> Attempting to learn mathematics as some sort of pattern matching, which is where having large sets of questions and answers to study is useful, does not work; it isn't mathematics.
You're right, but you need to know the basic mechanics pretty well in order to start to understand the deeper philosophies and ways of thinking that math _is_.
It's like learning to ride a motorcycle without ever having ridden a bike; Riding a bike is not riding a motorcycle, but you're going to really struggle to make progress past a certain point of learning since you're mastering the absolute basics of _both_ things at the _same_ time.
It's the same thing with math. If I never see what well-formed answers to problems look like, never gain familiarity with the symbology or jargon, then I can never start to even learn proper math because the professor can't communicate with me.
You're right, but you need to know the basic mechanics pretty well in order to start to understand the deeper philosophies and ways of thinking that math _is_.
It's like learning to ride a motorcycle without ever having ridden a bike; Riding a bike is not riding a motorcycle, but you're going to really struggle to make progress past a certain point of learning since you're mastering the absolute basics of _both_ things at the _same_ time.
It's the same thing with math. If I never see what well-formed answers to problems look like, never gain familiarity with the symbology or jargon, then I can never start to even learn proper math because the professor can't communicate with me.