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by 47uF 4979 days ago
Agreed. I had an interesting experience recently when I decided to "relearn" math. I had taken calculus courses in high school and university, and aced all the exams. But when I eventually came back to calculus out of personal interest, I realized that I didn't know what a derivative was! I didn't know what a limit was! How did I pass those classes? And if someone who got the highest marks didn't learn anything, what about the people who were actually struggling? How many people in that class actually learned anything?

And I could say the same for my science classes, foreign language classes, etc. I don't think you really learn anything unless you really want to understand the material and you work hard to do so. And if that were the case, hour for hour you'll get what you put into it. You wouldn't be studying to an exam. You wouldn't be satisfied with 60%+ on that exam. You wouldn't restrict yourself to a specific curriculum. You wouldn't put time limits on your learning. Instead you would learn the thing that you decided you wanted or needed to learn, and however long it took for you to really understand it, that's how much time you would spend.
2 comments
rtkwe 4979 days ago
The real test is how well you were able to pick up the concepts again. Not using it for, how ever many, years it's natural to forget. However if you can quickly reacquire the knowledge then you did learn it atrophied so to speak.
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47uF 4978 days ago
But I really think that I never learned those concepts in the first place. All I learned were rules to solve the problems given to me. For example I actually did remember the "chain rule". But those rules had no meaning to me, just moving numbers around. Which means I would never be able apply it to anything. For example, calculus clearly has applications all across basic physics. But I never really made that connection. All this makes me think that exams are much, MUCH less effective at measuring comprehension than we think.
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mangostache2 4979 days ago
“Nothing that is worth knowing can be taught.” -- Oscar Wilde

What materials did you consult when relearning math?

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