What mathematics understanding means to Asians and to the West

The academic success in Mathematics of countries like China, Taiwan, Singapore, and Korea over the Western countries in general sparked some research a few years ago.  Interestingly, there was a general suspicion that Asian learners are only used to drilling and may not be engaging in a deep level of understanding, though some are still cautious in jumping to the conclusion.

Generally high achievement in Mathematics among the mentioned countries may be partially attributable to how they conceive “understanding mathematics” which might be described as getting the right answer through revising and working hard.  Such thinking enables them to continually practice and to identify the right rules and apply them correctly to arrive at the correct answer.  It is thinkable that when mathematics is regarded as a body of absolute truth and a set of rules for playing around with symbols, students will learn through memorization and problem solving becomes searching for appropriate rules by picking up clues from questions.

In contrast, the Western view of understanding mathematics “is a sudden process requiring insight rather than effort” (http://www.tandfonline.com/doi/pdf/10.1080/13632430050011407.  This can be seen at play when every time students in the West do arithmetic, they reach for the calculators and they tend to not memorize mathematical formulas.