> Why are you enrolled in the degree course if you are critical of it instead of wanting to learn the material?
Maybe you want to learn why it is true?
Since Euclid, mathematics is about proof i.e. being convinced. If you really understand the material, you see it must be true - and need not blindly accept it.
What is taught in high school and many university courses is not mathematics, but how to use it. Like how to use Word, not how to write Word.
When you understand something, it becomes yours. You remember it longer, and can adjust and generalize it.
Unfortunately, it can be many times as much work to understand some mathematics, even some from early high school, and requires higher mathematics. So you can't understand til after you've understood it... It makes sense mathematics is taught the way it is... especially when most people are users, anyway.
But bad luck for those who need to understand and be convinced, which was so important to the developers of mathematics.
i.e. mathematics filters out mathematicians.
> Since Euclid, mathematics is about proof i.e. being convinced. If you really understand the material, you see it must be true - and need not blindly accept it.
I agree. Learning mathematics means learning the proofs. This is pure learning and has nothing to do with critical thinking (at least to me and I am a mathematician).
Maybe we mean different things by "critical thinking"?
To me, an essential part of a proof is checking that it is correct yourself... as opposed to "learning" it i.e. taking it on faith, believing it is correct because someone said it was. (Of course, in practice you can't verify everything yourself... but nonetheless that's the idea of mathematics, in theory).
Is that not the purest form of critical thinking?
OTOH I suppose when a proof uses a clever change in perspective, to show that it must be true (such as non-constructive proofs), it refutes many possible objections without ezplicitly considering them. So formulating those objections (or "criticisms") isn't needed.
Please keep in mind that you therefore have an inevitable non-zero amount of survivor bias there, and may have some trouble seeing why everyone else had trouble with the material.
Maybe you want to learn why it is true?
Since Euclid, mathematics is about proof i.e. being convinced. If you really understand the material, you see it must be true - and need not blindly accept it.
What is taught in high school and many university courses is not mathematics, but how to use it. Like how to use Word, not how to write Word.
When you understand something, it becomes yours. You remember it longer, and can adjust and generalize it.
Unfortunately, it can be many times as much work to understand some mathematics, even some from early high school, and requires higher mathematics. So you can't understand til after you've understood it... It makes sense mathematics is taught the way it is... especially when most people are users, anyway.
But bad luck for those who need to understand and be convinced, which was so important to the developers of mathematics. i.e. mathematics filters out mathematicians.