# Design of a math exam using multiple choice or computer

I'm teaching math in first years of university (matrix algebra, differential analysis, etc.) since maybe 5 years, and I usually give written (paper) exams to the students.

I'm looking for ideas to change a little bit my practice: I would like to do more exams, i.e. more tests during the semester to test the continuous work of the students, but without doubling or multiplying by 3 the exam-marking job.

Have you seen good examples of math exams using a computer, or multiple choice questions? for example for a basic matrix algebra course (matrix operations, rank, linear systems)

• My two cents: they're hard to write well - either the wrong answers are obviously so, or there is a brutally high penalty for (relatively) minor errors e.g. of sign. – kcrisman Dec 9 '16 at 13:21

## 3 Answers

Here are some examples of using WeBWorK for homework in matrix linear algebra and ordinary differential equations. (MTH165 at University of Rochester)

1. The current MTH165 course is here. You can login as guest. You can print out a pdf of any of the assignments.

2. You can use Moodle as a front end and us WeBWorK to provide the assignments: Here is an example (you can log in as guest and see the assignment version of the WeBWorK questions). You can also print out pdf versions of the assignments from this version of the course.

3. To see the pure moodle version of the questions (the "quizzes") where WeBWorK is completely hidden, you will need to login to the address above with the login visitor and the password visitor. Moodle does not allow guests to view quizzes.

4. If you want to look behind the scenes you can visit hosted2.webwork.rochester.edu, and look at UR101, UR102, etc. Use profa as login and profa as password. These are demo courses and not specifically linear algebra. Don't expect any changes to be saved. :-) Check out the Library browser and look for problems involving matrices or linear algebra.

5. Have a little patience with the free trial signup at webwork.maa.org. I think something failed over the weekend and they haven't noticed the outage yet. It's a busy time for them with the Joint Math meetings coming up soon. (Added 12/12/2016 10am) At this time the link at forms.maa.org/r/webworktrial/add.aspx for requesting a free trial was accepting submissions.

You may be able to construct a multiple choice computer exam using WeBWorK. There certainly are multiple choice ones in its library, but whether there were enough for a given exam would depend a lot upon the subject. Of course, you could learn to write your own. It is used for placement exams some places, at any rate.

• Thanks for this reference. Do you have an example of exam? It seems that it's either paid (with a fee) or free (but this requires a subscription, or it seems to be a version on github too). How does it look like (maybe is there a sample PDF?)? How do you use it? – user7559 Dec 9 '16 at 16:25
• WW is free as in beer and as in free speech. However, naturally to set up a server takes time and bandwidth. The MAA provides one free semester, I think, as a trial, but your local IT may be able to help you do it longer term. In any case, there is a way to use a sample account to try it out, if you poke around the website a bit. – kcrisman Dec 9 '16 at 18:47
• I must admit that my prior attempt at experiencing WebWork failed (a few weeks ago). My local IT won't set it up, and the offered trial login didn't work. If anyone had more specific, currently-working knowledge, I think that many of us would benefit. – Daniel R. Collins Dec 9 '16 at 19:46
• Maybe just an example PDF or HTML of how it will look like at the end would help convincing my local IT to accept doing it. Would someone have such an example? – user7559 Dec 10 '16 at 10:06

Concerning the time issue, you can use AutoMultipleChoice to write multiple choice exams in LaTeX, with randomization of questions (or simply randomization of their order and the order of answers), and which can be automatically graded using a simple scanner. It will take some time at first but you should gradually build a database of exercises that should be reusable. These might exist available, but I don't know a source.

Concerning the proper construction of the questions, there are several ways. If you want to test particular mistakes, propose an answer that follows from that mistake (e.g. I ask in almost all my calculus tests to differentiate $f(x)=2^x$ and I always propose $f'(x)=x2^{x-1}$). If you want to test computations of a certain sort, do the computation once for each proposed answer but each time add one mistake you really want your student not to do (this depends on your goal: you may include small silly mistakes if you want them to be flawless, or only include really bad mistakes).