How should I structure exams when individual problems could use up the entire class time?

Question

I am currently preparing for a new class in an area in which the individual problems can be very long. (My writeups for individual homework problems were often three or four pages long when I took the same course as a student!)

Solving a typical problem involves:

1. Identifying the correct differential equations and boundary conditions to solve.

2. Making the correct assumptions and simplifications.

3. Identifying the correct solution strategy.

4. Implementing the strategy and solving the problem.

All of the above steps are of critical importance, as we introduce new methods and approaches for each.

Given that, an in-class exam would only have enough time for one problem—so there would be no easy way to evaluate mastery of the breadth of the material. So I’ve been thinking of doing an out-of-class exam. The time would be long enough that the students would have time to think through things, but not long enough that they could spend a lot of time trying to look things up on the internet. The class is also small enough that it would be fairly easy to detect plagiarized work or students copying off of one another. (I suspect four to six hours is sufficient.)

Are there more viable or effective strategies for testing in such circumstances?

Answer 1

The most time-consuming and least information-bearing step (at least for the purpose of evaluating understanding of the material) is 4. In this situation I've often just given questions asking the students to do 1-3 and explicitly told them to not go through the calculation. It's better if you prep them for this by giving such a question on a quiz first since many students tend to go on autopilot after a couple of decades of being trained to come up with an answer.

Answer 2

Split up the question into subsections that, in total, are the initial large question. Turn these into individual questions, in-place of the expected components of the large question.

1. Identifying the correct differential equations and boundary conditions to solve.

2. Making the correct assumptions and simplifications.

3. Identifying the correct solution strategy.

4. Implementing the strategy and solving the problem.

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Wait. Do you want us to tell you how to test with a single large question, or how to make a test that would "evaluate mastery of the breadth of the material"?

Answer 3

One alternative would be to have multiple problems and with the steps necessary for the resolution in multiple choice questions regarding the process. This way it could be a matter of reading and thinking fast.

At the end they could one of the problems (let's say you proposed 4) and solve it completely.

-- EDIT --

Considering the new information, you could use in-class time for them to get to step 3 and let them solve step 4 out-of-class, maybe with MatLab or Octave (if that fits the course).