The job of a good teacher is to find a slightly less challenging problem, and to give you that problem first. Ideally, to find a sequence of problems very smoothly increasing in difficulty.
No. Being good at math is about being able to keep your attention on a complicated proof even if it's very challenging and your head seems like it's going to burst.
If you want to build muscles you don't slowly increase the amount of weight and keep it at a level where it's effortless. You train to exhaustion of given muscles.
Building mental stamina to tackle very complicated abstract problems that aren't solvable in five minutes is part of a good math education.
Deliberate practice is supposed to feel hard. A computer game is supposed to feel fun. You can play a computer game for 12 hours. A few hours of delibrate practice are on the other usually enough to get someone to the rand of exhaustion.
If you only face problems in your education that are smooth like a computer game, you aren't well prepared for facing hard problems in reality. A good math education teaches you the mindset that's required to stick with a tough abstract problem and tackle it head on even if you can't fully grasp it after looking 30 minutes at it.
You might not use calculus at your job, but if your math education teaches you the ability to stay focused on hard abstract problems than it fulfilled it's purpose.
You can teach calculus by giving the student concrete real world examples but that defeats the point of the exercise. If we are honest most students won't need the calculus at their job. It's not the point of math education. At least in the mindset in which I got taught math at school in Germany.
This kind of philosophy sounds like it's going to make a few people very good at tackling hard problems, while causing everyone else to become demotivated and hate math.
Another month has passed and here is a new rationality quotes thread. The usual rules are:
And one new rule: