www.singaporemath.com/Singapore‗*‗Story‗s/10.htm.