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.”