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MAKING NUMERICAL SENSE
Mathematics is, in many important ways, a language like English or French or Chinese. It has a vocabulary (numbers and symbols), grammar (operations and rules), and sentences (equations). It tells us about the universe around us, just as story or a poem might - but in a different and powerful way. Five year old children speak Russian fluently, but I do not; does this mean that I am unintelligent compared with five year old Russian children? Or that I am "bad" at Russian? Or that "my father was no good at Russian, so it makes sense that I'm no good at it either?" Obviously not. I just have too little exposure to Russian at this point in my life. If I went to Russia and did nothing but speak, read and write Russian, there's a very good chance I'd be fluent in Russian after five years. I have nothing to fear from Russian - I just need either to get used to it, or have a good translator. So if we approach mathematics with the same attitude as we might approach a foreign language, there's no need ever to be afraid of it. The key is to realize that if we don't speak it often, we might get a phrase wrong once in a while. It's no big deal; as long as we communicate the main ideas, we'll be all right. You'll be happy to know that, whether you realize it or not, you use math all the time - and well. If you live in a reasonably large city and you want to get across town by noon, would you leave your home at 11:59 A.M., 11:00 A.M., or 6 A.M.? You use math to figure that out. If you want to buy a medium-priced house, should you plan to spend $100, $100,000 or $100,000,000? Of course, you probably won't compute beforehand that you need to leave at precisely 11:06 A.M. to arrive precisely at noon, or that you'll spend $123,692.00 for your house. Rather, you find an answer that "feels right" or "makes sense." Using that "common sense" is the most important part of using mathematics as a language to help translate the universe. Having some general idea of what numbers are appropriate to answering a question or solving a problem is 90% of the battle. Use that common sense! |