A free report from 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
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
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
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
30o is 0.5.
mathwizz.com has a few sections devoted to helping students learn the
basics. The site is divided into these basic categories:
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.