## Exam Format

I had (exactly) two good ideas from last year. I already wrote about Weekly Writing Homework, which I am pretty sure I have never heard of before (but I am also pretty sure this is a new idea). My second idea is one I am certain that I have heard before, but I don’t remember where. It is an exam format that worked really well for me—students came back after the semester ended and told me that the exams really helped them learn.

Here is the basic outline— you can adjust as needed.

1. Assign the students four problems one week before exam date. These are problems that could be on the exam.
2. Students can work together to solve the problems. In fact, I encourage students to work together to solve the problems.
3. Each student picks one of the four problems to write up prior to the exam in $\LaTeX$. I make it clear that this write up cannot be done with other students—students can develop the ideas together on, say, a blackboard, but the students need to separate and write up the problem alone.
4. The student comes to the exam and hands in the $\LaTeX$ed solution immediately.
5. The student gets a copy of the in-class exam. Of the remaining three problems the student did not write up, I assign them one to do for the in-class exam (My exam instructions are roughly: “If you did not submit a $\LaTeX$ed version of Problem 1, do Problem 1; otherwise, do Problem 2.”). Since they have already discussed the solution with other students (hopefully), they just need to re-create and write down the answer.
6. So one problem was written in $\LaTeX$ and one was assigned to them for the in-class exam. This leaves two of the original four problems; students need to pick one of the remaining two to do.
7. I also give the students a simple problem that they did not see before.
8. If there is enough time and it is appropriate, I might ask students to state some definitions, along with examples and nonexamples. (h/t Robert Campbell for this).

I like that I can give students challenging problems, and they can rally to do them; if one of the problems is too hard for a student, they might not need to do that problem on the exam. Students learn a lot from working together, but they also know that they will be held individually accountable.

Can you see ways this can be improved? What are the flaws?

### 8 Responses to “Exam Format”

1. thehabyss Says:

Bret describes this well. I have stolen this idea from him and am using this in my analysis course currently. The students really appreciate it.
I think it is worth mentioning that Bret and I are both using specifications grading to score the problems.

2. Andy Rundquist Says:

On my first read, the weak point appears to be “but the students need to separate and write up the problem alone.” Is your sense that you have to police that very much? I love the collaborations they’re likely participating in during that week, I guess I’m just wondering how similar their LaTeX files are.

• bretbenesh Says:

You basically have it. We can get identical write-ups from people. At that point, I don’t have confidence both (all) students understand the problem. In theory (and sometimes in practice), one student will just write it up and email the file to others.

Here is what is okay to do that perhaps I did not make clear: students could write up the entire thing on a chalkboard together, say. Then they could fine-tune how to write it. But then I don’t want students to just take a photo of the chalkboard and then type that up. Again, a student could be present with no understanding, and then I wouldn’t be able to tell (and perhaps neither could they).

Students might do this anyway, but my (possibly) naive sense is that usually students who submit identical versions of the paper do so out of ignorance of the “rules” rather than because they are trying to cheat. Explicitly tell them what the “rules” are eliminates most of the problem. The few remaining cheaters are, well, going to cheat no matter what I say, and I will either figure it out or not.

Can you give me an alternative? Just let it go and assume that a well-written problem indicates that the student who submitted it understands it?

• Andy Rundquist Says:

I’m not sure of any really good alternatives. You know that I use oral exams to get to the bottom of that, but those don’t get at something I think you care about which is the students learning from doing the write up. For me, I would accept a vid of them walking me through the write up in lieu of a write up from each person, but I’m not sure that gets at what you’re looking for.

• bretbenesh Says:

Thanks for reminding me about oral exams. Those are great for identifying conceptual understanding, and I shouldn’t forget about them.

You are right, though: in several of the courses, the _writing_ is also important. And this is what I am trying to get at (in addition to other stuff).

I should think about relying on oral exams more, though. Thanks for reminding me!

• thehabyss Says:

I have a similar concern. This past Fall I had an issue with this. This semester, though, I have been very clear with my students about the rules and expectations, as Bret explained. I explain to them that they could put themself into a moral quandry and I want to eliminate even the potential for that. I give them this example to help explain my point:

Say you write up the proof for theorem 3. You are done and happy with your proof. You intend to turn it in soon. Your friend asks you to review their proof, knowing that you have finished the proof. Knowing that you are done with your proof you don’t see the harm in reviewing their proof, since your proof is your own ideas. You look at your friend’s proof. They have included a case that you haven’t yet considered. You realize that your proof is incomplete. Do you add this proof to your own?

My students see the potential dilemma and I haven’t yet had any issues with similarity in proof this semester.

• bretbenesh Says:

Yeah—our students collaborate really well—sometimes too well. They are (usually) not being malicious or trying to cheat, but one needs to give clear instructions, as Robert thehabyss does.