I added two comments.
Of course, students “think” they are better prepared than they are. That’s what we professors are there for, to make sure they all “think” they are getting a good education. Here is how it is done.
How to Make Calculus Students Believe They Know Calculus When They Don’t
Step One: Teach at a selective (or, better yet, highly selective) school. That way the students start off feeling they are specially gifted. (They may be brilliant but calculus is hard for most people; that is, the real thing is hard. “Hard” simply means it takes work and study to understand it and get good at it. And it is worth the work for many, many reasons.)
Step Two: Make sure that they understand that you, the professor, are an outstanding mathematician.
Step Three: Never tell them anything really hard. If you do, they won’t understand it right away, and many of them will think the problem is you, not calculus. They will say, “That prof. can’t explain anything.” (Of course, by not telling them anything that is a challenge to understand, you are ensuring that very few will learn calculus.)
Step Four: Reinforce that calculus is easy because they are smart and you explain it really well because you, the professor, are such a brilliant mathematician and teacher. (They want to believe all these things.)
Now, for the icing on the cake. Tell them that a representative of the math profession has determined that they have learned calculus really well. Who is that representative. It is you, of course! You get to make up and grade the test that proves you did a great job of teaching! (If you made a mistake and challenged them to understand something hard – like the formal definition of a limit; by all means, don’t test them on it.)
Then, they will “think” they have learned a lot, the Deans will be happy, nobody will distract you from your research, and you can go off and be irate about unscrupulous bankers.
These two very important facts should be added to Mr. Selingo’s data.
In their seminal book, “Academically Adrift”, the authors, Arum and Roksa, show that students in the 60’s had to study 25 hours a week to learn what was required of them by their professors. Now it is 13 hours a week – and the grades are higher.
The result: the increase in critical thinking has dropped from one sigma (above what students came in with) to almost zero.
From my experience of teaching for over two decades, it is NOT the fault of the students . It is the fault of scoundrels; some called “administrators”, some called “professors” (researchers ok, but not professors).
(Taken from the post on my blog inside-higher-ed )