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Pattern-matching syntax trees

I’m doing some very fun things with pattern-matching syntax trees today.

For context: I write a computer-based assessment system called Numbas, and it’s focused on assessing mathematics. A big part of that assessment involves asking the student to enter an algebraic expression as the answer to a question. How do you decide whether to mark the student’s answer as correct or not? Historically, there have been two approaches, given a representative “correct” expression written by the teacher:

  • Put the student’s answer and the correct answer into a canonical form. If their syntax trees are exactly the same, then the student’s answer is the same as the teacher’s. This is the model used by, for example, STACK.
  • Identify the variables used in the student’s answer and the teacher’s. Pick a few random numbers as values for those variables, and evaluate both expressions. If they come out to the same number, then the student’s answer is the same as the teacher’s. This is the model used by systems in the CALM line.

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Resources for first-year engineers

Maths-Aid, the drop-in maths help service at Newcastle University where I do a bit of work, commissioned some worksheets and accompanying videos for engineers, to be completed over the Summer. The idea was that they would cover the most commonly-requested topics at Maths-Aid, providing pretty much the same information as we would give in a one-to-one session but not acting as a replacement for lecture notes and textbooks.

They’re finally just about finished after a lot of employee-herding and you can see them on the Maths-Aid website. Each worksheet consists of a brief introduction followed by worked example questions. Embedded in each question is a video of me going through the solution from start to finish. They were very quick to produce, and I think they will be very useful. By the way, all these videos and a few others I’ve made are available on our Vimeo account.

The original worksheets were written in Word, so I translated them to HTML+MathJax because it’s much much more convenient. I’ve left links to the Word documents on the page in case people want to print it out, but there’s a nice print stylesheet so just printing out the page itself produces good results.

Now that the worksheets and videos are finished, we’re adding some interactive revision questions using Numbas. At the moment there’s one for the simple second-order ODEs sheet. It produces a randomly generated ODE to solve each time you run it, and can give hints or a full worked solution if you get stuck. There’s a button to re-randomise each question, so you can just stick at it for as long as you like.

I’m trying to make a case in the E-Learning Unit for more of this kind of thing being produced: I think they’re very useful, and complement lecture notes and textbooks very well.

Another Numbas presentation

I gave another presentation about Numbas last week at the e-Assessment Scotland conference in Dundee. I revised my old slides and created a better demo exam, so I thought I’d better link to them from here. I’m thinking about recording a screencast of how to use Numbas – would that interest anybody?

Anyway, those slides – click here.

My Numbas presentation

I’ll try and make this my last Numbas post for a while, but I’ve had to give a few presentations about Numbas at various places in the past month, so I wrote a quick set of slides. I’ve just uploaded it here.

I created the slideshow using Slidy, which is much better at using HTML for slideshows than my attempt.

A demo of the Numbas maths exam system

As part of one of the many jobs I’m doing at the moment for Newcastle University, I’ve written a web-based maths exam system which runs entirely in the browser, with no plugins, and is SCORM compatible. It uses the excellent MathJax for displaying mathematics; there’s a load of clever programming to allow fully randomised, algebraic answers to questions; and exams are written in a fairly easy-to-understand plaintext format.

Here’s an example of an exam written using Numbas, and here’s the file which generated it. The exam should run in modern Firefoxes, Safaris and Chromes, and IEs 8 and 9. Press the ‘Reveal’ button at the top of the page to see the answers to the questions.

We’re still clearing up exactly who owns the copyright to all this and under what terms it can be distributed, so I can’t provide much more material than this, but someone came to visit us yesterday (to give Bill Foster an award for pioneering e-assessment!) and he said that we should be a lot more public with what we’re doing, so that’s what I’m doing.