Final Exam

In the end, I was disappointed in the written portion of the final exam for the course. As the three sets of papers show, the exam did differentiat between the students somewhat. However, on the finer scale, I felt the exam did not do a good job of differentiating among the students. In particular, because problem 3 was dramatically more difficult than the problem it was ideally meant to be paired with, problem 7, the exam penalized students that chose to do problem 3. The other problem with the take home final from my perspective, was that by avoiding problem 3, students could avoid showing their problem solving skills. On the positive side, the final exam did do a good job of addressing the issue of transforming knowledge to pedagogical knowledge in questions 1 and 2. These problems showed that not all students were able to make this transformation, but on average students did. Below we shall analyze each of these.

The other issue is what does my experience with thsi final tell me for the future. The next time through the course, I will include problems like the first two, although I may require both, but I will try and put two problem solving problems on the exam, or force all students to do one problem solving type question. As mentioned in the introduction to this section, I find final exams to be somewhat problematic in advanced mathematics courses, which is part of the reason why I plan on keeping the final exam worth around 20% of the grade.

Next we analyze how the final played in to each of the course objectives:

All in all, most outcomes were addressed in some way by the final, although no student was required to respond on any particular problem. In the future, I may require a different final exam set up to be sure that certain outcomes can be assessed for all students, independent of how they choose problems.