China has a long history of being at the forefront of many technological advances including mathematical ones. Chinese primary and secondary school students are seemingly unsurpassable in their mathematics results according to many world rankings and indexes but China’s role in further extending the field at those crucial boundaries of innovation and mathematical breakthrough has been less pronounced. China has not yet had a Fields medal winner, mathematics’ version of the Nobel Prize that is awarded every four years, unless you count Chinese-American Shing Tung-Yau (1982) or the Australian-born Chinese prodigy Terence Tao (2006). Historians would argue that China got left behind the west in terms of mathematical innovation even before their technological peak at the height of the Ming dynasty (see the extensive writings of Joseph Needham on this topic). So why is there a seeming contradiction given the importance placed on maths in Chinese schools and achievements in world benchmarking exercises such as Programme for International Student Assessment (PISA) where Shanghai had the highest achievement in maths (the programme covered 12 of China’s 32 provinces)? We posed these questions to some of our staff including Mr. Simon Lewis, who read Mathematics at Cambridge University, and teaches the subject to over 300 local Chinese students at the Dulwich College High School Programme in Suzhou; Mr. Jonathan Taylor, Director of our Dulwich College High School Programme in Zhuhai; and Dr. Zhang Xiaolu and Dr. Peter Le Masurier based at the Dulwich College International’s office in Shanghai. Simon Lewis and some Chinese mathematics history “In the 11th Century and leading up to the 13th century AD – the Song Dynasty – China was very much at the forefront of Mathematics. The Chinese Remainder Theorem was developed then by Qin Jiu Shao, who was considered as great a mathematician of that age as Newton in the 17th century. For just over a thousand years until their abolition in 1905 progression in Chinese society was dependent on passing the Chinese Imperial Examinations, and entering into Civil Administration. This is described in the book Mission to China: Matteo Ricci and the Jesuit Encounter with the East by Mary Laven (2012). These examinations, taken by students across China, consisted of writing formal philosophical and literary arguments and required extensive training and the memorising of large amounts of text. There was very little mathematical content. The career mathematician was not respected in China and it was an unpopular career path. Laven (and others) posit that as a consequence mathematics was held in relatively low esteem in China. Of course, another contributing factor is that the first modern university in China that challenged the traditional education model was not founded until the end of the 19 century; what is now known as Peking University or Beida. In contrast, mathematics had a long tradition of being held in high esteem in Western Europe ever since the foundation of the Great Library of Alexander the Great in Alexandria in 300 BC. With the boom in trade and development of navigation in the Middle Ages (which in turn required an understanding of how the solar system worked; remembering that the discovery of Australia and New Zealand was in some ways the by-product of a voyage to observe the transit of Venus across the sun) there were even more demands for everyday applications of mathematics. Isaac Newton was not only Professor of Mathematics at Cambridge but also Master of the Royal Mint. Maths was employed in those times to detect the highly profitable activity of coin-forging. Pure maths also was prestigious; universities in Italy in the 16th century held contests to solve cubic equations which guaranteed the winner the sort of fame reserved today for winners of the X factor (Editor – well that is a “fame” of some kind I guess). China’s renown in modern mathematics history is much more recent and probably of a lower profile than their forebears. Some examples include the founder of differential geometry Shiing-Shen Chern (1911-2004), whose doctoral student was Shing-Tung Yau, won the Field’s medal in 1982. The 2006 Fields Medal winner, the Australian-born Terence Tao, is also of Chinese heritage. Terence Tao’s father was born and grew up in Shanghai before migrating to Australia and he is the youngest person to be awarded tenure at UCLA at the ripe old age of 24.
