I suspect most of [EDIT: many?] HN readers breezed through calculus using nothing but free online resources. With zero attitude, I say that I am truly impressed. I wish I was that amazing of a student.
I followed the more typical educational path of taking calculus in college. Some of it was easy, some of it was hard, but I seriously doubt that I would have been self-motivated enough to go through the entire sequence of calculus course material on my own. The pressure induced by being part of an in-person class, for a grade, and not for free, made me feel like I had to learn the material, and avail myself of whatever resources I needed, be it asking questions of the professor, going to tutoring sessions, reading extra books, whatever, to make sure that I learned it.
I totally wish I was so self-motivated that I could learn absolutely anything at any breadth and at any depth without any external reason to do so. But on my own, there are limits to what I make myself study. Which isn't to say that I'm stupid on my own, but rather, I appreciated the in-person college experience mainly for applying pressure on me to learn things that I wouldn't have otherwise. (And as a result, I did become more inclined to study broader and deeper on my own.)
In my cursory experience with MOOCs thus far, I don't see them applying that same pressure. Maybe they can; I'm not sure. But unless they do, I think that a lot of people (especially outside of HN, etc.) will find value in actually going to school.
Yes. If you draw a bell curve of all first year students, say at schools where the entering avg Math SAT is 500 or above, then the shaded area of those who struggle with Calculus would, in my estimation, encompass .9 or more of the area below that curve.
This is despite hundreds of years of effort by well-meaning, perceptive, and hard-working teachers and students to refine the presentation to make the subject as clear as possible. Because most teachers and most texts are not the dipshits of the world. In short, Calculus is hard.
The thing about massive courses is that they are massive. When you get big, you cannot help but get average. In my experience average students (say at the schools I mentioned above) need support, including reasonably intensive personal attention from an experienced and knowledgable teacher. I don't believe the typical person in my course can pick it up on their own. (Not to dismiss the potential; I think there is a lot of exciting stuff happening that can help people learn. But I've seen nothing that would make attention unneeded.)
I do perceive that many HN readers could just pick Calc up, and frankly so could I, which is a good reason to read HN. People here pique my interest every day. But often in the discussions following articles like the one here missing is an understanding that you (speaking to a typical reader) are not average.
I majored in math and had pretty good ACT and SAT scores but I still find Calculus and related math very difficult.
My unscientific observation is that some people find the analytical/continuous parts of math difficult but can still do really well with stuff like abstract algebra, combinatorics, linear algebra, and so forth. Other people (i.e. physics & engineering majors) are the exact opposite.
Then of course there are a select few who are good at both.
My brother is a math teacher and was more of a physics guy and his claim is that people who struggle with calc generally had poor instruction in trigonometry in their youth. I'm not sure how true this could be but I definitely hated my trig instructor the most out of any teacher I've ever had.
I simply have to disagree. I've only met two teachers I didn't think were dipshits and that's over the course of a B.S. in bioengineering, a masters in CS, and a trip through an MD/PhD program. These are all at top ranked schools, too. These people may have been smart, but they certainly weren't quality instructors. In my opinion, teaching should be something people do when they retire for fun. The two non-dipshits were doing exactly that.
Students should absolutely be able to pick it up on their own, but most classes use crappy textbooks and the teachers recite from the crappy textbooks. Stewart's Calculus is used by a ton of schools and that book is utter garbage. The guy is using it as a way to print money, which is fine, but you'd think after 10 versions, he'd eventually get things right.
I'd say our posts are completely opposite in thinking. You think most texts and instructors aren't dipshits, I think they are. You think Calculus is hard to learn, I think it's easy.
I think that on HN some people do not understand what the academic experience is like for the majority of students and you've provided confirmation of that.
I know what the academic experience is like for the majority of students, it was me my first year of college. I realized that almost all teachers are dogshit after that and only attended class when it was required, studying on my own. Most people don't come to that realization until it's too late, though.
