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The abstract concepts of calculus are useful and will shape the way you think about and go about solving problems, even if you don't explicitly employ an integr
by dymk 5y ago
The abstract concepts of calculus are useful and will shape the way you think about and go about solving problems, even if you don't explicitly employ an integral or derivative. Rates, sums, areas, volumes, etc.
Learn the nuts and bolts in highschool, use the intuition for the rest of your life.
- arcbyte 5y agoSeriously this. The average American doesn't grasp how basic graphs work. This simple idea of trends and how different functions imply graph differences is a powerful basic thought model. "Is this a linear or exponential curve curve problem?"
- mrob 5y agoThe abstract concepts are useful, but in practice most effort is spent on applying rote symbol manipulation rules to questions specifically designed such that applying the most obvious rule at each step will reach the solution. The idea of a tree search in symbol manipulation is never taught, so if you try solving non-trivial real-world problems you will likely manipulate yourself into a dead end. Highschool calculus should be taught with computer algebra software. That's what you'll use in real life as soon as you find an even slightly difficult calculus problem. There's not enough time to teach both the symbol manipulation rules and the intuition.