Anecdotally, I've heard it said that in (Australian) grades 11 and 12 calculus needs to be taught in a procedural way involving merely recipes for doing calculus, rather than teaching for understanding common in lower grades.
In primary school there is a lot of emphasis on relational understanding, perhaps at the expense of rote learning (eg times tables) or procedures (eg long division). But on reaching senior school this is not expected.
Is there too much content in the curriculum? Is there an emphasis on exam preparation, including revision at the expense of understanding? Is the content not amenable to relational understanding (cf complex numbers just are)? Perhaps relational understanding only comes after a mastery of procedural techniques (of differentiation and integration). Does it need just to be taken on faith? What role does proof play? What role do algorithms play (Differentiation if easy but integration is hard)? Is relational understanding even necessary? - historically calculus was used successfully without proper underpinnings. Is instrumental understanding necessary without introducing further abstraction or esoteric machinery (logic and set theory)?
Is anyone aware of arguments or research supporting any of these claims?
A related question is regarding teacher (and student) attitudes to these things.
(Of course, I believe in the importance of imparting a relational understanding, but (for an essay I was writing) I was looking for some evidence of teachers attitudes regarding the necessity of teaching calculus in an instrumental way.)
I'm sorry if any of you misinterpreted my inquiry as dissent. I was merely looking for evidence of what teachers actually thought. I was looking for a representative sample of what teachers thought not just the opinion of a few.
Also I was looking for evidence to support the proposal that calculus needs to be taught in a particular way. I wasn't making that proposal!