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[quote=Anonymous][quote=Anonymous][quote=Anonymous]I actually teach a college STEM subject at Mason.

Here is my 10,000 foot view and what we tend to see. Even with AP calc or post-calc courses, many, many of our students are repeating calc and other courses like linear alg. because their foundations aren't strong enough. I'd say, these students tend to do well repeating because it's another pass on the material and reinforces what they already know. For the students who take the credit and move up, I've seen them struggle, but they do complete their programs. You tend to see more C's in things like material science & engineering courses and physics but they do finish and end up employed fwiw. The kids who are repeating tend to get higher grades (based on the students I have counseled/mentored for 10 years or so).
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How do the kids retaking Calc perform compared to kids taking Calc for the first time in college?  It seems to me that the advantage of taking AP Calc, perhaps AP Stats, and post-AP classes is not the ability to skip them but rather to have a quasi review, easyish A in coursework that would otherwise be a weed out class.  I'd hate to be the kid seeing the material in BC Calc or Linear Algebra for the first time in a class filled with kids who already somewhat know the material.

If having good foundations is important, wouldn't passing through calculus and linear algebra twice be the most helpful?  Kids would learn the material more superficially in high school, and then really dial the material in when they take the college classes.  [/quote]

Mason professor here.

My advisees who went into college and took calculus for the first time had a mix of outcomes. Some struggled because they needed support in math. Some did really well because they were ready to take on the material even if they only got to precalc in high school. It really was a mix.

The biggest thing that drove success was three things: (1) a willingness to engage with math conceptually -- showing their work, their thinking and being flexible; (2) an understanding that some things won't come easily and they need help and understood how to ask for help, accept help, and follow the suggestions of their TAs, tutors, professors; and (3) maturity...that latter point is something I've seen over and over again -- the older students -- especially the kids who went to NOVA and slowly made their way to GMU -- have the highest success when I think through things. I've seen far fewer of these students flounder compared to the student who opted to skip calc and other fundamental math courses and charge into the higher level classes in our department. In terms of buckets, the most successful students (as in the highest GPAs) as a whole;

1) the group that took calc and/or higher level math & science courses and decided to redo some or all of them to get a better grounding;
2) the NOVA/community college kids who slowly went through math and then took the entry level courses in STEM at Mason before moving up (I attribute this to maturity)
3) the Mason direct admits who went through the basic math classes and science classes and entered Mason without calc or just AB calc; (I attribute the difference from the previous group to maturity).
4) the Mason kids who took the credits and went into the higher level classes (I would say 75 percent of them struggled...about a quarter did amazing like group one, fwiw).[/quote]

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