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>> Most teachers are not good, so self-study is essential.

It's not even about teachers being good or bad. It's about something called "illusion of competence". Basically, everything seems easy while teacher is explaining it on whiteboard, but when facing similar task on your own, outside of the classroom you are completely lost, don't know where to start. Homework helps dispell that illusion.

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Tests get the same result. It is better to regularly tell the kids to solve problems without help than to make them to do it at home, since many kids wont do it at home.

but homework gets checked by teachers, right? I mean, from what I remember from my own high school teacher would spend first few minutes of each class asking about homework, somethimes simply providing the correct answers, sometimes randomly asking a kid in class to provide an answer. It wasn't graded, so much less stress than taking a test, but still you could verify that your solution to the assignment was correct.

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