“It is so refreshing to hear someone talking sensibly about the learning of basic arithmetic. I agree 100% with everything Audrey Tan says, not least her point that column addition is an easy and reliable way to add. Its structure is adapted to the way we write numbers. We have this wonderful decimal system which took tens of thousands of years to bring to perfection and to not take advantage of it for basic operations is nothing short of folly! Would one try to teach addition and multiplication using roman numerals? Not a chance.
One must understand that all of mathematics, beyond the ability to recognise fairly small numbers of objects, has been invented over a period of probably hundreds of thousands of years. The column-based techniques of calculation thus produced are highly refined and optimised. They should be celebrated! Trying to improve understanding by looking at different, almost certainly inferior, techniques is an unproductive waste of time.
As one who has been learning mathematics nonstop for the last 60 years, I can say that learning a topic never begins with broad general principles. Rather, you learn by much practice which builds familiarity and confidence. If that means a certain amount of repetition, so be it. Would anyone attempt to learn how to play the piano without practice? I don’t think so. For one who has mastered a technique, it is an easy trap to fall into to think that one’s own understanding can be imparted with a few quick strokes of the brush. Those strokes may be all that is needed once understanding has been achieved, but virtually useless as a pathway to understanding.”
Professor Sir Vaughan Jones
Sir Vaughan Jones, KNZM, FRS, FRSNZ, New Zealand mathematician and Fields Medallist, is a Distinguished Professor of Mathematics at Vanderbilt University, Nashville, TN, USA, and Professor Emeritus at the University of California, Berkeley, CA, USA.
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