Do math teachers, mathbook writers AND math textbook writers generally target students who show a math aptitude initially? Are students who show lack of interest weeded out? I remember seeing the movie STAND and DELIVER with Edward James Olmos (forgive the spelling), where he was a high school teacher and he wanted to teach calculus to his grade 12 students. The faculty was against him but he managed to make his students proficient in Calculus; A LOT of them initially disliked it. Why can't calculus be taught in grade 12 or 11?
Yes. In many places, students who are more capable get more resources allocated to help them excel. The textbooks do not discriminate between different students, but the teachers can, and quite often do.
It is not unheard of for 9th graders to take Advanced Placement Calculus BC. It's just a matter of how ready they are to take the course. I don't think that anyone is really neglected, it's just that the "smarter" kids get put into more advanced classes, which get more resources, allowing them to do even better. It comes down to ability more than anything.
It's not necessarily the case that people are trying intentionally to target a certain type of student. However there is evidence that certain traditional methods of mathematics instruction do cater to certain kinds of people and it is not as simple as selecting for the more apt students.
In the process of learning, students form ideas about what mathematics is and who they are in relation to it. Many get an impoverished view of mathematics because of an approach that focuses on certainty, having a single answer, rigid procedural action (so-called "machine agency"). Some decide that this inaccurate view of math is just what they're looking for for themselves and their future. Others want a future in which they feel they can express themselves in their work and use their interpretive, meaning-making ability. Not surprisingly, those people think math is not for them.
So, it turns out you're not getting the most "apt" students, and it's not necessarily intentional targeting.
For more details, and references to that evidence, see this other MESE answer:
No, they aren't. That said, some subjects are genuinely difficult such that even the clearest writer cannot simplify concepts further. You cannot distinguish your readers in a text. Authors attempt to narrow the prerequisites for learning their area to their bare minimum, which may not account for the true amount of background knowledge and/or mathematical maturity (often invoked) necessary for dealing and struggling with the naturally presented difficulties.
As for your anecdote regarding calculus in grades 11 and 12, I am not from the USA but I believe this stands: it's not about age but about readiness and willingness to work through the concepts. I feel that whoever learns calculus earlier than usual is better prepared and nurtured to do so than most people, not that they are more capable than anyone else.
It is just that someone talented/very interested will be able to learn even from an awful book or teacher, and that teaching those is a lot more fun than dealing with the bottom fifth of the class. Given Sturgeon's revelation, and teachers being just human beings explains your observation.
Don't believe what Hollywood shows you. A modicum of knowledge in a given area (or just a bit of common sense) will show innumerable howlers in your random film. I'm not saying it can't happen; but if it was reasonably common, it won't make a good story...
The text itself isn't the issue. In my opinion, student's aptitude fits a bell curve fairly well, and the struggle for teachers is to keep that lowest 1/6 passing, while not losing the top 1/6 to boredom.
In my school, the advanced track has calculus as an offering for seniors (12th grade). I also see seniors who are struggling with algebra, of basic trig. A student's problem on solving simple trigonometric operations is an example of this. The text and the teacher are expecting students proficient at basic manipulation, yet, the teacher will likely need to pause to give this a review.
An answer to that question (Chris) suggests that mastery isn't the right expectation. My opinion is that his response is correct and forms the basis of the full high school curriculum. i.e. that a certain fraction of class time spent on review reduces the amount of new material that can be delivered.
Do teachers and books target more apt students?
I am shocked at people either saying or implying that the answer is no.
I have discussed this topic several times with my former fellow students and to me it's quite obvious the answer is yes.
In first grade everyone, except for a few rare exceptions, learns the material. This is the kind of success rate any normal academic school should aim at.
In university, only a handful of people learn the material properly (and not just passing). How can people claim that the courses aren't out of the average students reach? They are so by definition. Arguments such as "students just don't study" aren't good because students don't study in first grade either, yet they learn.
With respect to books, the same happens. Take a regular mathematics book about a subject you don't know and you (unless you are one of those handful of people) will struggle. Take a non-regular mathematics book like How to Prove It: A Structured Approach and things are very different. You can actually read this book like a novel. The level of detail is actually adequate for someone who doesn't know anything about it.
Picture yourself teaching a group of thirty people how to turn your water heater on. Would you really believe that you're teaching was adequate if only two or three people really learned it and ten somehow managed to 'barely' turn it on while the others simply couldn't? The difference in difficulty between turning a water heater on and learning calculus is of no concern here, results are what matter.
Throughout my rationale I basically assumed that students should be learning without studying at home. I do not commit to this view, but if you reject it, I still maintain my position. If one removes people who don't study at home, there will still be a huge amount of people failing. (I can't support this claim with evidence, this is just something I observed during my undergraduate degree).
On a more personal note, I had good grades throughout my BSc I had good grades, but I had to work hard to get them, so did my most of my friends who had good grades and I know about lots of people who worked hard and didn't get good grades. Wouldn't you expect, if you pick one of the best students, that he/she would be someone who learns easily? This isn't so...