Last Friday, Reuters reported that more than half of the students involved in last year’s cheating scandal at Harvard have been suspended. This was even labeled “the largest academic scandal to hit the Ivy League school in recent memory”. In this post, I wanted to discuss my own thoughts on the matter, and more importantly on the general idea of giving take-home exams in a mathematics class.
As you may or may not recall, in the Spring 2012 term course on “Introduction to Congress”, 279 students were given a take-home final exam. The professor for the class, Matthew B. Platt, started noticing similarities in the responses to the questions, which indicated they had collaborated, something they were specifically instructed not to do. After this, of the 100 students implicated, 60 were suspended and the rest received some sort of probation.
The large scale of the cheating has led to much speculation as to whether the students were really at fault, or whether it was wrong for the professor to assign such difficult take-home questions and then expect the students to work alone. In September, Farhad Manjoo wrote a piece arguing that the students should be encouraged to collaborate on an “unfair test”, and if individual responses were required then the test should be taken in class.
I disagree with Manjoo for a few different reasons. First of all, I do not think that cheating is a good way to take any sort of stance against something you find unfair. If it really is unfair there are other channels, like talking directly to the professor, and students have lots of advocates they can approach, like the Dean of Students, Ombudsman, etc. As demonstrated by this case, by cheating they only hurt themselves and in the end didn’t change the system in any significant way (although I don’t know what, if any, were the repercussions for the professor of this class).
Secondly, I think that take-home exams are a valuable testing and teaching tool. I myself really like this for upper lever courses, since I can do exactly what the professor for Intro to Congress did, I can ask harder questions. Especially in mathematics, but I imagine in other disciplines, too, it is important to let the students let the question sink in and try several approaches (the first few may fail) before finding the correct answer. For a proof-based course, it is sometimes important to let the students use their notes and books (I don’t let them use the internet because there are too many people on there willing to give you the answer). Unless you are having them do computations or write proofs that they have already seen in class, it is hard to tell how much time someone will need to solve a problem. I think this is a useful teaching tool because it allows them to work like mathematicians, trying to figure out a brand new proof at home, using the material from class.
Of course, mathematicians collaborate sometimes, they don’t always just work on their own. And this is another point Manjoo makes, that we should encourage collaboration as it is going to be an important skill in the “real world”. Unfortunately, collaboration sometimes turns into a few students leading the others through the answers. Students don’t have the same understanding of pedagogy, and are more inclined to help their peers by giving them the answers (I really think most cheating comes from a sense of loyalty of students with students than from any malicious intent). But the point is, as instructors we want to know how much each student knows, and thus we need to at some point evaluate them individually. I am a big supporter of collaboration, since it is another important part of doing mathematics, and I encourage them to work together on homework and on final projects (which I do for many classes instead of a final exam).
Taking Manjoo’s side for a second, I do know some people who allow collaboration on take-homes, and then the individual assessment is in the form of an oral exam (based on the take-home). That is a pretty good tool for knowing how much each student contributed to the answers, but is quite time-consuming (and intimidating to the shier students). Catherine Roberts wrote about some examples of collaborative assessment. Some seem to work well, but she does point out that “one danger with collaborative exams is that students frequently defer to the person who is perceived as the “smartest”—they don’t want to waste precious time learning the material but rather hope to get the best score possible by relying on the class genius.” In any case, even if we allow collaboration on exams, there needs to be some individual accountability. It is my job to teach mathematics, it is the student’s job to learn mathematics, and I need some way to know if we’re all doing our job!
But I still wonder, why were so many students inclined to cheat in the first place? It seems like there is a deeper problem here, which has to do with the students’ philosophy of learning. This reminds me of something I learned in a math ed class in grad school: the difference between learning oriented and performance oriented students. Performance oriented students were more worried about the grades in the class than learning the material in the class. It’s not surprising that learning oriented students actually tend to do better in classes, and are also more likely to succeed, especially in mathematics. So I can imagine that if I were a performance oriented student, was given a very hard take-home exam, and a friend was in the same class, I would be tempted to collaborate so that we could both get a better grade. But if I were a learning oriented student, and possibly understood why our professor was giving us a take-home exam full of difficult questions, I would just work as hard as I could on my own and hope for the best. Applying this to the Intro to Congress class, which Manjoo says “had a reputation for being easy”, I am not surprised if many of the students who enrolled were more performance oriented (this was supposed to be an easy A).
At any rate, this leads me to the only thing I think I learned from the cheating scandal, and maybe my one criticism of the Harvard professor involved (of whom I know very little). It seems like the instructions for what was allowed for the test were clear, but maybe not the reasons for having such a test in the first place. From now on I will try to be painfully clear about my own goals as a teacher (I do this already, but it can’t hurt to try harder). If you’re giving a hard take-home exam, which many students will be tempted to cheat on, you should be clear about why you’re doing it. That is, explain your pedagogy, share your philosophy of teaching, make yourself an ally (I’m doing this because it’s the best way for you to learn or for me to assess what you’ve learned) rather than their adversary (I’m giving you this test so you will fail). I have also tried to make cheating less tempting by giving exams in two parts, an in-class worth about 60-70% of the grade, and a take-home with harder questions for the rest of the grade. I think this takes some of the pressure away, but allows me to assess (and teach) the way I want to.
By the way, I have caught very few students cheating on my take-home exams, but that doesn’t mean they’re not doing it! The fact is I can’t police and control all of my students, nor do I want to. In the end, what bothers me most about cheating is that they are avoiding learning the material. If they get through my class by cheating, they will be stuck with not knowing very much in the future. They may pass my class and graduate college by cheating, but mediocrity is harder to hide when you are out there in the “real world”. Or at least that’s what I tell myself to feel better about the whole thing.
1- introduction ( author, title, sourse, data, and main idea.
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