Image: Dennis Skley, vie Flickr.
Last year, I had my math history students write a blog. The course counts as a writing credit, so blog posts seemed like good short writing assignments. But what about blogging in a math class that’s just a math class? My academic sibling Casey Douglas, who teaches at St. Mary’s College of Maryland, incorporates blogging into his Foundations of Math class, and I decided to ask him a few questions about it. If you want to jump down for links to some of his students’ posts, click here.
I hope other teachers interested in class blogging will get some ideas from him. If you’ve used blogs in your classes, feel free to share in the comments!
EL: First, can you say a little bit about the class that’s blogging: size, typical student majors, main topics covered, main learning goals?
CD: This is class called Foundations of Mathematics, a relatively fancy name for a standard proofs-writing course. The class size can vary, anywhere from 15 students to 30-ish students (this semester I have 21 students). Roughly half of the students are math majors (or will be.. this class tends to hook them), and all of them are at least math minors. (St. Mary’s offers an especially schedule-friendly math minor, one that requires Calc 1, Calc 2, Linear Algebra, Vector Calculus, and Foundations of Math (FOM); students who are already majoring in subjects that require some of these classes find it very tempting to complete the minor. Our department uses this as an opportunity to recruit more majors, encouraging students to take just one more course.) That said, the vast majority of students in this class are a bit “on the fence” when it comes to math, most being fairly nervous about the course as they’ve heard “it’s like no other math class before.” My primary learning goals are (1) to have students learn to critically assess logical arguments (especially proofs), (2) to have students learn to compose their own precise, logical arguments (in particular, mathematical proofs), (3) to have students understand the value and idea of a mathematical proof, and (4) to expose students to a wide variety of mathematics (including history and current research).
EL: What are your goals for students’ blog posts? Or to put it another way, why did you choose blogging rather than more traditional writing assignments or in-class presentations?
CD: This class was first devised quite a while before I arrived at St. Mary’s, and it’s undergone a number of revisions since then. For much of the past decade or so, instructors for the course had students maintain a journal. They were expected to make regular entries where they could record their thoughts on/reactions to readings, assignments, and in class activities. One of the main points or benefits to this was having students regularly thinking and writing about this course; it encouraged (perhaps forced?) them to develop important habits—reading, re-reading, engaging with the text, working out examples—and kept the challenging topics on their mind. There was a significant drawback, though. At a few times during the semester, the instructor would collect these journals and assess them (how many entries, how in depth they were, etc.), and this left them with a daunting pile of books to sort through.
When I first had the opportunity to teach this course, I knew I wanted to avoid those piles, and requiring regular blog posts from my students seemed like an ideal way to do this. Like many others, I spend a great deal of time reading things online anyways, especially math blogs. I figured it would be easy to keep frequent tabs on my students’ blogs by incorporating them into my media diet. Its also easy to read through blog posts while, say, doing some other activity (like waiting for a child to doze off to sleep or washing dishes). I have them use WordPress, which supports (a version of) LaTeX, and so many of them also get the benefit of learning mathematical typesetting. Another benefit to the blogs is the creation of a community. Student bloggers often consult with others by reading through their old posts and commenting on them. (This usually takes some time, though, roughly about 2/3 the way into a given semester.) Finally, regularly-updated student blogs help me better assess students’ needs, struggles, and progress far better than homework assignments and nerve-wracking exams; I am able to customize class activities, lectures and discussions, I am able to write especially rewarding exams and I am able to create more helpful activities as a result. For all of these reasons I now require FOM students to maintain a blog whenever I have the pleasure of teaching the course.
EL: Is this the first time you’ve had students blog in class? If not, how did the earlier iterations go and have you made any changes as a result?
CD: This is my fourth time teaching FOM, and it is my fourth time requiring blogs. I have not implemented too many changes since the first time doing this (back in the Fall of 2012). After using this the first time, though, I realized one potentially serious issue: students may not wish to participate in such a public activity. I now make it very clear to students that, while they need to maintain a blog for this course, they do not have to use any identifying information, so they are not required to use their name, my name, the name of our school, etc. I think the next change I will implement for next semester’s FOM class is, in addition to regular blog posts, requiring students to comment on others’ blogs. Perhaps this will help establish a sense of community in a more timely manner.
