At colleges like Cal Tech and Ivy League, where virtually all students in Calc 1 will have already had experience with it in high school, do teachers grade harder, or just give everyone an A who has mastered the material? Is there higher expectations or an accelerated pace in courses where most students have a high level of background knowledge?
Usually grades are based on learning objectives for the current course. If it is a regular Calc 1 class then the learning objectives should reflect that and those who demonstrate they have met the objectives would get high grades. Students with a strong background in Calc 1 would likely test out of it via a placement test or high AP/IB score and start with Calc 2.
Of course, high school and college classes are different, so it is possible that a student who took a class in high school might not walk into the college class with much of an advantage (at least that’s what I see when I teach introductory psychology–often those who had it in college do worse perhaps because they assume they don’t need to study because they “already learned it”?)
I took college algebra during my freshman year, and it was similar to my Algebra II class in high school.
The college equivalent of a class will likely be accelerated and more advanced. Professors will most likely teach a new lesson each class; my high school math teachers would spend multiple days on one lesson.
College courses also have the ability to delve deeper into material. I know that my high-school math teachers were limited because they had to cover certain material because only certain things would be on the standardized tests. It was unfortunate because my Alg II teacher loved the chapter on matrices, but she skipped over it because it wouldn’t be on the standardized tests. College professors have more freedom in what they can teach.
Caltech “calculus” is far more theoretical than most high school or college calculus courses, and expects that entering frosh have seen calculus before in a more ordinary high school or college calculus course.
At other highly selective colleges with more ordinary calculus courses, many of those who took calculus in high school are able to place into a more advanced math course than calculus 1 (through AP or other placement tests).
Interesting thanks @WildLupine @NewBeginnings3 @ucbalumnus
I’m not quite at an ivy-level school (Case Western), but most of my friends took at least Calc AB in high school. I took Calc BC but decided to start back in Calc I in college. Most students in the class had learned the material before, but I didn’t notice any differences in how the class was taught or graded. I actually got a B, becasue I initially assumed it would be an easy A and I slacked off.
I’d say the biggest difference between a class that most students have already taken and one that most hadn’t was that there were less kids at office hours in the former. The grade distribution was similar, and the professor didn’t make any major adjustments in how he taught things.
My firends who only took Calc AB thought that the pace was really fast, but that’s since they learned Calc I in the equivalent of two semesters in high school when the college course is taught in one semester. I, having taken the equivalent of Calc I and II in high school, thought it went at a pretty slow pace. But that’s because my high school teacher moved onto Calc III topics at the end of the year to prepare my peers for skipping both Calc I and II in college.