This is a very interesting study, thanks for sharing it. With risk to go against what I said earlier, I have to admit that I've seen the same thing in my own le

This is a very interesting study, thanks for sharing it. With risk to go against what I said earlier, I have to admit that I've seen the same thing in my own learning and that of some of my peers in my math program. The first two years of math courses were great and we did well and the more advanced ones were, of course, harder but we just couldn't do as well on them as we wanted. However, I'll argue strongly that it's not because our first few teachers were so good, from perspective of evaluation but because the later professors were not up to par. You see, Calculus courses are taught so much that the material has been developed and optimized to an extent that when I took my Calculus courses, I fell in love with math. Even somewhat more advanced courses like Linear Algebra and Complex Analysis are quite optimized for learning. Go in a little deeper into things like Real Analysis, Group Theory, Abstract Algebra and Galois Theory, and all of a sudden, everybody teaches these courses differently. Of course, these courses are taught less and they are not as optimized. THIS, I will argue is the reason for the decreased performance in the "deeper subjects". Let me use an analogy. Let's say your first big relationship is with a really easy-going happy person and you have great times but eventually you have to part ways for some arbitrary reasons. Some time later you get into a second big relationship and this time the other person is difficult. They are battling through a lot of childhood issues and have problems with self-esteem. All of a sudden, you find yourself unable to deal well with this person, eventually you break it off. Now, was your lack of "performance" in the second relationship due to the first one being so good or due to the second one being so crap? Now, from the paper's conclusion: > A final, more cynical, explanation could also relate to student effort. Students of low-value-added professors in the introductory course may increase effort in follow-on courses to help “erase” their lower than expected grade in the introductory course. I have seen and experienced this all too often. Case in point - one of my friends got a C in Calc 1 but went on to get A's in the next few Calc courses.