Homework strategies to improve problem solving skills

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Howers
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Just a question... to learn math/physics, is it better to do ~10 medium-challenging problems that invoke some thought, or doing 2-3 really hard problems that require deep thought and lots of time. Up to now I've been doing both, but it just isn't possible to keep up with UT's supplementary problems... I'm 2 weeks behind in many courses because of my stubborn attempt to do so. It seems schools don't value learning so much as rapid routine.

So what do I do? A bunch of routine calculations and some moderate problems or the really hard ones?
 
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depends on what you feel. I usally warm up with some easy ones, then intermediate and try to do as many "really hard" problems as i can. But it depends on what level the course is, and what exercises is recomended by the teacher and so on.

Just feel for yourself, but you should aim for the thoughest ones. And if you get stuck, ask your teacher for help. If you never run into problems, then you never learn something is my philosophy :)