Mathematics of Eastern Asia
The "Mathematics of Eastern Asia" refers to the diverse mathematical traditions and educational practices observed in the culturally rich and populous region of Eastern Asia, which includes countries such as China, Japan, South Korea, Mongolia, North Korea, Hong Kong, Macau, and Taiwan. While the region shares influences from the Chinese cultural sphere, it is characterized by distinct educational philosophies and systems. In many Eastern Asian countries, mathematics education adheres to a Confucian model that emphasizes memorization, repetition, and teacher-led instruction, often resulting in high performance in standardized tests, such as the International Mathematical Olympiad. The region employs a decimal number system with unique linguistic structures that facilitate understanding place value among students, alongside traditional tools like the abacus.
In recent years, there has been a shift towards incorporating problem-solving and practical applications into the curriculum, particularly in response to identified weaknesses in creative mathematical thinking. While traditional methods remain prevalent, countries like Hong Kong and Taiwan are adapting their educational approaches to better engage students beyond rote learning. Notable achievements in mathematics, such as the recognition of individuals through prestigious awards like the Fields Medal and the Wolf Prize, highlight the region's contributions to the global mathematical community. Overall, the mathematics of Eastern Asia presents a complex interplay of historical traditions, cultural influences, and evolving educational practices.
Mathematics of Eastern Asia
Summary: Across eastern Asia, mathematics education is given a high priority, with the goal of continuing the region’s tradition of excellence.
Eastern Asia is one of the most populated regions of the world, lagging behind only southern Asia, and includes the Chinese cultural sphere once called the “Far eastern civilizations”: China, Hong Kong, Macau, Taiwan, Japan, Mongolia, North Korea, and South Korea. The region is by no means homogeneous but has certainly been influenced to varying degrees by China in its writing systems, its cuisine, its architecture, and its religion. These influences are principally historical, cultural exchange being less centralized now, and influences like the Western world and the Soviet Union (in the case of Mongolia and North Korea) having been significant in the recent past. The technology sector is important in much of this region and mathematics education is a priority. Mathematics education in most of east Asia follows the Confucian model.
Number System
The number system in all Chinese-based east Asian languages centers on the same decimal system as the West but with stricter adherence to simple place-value patterns. For example, employing literal translations, the word for the number 12 is ten-two, 20 is two-ten, 37 is three-ten, seven, and 533 is five-hundred, three-ten, three. This system, along with the use of an abacus, facilitates the understanding of place value among east Asian elementary students. east Asian countries also follow the Chinese myriad-grouping system, which groups large numbers by ten thousands, rather than thousands. In other words, these languages have single words for the numbers “ten thousand” and “one-hundred million,” but not for “million” or “billion.”
Educational Philosophy
Historically, public east Asian mathematics classrooms could be generalized as teachers delivering lectures to large classes of students who are expected to master calculations and grasp theory through repetition and memorization. Inherent in this Confucian approach is the assumption among students, parents, and teachers that mathematical success results more from diligent studying than natural talent. Student-centric and practical applications of mathematics are not a primary focus in east Asia, as they sometimes are in the West. This educational philosophy is true not only of the textbooks, which in east Asia are succinct and cover the minimal core set forth by each of the national governments but also of the classrooms, which must closely follow the textbooks. However, since the international test results illuminated relative weaknesses in problem solving, creativity, and practical applications, the east Asian governments have been working to adapt curricula in various ways.
China
Chinese children’s task of memorizing thousands of Chinese characters naturally seems to transfer to the subject of mathematics where memorization of formulas and processes is assumed to lead to understanding and discovery.
While mainland China did not participate in some international comparisons, the Chinese team has performed exceptionally well in the annual International Mathematical Olympiad (IMO), a competition among high school students, where it placed first almost every year between 1990 and 2010. But these achievements in mathematics are not limited to Chinese students; two Chinese mathematicians have received the distinguished Wolf Prize in Mathematics: Shiing-Shen Chern in 1983–1984 and Shing-Tung Yau in 2010.
Hong Kong
The mathematics education system in Hong Kong employs elements both from mainland China and Great Britain. Despite the fact that international test scores ranked students from Hong Kong as years ahead of many Western countries, there is widespread concern about students viewing mathematics as irrelevant beyond testing. This concern has been leading to a curriculum that emulates the Western approach to teaching more mathematics related to problem solving and practical abilities.
Japan
While Japan distinguished itself in mathematics from the other east Asian countries during the Edo period (1603–1868), modern Japanese mathematics carries few remnants of this period. One such remnant is the soroban, a Japanese modification of an abacus. Japanese schoolchildren continue to use this beaded calculation device as a means of mastering the decimal system. Like in all east Asian countries, private schools (called juku) are attended widely by Japanese students. Japan has produced some of Asia’s best mathematicians of the past century, including three winners of the Wolf Prize (Kunihiko Kodaira in 1984–1985, Kiyoshi Ito in 1987, and Mikio Sato in 2002–2003), and three winners of mathematics’ most revered award, the Fields Medal (Kunihiko Kodaira in 1954, Heisuke Hironaka in 1970, and Shigefumi Mori in 1990).
Mongolia
Geographically, Mongolia lies between China and Russia. Until the early twentieth century, it was largely under the control of China and was later strongly influenced by Russia and the Soviet Union, adopting a Soviet-style government until 1990. Mongolian teams began participating in the International Mathematical Olympiad in 1964. Ming Antu was a Mongolian mathematician and astronomer, though he has been referred to as Chinese in the past. He worked on infinite series in the eighteenth century, among other accomplishments.
North Korea
While North Korea has the same Confucian background as the other east Asian countries, the former Soviet Union played a significant role in sculpting the modern approach to mathematics education. As do most countries around the world, the North Korean education system upholds mathematics as a central focus for both primary and secondary students, although North Korean story problems tend to be phrased in a nationalistic context. Students who excel in mathematics during their secondary school education may be admitted into the esteemed Kim Il-Sung University. In terms of global rankings, North Korea has sporadically entered a team into the International Mathematics Olympiad, some of which placed in the top 10.
South Korea
From childhood, South Koreans grow up using two separate number systems in their daily lives. The first one, a purely Korean system, is used mainly for counting objects, animals, and people and is no longer used for numbers larger than 99. It is worth noting that the numerals in this Korean system do not follow the same simple place-holding constructions as the number systems rooted in the Chinese language. The Sino-Korean number system, on the other hand, does follow these rules, and is most commonly used with money and large numbers. In school, many South Korean students receive just as much, if not more, of their mathematics instruction from private tutors or hagwons (academies) as from the public school environment. This system stems from the inextricable link between a student’s mathematics performance on entrance exams and his or her eventual place in society. Some people cite this pressure as an explanation for why South Korean and Japanese students, despite performing exceptionally well on international tests, also rank the highest in their professed dislike for mathematics.
Taiwan
Private mathematics academies in Taiwan are referred to as buxiban (cram schools), suggesting their primary, but not exclusive, role of preparing Taiwanese students for entrance examinations. With electronics as a major industry, there has been a recent overhaul of the Taiwanese education system to focus on practical applications of mathematics instead of only theoretical mathematics.
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