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I'm considering increasing the online component of my mathematics courses (I teach at the university level). I'd like to know what my options are to avoid reinventing the wheel.

The features I would like are:

  1. A unified system. I could cobble together a system using a bit of this and a bit of that, but it would be better if it were all under the same roof to make it easier for students to navigate.

  2. The ability to put actual material and quizzes in the system. The material might be in the form of a video or a webpage. I'm using "quiz" quite generically with nothing beyond "Questions to be answered" in mind.

  3. The ability to get feedback both for the students and the instructor. The latter is crucial in this endeavour. I don't simply want to put stuff on the web and leave it there, I want to know how it is being used and more. Ideally, there would be the opportunity for students to leave comments (for the instructor) as they go through the material and for the instructor to get summaries of the results of the quizzes.

  4. Easy to do maths. There are systems that do all the above, but maths support is somewhat lacking. This is not just about being able to write maths, in the quizzes then the students should be able to enter mathematical answers and any answer-checking needs to be mathematically robust.

I realise that this is something of a "big-list" question - though I suspect that the list is actually quite small - but it is also something that is hard to find out about, particularly with regard to the last criterion. I'm particularly interested in systems that have been used by mathematicians and what they found most useful and most frustrating about the system.

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  • $\begingroup$ Are you looking for something like Coursera or edX? $\endgroup$ – Jill-Jênn Vie Mar 20 '14 at 9:49
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    $\begingroup$ @Jill-JênnVie While I wouldn't rule them out, I'd be more interested in something where I would have full control. In particular, I'm not interested in making the material available to anyone other than my students (I'm not bothered if they have access to the bare material, but I certainly don't want to get any feedback from them). $\endgroup$ – Loop Space Mar 20 '14 at 10:00
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    $\begingroup$ 1 through 3 are supposedly supported by Moodle (which I only know about since it is the official one deployed by my institution); though I've been avoiding trying to learn it well enough to make full use of the system. 4, IMHO, is the hardest one to satisfy. $\endgroup$ – Willie Wong Mar 20 '14 at 10:06
  • $\begingroup$ @AndrewStacey I mean, it might be a bit overkill, but you still can install the whole platform somewhere and host your lessons on it :) All of your 4 points will be covered. $\endgroup$ – Jill-Jênn Vie Mar 21 '14 at 11:08
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Have you considered the online homework system WeBWorK? From the MAA's WeBWorK site:

WeBWorK is an open-source online homework system for math and sciences courses. WeBWorK is supported by the MAA and the NSF and comes with a National Problem Library (NPL) of over 20,000 homework problems. Problems in the NPL target most lower division undergraduate math courses and some advanced courses. Supported courses include college algebra, discrete mathematics, probability and statistics, single and multivariable calculus, differential equations, linear algebra and complex analysis.

Here is how the features of WeBWorK measure up with your desired features:

  1. A unified system: WeBWorK can be integrated with Moodle and Blackboard.

  2. The ability to put actual material and quizzes in the system: WeBWorK now has a problem library of over 25,000 questions (the MAA quote above is dated) and it is easy to create homework sets and timed quizzes. You can also write your own questions and easily include links to videos, web pages, etc.

  3. The ability to get feedback both for the students and the instructor: The WeBWorK statistics, student progress, and gradebook pages offer students and instructors access to student progress in real time. At the bottom of each homework problem, students can click an "email instructor" button to share their work and questions about the problem with their instructors. It is also possible to write essay questions that allow students to input mathematics using LaTeX syntax, but these questions require a human to grade them.

  4. Easy to do maths: WeBWorK was originally built by mathematicians at the University of Rochester (Michael Gage and Arnold Pizer) for mathematics students and has expanded over the past ~15 years to meet other STEM education needs. In my opinion, WeBWorK has the most reliable and robust answer checkers thanks to the hard work of Davide Cervone at Union College (who also created MathJax). Since WeBWorK allows any answer that uses standard math syntax (and gives students feedback when their syntax is incorrect), students who have worked with calculators before find the transition to WeBWorK very easy. The current WeBWorK user interface is good and easy enough to use, but it will be improved in the near future (hopefully available by Fall 2014) so that it becomes more intuitive and streamlined. Also, for instructors who do not want to put together their own homework sets from WeBWorK's problem library, WeBWorK has begun to put together model courses that are essentially pre-packaged homework sets (which can of course be modified to suit the needs of a course).

