  An assumed attribute of expert physicists is that they learn readily from
their own mistakes. Experts are unlikely to make the same mistakes when asked
to solve a problem a second time, especially if they have had access to a
correct solution. Here, we discuss a case study in which fourteen advanced
undergraduate physics students taking an honors-level quantum mechanics course
were given the same four problems in both a midterm and final exam. The
solutions to the midterm problems were provided to students. The performance on
the final exam shows that while some advanced students performed equally well
or improved compared to their performance on the midterm exam on the questions
administered a second time, a comparable number performed less well on the
final exam than on the midterm exam. The wide distribution of students'
performance on problems administered a second time suggests that most advanced
students do not automatically exploit their mistakes as an opportunity for
learning, and for repairing, extending, and organizing their knowledge
structure. Interviews with a subset of students revealed attitudes towards
problem-solving and gave insight into their approach to learning.
