Making up Problems

Guest Blogger: Bill Gasarch

HW AND EXAMS:
1. While making up the lecture notes problems may arise naturally. Such as ``OH, I don't want to bother proving this, but it would make a good HW'' or ``OH, I can do example 1 in class and leave example 2 for the HW, and 3 for exam''
2. OR the reverse- I want to ask THIS HW/exam problem, so I'll cover THAT in class.
3. If a paper you are reading for your research says `by a trivial induction XXX' then XXX might make a fine HW or exam problem. Same for other `easy' things that papers skip.
4. Do you allow your students open books? A sheet of notes? Calculators? Whichever it is, tune your questions to it, and view it as an OPPORTUNITY, not a restriction.
5. Just changing the numbers around might not be sufficient. Better to change the concepts around. EXAMPLE In class and HW I do Given Random Var X, and Dist D, find Expected value. On exam do Given Random Var X and you want Exp Value E, what should be the distribution.
6. Exams: Make it clear that you take off for clarity. This way you don't have to try to figure out if a complete mess has some idea in it.
7. Scoring: On a 20 point problem I tend to give either a 0 or a 10 or a 20. Getting the base case of an induction is NOT worth anything. Making an obvious typo is not worth taking ANYTHING off. This makes grading easier, but also you are spared having to make arbitrary distinctions that don't mean much. Do you really want to say ``On the way to a proof that wouldn't work'' vs ``On the way to a proof that might work'' vs ``On the way to a proof that would work'' are worth diff values? And then try to discern which it was? ALSO, If one student really didn't know much, and another one knew alot, I would rather the point DIFF by 20 points, rather than give 5 sympathy points, and take off 5 points for minor things, and end up with a 10 point difference.
8. There are two kinds of questions (actually I'm sure there are more) Those that test MASTERY of the material Those that test CREATIVITY- going beyond the material. I tend to ask more MASTERY questions, especially on exams.
9. What to do about students getting help from the web?
   1. Ask old questions in new ways to avoid the usual search terms.
   2. Tell students they must TELL you the sources they used. The problem here is if they DO tell you, then what do you do? You wanted them to do it on their own.
   3. HW not worth much, but ask similar questions on exams. For lower level courses you can also have short quizes.
   4. For a graduate course you can even say ``If you can understand the paper this came from and write it in your own words, AND UNDERSTAND IT then you will get full credit. But be forewarned, it may be easier to just DO it on your own.'' This WORKS for MASTERY type questions, not for problems that just need one insight, and you want the students to get that insight on their own.
RESEARCH PROJECTS:
1. ``Code it up and see what happens'' could be a basis for a research project.
2. As a warmup and confidence builder I would have a student read and UNDERSTAND two (maybe more) papers and COMBINE them. This could lead to very good research, but might not. But in any case the student KNOWS something and has DONE something.
3. If a problem dawns on you that you think someone else MUST have worked on then LOOK INTO IT. You may well find that nobody has worked on it--- what dawns on you as an `obvious' problem to work on might not dawn on others as such. Peoples motivations differ.
4. If there is some paper you've always wanted to get around to reading but never did, have a graduate student read it and explain it to you. This will be good for him and for you. Can also work with very good ugrads. Might result in survey papers if they read a series of papers. WARNING: You may end up doing more work in correcting the student, and seeing what he really meant, etc. But in the end you'll both learn the paper.