Real-World Calculations
The employers' lobby group VECCI has announced that current graduates have poor mathematical skills, on the basis of their competence with manual and mental arithmetic (The Age, 2/5). In my experience as a professional engineer, all significant calculations must be done with increasingly complex software packages, often of incredible sophistication. While there will always be a place in engineering for "the back of the envelope", mastery of these commercial-grade systems is where the "real world" is at - not long division by hand.
VECCI must know this, so why is it pushing this barrow? Perhaps it has an old-fashioned view of what it means to be educated - good at toting up figures, able to recite a Wordsworth poem and knowing the coronation dates of key English monarchs. We need creative and innovative engineers, not good clerks.
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4 Comments:
You're spot-on about the relevance of these high-end packages and the need for scientists and engineers to be skilled with them.
I think you're underestimating the importance of being good at the "back of the envelope" stuff. For example, someone who can't calculate standard deviation by hand can only be dangerous to whatever task they apply software that calculates it for them.
Not every software tool or math technique needs to be studied from the bottom up to be useful of course, but basic arithmetic had better be second nature to any practicing engineer, if only to assist their intuition.
To my mind, competence with the "back of the envelope" stuff is useful as an indicator of certain other qualities: solid grounding in theory, quickness of wit, mental agility, frequent and/or recent practice with numbers.
It's similar to the relationship between professional footballers and chin-ups. I expect they can all do quite a few and the selectors would no doubt be impressed by the guy that can do 50 without breaking a sweat.
So it's probably useful at a crude level for sifting the men from the boys but it's no criteria for judging whether or not they get on the field that day. Chin-ups are an artificial test of football prowess.
Re: calculating standard deviations by hand. Here's a little anecdote I heard from a former mentor in the corporate world. Once he had a meeting with some Very Senior Executives considering a vendor bid (capacity planning for voice traffic). In the middle of the meeting, he grabbed a piece of paper and worked out the Quality of Service (blocking probability) of the vendor's proposal using some basic queueing theory to show that they were way off the mark. Said Big Wigs were blown away and he gained enormous esteem for this. Hence, this is one time where calculating the standard deviation by hand turned out to be useful!
(NB: Since the Poisson distribution that arises in markovian queues has equal mean and variance, and any distribution can be approximated as Gaussian thanks to the Central Limit Theorem, working out the 99.5th percentile as 3sd above the mean involves only a single square root. Still - he had to know that he could make that approximation ... probably because he has a PhD in that kind of thing.)
Staying with your chin-up analogy for a moment, if a coach finds that his team's average chin-up ability has dropped 25% from the previous season, it is definitely a cause for concern. No doubt a player's innate ability can (and sometimes does) make up for a lack of basic fitness, but fitness as an indicator of a systemic problem is pretty good.
In my experience of white-collar work, it is not necessary to be able to work out complex calculations by hand, but getting millions and billions mixed up in a meeting is very bad form (and it happens!)
I think that being able to work out simple arithmatic in your head (eg: percentages, multiplications, divisions)is very useful as a litmus test for determining whether a particular statement is plausible, and hence very useful in a professional setting.
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