mathwizz.com

A article appeared on the front page of The Globe and Mail, a nationally distributed newspaper in Canada on March 20, 2001. It was written by Anne McIlroy, a science reporter with the paper. The title was "Asians' practice of math equates to higher scores". The article addressed the question of why it is that Asians consistently outperform non-Asians in math.

The article highlighted a study to be published in an edition of the Journal of Experimental Psychology: General, conducted by Dr. Jamie Campbell, a psychologist at the University of Saskatchewan. The study tested the basic math skills of 72 university students divided into 3 groups: students educated in China, Canadian students of Chinese origin and non-Asian Canadian students.

In the first part of the study, the students were asked to do basic arithmetic in their head, stuff like 14 divided by 2, 3 times 7, 8 plus 9. The non-Asians were about 25% slower than the Asians. The reason? The Asians had the answers memorized. On average, the 2 Asian groups used their memory to recall the answer 85% of the time, compared to 70% for the non-Asians. For example, if the question was "What is 6 + 7?", a strategy used by some was to recall that 6 + 6 = 12 and then add 1 to come up with 13, rather than just remember that 6 + 7 = 13.

The next part of the study were multi-step questions such as 3 + 12 + 13. In this part, the students educated in China had 58% more correct answers than the non-Asian students, while Canadian students of Asian origin had 19% more correct answers than their non-Asian Canadian counterparts.

At the end of the day, Dr. Campbell's study found that the Asian students did better on the more complicated math test because they relied more on their memory. It was noted that these students did not use calculators in their elementary or secondary school education before coming to university in Canada, unlike their Canadian counterparts.

Speaking from personal experience as a math tutor, I would have to agree with the results of Dr. Campbell's experiment. More often than not, I have found that students who are firmly grounded in the basics can free up their mind to concentrate on the more difficult aspects of a problem. The more time a student has to spend on calculating basic math, the less time there is to devote to more complicated matters. This is particularly important in writing tests where students are always pressed for time.

What are the basics a student should know? Here is my suggested list:
elementary: basic add/subtract/multiply/divide.
middle: the above operations with integers and decimals. For example, a student should know that -1-(-2) = -1+2 = 1 or that (-3)(-5) = 15. Depending on when they learn it, basic formula knowledge for basic geometric shapes should be second nature, such as the formula for the area of a rectangle or circumference of a circle. As well, knowing how to add, subtract, multiply and divide fractions should be required knowledge.
high: Depending on when they learn it, they should know the basic facts of whatever discipline they are learning. For example, if the students are learning trigonometry, they should know that the sine of 30^o is 0.5.

mathwizz.com has a few sections devoted to helping students learn the basics. The site is divided into these basic categories:
Arithmetic
Fractions
Integers
Decimals
Algebra
Geometry
as well as statistics and imperial/metric conversion. Each basic category has help pages to help students learn the basics as well as interactive pages to allow students to hone their basic skills. You are invited to peruse the sections at your leisure.