Wrapup: Math Software Course for Math Teachers

08Jan13

Stephen Tosh and I co-taught the online course Math 600 for the University of Waterloo last term, in September and October. The course is part of the Master’s of Mathematics for Teachers program, which is an online Master’s degree for high-school math teachers. The students were a very interesting mix of people from all over the globe, ranging from freshly-graduated to very experienced. I just finished the very last part of the course administrivia, which was reading the results of a survey we sent to them, and it’s a good time to reflect on it before the next term starts here at Princeton.

So what was this course, exactly? It serves to introduce three pieces of software: LaTeX which is a typesetting system, Maple which is a programming language oriented around math and algebra, and GeoGebra which is a interactive system for setting up geometric and algebraic objects in the plane. We spent three weeks on LaTeX, two on Maple and one on GeoGebra, and gave out either short exercises or an open-ended project each week. The general idea is that we choose these technologies because they are useful for teachers in the classroom and/or they will be useful for teachers in future MMT courses that they take.

We hosted the course content on a WordPress installation at

http://cemclinux1.math.uwaterloo.ca/~math600

and WordPress turned out to be a pretty great tool for hosting an online textbook. We didn’t do any interactive stuff, just reading material in a nice searchable, universally accessible format. Along the lines of CS Circles we tried putting exercises sprinkled throughout each lesson, rather than bunched-up in problem sets at the end, which seemed to work well. We used LaTeX-generated typography in WordPress three ways:

  1. copying-and-pasting images
  2. using the built-in LaTeX plugin for WordPress to render text as images
  3. using MathJax to render text as MathML

Only the dumbest solution, #1, worked flawlessly for all students. But the other two approaches were also good: #2 only failed for one student behind the Great Firewall of China, and #3’s issues were limited to just a couple of students plus a couple of complex fraction formulas that were not rendered correctly.

It would be lovely, some day, to be able to automatically grade LaTeX, Maple, and GeoGebra in the same way that auto-graders currently exist for C++, Java, and Python. That day is a long way off, so I have to give a lot of credit to our teaching assistant Burcu Karabina’s excellent attention to detail in the manual grading process.

Here’s a couple of questions that I wanted to find out about in the end-of-course feedback:

  • Did students use LaTeX on their own computer or “in the cloud?” We showed students that they could download LaTeX software either to their own computer, or use a web-based version. Sadly the fabulous ScribTeX stopped accepting registrations just before the term started, but thankfully ShareLaTeX was a good remaining option. The students were equally split 3 ways between using ShareLaTeX, using TeXWorks in Windows, and using Mac-based options. If I taught the course again I would pursue Sage as a replacement for Maple, since Sage also can be run in the cloud.
  • How should you support students in an online course? We had forums built in to UW’s Blackboard Learn system, scheduled office hours for google/skype chats, and we allowed students to directly e-mail us. By far, the forums were the most utilized and successful option, and students indicated that we they would be happy if we stopped the office hours entirely.
  • Can you get students more engaged with each other despite being so far away from one another? This is more challenging. Based on questions that we asked, the students are not very supportive of group projects or peer reviews. A great idea mentioned by a couple of students was to let students share their completed projects with the others, which I would have loved to do and skipped only for lack of time.

For the latter two findings, it might be relevant that we’re teaching teachers in particular; younger students without a full-time job might want more close support and more interactivity. At this point I don’t have enough experience to say for sure.

In terms of the material, it seems like UW’s chosen combination of LaTeX, Maple and GeoGebra was pretty good. People expressed a love-or-hate relationship with LaTeX… two students said

LaTeX is not, and will not, be the preferred method for high school teachers. Keep in mind that we using Word and Equation Editor, there is no use, to most of us, to put in the numerous hours to use/learn LaTeX at the level to create something we can do in minutes in Word.

versus

LaTeX felt like a really useful program to know given its versatility. It was a very intuitive program.

The general feedback was appreciative of the course, and I was happy to see that students said they enjoyed doing the homework, which I consider a very excellent compliment. We seemed to do a pretty good job of one of our main goals, which was to give teachers tools that they actually would find useful in the classroom. GeoGebra and LaTeX were singled out for this… I do think that using programming is harder in a math course due to the extensive training and teaching needed, and probably could sit inside of its own separate course. It might be interesting to explore the various tools and mini-applications that Maple has inside of it for doing math and science explanations, although I know very little about that.

What else can I say? Go check out the site and see if you can figure out the Easter eggs at the top of each page.

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6 Responses to “Wrapup: Math Software Course for Math Teachers”

  1. Thanks for the report. I work closely with the MathJax team, and I’d like to get more information about the “complex fraction formulas that were not rendered correctly”. What was the configuration (browser/OS)? What were the fractions?

    • I just updated to the latest version (via git pull) and alternatively tried loading from the MathJaX CDN.

      With the latest git version, the fraction lines are too long. With the CDN version, some problems are resolved but there are other weird clipping and spacing issues.

      You can see the example here:
      http://cemclinux1.math.uwaterloo.ca/~math600/wp/test/
      it’s currently running from the local version (rather than the CDN) but I’ve posted screenshots of what both versions look like on my machine (Windows 7 + Chrome).

  2. Thanks Dave. Tried a couple of things…

    Used MathJax to copy the source code from each of your example equations. I then put it into a page of my own, referencing the CDN. No rendering problems.

    Saved your test page locally. I see the rendering problems in Firefox 18 on Windows and Mac, and on Safari 6 on Mac. I then commented out the CSS, and saw no rendering problems on any browser.

    This would lead to the conclusion is that there’s something in the CSS that’s conflicting with MathJax’s HTML-CSS rendering. Changing the rendering to MathML works fine with or without the CSS.

    • As a follow-up, the MathJax creator offered this observation:

      “OK, I checked the file that you link to, and the I suspect the issue is that they set the style

      .MathJax_Display {
      font-size: 125%;
      }

      in their style.css file. That will through off MathJax’s measurements, and produce exactly the types of issues that they are seeing. They should NOT style the MathJax_Display class in that way.

      “It may be that they are trying to get a different scaling factor for displayed equations from in-line equations, but this is not the way to do it. If that’s it, I can try to work something else out for them, but there is no current mechanism to get different scalings for the two situations.”

      Hope that’s helpful.


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