I realize you have probably had people tell you this already, and their attempts to explain Calculus to you have left you frustrated and more firmly convinced that it was beyond your capacity. But I don’t propose to demonstrate my hypothesis in that way. Rather, I can try to double-crux this by showing you that your understanding of regular school mathematics isn’t really what it should be and is what might actually be holding you back. In the spirit of your 3-question cognitive abilities quiz, here is a 3-question “ready for Calculus” diagnostic test I just made up (but which is informed by many years of teaching and tutoring students at many different levels of math understanding).
1) Can you explain why a real number has a decimal expansion that eventually repeats cyclically if and only if it is a rational number? (If you can’t do both directions confidently, your understanding of rational and real arithmetic isn’t good enough for calculus.)
2) Could you explain why the Pythagorean Theorem is true in a way that would completely satisfy the curiosity of a typical intelligent 12-year-old? (If you can’t, your understanding of plane geometry and area isn’t good enough for calculus.)
3) Can you state a version of the Binomial Theorem completely precisely? (Only state, not prove—if you can’t, your understanding of polynomial algebra and math notation isn’t good enough for calculus.)
All these things are definitely PRE calculus mathematics, and they are taught in high school, but rarely taught well enough that students could comfortably answer all three questions.
I attended a university where the median entering student had a perfect score on the math SAT and all students were required to take several calculus classes regardless of major (the first class involved epsilon-delta proofs). I never felt I had any particular problem with calculus; mostly got As. Majored in a math-adjacent field (though not one that uses calculus) and graduated with honors.
I’m not sure I could answer ANY of your 3 questions. Possibly if I spent a considerable time carefully thinking about them.
It’s possible that I could have answered them at the time and have since forgotten, but I don’t feel like that’s the case.
I realize you have probably had people tell you this already, and their attempts to explain Calculus to you have left you frustrated and more firmly convinced that it was beyond your capacity. But I don’t propose to demonstrate my hypothesis in that way. Rather, I can try to double-crux this by showing you that your understanding of regular school mathematics isn’t really what it should be and is what might actually be holding you back. In the spirit of your 3-question cognitive abilities quiz, here is a 3-question “ready for Calculus” diagnostic test I just made up (but which is informed by many years of teaching and tutoring students at many different levels of math understanding).
1) Can you explain why a real number has a decimal expansion that eventually repeats cyclically if and only if it is a rational number? (If you can’t do both directions confidently, your understanding of rational and real arithmetic isn’t good enough for calculus.)
2) Could you explain why the Pythagorean Theorem is true in a way that would completely satisfy the curiosity of a typical intelligent 12-year-old? (If you can’t, your understanding of plane geometry and area isn’t good enough for calculus.)
3) Can you state a version of the Binomial Theorem completely precisely? (Only state, not prove—if you can’t, your understanding of polynomial algebra and math notation isn’t good enough for calculus.)
All these things are definitely PRE calculus mathematics, and they are taught in high school, but rarely taught well enough that students could comfortably answer all three questions.
I attended a university where the median entering student had a perfect score on the math SAT and all students were required to take several calculus classes regardless of major (the first class involved epsilon-delta proofs). I never felt I had any particular problem with calculus; mostly got As. Majored in a math-adjacent field (though not one that uses calculus) and graduated with honors.
I’m not sure I could answer ANY of your 3 questions. Possibly if I spent a considerable time carefully thinking about them.
It’s possible that I could have answered them at the time and have since forgotten, but I don’t feel like that’s the case.