“The science and technology of the 21st century (and beyond) will be about the manipulation, handling, analysis and interpretation of physical and computational data. No-one doubts those with strong mathematical and analytical skills are going to command a premium in economies of the future. The skills we teach in higher level mathematics are to analyse, synthesise, abstract, induce, deduce, generalise, specialise and observe analogies. Future economies are going to become more and more reliant on educated populaces with these skills.
But to gain these skills one simply must have a good handle on basic mathematics. One should never confuse knowing about something with knowing the thing itself. Broad principles and higher level discussions may give a glimpse into what mathematics is about, but absolutely useless when it comes to the doing. And it is the doing which is important. For millennia, craftsmen have been aware of this. You build on skills, and you reinforce these skills by doing things over and over again. The same is true of mathematics. This is not “rote learning”, this is building “muscle memory” but within the mind.
The Finnish have a saying, “Tyvestä puuhun noustaan”, and it means “a tree is climbed from its base”. This underpins their educational system, widely regarded as the best in the world. You have to have the basic skills before you can “reach for the apples on the branches”. Actually, this analogy goes further. You might get to pick a few low hanging fruit but you’ll never get the best fruit unless you can climb. Some-one who can climb is always going to be better off.
Over literally millennia, we have built a strong and effective methodology to impart these basic skills – column addition, long division, times tables, basic geometry. Modern tricks that are mentioned as alternatives to building these basic skills have actually been known for millennia also – and rejected. I understand why educationalists want to try new things, and they should. But we tinker with the basics at our own and society’s peril. Further, it is now clear that many of the new teaching methods adopted in lower level mathematics are not aligned with what cognitive science tells us about the brain (our limitations on working memory) and how learning happens (the need for extensive practice to gain mastery in just about anything).
Get the basics right, and the rest will follow.”
Professor Gaven Martin
July 2013
Gaven Martin, FRSNZ, is a New Zealander and a Distinguished Professor of Mathematics and Director of the New Zealand Institute for Advanced Study at Massey University (Albany).
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