While I would agree that a basic programming course might be helpful as a required course for all schools, I don't understand why it should replace Calculus? There is room for both, and they have different goals and advantages/disadvantages. You say yourself that calculus is awesome for several reasons - why do you think we should replace it?
If it is only because a different course might be more practical, you have entered a slippery slope. College is not the same as trade school - we don't learn things because they are practical, but because there is an advantage simply to learning. I believe that all basic college courses should aim to promote critical thinking above all else, as the practicability of any given subject will vary widely between students.
I'm just trying to be charitable to people who don't want music, drama, driver's ed, health class, ........ cut out.
Why should recreational mathematics replace calculus, either? Ideally math would be taught well and written so that people could engage with it throughout life. (But how many adults do you see reading those yellow spiney Kluwer books at coffee shops?)
slippery slope
Thought Vi Hart was talking about high school. Maybe I was wrong. I agree that calculus is the right kind of brain-stretching for college.
I agree completely. I don't think that recreational mathematics should replace calculus. I think that there are some definite changes that should be made to mathematics education, but that the majority of these should take place at a much younger age, even grade school. Early education is the perfect place for recreational mathematics. Fostering an interest at a young age (rather than force memorization of formulas, algorithms, and tables) can help a lot to keep people engaged throughout their lives.
I think that by the time students reach the college level (which I think starts with Calculus, even if they reach this level in high school), they should be able to deal with some of the more boring parts of mathematics, sustained only by nuggets of usefulness and beauty. After all, not all mathematics is wondrous joy.
I also agree that many of these problems could be fixed simply by teaching better. In calculus, for example, the beautiful thing is how closely it mirrors nature. Calculus states that if we know the position of an object at all times, we also know the velocity of the object at all times. This is a beautiful and fundamental result, one that I feel is not stressed enough during a first-year calculus course. I think that it is amazing not just that we know (in theory) the velocity, but that we can actually calculate it explicitly (in most circumstances) or approximate it numerically (in most circumstances). The parts of calculus on how to do that are somewhat less beautiful and paradigm-shifting, but are necessary, and adult students ought to be able to deal with that.
If it is only because a different course might be more practical, you have entered a slippery slope. College is not the same as trade school - we don't learn things because they are practical, but because there is an advantage simply to learning. I believe that all basic college courses should aim to promote critical thinking above all else, as the practicability of any given subject will vary widely between students.