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Speaking as someone who always "got" math, the understanding really needs to come from you. You can't expect to get it from a book or from the teacher. I had tw
by hackinthebochs 16y ago
Speaking as someone who always "got" math, the understanding really needs to come from you. You can't expect to get it from a book or from the teacher. I had two tricks that has served me well: always ask yourself "why" until you reach that critical "a-ha" point, and secondly, visualize visualize visualize.
What I always did for new concepts was to ask myself "why". And I'd just think about it and visualize it until a reasonable explanation came to me. It doesn't necessarily have to be completely "right", but it just needs to make sense to you.
As an example from high school, everyone seemed to struggle learning basic algebra. The basic idea to learn from algebra is that you can do the same thing to both sides of an equation and the "truth" of it remains in-tact. This fact covers about 90% of everything you'll learn in Algebra I and II. The rest is basically just learning tricks for different situations.
The problem is you can't really be made to "get" this critical idea, the understanding has to come from you. The takeaway from all this is to focus on finding that a-ha moment for every new concept you learn.
As far as proofs go, again you can't be taught to do them well. You have to find your way on your own. The first step is to just convince yourself what you're trying to prove is true. Either by working out many different special cases and finding some pattern, or by visualizing whatever process you're trying to prove. Then you "formalize" your intuitive understanding by writing a proof. Convincing yourself that something is true is the crucial part.