There seems to be a consensus in the sense that it is unrealistic to introduce this type of arguments in an introductory calculus
course, not only in the U.S.
They manage this by putting the more advanced derivations in appendices that are accessible to a reader with knowledge of introductory calculus
and vector analysis.
(Interlake is the only high school in the district to offer the International Baccalaureate.) Those with one more year of high school take either AP calculus, AP statistics, or an introductory calculus
A well-developed understanding of rate is foundational to conceptual understanding of introductory calculus
. Many students achieve procedural competence with the application of rules for differentiation without developing an awareness of the connection between derivative and rate.
The effect of using graphics calculators on student's attitudes towards mathematics and students' achievement in introductory calculus
. Dissertation Abstracts International, 56, 2155.
My high school was certified as "college preparatory." I was able to take introductory calculus
, advanced chemistry and biology, and even several English literature courses for college credit, I graduated as valedictorian of my decent-sized class, with just over a 3.9 GPA.
He candidly observes that the most difficult hurdle for ordinary (rather than honors) mathematics students is introductory calculus
. Combinations of math and computer phobia, and even poor keyboard skills, can cause students to be overwhelmed.