Wikipedia describes a wiki as

a website that allows the easy creation and editing of any number of interlinked web pages… [Wikis] are often used to create collaborative websites, to power community websites, for personal note taking, in corporate intranets, and in knowledge management systems.

I have used wikis in three of my classes: two Discrete Mathematics courses (Fall 2008 and Fall 2009) and one Knot Theory course (Spring 2009). In the Discrete Mathematics class the students collaborated to create a homework “solutions manual” on the wiki. In the Knot Theory class each student had a “pet knot” and created a wiki page containing biographical information about their knot.

I used Wikidot to host the wikis. Their wikis are free and ad-free for educational use. You can make the wiki private if you want to. (I did this for Discrete Math because I figured the textbook author wouldn’t want the solutions available on the web.) Also, one of the deciding factors for me was that you can write mathematics in Wikidot using a modified version of LaTeX. (Here’s a Wikidot LaTeX help page that I created.)

Discrete Mathematics

Discrete Mathematics is our gateway course to the mathematics major, so it is in this course we teach the students how to write mathematical arguments (proofs).

I used the wiki as a place for the class to create an online solution manual for the homework. I made a page for each section of the textbook. As the semester progressed I listed the problems that needed solutions. I chose only problems that did not have answers in the back of the book. All of the problems were ones that I had assigned for homework, but I waited until after the students turned in their homework to list the problems on the wiki.

Every couple of weeks (once we’d accumulated enough problems) I required each student to contribute one major edit and two minor edits to the wiki.

Examples of major edits include:

• Typing in the statement of a problem and a complete solution.
• Making substantial changes to an existing solution. Fixing or cleaning up a proof is not sufficient for a major edit, it must be modified in a fundamental way.

Examples of minor edits include:

• Typing in the statement of a problem and a complete solution to a non-assigned problem.
• Correcting all mathematical errors in a solution.
• Correcting all typographical errors in a solution.
• Fixing badly-coded text.
• Modifying text to conform to our style guidelines.
• Starting a new solution, but not making much progress.
• Adding a picture that they created.

Periodically I went through the wiki and read the solutions. I wrote comments on the “talk page” and added banners (complete with goofy clipart) underneath each solution. The banners would say:

• Error. There are one or more errors in this solution. There is probably a discussion of the error on the talk page. When you have corrected the error, you should remove this banner.
• Messy. This text is messy. It might need better math formatting or structural repair. There may be typographical errors. Look on the talk page for more information. Once you have cleaned things up, you should remove this banner.
• Suggestion. I have suggested improvements for this text. The suggestions are described on the talk page. Please read the discussion there for ideas on improving the writing. Once you make the changes, you should remove this banner.
• Not started. This homework problem (or a part of this homework problem) has not been started. After you have written the solution, you should remove this banner.
• Checkmark. (If the solution to a problem is correct, I put a red checkmark underneath it. Once I signed off on it, they do not have to edit it further.)

I graded the students on participation, and not on the quality of their edits. Thus I only kept track of whether they did the required major and minor edits. Even for this I trusted their honesty. Each student had their own page on the wiki where they kept a log of which major and minor edits they made, and the dates they made them. Of course, wikis have excellent version histories, so I could always go back and see who edited what, when.

I was surprised (although in retrospect it isn’t too surprising) to discover that many students would rather type the solution to a non-assigned problem for their minor edit than to read through an existing solution in search of an error. I ended up not allowing this type of minor edit in the latter part of the semester because there were so many lingering non-corrected errors.

The students quickly realized that there was incentive to make their edits early. If they waited until the night before the edits were due, then only the more challenging (or more time-consuming) problems were available.

When we got close to exam times I would assign extra minor edits so that the solutions could be used as a reliable study guide.

Did it work and was it worth it? I think it worked pretty well. By the end of the semester we had a pretty good solution manual for the course. This was a nice resource for the students to study from. However, I wouldn’t say that the students were overly excited by the process. Most students did the bare minimum that was required of them. In neither year did I find any students who went out of their way to clean up the wiki beyond what was required of them. On the other hand, I think that it wasn’t too time consuming for any individual student.

Knot Theory

I taught a low-level mathematics elective on Knot Theory. There were seven students in the class of varying mathematical abilities.

The wiki for this class (which is still available online) was not collaborative. At the beginning of the semester each student chose a “pet knot” and created a wiki page for it. At first they just chose a name for their knot and used KnotPlot to generate a picture of it. Then, as we progressed through the semester and learned about new knot invariants (tricolorability, unknotting number, crossing number, etc.) the students would compute the invariants for their knot and write about them on their pet knot page. For example, here is one student’s pet knot page and another student’s.

One might imagine that some students would have trickier knots than others. That was true for certain invariants, but since they were doing so many different things with their knots, I think it all averaged out in the end. It was fortunate that there were seven students in the class and there are exactly seven 7-crossing knots, so I assigned each student a 7-crossing knot. This made things more fair.

One sticky point was drawing the drawing of knots, graphs, and surfaces and putting them online. In the end the students used a variety of drawing programs: EazyDraw, InkScape, PowerPoint, Adobe Illustrator, etc.

I think the wiki worked pretty well in this class. I could have accomplished the same thing without a wiki—have students turn in solutions for their pet knot on paper during the semester or at the end of the semester—but the online approach worked well. It was nice to see the knot biographies fill up as the course progressed.