Mathematics in the western tradition began with the Greeks; they were the earliest engineers of our modern culture. They lived in a day where no formal method of numbers existed. Where we can simply memorize formulas and procedures without question, they had to figure out and prove how mathematics even worked. They had a lot of questions and didn't take what "math teachers" said on face value. They were men of logic. It would have been foolish for a student to take math on faith.
It is sad that, in our modernity, we lost that faculty to question math. We take everything the math professor says on faith. The teacher says that as long as you follow these steps you will get this answer, which is right. However, none of us know why it is right, or how to use it, or where it came from. Is it really any wonder why math students struggle?
If english were to follow this pattern, then the student would be expected to memorize the dictionary. after years of doing that, they can than start to compile an encyclopedia of syntax, where any sentence they would ever want to use is already listed. It would be absurd. What math teachers really need to do, is teach the principles of mathematics, beyond the mere performance. They need to teach how to independently use math to accomplish the ends of students. This would significantly increase the calculating ability of students world wide.
Euclid, a greek mathematician, was a great example of this. He wrote a book simply called "Elements" in which he used logic to prove why and how geometry works. He took nothing on faith, but took everything as an axiom to be proved. Because of men like Euclid, we have a tradition of mathematics. For our world to move forward, we need more teachers to teach and learn like Euclid.
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