Yang Hui triangle (Pascal's triangle) using rod numerals, as depicted in a publication of Zhu Shijie in 1303 AD. It was used to generate binomial coefficients. Are Chinese students the best mathematics students in the world? Simon Lewis: China has won the International Olympiad 11 times since 1992, compared to Russia and America (2 wins each). China, well Shanghai as only their results were made public, also topped the reading, mathematics, and science categories of the OECD’s Programme for International Student Assessment (PISA) in 2009. What about China’s involvement research and advancing mathematics in new areas? Simon Lewis: Interestingly, although solving the Poincaré Conjecture in 2006 was accomplished by the Russian mathematician Perelman, two of the three groups who contributed to the solution were Chinese. The group consisting of Huai-Dong Cao and Xi-Ping Zhu was led by the aforementioned Fields Medal Winner Shing-Tung Yau. Are Chinese students naturally gifted for mathematics? Or are they more focused on mathematics from a young age? Simon Lewis: This last statement is more true. There are many anecdotal reasons for this. Chinese families pay a lot of attention to mathematics, because it is one of the three most important courses at school; Chinese language, English and mathematics. All other courses are supplementary. These are compulsory courses. Of course, the one child policy has had the effect of focussing the hopes of families on one child, and school performance is highly competitive. At the weekend, many Chinese students attend English and/or mathematics training courses. Education Professor Yong Zhao noted that the PISA 2009 did not receive much attention in the Chinese media, and that the high scores in China are due to excessive workload and testing, adding that it's "no news that the Chinese education system is excellent in preparing outstanding test takers, just like other education systems within the Confucian cultural circle: Singapore, Korea, Japan, and Hong Kong." (see www.zhaolearning.com; December 2010) Dr Zhang Xiaolu: As a mother of an 11 year old daughter going to primary school in Shanghai I would agree with the statements that in China educationalists pay a lot of attention to students preparing for examinations and getting good grades. This is largely because the Chinese education system is geared towards examinations as gateways to the next stage in life, good junior school results help you get in to good junior high schools, good junior school grades get you in to the better high schools and so on. Taking my 11 year old, (Year 6) daughter as an example she goes to school a bit after 7am and is home at around 6pm; she would have around 3 hours of homework per school evening, 2 hours of which is devoted to maths. There is definitely a difference between Chinese and western cultures in the teaching of maths. For example Chinese maths teachers often spend their whole lunch hour working with their students on the problems that got incorrect the evening before. Students would line up with their corrected homework and then go through what questions they got wrong with their teachers who would explain to them where they went wrong. So the Chinese teacher devotes a lot of time and energy to making sure their students are thoroughly prepared for the examinations. Though, of course, timetables and teacher workloads may vary quite a lot between Chinese schools and other countries. My daughter is only 11 but her mathematics teacher is already preparing them for their zhong kao exams which are at least 2 to 3 years away. I think a big difference between the western and Chinese approach to learning mathematics is that in China we simply devote a lot more time to learning how to solve problems from the text book; that is developing skills and experience in methods until it is known off by heart. I should note here that we help Chinese high school students applying to do maths or similar courses at foreign Universities by giving them a lot of resources that explain the history and philosophy of mathematics. This appreciation of mathematics and developing a passion for mathematics is where their Chinese curriculum maybe lacking. Jonathan Taylor: I think there is still a major issue with translating Chinese mathematics ‘learning’ into creative solutions. I took two of our best students for lunch with an Old Alleynian (OA) who studied Engineering at Oxford and despite the fact they are A* Maths students they were simply unable to produce solutions to problems that weren’t framed as exam type questions. Dr Peter Le Masurier: It would be interesting to compare the number of hours Chinese students spend on maths during their life compared to international students. I believe this will give a very simple answer as to why they are also held up as being better at maths. Jonathan Taylor: I agree with Peter. I also believe however that the Chinese emphasis on rote learning translates better into subjects like mathematics than it does in say, social sciences. Creative problem solving remains an issue for our best mathematicians. Does China’s language and language structure suit mathematics teaching better than say English? Simon Lewis: This is the thesis of Outliers by Malcolm Gladwell. Certainly this may be true of the early counting of a child but beyond this the language gives no advantage. Without a calculator the Chinese language helps students get introduced to [the concepts of] addition and subtraction very quickly. Perhaps a better reason for the success of Chinese schoolchildren is the better training of mathematics teachers, especially in Primary and Middle School which all have specialist mathematics teachers. In addition Chinese students spend more hours doing mathematics than UK and American students and at Middle School are expected to complete mathematics homework every evening for the next day. So, they are perhaps more formally taught and, spend more hours doing Maths, and are expected to complete more work [than their western counterparts]. So what does the future of mathematics hold – where is the field going? How have curricula changed, if at all? Peter Le Masurier: Some, such as Harvard Professor O. E Wilson, would argue that despite a widely held perception of needing high level mathematics qualifications, you do not really need advanced mathematics to succeed in the field of science. Wilson suggests that mathematics is a useful tool but that solid, innovative science really requires creativity to advance thinking on a particular problem. In Wilson’s recent article “Great Scientist ≠ Good at Math” he states provides examples of great scientific thinkers like Darwin as examples of great scientists who were not strong at mathematics. You could argue the toss ad infinitum (that did send people like the German mathematician Georg Cantor a little mad) but there is no doubting that mathematics remains as important as ever. China has addressed many issues in its delivery of mathematics curriculum in recent years, as evidenced by the OECD report on their PISA 2009 results. That report described Shanghai as a pioneer of educational reform, noting that "there has been a sea change in pedagogy". The OECD point out that Shanghai’s education establishment: "abandoned their focus on educating a small elite, and instead worked to construct a more inclusive system. They also significantly increased teacher pay and training, reducing the emphasis on rote learning and focusing classroom activities on problem solving." (OECD PISA Report, 2010). There is no doubt the Chinese government and educators are listening and changing their pedagogy methods. The Fields Medal will be awarded in Seoul next year to another batch of four brilliant mathematical minds. The Chinese flag may or may not be waving next year but the trend and increasing internationalisation of China would suggest that this is not far away. Chinese Remainder Theorem.