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As I learn math, It feels important to me to get a solid grasp of theory rather than just memorize rules. I see it as a language, and I want to be able to confidently read sentences instead of piecing out words, letter by letter, as I go. I guess I'm limited in that approach by a certain factor I don't have a name or description for: it's the ability to turn rote rules and explanations into a visual-intuitive concept.
When I last looked at Khan Academy, before a stretch of stressy days kept me away, I was working on internalizing how to create an equation for a function that describes another function with x and y offsets. It's straight forward enough to do by following the rules, but I didn't want to move on until I could look at related graphs with one equation and do the mental translation into a second equation just based on theoretical understanding.
I kept getting stuck on that bit of mathematical vocabulary, for quite a while. Today, I can almost speak it fluently. Yay! On to the next bit of metaphorical grammar.
When I last looked at Khan Academy, before a stretch of stressy days kept me away, I was working on internalizing how to create an equation for a function that describes another function with x and y offsets. It's straight forward enough to do by following the rules, but I didn't want to move on until I could look at related graphs with one equation and do the mental translation into a second equation just based on theoretical understanding.
I kept getting stuck on that bit of mathematical vocabulary, for quite a while. Today, I can almost speak it fluently. Yay! On to the next bit of metaphorical grammar.