Calculus is just no fun at all, to either teach or take, when you have a poor grasp of algebra in particular, and a poor grasp of what makes sense and what doesn’t in quantitative terms in general. It’s like traveling in an extremely exotic country — or being an alien on another planet — without having a firm grasp of the language or customs. Possibly exhilarating in a way for a while, but pretty soon it just gets infuriating. You miss all the good stuff because the only thing you can think about is how poorly you grasp things.
Calculus is a lot more than applied algebra, and yet algebra is a massive bottleneck in teh course, and the majority of students I have had have such a poor handle on algebra that they miss the important and beautiful ideas in the course — continuity, the Intermediate Value Theorem, the concept of the infinitesimal, etc. — because they can’t remember how to simplify ((3/(3+h) – 1)/h in order to take the limit as h-> 0, and then having no idea what this limit is supposed to be or represent.
And what’s sad is that this algebra trickery isn’t even the point. But it does become the make-or-break component of the course, which seems to me to indicate a major flaw with the way calculus courses and books are designed.