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Education needs to focus on comprehension and thinking.
Yes, thinking and comprehension are important, but not only them. Numeracy is also important and kids cannot get it without knowing how to be human calculators. Experiences at the cash register when dealing with cash, have be less that satisfactory when the people cannot even think that what they are doing is a huge mistake. People need some number sense to get along in this world. Also, mathematicians have to start somewhere and that somewhere is with rote learning about basic arithmetic. It is just like dealing with a slide rule, you have to have a sense of some kind of result to get accuracy.
I do agree that you want to teach basic numeracy. I more meant that in higher level courses, it's silly to not allow calculators and other advanced computational tools. When you allow students to use powerful cognitive tools, then they can apply their intelligence to more interesting aspects.
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Ok, I can see that. What about slide rules?
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By any means necessary
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That's how it's done!!
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