I don't know, man. My grades always seemed to reflect my understanding pretty damn well. If it wasn't reflecting my understanding, I knew it wasn't.
To be fair to the writer, it'd be a much longer and more difficult article if it was called "Tips for understanding concepts in math." I don't even know how you could approach that.
Also, what the heck is wrong with memorizing definitions? You can't prove something using nothing. Eventually, after doing enough proofs employing the definition (or axiom or theorem or whatever else you memorized), you won't have to even think about it anymore - similar to how you or I could find the first derivative of a polynomial without thinking about it or know the definition of an even number.
To be fair to the writer, it'd be a much longer and more difficult article if it was called "Tips for understanding concepts in math." I don't even know how you could approach that.
Also, what the heck is wrong with memorizing definitions? You can't prove something using nothing. Eventually, after doing enough proofs employing the definition (or axiom or theorem or whatever else you memorized), you won't have to even think about it anymore - similar to how you or I could find the first derivative of a polynomial without thinking about it or know the definition of an even number.