The rise and fall of a good idea

Last year (late 2008) I applied for a Teaching and Learning grant to embed mathematical software in all aspects of one of my first year subjects. (This subject is mostly calculus, with a smattering of combinatorics and complex numbers thrown in.) My University for some time has had a lab license for Maple; at the time we originally purchased Maple we had tried Mathematica, and been disappointed with the level of support from Wolfram Inc; and the freeware software such as Maxima, Axiom or Sage, were not as robust as they are now. Anyway, we had built up a fair amount of local expertise in the use of Maple as an adjunct to lectures and tutorial, in lab classes.

The idea of this grant was to embed Maple more solidly in the subject: to include it in the notes, and to use Maple T.A. for assessment. Basically, the entire subject was to built around Maple. I should point out here that I have no special alliance to Maple or its parent company; this was more of an historical decision, based on the current expertise of our mathematics staff.

Maple and Maple T.A.

Maple is a computer algebra system; that is, a computer system which as well as allowing numerical calculations, also allows symbolic and graphical work, all nicely integrated into a "worksheet" interface:

elementary Maple

A symbolic example with differential equations can be seen here. And here's one with Laplace transforms:

Maple can also draw nice graphs (the spelling error is not mine!):

Maple graphic

which can be rotated, zoomed into and out from, in real time all with the mouse. Here's another picture:

Maple 3d plots

Maple T.A. (the "T.A." stands for "Teaching and Assessment") is an add-on package, sold separately, which allows mathematical tests to be administered online. Tests may contain open-ended questions, multiple-choice questions, questions whose answer may be a number or a formula, questions which may contain graphics, questoins built of random elements so that each student gets a different question. Maple T.A. is designed to work with Maple in the background, so the mathematical "engine" of Maple checks to see if the answer entered by the student was correct or not. Maple T.A. comes with a powerful authoring system, where questions can be created by filling in blanks, as you can see here. And of course it does automatic grading, and collation and analysis of results. It is supposed to scale well, so whether you have 30 students or 3000, Maple T.A. should be able to handle them with ease.

My project

I applied for 10,000 - not a plethoric amount - and interestingly, one of my colleagues, to whom I showed the application, commented that he thought it was somewhat over-ambitious, given the money and time I'd allocated for it.    	Initially the project went well. I got a new set of lab materials up and running, and ran the labs with a group mostly of Education students, all training to become high school maths teachers. I decided not to include too much Maple scattered through the notes; what I did was produce a new chapter introducing Maple, and used Maple as often as I could in lectures to illustrate a point (limits for example). I bought the new version of Maple T.A., and hired a research assistant (whose blog you can read <a href="http://mvngu.wordpress.com/">here</a>), who was able to help investigate creating some <a href="http://www.maplesoft.com/tacontent/">question banks</a> to be used with Maple T.A. It's been my experience that the students and subjects we have are not well served by "off the shelf" materials, either in terms of textbooks, or any other material. So to best serve the needs of the students and their diverse backgrounds, specially written material was needed.    	The running of the labs brought up an aspect of my teaching - especially in the use of technology - which I need to fight against, and that's being too ambitious with the students, pushing them at too fast a pace, and expecting too much of them. It was becoming apparent after a few weeks of Maple labs that I was simply expecting too much Maple expertise of the students. This was a turn-off for them. The idea of any computer algebra system (such as Maple) is that it should allow the students the opportunity to explore, to play with mathematical concepts, and let the system handle all the messy algebra. But I had made the mistake of making my lab sheets require too many different Maple commands, and so the students spent most of the labs wrestling with Maple, instead of playing with it.    	Our first stumbling block was the extraordinary difficulty of installing Maple T.A. on our servers. Being commercial software, we couldn't just compile source code, using our own libraries, we had to shoehorn Maple T.A. onto our running system. This turned out to cause endless errors and total confusion on the part of our very experienced and knowledgeable systems administrator, who had installed, maintained and upgraded many many larger and more diverse packages than this. Over a month of anguished phone calls and emails went between our sys admin and the <a href="http://www.ceanet.com.au/">local distributors</a> of Maple T.A., who were at all times helpful, professional, and approachable. However, they were as much at a loss as we were. Eventually, though, but vastly behind time (according to the timeline in my grant application) we were able to get Maple T.A. installed, and could attempt to use it.    	My plan was to get Maple T.A. installed and tested in first semester, and write some question banks, so that we could "roll it out" with the cohort of students in second semester. (This subject was running in both semesters, with different students each time.)    	It turned out that this new version of Maple T.A. was hopelessly buggy. The software should allow mathematical formulas to be properly typeset:    	<img alt="Maple T.A. sums" src="http://www.adeptscience.com/products/mathsim/mapleta/images/summation_lg.jpg" />    	and the formulas displayed may be built up of random elements, so each student will obtain a different question, as you can <a href="http://www.numbersandshapes.net/wp-content/uploads/2009/12/mapletacreation.jpg">see here</a>. Our experience was that equations and formulas were not so typeset, and to obtain typeset formulas on the screen, they had to be created with separate software, and pasted in place - a messy, time-consuming, and annoying process, and impossible to do with random elements. So immediately part of the power and promise of Maple T.A. was lost to us.    	To add to the difficulties, I started spending more and more time fighting the University's egregious Change Plans, of which you can read my comments <a href="http://amca01.wordpress.com/2009/06/13/the-mathematics-change-plan/">here</a> and <a href="http://amca01.wordpress.com/2009/08/04/the-mathematics-change-plan-take-2/">here</a>. The extraordinary worries caused by these Plans made concerted work impossible for me and for my colleagues.    	Of the10,000, I'd allocated some to buying Maple T.A. (to be precise, upgrading it, as we'd bought a license some years ago with another grant), some for a little time-release for me, and some for the research assistant. My own time-release was quickly used up in planning, implementing, and supporting the students in the labs, which, as I said above, I made too hard. My research assistant, who did about three times the amount of work I paid him, wrestled with Maple T.A. until he was totally sick of it. By the end of year, we had run out of time and money, and still didn't have an assessment system we could easily use.

