Why am I good at mind calculations but bad at problem solving?

From: https://www.quora.com/Why-am-I-good-at-mind-calculations-but-bad-at-problem-solving

I have this friend who is great at cutting vegetables. You give her whatever you want, she can shred it in seconds. However, when it comes to cooking, she needs to be shown how to combine the vegetables and understand the differences in taste and acidity of each one, etc. Otherwise she can’t progress, she is almost paralyzed by fear. Why doesn’t her great cutting skill translate to great cooking skill?

The answer is that, fundamentally, the two skills are different. Mind calculations take time to do, and you can get better with practice. The same is true of problem solving. However, just because both are parts of mathematics doesn’t mean that practicing one also gives you practice in the other. If you feel weak in problem solving, then the only solution is to practice more in that direction. Try to solve easier problems first, make sure that you understand the theory well, and then work your way up.

As far as I can tell from mine and my students’ work, when you can’t decide what way to go on a problem, most of the time it’s because you are missing some clue from theory.

It would also be helpful to read books on problem solving, like Polya’s “How to solve it”.

 

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