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I am teaching one of my friends in high school mathematics, namely algebra, trigonometry, logarithms, exponential growth etc. But he is having a hard time to make connection between the things he learns. When he learn new things, he just tries to memorize them instead of understanding them, and when he does exercises in the books it all goes wrong. He is memorizing rules instead of understanding the deeper structures behind. And it is really difficult for him to understand the rules that makes sense for other people. I have tried to explain him how to find a common factor. For example he simply just don't understand why pq^2+p = p*(q^2+1) He says it makes much more sense with pq^2+p = p*(q^2+p) which is obviously wrong. How should I teach my friend mathematics, and how can he benefit most from my teaching? Anything would be helpful! Thanks!
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