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I'm studying Precalculus Algebra(around factoring quadratics at this point).

I want to know if it's worth banging your head for 2-3 days stuck on a hard problem or skipping them and doing all other thing that you seem that you're able to solve.

justification to your answer would be much appreciated

Abdul Kalam
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  • The curriculum that I teach grade separately on Knowledge type questions and on Inquiry type questions. What do you consider a normal/hard problem? Can you give examples? – Andrew Chin Aug 13 '20 at 21:55

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Both have their own merits. But for the former please pay attention to this quote by Terence Tao which I always find comforting.

It's like if you want to be a good pianist, you have to do a lot of scales and a lot of practice, and a lot of that is kind of boring, it's work. But you need to do that before you can really be very expressive and really play beautiful music. You have to go through that phase of practice and drill.

Hope this helps. :$)$

Khashayar Baghizadeh
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What's your definition of normal problems?questions you feel comfortable with? I feel the other way it's better the essence of solving in the first place is that we learn new ways,knowledge and acquire new skills I don't see how you can accomplish this by doing questions you are familiar with. The only thing you end up doing is exercising your already acquired skills.so it's better if you work up new challenging problems,you could also devise means to go about this

Vector
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I have profited the most from challenging problems that also required me to apply one or two core ideas of a field. When things get too obscure, it is a nice feeling solving the problem, but it may not help me understand the mathematics behind it any better.

Personally, I always try to prove statements from my lecture that are a consequence of some main theorem, without looking at the notes from class.

This helps me figure out the general ideas behind the theorems and definitions while often still requiring some nice idea I have to come up with.

Claudio Moneo
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