Sunday, 18 January 2015

Using Computer to Teach Maths: Good or Bad? (Discussion)

The topic of using computer to teach mathematics is a controversial one. Yes, there are many benefits of using computers for calculation, but also some drawbacks.

Conrad Wolfram (in the above video) presents an excellent case of using computer to teach mathematics. This is really a good idea, to be honest. (The caveat is that Conrad is linked to the company Wolfram founded by his brother Stephen Wolfram. Wolfram is a computational math software company.)

Personally, I feel that once a student has mastered a skill to a certain degree, for example solving quadratic equations, there is no point making him/her solve quadratic equations ad infinitum over and over again. Using a computer/calculator that can solve quadratic equations is perfectly acceptable.
On a higher level, once a student knows how to compute eigenvalues/eigenvectors of a matrix, there is really little point in calculating eigenvalues by hand, which can be really tedious.

However, on the other hand, manual/mental calculation is an essential skill that is at the foundation of mathematics. Many mathematical theorems, no matter how abstract, have roots in calculation. To come up with a theorem, many mathematicians do extensive calculations to come up numerical evidence that a theorem is probably true, then try to prove it. Riemann came up with his famous Riemann Hypothesis after some calculation that the real part of the non-trivial zeroes of the Riemann Zeta function is always half. If you are interested in learning more about the Riemann Hypothesis, this book Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics is an excellent introduction to the subject for laymen.

Finally, manual calculation, despite being tedious and cumbersome, is also a skill. As a maths tutor over the years, I have seen some subtle changes in the average mental calculation skills of students after the calculator was permitted in Grade 5 (11 years old) in Singapore. Students who have memorized their time tables and used to mental calculation would have no problem telling what is 8x7, and what is 50-36.20, mentally. However, there are some students who are too used to calculators who may not be able (or willing) to calculate the above sums mentally. However, we must note that there are many great mathematicians who are poor at mental calculation. Grothendieck, one of the top mathematicians in the 1900s, once claimed that "57 is a prime number". As a result, 57 is known as a "Grothendieck prime".

What do you think about using computer to teach maths? Please write your comments below!

Also, check out this controversial book by Stephen Wolfram:
Although criticized by many for "pretending that he is the inventor of standard ideas and facts in computer science", there are some merits to this book. Galileo proclaimed that nature is written in the language of mathematics, but Wolfram would argue that it is written in the language of programs and, remarkably, simple ones at that. Sounds interesting...

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