Another Change Plan – this time for technical staff – meant that suddenly all our computing support vanished, and in particular our sys admin, who'd so valiantly fought the good fight with Maple T.A. was relieved of his position. So at the time of writing, Maple T.A. is off-line, and can't be brought back, as the one person who knows how to do it no longer works here.

Failures

Well, we have certainly not managed to achieve our aims. We have not incorporated Maple T.A. into the assessment of the subject. A small pilot study I ran two years ago (with another grant) demonstrated that this was certainly feasible, but it was not brought to fruition with this current project.

Successes

Apart from my tendency to get over-excited with software, and make things too hard for the students, we have successfully demonstrated the powerful use of mathematical tools in first year subjects. The students, once over their initial lack of enthusiasm (read: "animosity") to the software, became happier with it over the semester, and by the end were very pleased to be using it. In a sense, the major outcome of this project was a paradigm shift, from software as being an adjunct to a subject, to becoming an integral part of it, even if not in the way I'd envisaged in the grant application.

Future plans

Now that the project has finished, we need to look ahead. To y way of thinking, teaching mathematics without using modern software tools would be like teaching carpentry without power tools. However, it is clear that Maple and Maple T.A. are not the way to go. There are several reasons for this:

  1. Being commercial software, we would be locked into expensive licensing agreements, which the University would be unwilling to maintain.
  2. Our current license (for 40 concurrent users) is not really sufficient for projected demand. We thus need a system which is highly scalable, without a huge increase in cost.
  3. Commercial also means possible difficulties in installation and maintenance, as we have seen.
  4. So far, I haven't met anybody who's used Maple T.A. and liked it.

So, some possibilities for further work include:

  1. Using WebWork, or STACK, which uses Maxima as its engine. Both of these are open source, and both are known to work well.
  2. Create an entirely new product which uses Sage as its engine. This may be done by rewriting STACK so that the system calls are to Sage, instead of Maxima. Given the current high interest in Sage, this may be a preferred solution.

9 thoughts on “The rise and fall of a good idea

  1. A couple of my colleagues and I started using WeBWorK in our calculus classes (and in one discrete math class) this semester, and it was fantastic. Very easy to use for both students and faculty (and IT people) and it did exactly what we needed it to without bugs. Highly recommended.

    I share your pain with issues with concurrent Maple licenses. We dropped Mathematica some years ago (same reasons as you) and got a network license for Maple, only to find out that the server software that handles the concurrent usage was broken, and Maple refused to fix it because the server was written by a third-party developer. Maple’s great…when it works. I am teaching a MATLAB course for freshmen next semester and I dread the same kind of thing happening.

    I’ve been extremely impressed with Sage and how it’s developed. I think it’s still a little beyond what our students are ready for, but I would not be surprised if in the near future we dump Maple and go with Sage. I’d use Sage instead of MATLAB for my course, but the course is in conjunction with the engineering department at a local large university and they insist on MATLAB and nothing else. Maybe that will change in the future too.

  2. > Create an entirely new product which uses Sage as its engine.

    I’m all for helping to do that! The time is right for Sage to get such functionality.

    — William Stein (Sage developer)

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