1. If two classes are identical in performance during the year, do you think their performance on finals will be the same?
2. If the "better" (e.g., higher-average-grade) class meets period 3 and the "worse" class meets period 8, will you expect their average grades on the final to differ by the "usual" amounts?
3. If the opposite situation holds to #2, what would you expect?
4. If there are differences beyond "expected" ones in #1, 2, 3, what do you think the cause (or causes) is/are?
perfect ideal rational world, yes, performance on finals would simply correlate with performance (as a group) over the course of the year. But the world is not rational. Several commenters to my post addressed the issue of "soft cheating" and time issues, and I agree with them. There will be differences (see #4), and in my opinion those differences will largely be due to the time that the final is actually given. It's been my experience that the later in the week the final occurs, the worse the students do, soft cheating or no.
The last question is more interesting, in my mind:
5. Should anything be done about [the existence of differences beyond expected ones] if so?
Yes, yes, yes it should. But it's not changing the final, or making multiple versions, or rescheduling things; it's bigger than that. I think finals should not be structured as they are now; they should not be simply opportunities for students to regurgitate knowledge they've stuffed into their heads, quickly to be forgotten. They should allow students to discuss, demonstrate, interact, and in short authentically show me what they've learned. That requires that my courses must:
- ...be ones in which students have opportunities throughout the year, not just at finals time, to genuinely demonstrate what they know.
- ...have a narrative - a beginning, middle, and end, with all of the metaphors taken over from works of literature intact. There should be crises; there should be characters; there should be a plot with a denouement. Storytelling is an old and honorable way of transmitting knowledge. I see no reason to believe that model would not apply to a mathematics course.
- ...have a practical and genuine way of figuring out what a particular student has learned at the conclusion. That is, what does a final for a course thought of in this way look like?
I don't have a lot of answers to these requirements right now. The first one seems to dovetail with standards-based grading; the last may lend itself to a "capstone" model of final projects instead of an exam; and I'm not at all sure what to do with the "narrative" requirement. Maybe a subject for a future post.