## On Midterms

I am in the middle of midterms. I tend to write three different types of exams: two types of in-class exams, and one time of take-home exam. I will mix the take-home with either type of in-class midterm.

The first type of in-class midterm is a check that students are able to do the basic things from the course. This includes recalling definitions and answering straightforward questions. In a calculus class, I might include a question like “What is the derivative of f(x)=x^2?” The purpose of this in-class exam is to act as an incentive for the students to take time to learn the course material.

The take-home exam has a different purpose. Here, I’ll ask questions that require students to think about concepts in novel ways. I often make these open book, open notes, group exams. In a calculus class, I might include a problem like: “Find the equation of a tangent line to f(x)=x^2+1 that goes through the point (4,8).” The purpose of this type of midterm is less to assess the student’s knowledge than to help her acquire more. I hope that thinking about these questions leads to a greater understanding of the material.

The second type of in-class midterm is like the take-home, only it is in-class and not a group test (with a couple of exceptions). The main lesson I have learned here is to only give a small number of questions, since each of the questions is fairly involved.

I have given all three types of midterms so far this semester. I tend to always include a component of “learning exam” (rather than “accessing exam”), as my main goal is to help students learn. However, I also need to assign grades, and this is the reason for the pure assessing exams.

I don’t feel great about giving the assessing exams. I do not like the idea of making the students demonstrate that they learned the material, largely because I have read psychology results that say this type of “incentive” (a bad grade is a “stick,” or a good grade is a “carrot”) decreases student learning. I would love to hear of creative ways of having students learn mathematics, assessing what they know, and having the two complement—rather than work against—each other.

Please leave comments, although please offer evidence if you say “students would never learn if I don’t give them exams/homework/etc.”

### 9 Responses to “On Midterms”

1. Anonymous Says:

A few days before the test, I give a worksheet/practice test that has the same type and number (or thereabouts) of questions as the test. They take it home and work on it with each other, with people who aren’t in the class, or alone.
The next 1-2 days they can ask questions about the practice test at the beginning of class and we work through the answers on the board. I remind them that the practice test has a low number of points and is basically inconsequential to their grade, but that the reason it exists is so they can test themselves / review / prepare for the test.
Then I give the test. It is always open book and open notes. I figure that the books don’t have the test answers in them; they have the tools to get the answers. If the student didn’t know how to use the tools before the test but figures it out during the test, then some learning has taken place and that is my goal.
Most students use the practice test wisely. This is sort of the example that you didn’t want to hear, but I’ve had students who seemed as though they couldn’t apply the material towards getting the correct answers until the moment of the test, and the test period is when they spend the time figuring it out. I’m OK with that.
I’ve also had students who couldn’t apply the material we learned to new situations, AND had no idea how to use the book to help them do this, i.e., did not know what page to use, or could not discern what examples from the book were pretty similar to the test questions. I find these students either need help with study skills / reading skills / test-taking skills / general problem-solving skills, or they are in an inappropriate level of class and the material is not yet comprehensible to them.

• Anonymous Says:

(directed towards anonymous guy) Just out of curiosity, what level of education do you teach (elementary school, high school, college)? Also, what level of courses do you generally teach?

• bretbenesh Says:

Thanks for the new idea! I like the fact that your method teaches students to use resources as well as learn the material. This is almost certainly a more valuable skill than the particular bit of content being tested.
A couple of questions or comments:

What subject do you teach?
I actually don’t get too worked up over students learning the material immediately before the exam. One justification for giving exams is that they motivate students to study; it sounds like your model does this for students.
Exactly how similar are the practice test questions to the test questions? Do they differ by just a couple of words or numbers, or are they just similar in “spirit?”
You said that the practice test counts a little toward their grades: how to do you grade it? Do you basically treat it like a regular exam?
On a related note: how much time does it take for you to make up and grade the practice exam?

Thanks!
Bret

• Anonymous Says:

1. If I would’ve signed my post, you might have known that I teach English as a Second Language to community college students. The specific classes I was writing about were high beginner and intermediate grammar classes.
2. I agree.
3. The practice test questions are on the same grammar point and in the same format as the test questions.
Example practice test question:
Change the active sentences to passive. Use the by-phrase only if necessary.
People speak French and English in Canada.
Example test question:
Change the active sentences to passive. Use the by-phrase only if necessary.
People check out books at a library.
4. The practice test is worth five points and it goes into their homework score. The entire class has 1000 points total, so five is not a big percentage.
5. I make up the practice test and the test at the same time. Together they probably take 2-3 hours to write. The practice test probably takes about an hour or hour and a half to grade.

• bretbenesh Says:

Thanks, Bad Z. It is nice to see you on this site. Thanks for the clarifications!

2. ericakathryn Says:

We’ve talked about this before, but I suspect you might be overestimating the disincentive of “external” motivation. Some (though, of course, not all) people like the opportunity to demonstrate their knowledge on an assessment-type exam, and if you’re using them in conjunction with others (as some of your commenters have suggested) I don’t see anything too bad about them.

• bretbenesh Says:

Perhaps I should clarify my thoughts here. I think that whether or not I am overestimating here depends on the outcome we want to measure. I completely agree that external motivation gets most students (at our college, at least) to study. I am not disputing this. In fact, I’ll one-up you: I think that this effect even happens to students who don’t like demonstrating their knowledge. So I do think that exams lead to learning…in the short term.
However, I think that there may be a cost that is tough to notice immediately (and research backs me up). I think that this cost may be that students are more concerned about “doing well” than “learning the material.” It can be very difficult (impossible?) to tell the difference when observing a student. If the research is correct, and these external motivations sap ones interest in the subject, we might be trading a lifetime’s worth of studying for a semester’s. This seems to me to be penny wise and pound foolish. Again, assuming that the research is correct.

• Anonymous Says:

That’s a really great point Bret. I have seen so many fellow physics majors be “weeded out” due to high pressure exams and being told that your grade equals your success level. It really does squeeze the life out of the field. Even this semester as a junior, I have seen 3 (of around 15) physics majors drop because they just don’t enjoy it anymore. I think this is true (and so do many others) that the US has a big problem with teaching science and math. Both these fields make most people cringe upon mention. They are made out to be difficult and only to be pursued by a gifted few. This is not how it should be.
Grant

• bretbenesh Says:

Hi Grant,
It is nice to see you here. Do you have suggestions on how the math and/or science could be made easier?
Bret