As a WeBWorK developer and long time user, I have a strong positive bias for it. I was forced to use another commercial online homework system for one semester, and it was clearly inferior to WeBWorK in terms of quality of questions available and reliability / robustness of answer checking. Students of mine who have used WeBWorK and another online homework system have universally said that WeBWorK was better.

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You are in luck! I am part of a team creating "Ximera", a system for converting latex documents into interactive web based learning courses. We are still sort of at the early stages, but the homepage is here:

http://ximera.osu.edu/

and the link to a multivariable calculus course we are running in this system is here:

http://ximera.osu.edu/course/kisonecat/m2o2c2/course/

Features:

  1. Questions with solutions which are functions or matrices of functions

  2. Multiple choice questions

  3. Free response questions, where they have access to a Latex editor.

  4. Python coding exercises, which have machine checked answers (Ex: implement power iteration to approximate eigenvalue)

  5. Hints for questions, which can themselves contain more questions (for a more "socratic" learning experience)

  6. Forum attached to each page

  7. Ability to view source of each page, along with a link to github. We have already had several students correct typos and such, in the first week!

  8. Easy to embed youtube videos

Currently the whole system is not really user friendly enough that I would recommend you start using it now. Writing the content is fine, but we have not streamlined the process of taking the latex files and converting them into html pages. I would imagine that the whole system should be streamlined enough for general use by the beginning of the next academic year.

The Multivariable calculus course will cover the following topics, just in case you are interested enough to follow its development:

Week 1: Linear transformation, matrices, dot product

Week 2: Derivative as a linear transformation, partial derivatives,gradient, chain rule

Week 3: Abstract vector spaces, subspaces, eigenvectors

Week 4: Adjoints, bilinear maps, real spectral theorem

Week 5: Second derivative as a bilinear map, second derivative test, lagrange multipliers

Week 6: Multilinear functions, higher derivatives as multilinear functions, full taylors theorem

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  • $\begingroup$ Would I need to use your system for converting LaTeX documents in to web pages? I have my own system for that (github.com/loopspace/latex-to-internet if you want to look at it). $\endgroup$ – Loop Space Mar 20 '14 at 11:30
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    $\begingroup$ Well, our system includes things like "\frac{d}{dx} \sin(x) =$ \answer{cos(x)}", which would generate a question with a solution box. The student has to type in "cos(x)" (or ex. cos(x+1-1)) to get the question correct. $\endgroup$ – Steven Gubkin Mar 20 '14 at 11:34
  • $\begingroup$ Probably it would be best just to check out one of the more complicated pages (like ximera.osu.edu/course/kisonecat/m2o2c2/course/activity/week1/…), see if the format interests you, and have a look at the source file to see if you would be willing to write such things to achieve that effect. Also, although I know you said you don't want to reinvent the wheel, we would be very happy to have you invent the wheel with us! $\endgroup$ – Steven Gubkin Mar 20 '14 at 11:38
  • $\begingroup$ From your previous comment, it sound like you have a way to automatically evaluate the free response questions? How robust is the parsing? $\endgroup$ – Willie Wong Mar 20 '14 at 12:49
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    $\begingroup$ We can automatically check expressions which are matrices of formulas given by elementary functions. We currently just evaluate their response and our answer at a bunch of randomly selected complex points, and see if they agree to some specified error. For low complexity functions (of the sort of complexity you would expect for reasonable questions) it seems to be working well. One problem is that it does not deal with very large numbers well (x^100 would throw things off). We hope to improve the parser by doing some syntactic reducations on both strings first. $\endgroup$ – Steven Gubkin Mar 20 '14 at 13:35

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