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I'm teaching a graduate course in mathematics next semester. I'm planning to have a midterm and a final exam. But I'm thinking about having weekly (or once-every-two-weeks) in-class quizzes instead of homework assignments. My plan (for each week) is to post five problems for the students and one week later randomly select one of the problems for the students to solve during a 10-minute closed-book quiz in class.

I've done this type of thing before in first-year calculus and linear algebra classes without issues. Some students reported that they liked the quizzes because it forced them to keep up and internalize the material more than homework does. I agree with them on that point. I also like quizzes over homework because it is more difficult to cheat and that there is less grading to do.

Is doing quizzes instead of homework a good idea or a bad idea in a graduate course? What are the pros and cons?

Edit: It's a standard first-year lecture-style graduate course. Think complex analysis or abstract algebra or measure theory. I expect 10-20 students, mostly graduate students, but a few senior undergraduates.

Edit: A valid answer could be neither. I'm open to hearing the case for that.

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    $\begingroup$ A valid answer might depend on a few unsaid things. What is the scale of the class? A few students or quite a lot. More like a seminar or more like a lecture? What is the level of the course? Is it an early course or one that would normally come later in your curriculum? $\endgroup$ – Buffy Jun 27 '18 at 13:44
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    $\begingroup$ What is the goal of giving graded homework or quizzes? These seem like formative assessments, and I typically feel that assigning a grade to a formative assessment is a way of getting students motivated to actually study (the actual grade for a course should be based on summative assessments). By the time a student is in graduate school, it seems a little condescending (to me) to give them graded quizzes and homework---they're grownups, and already know that they have to study. $\endgroup$ – Xander Henderson Jun 27 '18 at 15:16
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    $\begingroup$ @MichaelGaudreau Most of the graduate courses that I have taken have homework; very few of them have graded homework. In the classes with graded homework, the work tended to involve tackling more interesting / difficult problems that simply couldn't be done in a 10 minute (or 90 minute) quiz. Obviously, there is likely quite a lot of variation from institution-to-institution, and from instructor-to-instructor. That being said, I, personally, would find graded homework to be much less condescending than quizzes. Quizzes seem punitive, somehow. $\endgroup$ – Xander Henderson Jun 27 '18 at 16:31
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    $\begingroup$ @MichaelGaudreau If you tell me that I am going to have to regurgitate the solution to one of five problems during a 10 minute quiz, I'm going to organize a rebellion. By forcing me to do this as a quiz, you are taking instructional time away from me (I want to hear your lectures!) and suggesting that I don't have the integrity to turn in my own homework. Please, treat me like the adult that I am. If I fail your exams because I never did my homework (or cheated on it, even), that's my problem. Again, graded homework is preferable to quizzes (IMNSHO). $\endgroup$ – Xander Henderson Jun 27 '18 at 16:46
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    $\begingroup$ No. Undergraduates are very different from graduates. Most undergrads are coming straight out of high school. They often don't have very good study habits, and a little bit of hand-holding is appropriate. By the time students are in graduate school, they really don't need that much support. Many of your students will have written undergraduate theses or have presented posters or talks at conferences (the MAA, for example, has many conferences for undergrads). They should know what they are doing. The phrase "instructional scaffolding" might be good for Googling. $\endgroup$ – Xander Henderson Jun 27 '18 at 16:54
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This is rather rare, but I have had two or three graduate classes that did this (out of an unusually lengthy graduate career spanning several universities). The best use of this for me was in the first semester of a two-semester graduate algebra course that used Hungerford's book. I thought it worked extremely well in that case because Hungerford's book (especially Chapter I and Chapter III) contains a lot of fairly simple and short techniques in the text proofs and exercises that one should master before they pile up too much and one gets overwhelmed by all the important and unimportant details. This was a MWF class, and there were at least 2 quizzes each week, except maybe the week of an hour test (there were probably 2 hour tests, and 1 final exam), when at most one quiz was given, and probably none if the hour test was on a Wednesday (since a Monday quiz wouldn’t get handed back to us until Wednesday, too late to help in studying for the hour test, and there would be no new material to base a Friday quiz on).

Incidentally, this reminds me of when I taught an elementary differential equations course (4 times), when so many methods for solving ODE’s pop up at the beginning --- separable equations, exact equations, homogeneous equations, first order linear equations, integrating factors, Bernoulli equations, etc. I gave a short quiz nearly each class meeting in which they knew which method I would be asking them to use. The more difficult task in which the students had to determine which method (or methods, as often more than one method could be used to solve an equation) to use on a particular differential equation, without being told, was dealt with in the first major test (and the review for that test).

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I think this is a great approach. Just because you are in fancy schmancy grad school doesn't mean basic pedagogy or psychology has changed. I don't know much about measure theory but for complex analysis or modern algebra, think it would be easy to write questions of appropriate time length that test something relevant (drill problems from the homework). You go, girl!

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I had a graduate abstract algebra course (part of my minor to a PhD in Computer Science), in which weekly (or each two weeks, it was long ago) we got homework. Usually four quite tough questions (not "exam style"!), and only one (chosen at random each time) was graded. If some question gave too much grief, it was discussed in class after handing homework in.

One particular point that stuck was that often it was asked to prove something, and your first reaction was "That can't possibly be true!". I enjoyed the course immensely.

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