[woolvalley]

Math education from the undergraduate level on is fairly horrible and not communicated well. Just go read the typical calculus textbook and realize that they reference a lot of stuff that no pre-calculus student would typically know, such as proof by induction, lemmas and so on. The textbooks are written to the professors, not the actual students.

Various non-intuitive concepts are handwaved, the foundations skipped over and students then start struggling because they don't understand the foundation of what they are trying to learn. Reading from the textbook is fairly useless and it ends up being used as a problem set source.

I argued to a few math professors about teaching things like calculus with the textbooks referencing concepts that were not actually taught until 5 classes later is a bad idea.

In return I got a shrug of indifference telling me that's just the status quo and the status quo is OK.

Thank god khan academy exists now.

[jessaustin]

I attended a not-superb high school in rural Missouri, and we studied proof by induction in 11th grade, before calculus in 12th. (Only over the naturals, but that's enough to get the flavor...) Lemmas came in 10-grade geometry, although frankly I may not understand what you mean because that's not really a full "concept", just kind of an arbitrary detail. That was the early 90s, though, so perhaps standards have slipped.

Of course, colleges should cater to a range of preparatory educations, but the textbooks you're talking about are pitched at the correct level for somebody.

[woolvalley]

My recollection is vague, since it was quite a while ago, but there were other things that weren't introduced in my high school curriculum that I remember my calculus textbook containing. I'm glad your school taught you proof of induction and other such things although. I also remember talking to my classmates about how near indecipherable our calculus textbook was.

[jessaustin]

First semester of college, I took multivariate. That was kind of a mess, because instead of a textbook we got a "bound" compilation of our professor's notes that he was trying to turn into a textbook. It has been some time, but I kept lots of math books from college, and I specifically threw that thing out. My recollection is that it was pretty much worthless.