In the latest Quacquarelli Symonds (QS) World University Rankings by Subject (2014), NUS Math is ranked among the best mathematics departments in Asia.
Knowing and Teaching Elementary Mathematics: Teachers’ Understanding of Fundamental Mathematics in China and the United States (Studies in Mathematical Thinking and Learning Series)
Chinese students typically outperform U.S. students on international comparisons of mathematics competency. Paradoxically, Chinese teachers receive far less education than U.S. teachers–11 to 12 years of schooling versus 16 to 18 years of schooling.
Studies of U.S. teacher knowledge often document insufficient subject matter knowledge in mathematics. But, they give few examples of the knowledge teachers need to support teaching, particularly the kind of teaching demanded by recent reforms in mathematics education.
This book describes the nature and development of the “profound understanding of fundamental mathematics” that elementary teachers need to become accomplished mathematics teachers, and suggests why such teaching knowledge is much more common in China than the United States, despite the fact that Chinese teachers have less formal education than their U.S. counterparts.
Studying Mathematics is totally different from studying Humanities, this is the reason why humanities students often don’t do well in maths. But with the right studying techniques (i.e. practising doing mathematics), humanities students can be very good at maths. Together with their creativity and good memory, humanities students have the potential to achieve the top grades in maths exams.
I have taught Pure Literature students and found that they definitely have the potential to do well in Maths once they learn the correct method of mathematical studying and thinking, and how to approach solving Maths questions.
One of the top mathematical physicists, Edward Witten, majored in history and minored in linguistics! (http://en.wikipedia.org/wiki/Edward_Witten)
Mathematics is not a spectator sport
Even if you understand every word in lecture and in the textbook, the only way to really learn mathematics is by doing mathematics. Sometimes this means doing even more than the assigned problems. (See “time committment” above.) This is how to avoid the common pitfall of “understanding everything in class but blanking out on the exams.”
I realize this isn’t welcome advice, and I admit that I haven’t always followed it myself. But in years of teaching (and 20+ years of learning) mathematics I haven’t found any shortcut.
‘Above all, it is a cultural thing.” Professor Lianghuo Fan is reflecting on the differences he has noticed between maths education in China and Singapore, where he lived and taught for 40 years, and in Britain, where he is now based. “In China, all parents know that maths is the number one subject in schools, and they expect that in a modern society everyone must be comfortable with maths, even if that means they have to work hard at it.“That attitude is passed on to their children. But here in Britain, you can feel students’ attitude about mathematics is different. They feel all right if they say they don’t like mathematics.”
Professor Fan is not alone in highlighting this national phobia of ours about maths. The government has this week shown itself determined to tackle the problem head on with the unveiling of a new “back-to-basics” primary school maths curriculum, with a renewed emphasis on times-tables, mental arithmetic, fractions and rote learning.
Most people over 40 will see the proposals as a return to the classroom practice of their childhood – but in its introductory remarks the Department for Education claimed inspiration from Asian model that Professor Fan knows so well: “I never heard a child in China or Singapore say that they don’t like maths’,” he stresses, “without a sense of embarrassment.”
We are sitting in a café near Southampton University – where 50-year-old Professor Fan has been head of the Mathematics and Science Education Research Centre since 2010 – as we try to decide if anything lies behind the popular stereotype that Asian children are “naturally” better at maths than those in the West. It is, for example, in the core storyline of Safe, the recent Hollywood blockbuster, starring Jason Statham. An 11-year-old girl, Mei (played by Chinese-born actress Catherine Chan), is a maths prodigy who can decode number sequences at a glance – and therefore has to be protected from the baddies.
When you have mastered numbers, you will in fact no longer be reading numbers, any more than you read words when reading books. You will be reading meanings. (W. E. B. Du Bois)
When learning mathematics as an undergraduate student, there is often a heavy emphasis on grade averages, and on exams which often emphasize memorisation of techniques and theory than on actual conceptual understanding, or on either intellectual or intuitive thought. There are good reasons for this; there is a certain amount of theory and technique that must be practiced before one can really get anywhere in mathematics (much as there is a certain amount of drill required before one can play a musical instrument well). It doesn’t matter how much innate mathematical talent and intuition you have; if you are unable to, say, compute a multidimensional integral, manipulate matrix equations, understand abstract definitions, or correctly set up a proof by induction, then it is unlikely that you will be able to work effectively with higher mathematics.
However, as you transition to graduate school you will see that there is a higher level of learning (and more importantly, doing) mathematics, which requires more of your intellectual faculties than merely the ability to memorise and study, or to copy an existing argument or worked example. This often necessitates that one discards (or at least revises) many undergraduate study habits; there is a much greater need for self-motivated study and experimentation to advance your own understanding, than to simply focus on artificial benchmarks such as examinations.
Continue reading at http://terrytao.wordpress.com/career-advice/there%E2%80%99s-more-to-mathematics-than-grades-and-exams-and-methods/