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It's not a question which is confined to economists. Maths teachers are also asking similar questions about the 'gap' that the increasing rate at which technology is being introduced is causing in the ability to do mathematics. I posted in March ( about some of the issues surrounding the problems that many parents have helping their children with homework. The search for machines to do calculations more quickly is not new (eg abacus). It is maybe the flexibility of the mind, to approach calculations based on arithmetic from a number of different directions, which is the advantage gained from mental arithmetic. Anyone who accepts an answer from any source, numerical or otherwise, without checking it elsewhere, deserves the errors which may or may not accompany it. Arithmetic is only one part, and perhaps a small if fundamental one, of mathematics and what mathematicians do. Many problems come from people who teach mathematics in the early years not understanding the underlying concepts of what they teach and so revert to teaching by algorithm. Use of calculating machines is incidental if you don't understand what it is you are calculating or whether what you have calculated is reasonable.
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This is clearly a 'hot topic' at moment! I agree with you about precision in the use of language (actually the impact of teaching language on the learning of Mathematics is my main research interest!). I have already made comments about this on two other blogs: Robert Talbert on "calculator syndrome" (as I call it) and George Woodbury's thoughts on simplification of algebraic expressions. Your readers may find them interesting too. Oh, and since you mentioned speed... does it annoy you when people talk about "driving at a high rate of speed"? Surely they mean acceleration, don't they? Or, do they just mean driving very fast... Colin
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Aug 13, 2010