Two years from now at my ten-year high school reunion, I'll be explaining to my former high school classmates that I am still in school. At the college level, I have taken over 200 semester credits. I have also had a chance to teach my own classes. My lifetime dedication to school and my focus on economic principles give me unique ideas on education.
Personally, I find these ideas useful both as a student and as a teacher. That's why I am posting about this. From my perspective, the process of teaching and learning is an economic problem. By this, I mean that teaching and learning are both guided by scarcity and optimization.
In my experience, this has been true whether I was receiving exceptionally poor instruction or exceptionally good instruction. I will save my thoughts on what makes good teaching good for another post. This post examines the question of when giving a difficult exam is good idea.
This is a normative (value-based) question, so depending on what you think is a good outcome from teaching, you may disagree with me. This also means that for a cohesive argument, I need to define what I mean by "good" versus "bad." In my view, a good teacher's objective is for students to learn as much as possible about the subject. I think this is a reasonable objective for a teacher (or an education system in general), so this is my criterion. Therefore, if a practice leads to more learning, I call it a good idea. If not, I call it a bad idea.
So, what of giving exams? Why do we give exams if our objective is to maximize student learning? After all, time spent administering an exam is time that cannot be spent learning new material. So, what's the point?
Is giving exams a bad idea? I don't think so. I think the point of giving an exam is that we really, really, really want our students to understand the material covered in class. If the subject is worth teaching, the median student probably did not sufficiently understand what was taught on the first go-around. Periodically, we need a status check. But, in an economic sense, it is more than that!
If the median student does not meet expectations prior to exam time, that does not imply bad teaching. In fact, most subjects worth teaching usually lead the median student into confusion before he eventually gets it. I think this happens because points of misunderstanding are annoying to clear up. Most people dread having to study something that they failed at understanding in the first place. This leads us to neglect important concepts and miss the big picture. As time goes on, the median student accumulates misunderstanding, and this leads to general confusion.
This is where exams come in. Viewed from an economic perspective, students in the previous paragraph do not face a high enough price for small points of misunderstanding. Most people need a credible threat that if they do not understand something important, they will be punished for that lack of comprehension. What's more threatening than a challenging exam? And, what more credible than doing it over and over again (year after year, final after midterm)?
This gives us a reason to challenge our students. Students who are held to the fire tend to learn more than otherwise. This is one reason why employers place a premium on hard degree programs. All else equal, we expect more value added.
That's all well and good, but can an exam be hard in the wrong way? I think so. Moreover, I think that well-intentioned instructors often write pointlessly hard exams.
To be sure, students need to be pushed hard to understand tough material, but exams should give students an incentive to review all that was covered to that point in class. To that end, it is counterproductive to write an exam that is intentionally vague or takes students to "new and interesting places." This is because such exams cannot be studied for, so students rationally do not study as much as they should. As a result, less learning takes place.
Being intentionally vague on an exam makes the exam difficult, but in the wrong way. Such exams are also painful for everyone involved: students feel dumb, and the grader has to make some tough choices. To me, it sounds like this practice uses more resources to get less learning. That's clearly a bad idea.
Tough exams have their place and I generally think they are a good idea. But, teachers should be careful about how they ask tough questions. Tough for its own sake is usually a bad idea, but tough for the sake of learning leads to better outcomes. How do I decide on whether to include a difficult question on an exam? I ask whether showing the question to next year's students will get them to study harder. If yes, that's a hard question that I can agree to asking.