EL: Overall, has blogging done what you hoped it would for your class? Have there been any unexpected difficulties or benefits to having the students write blogs?
CD: Overall, yes, I think having students maintain these blogs did achieve what I (and previous instructors for this course) wanted. (I mentioned several unexpected benefits in my answer to 2, so I won’t repeat them here.) There have not been any unexpected drawbacks, which is to say there have been some, but they were easy to anticipate. In particular, there are students who neglect their blogs and end up with a lower grade as a result. I am not especially bothered by this since it is usually easy to fix — a simple e-mail reminder to a student usually does the trick. Some teachers may not like the idea of students getting answers from others’ blogs, but I am unbothered by this; indeed, I view it as a net gain for the class.
EL: Were your students enthusiastic or reluctant about blogging? Have you had any privacy concerns or students who didn’t want to share their work publicly?
CD: Students are usually fairly reluctant to blog, mostly because it initially sounds like a lot of tedious work. However, the majority of them really get into it after two or three weeks. Many find great joy in developing their voice, their mathematical voice in particular, and quickly come to appreciate the benefits of regular blogging; they seem to agree that it helps them remember abstract ideas and definitions, and given the fact that FOM focuses so much on writing (especially proof writing), they also agree that their blogs provide them much needed opportunities to practice. While I have yet to have a student express privacy concerns, after my first semester doing this, I realized I needed to address this issue. I try to make it clear that blogs need not contain any identifying information, and I also provide them with the option of having their blog not listed on mine.
EL: Have you gotten any feedback from students about whether writing the blog and reading other students’ posts were helpful for them?
CD: At the end of all of my previous FOM courses, all of the written comments I received about the blogs were positive, and for precisely the reasons you mention. Students found it convenient to read what others in the class were doing by simply skimming their blogs; they also found it helpful to practice expressing their ideas in written form. They also appreciated how easy it was for me to provide feedback (in the form of comments on particular posts). Although negative comments were never offered on a written evaluation, I have talked one-on-one with students who remained staunchly anti-blog throughout the course and after it concluded. These students did not see a point in writing their thoughts and posting them online, since they thought homework assignments were helpful enough. And, who knows? They may have been exactly right; perhaps their understanding of the foundations of mathematics was not helped by this activity. Having to do something that you don’t especially value or agree with, though, is also a good experience to have, too, especially if you hope to work in any job or career.
Also, one other noteworthy and unexpected (though obvious in hindsight) benefit: reaching introverts. Although I enjoy speaking in certain public forms (like this interview, in my classes, at conferences), I am a pretty standard introvert. Talking and interacting with others exhausts me, and there are lots of students for whom participating in class (be it discussions or activities) is similarly challenging. Blogging their thoughts and ideas helps them participate in meaningful and sustainable ways, I’ve found, and it helps them feel included. Their work is often the best in this arena, too, often resulting in more thoughtful and helpful blog posts.
EL: Those of us who are interested in blogging in the classroom are probably curious about some logistical details: how do blog posts figure into a student’s grade, and how do you grade them? How do students submit their posts to you?
CD: I have a relatively simple way to incorporate blog grades into a students’ overall grade. Here is a copy of my syllabus for this semester (https://mathematicalypse.files.wordpress.com/2015/05/fomsyll-21.pdf), where the Blog is said to count for 20 percent of the final grade. Roughly speaking, I expect students to post at least one entry on their blogs per class period. How long should each post be? How much math talk should they include? These questions can only be answered subjectively, but I provide some rough guidelines (both in class and in a blog post explaining some details, which can be found here: https://mathematicalypse.wordpress.com/2012/08/26/guide-to-fom-blogging/). If you have three posts per week, and they contain a rigorous and/or helpful discussion of topics we’ve discussed in class, then you’ll be awarded full credit. Alternatively, if you post only once per week, but the entry is especially long and thoughtful—so much so that it read like three “regular sized” posts jammed into one—you can also earn full credit. Similarly, you can post 6 times per week, publishing shorter thoughts and reactions and rack up a full amount of credit that way. I also encourage students to post about mathematics from other classes and that they’ve been thinking about or reading about on their own, so there are lots of ways to rack up “blog points.”
