The current evidence clearly relates better maths results for students to a country’s higher GDP and incomes. Thus a key question relates to the best way to teach maths (or ‘math’ as our North American cousins refer to it). Further to this, a vital question is how to relate success in maths to success in your engineering job. Especially from a creative and innovation point of view. As we all know, creativity is highly prized in the world today (whether it be Bruce Springsteen, the Beatles, Bill Gates or Steve Jobs).
Mathematics is the language of engineering and science. The better skill one has of a language, the better one is able to express one’s thoughts and understand those of others.
However, it all good and well to turn out highly technically proficient maths robots from school and college but if you cannot solve problems or be innovative and creative you are not going to go far in your engineering job. For example, problem solving a tricky installation problem for your control system or designing the next programmable logic controller, iPhone or Google search engine.
The world schooling system is now driven to produce high quality maths graduates; but sadly this is not the only ingredient required to make them successful as an electrician, technician or electrical engineer.
Achieving outstanding results in your maths examinations at school does not translate into becoming a successful engineering entrepreneur where creativity and innovation are the keys to success. Importantly, in life and business, the single perfect answer prompted by maths is generally not the same as the questions posed in life and business. It is a much more ambiguous world with many potential answers.
New Technology is the Key to Success in Maths
A third of pupils tested in Shanghai (one of the top locations for the maths tables) where classical maths learning techniques such as drill and memorisation of formulae are key, show that they generally manage to successfully work with innovative, ambiguous and difficult problems (compared to a tiny 2% in North America and Europe).
But I honestly believe new technology renders much of the old rote learning of maths redundant. There is no doubt that it is important to learn how to do long hand division by hand but then to use a calculator to execute most of the work thereafter. Old fashioned methods such as long hand division are useful to understand but should not be the focus.
An intuitive feeling of the integrity of the results from a software program or calculator are critical; but one should then let the calculator do the mind numbingly grind work of a statistical calculation or least squares fitting of a graph.
It is also important to remember the key formulae but then to be able to access more complex variations on your tablet or calculator. It is also important to think logically and to be meticulous about assessment of a particular problem. After all, there is a massive difference between a solution to a power problem indicating that you need to size your generator to provide 300kW and not 420kW of power with 20% spare capacity. Simply being able to use a tablet without a deep understanding of how the underlying maths works is a recipe for a superficial approach and many mistakes.
Visualization is Also Fabulous
One of the most marvellous things of computing technology is the ability to allow one to visualize the result of a mathematical equation. One only needs to look at Maxwell’s equations which are extremely clever and link the world of electricity to electric and magnetic fields and then to see them actually displayed in graphical format which is so much easier to understand. This level of graphics and visualization was difficult to achieve a few decades ago and would help the learning experience.
A Faulty Premise
I thus do think though that the current debate between rote learning and use of calculators or tablets is missing something vital - most of these approaches to reform maths education are doomed to fail whatever way you go.
Students do need to be proficient in applying maths to real world (engineering) problems; be able to perform problem solving with finesse and to be creative and innovative. This is simply not happening in our education system.
Perhaps, the reason for the drive to reform maths education is that the people who are making decisions have absolutely no understanding of engineering or the industrial world as they are lawyers, accountants or in business. I would doubt the current president of the US could even perform a simple calculus exercise let alone understand the application of maths to the engineering world. Hence, if there were a few more mathematically literate people who have worked as tradesmen, technicians or engineers making decisions in the political world, we would have far more sensible decisions being made about more applied maths education.
Most Engineering Professionals do not need Advanced Maths to be successful
We undoubtedly need maths geeks – who drill down in exquisite detail into maths and spend all their entire careers researching exotic themes in maths. Similarly for those of us who are in dedicated R &D doing some exotic design of a spectrum analyser needing to make some tweaks to a Fast Fourier algorithm to apply it to a new computer processor.
However, it is questionable whether most of us in the engineering world need two or three intensive years of mathematics at college. Learning about exotic complex integrals or doing advanced calculus has limited value for most engineering professionals – whether you are an engineer or electrician. It would be better to use this time to teach the application of maths to problem solving and innovation in engineering.
A Challenge with our High School Teachers
One other problem with our teachers (even with the great ones) is that while they are probably outstanding (and indeed, passionate) at maths teaching, they have great difficulty in putting it all into a real world context. In other words, how you can apply maths to an engineering situation.
OK – I do understand that our high school (and indeed, college) teachers are unlikely to be familiar about the engineering world but it would be worthwhile them gaining some appreciation of the technology world and thus to change the requirements of the maths syllabus to be focussed on applications, problem solving, creativity and innovation particularly in the engineering world.
Thanks to The Economist (and especially the comments) for an interesting discussion on this vexed topic.
Most importantly, as Bill Beattie points out: The aim of education should be to teach us rather how to think, than what to think - rather to improve our minds, so as to enable us to think for ourselves, than to load the memory with thoughts of other men.
Yours in engineering learning,