Tuesday, April 13, 2004

The Challenge of Teaching Mathematics

The Challenge of Teaching Mathematics

My teaching experience is limited to an undergraduate course in information systems which I had the opportunity to conduct at a university in Jakarta. Even though the course was a simple one, I realised that the challenge in teaching the subject was making the students see the real-life relevance of some of the concepts taught.

Most of the students were familiar with computers and the Internet; they probably spent more hours on the Net than me, but yet they struggled to understand relatively basic enterprise computing concepts such as ERP, data warehousing or even client-server computing. This is because they did not have the experience of working in an enterprise and see how IT is applied in a business organization.

The challenge for me was to illustrate these concepts to them using clear examples in a jargon-free language which they could understand. A professor at the university once told us that we are all "analog" creatures--an analogy often help us to understand a concept better. Analogies that are close to the students' hearts also have a greater impact.

Example: What is the function of a crystal clock in a computer system? If you tell them that clocks help to synchronize the various electronic events that occur in the circuit system, it will definitely draw blank looks on their faces. You must remind yourself that you are talking to teenagers who frequent discotheques: So the computer system is like a pop band, and the clock is the drummer; all the parts in a computer are members of the band who perform according to a common rhythm set by the drummer. And computer applications are like the different types of music or songs that the band plays.

The challenge in teaching is to come up with good examples and analogies to help explain difficult concepts. For a practical course like information systems, it is not too difficult. But for subjects as "dry" as mathematics, it could be an uphill task. Which is why if I were to get an opportunity to teach again, I'd definitely want to attempt to teach mathematics.

Most students--except for a particular category of them which we normally refer to as geeks or nerds--are turned off by mathematics. It is dull and its concepts seem to have no relevance to the real world. Mathematics, especially pure mathematics, is full of weird-looking Greek symbols with lots of laboriously rigid rules for their manipulation. Why do we need to study for instance, the properties of a parabola? Why in the world would we want to learn set theory which seems like common-sense anyway? And why do want to struggle to manipulate "imaginary numbers", and bend our minds trying to picture what the square root of negative one is like?

It all seems very irrelevant to the world of people and emotions. Perhaps it is unfortunate that the approach to the teaching of mathematics has traditionally been rather dull and uninspiring--it is in actual fact a very intriguing subject. There's even adventure and excitement in mathematics: Those who have read Simon Singh's book describing how mathematics professor Andrew Wiles figured out a solution to Fermat's Last Theorem which for 350 years was thought unsolvable, would understand the exhiliration of mathematics.

And mathematics do have relevance to the world in which we live in. All the technological marvels that we see around us would not have been possible if say Newton and Leibniz had not invented the mathematics of calculus. I won't be typing these words on a Pentium notebook if the solid-state transistor was not invented; the behaviour of a modern transistor is based on the properties of the p-n junction which at the very fundamental level could only be understood using quantum mechanics, which requires a mastery of probability theory, wave theory and differential equations.

The study of mathematics is certainly not dull. The intellectual rapture one feels in comprehending the concepts of mathematics is not unlike the emotional ecstasy experienced by someone who listens to Beethoven's 9th Symphony . It is a great pity indeed if huge number students are turned off by mathematics just because generations of teachers have failed to convey the sheer grandeur, magnificence and excitement of this wonderful and important subject.

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