I check my students’ blogs multiple times a week, and blogs are graded on a weekly basis (on Fridays in this class). So every Friday I assess the number and quality of blog posts a student has done that week and assign a grade — usually its a nice round number, like 100, 90, 80, 70, 60, or 50.
By the way, I am not certain that 20% is the ideal number for this component, but it seems to work for my classes. People who are blog-negligent do not fail the class, but their grade does suffer, and no one is able to do well in the class by blogging alone.
EL: Any advice for math teachers who want to incorporate blogging into their classrooms?
CD: I think the most important advice I have is to maintain a blog yourself, and not just one about teaching. It can be a wonderful experience for teacher and student alike to share their thoughts on mathematics via their blogs, especially when the mathematics involves not just the topics discussed in class but the mathematics that happens to be on someone’s mind. For instance, I knew that I wanted to use my blog to keep track of some research interests I was pursuing the first time I taught FOM, and it was helpful for me to feel like a student again. I documented my progress, my setbacks, and my new ideas on my blog (never expecting or requiring students to read these entries, but never hiding them either), and it helped me understand better the progress, setbacks and ideas my own students were sharing on their blogs. It let me model for my students how to approach struggles and questions in mathematics, it also helped students view me as a member of their learning community.
EL: Can you share some of your favorite posts from students?
CD: There are so many to share. I actually asked some of my current students if they would have any objections to their blogs being mentioned in your post on this, and all were excited at the possibility. So feel free to explore other posts from the ones I mention here. Here is one by a current student, https://smcmfom.wordpress.com/2015/10/03/can-money-buy-happiness/ —in it she works out some examples of if-then statements (and their contrapositives), all on her own. The benefit of creating her own examples and sharing them with others is far more meaningful than that obtained by reading examples I come up with or our textbook uses. Here is another interesting post, https://scbergen.wordpress.com/2015/09/25/proof-of-math/, where a student wonders aloud about, essentially, metamathematics. When we spend some time talking about Gödel later this semester, I will be able to turn to this post to generate relevant discussion.
Here is one about a Problem of the Week (POW): https://tripletintegral.wordpress.com/2015/10/02/the-one-with-the-pow-oct-1/. What’s so great about this post is how helpful it could be/was to other students who struggled with this question. The student’s thought process is so clearly laid out that it will no doubt ring true for others in the class who also attempted this question.
This blog was from 2013, and the last two entries (on paradoxes and on blogging) are especially interesting, I think: https://cdmachlin.wordpress.com
In general feel free to pick through any of my old or current student FOM blogs for interesting posts. Warning: there are a fair number of expletives. Also, this 2013 student was obsessed with working in lots of cat pictures: https://myhypotamoose.wordpress.com/page/2/
[Editor’s note: Casey shared a couple more posts with me: https://fomdamentals.wordpress.com/2013/04/25/the-scavenger-hunt-solutions/, https://fompwomp.wordpress.com/2013/05/09/im-a-big-deal/. You can find the list of FOM blogs here: https://mathematicalypse.wordpress.com/2012/08/26/guide-to-fom-blogging/]
EL: Are there any questions you wanted to answer that I didn’t ask? Please feel free to add them!
CD: Maybe! So I’ve blabbed long enough about all of this, but I also do one other “unusual” thing for this FOM course. Their final exam is self-referential; the first question on the exam is to find the final exam. Students have to complete an elaborate, mathematical scavenger hunt to find the final exam. They are expected to blog about their successes and failures with this hunt and collaborate in completing it. This seemed to be one of the best uses of the blogs; students responded very positively to it.
I think that this is an amazing idea. When I read about the part where you talked of being able to customize the class activities based off of if the students are struggling I understood how helpful this could be. With students having to explain whatever they learned that day in their own words you can see where mistakes are going to come in before they do them on an exam as well as forcing them to reread their notes every day. I know this isn’t exactly the way you were discussing it, but for lower level math students rather than showing the proofs there they could post other homework assignments or such there as well.