Teaching with Tech
Can Math and Discussion Boards Compute?
Maria H. Andersen, December 2011 / January 2012
Several years ago I began using an online homework system with all my calculus sections. The basic premise is that each student receives algorithmically generated problems similar to each other in structure but different in numerical details. The system grades the problems, with points based on correctness, and it is a common practice to let students have multiple tries to complete each problem.
When I made the leap into online homework, I also shifted the homework Q&A portion of the class into the online world. In online discussion boards (also called forums), students could ask questions about any homework problem online by generating a new “topic” and could receive help from another student or myself in the “conversation thread” on that topic. Since no two students have the same two problems, students have to share their problem and some of their work when asking a question about homework.
At first I thought my foray into online discussion was a failure—my math discussion board conversations looked nothing like those I had seen in the online classes of my colleagues from English or the social sciences. Their discussion boards had rich conversation threads on a few topics, with the majority of the students participating for each topic. My discussion boards had a huge number of topics, with a short conversation thread on each topic and only a couple participants per thread.
I realized, however, that my boards were not flops; it’s just that the nature of completing a solvable math problem makes the conversation pretty short. When the problem is solved, the conversation may continue as one or two details are cleared up, but for all intents and purposes, the conversation is over. (But Tim Gowers has facilitated lengthy and rich discussions in comment threads on the Polymath Project that have led to solutions for previously unsolved problems in mathematics. See the article titled “Massively Collaborative Mathematics” in Nature [October 15, 2009; doi: 10.1038/461879a].
I also learned that there is a “sweet spot” for the number of participants in a discussion board. I’d put it roughly between 20 and 40 students. With fewer people, it is hard to get the discussion boards going at the beginning of the semester (you might have to “seed” the board with a few questions). With more, it’s harder for students to find unique questions to ask.
Table 1 shows the statistics from my current calculus course, which has 32 students enrolled in the traditional face-to-face format; it is pretty representative of the participation patterns I’ve seen for years now. Most conversation threads last for only three or four posts and have only two to three participants.
Benefits of Boards
At first, I made the discussion boards mandatory for online students and optional for face-to-face students (all of them had access to common boards). But later, as I saw the benefits, participation in discussion boards was required for everyone. In particular, I started to realize how many of those in-class questions boiled down to a missed negative sign or incorrect algebraic simplification. These types of mistakes weren’t worth the class time of the entire group but were important to address somehow.
When a student asks a question in class, there may be only a few students interested in seeing the answer at that moment, but other students may end up with the same question a day or two later. With discussion boards, there’s a history for every question asked, and a place to continue the conversation if something needs clarification.
Using discussion boards gives your students a good place to ask questions if they have been absent or if they are shy about asking questions in front of an audience. In addition, students begin to write about math as they pose and answer questions, they learn a lot from troubleshooting, and you have the opportunity to see where students are stumbling in the mathematical process.
Incidentally, by moving homework Q&A out of class time, I put that time to use for more engaging class activities.
RulesOver the years, I’ve developed three “must follow” rules if you want to have active and successful discussion boards in a math course.
Give students a simple way to share work.You must teach the students to use technology that provides them with an easy way to share their questions and work. They need a simple way to snip and quickly share an image of what’s on their computer screen without having to save and upload each image. Various program can do this; check out Jing (Mac or PC) and Shutter (Linux).
Assign points.If you want students to participate, you must assign points to this activity. Students in my classes get their discussion points from either asking a new question or adding something valuable to the conversation thread around a question.
Stop answering homework questions in class.
When a student asks a question about a homework question during class time, you should respond with, “Did you ask on the discussion board?”
This last rule is the toughest one for new users of discussion boards to follow (both for students and instructors). The most painless way for a student to do homework is to not do homework—many students have figured out that they can ask us about a homework problem in class and that we’ll do the problem. (I call this the “trained monkey” phenomenon—guess who the monkey is?) And in our defense, we’ve all been told “there’s no such thing as a stupid question,” so we answer all student questions during class time.
What should your role be in discussion boards? I participate actively at the beginning of the term, then gradually pull away as the course progresses. During the first unit, I try to check the discussion boards late at night. This demonstrates that help will be available to all the early adopters. It also models the behavior I want to see from students. Remember, you can set the tone for appropriate behavior on discussion boards. Make it clear that students are not to do the problems for other students, but can give hints or troubleshoot each other’s problems. Following this, I give hints (not answers), and I use Jing to share images of my mathematical work.
By the second unit, I’ve shifted to checking the discussion boards first thing in the morning and performing mop-up on questions that lack resolution. This lets the students take a more active role in answering each other’s questions (they are always doing their homework late at night). In the first unit, my post is often the last say on each thread. But by the end of the semester, my input is occasional and mostly involves correcting notation or clearing up muddy mathematical thoughts.
When I see a problem has generated more than 10 posts, I make time to give a few hints about the problem, either during class time or in a short screencast online. (For help with screencasting, see my August/September 2011 column, “Become a Screen-casting Star")
My grading for discussion boards is old-fashioned—I print a roster and go through each of the threads, tallying marks by each student’s name as I see his or her participation. I use a simple grading scale: 1 point for each question/post (defining a “post” as a meaningful contribution to the conversation). I cap the number of points that can be earned per unit (some students will participate a lot more than others), and I allow for a small number of extra credit points to be earned for students who participate more than others. You may find that some classes require you to tweak your grading slightly. For example, if your students only ask questions, you could make answering a question worth twice the value of asking a question.
So, does math lend itself to discussion boards? Yes! You can have a rich and rewarding experience using a discussion board as a homework helpline manned by your own students.
Picking a Venue for Online Discussions
Not all discussion boards are created equal. You’ll likely have two options for discussion boards, one inside the learning management system used by your campus, and one inside the online homework system used for the course. Consider the following options before deciding which to use; I’ve listed these in what I consider to be the order of importance:
Pain factor: How long does the discussion board take to load on to the screen, and how many “clicks” does it take to get from the homework problem to the discussion board?
Readability: How easy will it be for a student to see the entire thread of conversation on a topic?
Sharing: How easy will it be for student to share an image of their problems or work? Can students edit their posts?
Grading and Monitoring: How easy will it be to grade the discussion boards? How editable are the posts and subject lines? Can you edit or remove a post?
Maria H. Andersen is a math professor and the Learning Futurist at the LIFT Institute of Muskegon Community College, Michigan; email: email@example.com.
This column appeared in the December 2011/January 2012 issue of MAA FOCUS.
Maria H. Andersen is a Learning Futurist for The LIFT Institute and a Math Professor at Muskegon Community College. She is also president of Edge of Learning LLC (formerly Andersen Algebra Consulting LLC), an educational consulting business. Follow her on Twitter @busynessgirl or visit her official website.