How important is a strong foundation?

[Permanence]

As I enter college I'm faced with the choice of transferring the credits I've earned in high school taking AP exams. While I'm positive that I'll be taking credit for certain classes that I won't progress on with, like electives or courses that aren't related to my major, I'm not sure what I'll be doing with my other courses. I personally am tempted to take credit for Calc I-II and Physics I-II, but a few of my mentors are strongly against it. They are telling me that if I jump into these classes I will struggle and that the AP exams I took are absolute jokes when compared to college equivalents.

How do you feel about that? Better yet how do you feel about students jumping ahead? Lastly, for those of you who are instructors, is it evident to you that a student has skipped some material coming into your course?

Thank you.

 

[WannabeNewton]

I skipped past physics I-II using AP physics C credit, calc I-II using calc BC credit, and calc III via placement exam and it hasn't hurt me in the slightest as of yet (I will be starting my 2nd year after this summer so we'll see if it keeps up!). My high school teachers for physics C and calc BC were really awesome and went way beyond the standard curriculum so using the AP credit didn't seem to have much of a negative impact. On that note, it's hard to tell if you should skip or not without knowing how much you learned in your AP classes but you can easily look up the physics I-II material as well as calc I-II material on your future college's webpage and see if it aligns with or goes beyond what you have learned. Note that your college might offer an honors physics sequence (Kleppner, Purcell) and an honors calculus sequence (Spivak or Apostol). If they do then by all means do NOT skip and take these classes if you are interested. Best of luck!

 

[micromass]

It's very difficult to make a general statement here. It depends on so much. For example:

1) The quality of your high school courses. Some high schools have very good calculus and physics courses, other schools are very bad.

2) The quality of your college courses. In many cases, college calculus and high school calculus courses won't be much different.

3) Your motivation and capabilities to self-study concepts that you don't know yet or don't know well.

A strong foundation is extremely imporant. But the right question here is: do I alreay have the right foundation and to what extend can the college provide you with a stronger foundation?

A thing you can do is to test your calculus and physics knowledge. Take a look at the tests and exams of your college and see if you can do it. Take the calculus book that your college uses and try to solve some exercises. This will tell you whether you are ready or not.

 

[PhysicsWiz4]

I transferred credits and skipped ahead to calc 3 (physics department doesn't permit jumping ahead though, even with a 5 on C). I did well in all those classes. That being said, your preparation *does* matter. The AP BC test was a joke compared to what we were covering in the class -had I only known the material in the test I would not have been ready for calc 3. (If you're wondering what else we learned, it wasn't the breadth of what we covered, rather the depth. We learned what was on the AP test, but enough so that it would never be much of a challenge). Make sure you understand the fundamentals of calculus - this is more important that being able to do the calculations. Anyone can perform algorithmic algebra to find derivatives without knowing what it means. If you feel you have an intuitive understanding of what calculus is, and feel comfortable with generalizing that knowledge to more dimensions and objects(vectors), then you are ready for calc 3.

I can't speak much for skipping physics, but "retaking" mechanics and e+m helped (I eventually dual enrolled in second and third-year physics courses, mostly due to me skipping ahead in math). I have done well so far, so I wouldn't recommend against it.

You can always enroll in the harder class and then drop to the easier one if it gets too hard (before the deadline), but if you start with the easy one you're already behind schedule if you want to transfer up.

 

[DEvens]

[snips]
but a few of my mentors are strongly against it.

Depends on who your mentors are. If these are profs in the school you are attending or going to attend, then you should consider their input very carefully. If these are your pals from high school, well, they don't know any more than you. Your guidance councillor from high school is probably in the middle.

Talk to the profs at the college you want to attend. If possible, talk to the profs in the courses you are considering bypassing, and possibly the profs in the courses that require the classes you want to bypass. See what they think. If you get a uniform answer there, I'd say follow it. If they are mixed then you will have to figure it out for yourself.

In my undergrad days, there were three students who bypassed a number of first year classes. Mostly that was because (a) they were brilliant (more brilliant than me at least) and (b) they came from Quebec where they took extra credit in CEGEP.

http://en.wikipedia.org/wiki/CEGEP

The result was, they took a full load of courses in first year, taking classes they would not have been able to, and getting effectively 1.5 years worth of credit in first year. They were thus able to take classes that gave them many more options in later years, and helped a lot getting scholarships and positions for grad school. Now they all three are profs at respected universities.

So if you come from a really good high school, and you are brilliant, and you are keen to take those extra classes, sure, bypass classes using the exams.
Dan