We here at Hopkins give Advanced Placement credits for our calculus courses depending on the score one receives on the AP exams, offered in May of each year. The results come out in July. We give 8 total credits for Calculus I and Calculus II (a full year's worth) for a score on the BC-level exam of 4 or 5 (out of 5), and 4 total credits for Calculus I for a BC-level score of 3, or an AB-level score of 4 or 5 (again, out of 5).

Roughly speaking, the AB-level coincides with Calculus I and BC with Calculus II.

Well.... One of our own, Professor Stephen Wilson, performed a AP score verses grade in the next level course analysis which wound up being quite insightful. It turns out that getting a BC score of 5 is a good indication that the student is prepared to go directly to Calculus III. However, a BC score of 4 may not be. Almost no student who took Calculus III and brought in a BC score of 4 got an A in the class. Likewise, almost no student who brought in an AB score of 4 got an A in Calculus II (the logical next step).

It may be the case that not getting full marks on the AP exams means it is better to step back and re-evaluate the idea that you are really ready for the next level. We will certainly be keeping an eye on this over the next year or so. I thought I would put this out there now.

Advising must be a careful business, no?

## 4 comments:

Hi Richard,

I graduated from JHU majoring in what was then called 'Mathematical Sciences' and became a statistician. As such, I feel compelled to point out who you really want to compare is not grades for people who got 4s and people who got 5s, but people who got 4s and repeated all or part of Calculus I/II and people who got 4s and went straight into Calculus III. The question is whether the additional preparation helps the ultimate Calc III grade. (Actually, you really want to compare people who got 4s, wanted to take Calculus III, and were randomized into taking Calculus III and repeating Calculus II.) I know randomized experiment data doesn't exist, but if you have some information on the former (people who got 4s and elected to repeat Calculus II) it would be the more relevant comparison.

Best Regards,

Beatrix Jones

Very true, Beatrix.

We were concerned about the struggles of some of our students in Calculus III during their first semester here at Hopkins, and thought to look here for an indicator. In the chart for Calculus II performance vs. AP score, the BC3er's do very well. Hence the students who get a BC score of 4 and decide to retake Calculus II should be fine. But you are right. We are not statisticians and I am sure we did/do not design these studies properly. We are actively concerned about how our students do, however. Hence the attempt.

Thanks for your input. We will keep working on this.

And there is still the Math Sci. degree, over in the Applied Mathematics and Statistics Department in the Engineering School. Best regards also to you.

Just to be clear, I'm talking about the comparing the ultimate Calculus 3 grade obtained. The AP 4 grade students would do well in Calc 2, but does the extra preparation allow them to go on and do well in Calc 3? Or is Calc 3 just tougher, with or without the extra prep?

I think you are probably basing your conclusion on some background information that people who have done Calculus 2 at Hopkins do fine in Calc 3.

Its great that you can assume that students are mostly good students and want to do well. At my current university I have a lot of students who get B or even C because "that's good enough," so extra preparation doesn't necessarily change the end grade.

I am basing my conclusion on the idea that students who take Calculus II here generally do well in Calculus III here.

We do have a related issue, though. We cover our first semester grades, with the public view being only S and U (satisfactory and unsatisfactory). The main reason is to ease the transition from HS to college, I believe. However, some feel the effect is for students to only work for the S (given for a C- or up) instead of trying to excel. There is concern this leads to the development of poor study habits later on.

We have not addressed anything like that yet.

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