Unfortunately what we typically end up with when learning math is:
1. Explain some problem that is difficult to solve using other techniques. The problem is painfully abstract and completely absurd.
2. Propose a technique to solve it. Never mind how we got to this technique or why it makes sense, just apply this equation and you'll get the answer. Memorize the numbers and symbols, that's all that matters.
3. Show that the technique also works on different (but really the same) problems.
4. Exam time! Here's a problem that looks nothing like the ones you've seen so far, but use the magic technique you memorized! You did memorize it right? Even though you didn't understand it at all?
5. This class is over so you will never use that technique again--even though it's generally useful, but since you never learned how to actually apply it or why it's useful, you'll forget it the day the exam is finished.
1. Explain some problem that is difficult to solve using other techniques. The problem is painfully abstract and completely absurd.
2. Propose a technique to solve it. Never mind how we got to this technique or why it makes sense, just apply this equation and you'll get the answer. Memorize the numbers and symbols, that's all that matters.
3. Show that the technique also works on different (but really the same) problems.
4. Exam time! Here's a problem that looks nothing like the ones you've seen so far, but use the magic technique you memorized! You did memorize it right? Even though you didn't understand it at all?
5. This class is over so you will never use that technique again--even though it's generally useful, but since you never learned how to actually apply it or why it's useful, you'll forget it the day the exam is finished.
6. Math is great! Why don't people like math?!