All entries for July 2006

July 21, 2006

Transatlantic Tutorial

On Monday afternoon, five of us in Warwick's Elab and a member of the technical team at Adept Science hooked up to Waterloo in Canada for a 2-hour tutorial on Maple TA, the mathematical teaching and assessment software created by Maplesoft. It was my first exposure to web conferencing software (in this case Webex ): just a communal phone link and a real–time view of the tutor's desktop, but it was fast, effective and 100% fit for purpose. My only regret is that we didn't make a recording of the session.

In the Manner of the Banner?

Follow-up to City slogans and climate change from Computer-aided assessment for sciences

City slogan time again. This year the bright cylindrical banners sheathing the lamp posts at the Gibbet Hill junction exhort me thus: Coventry Banner 2006

COV '06 — be part of it!

While I idle at the traffic lights, I am prompted to ask: when earning my crust on campus, am I part of it?

Geographically I am, because the Mathematics Institute in the Zeeman Building is on the north side of Gibbet Hill Road. But emotionally? Hard to say. I have more contact with Coventry University than I used to; I deal with a Coventry solicitor; my sons watch hockey and skate at the Planet Ice Arena, and swim at the Pool; but from my Leamington base I can't yet claim to feel deeply and meaningfully about Lady Godiva's city in the way I do about London, where I was born.

The University got off to a bad start by naming itself after a county town eight miles away. For decades many citizens of Coventry didn't know where our campus was. Culture vultures found out when the Arts Centre got going, as did some of the city's great and good on the University Council, which occasionally got embroiled in local politics. (Jolly Jack's acquisition of Westwood for the University might merit the attentions of a racy historical/political novelist.)

But here's something exciting to redress the balance: Every Wednesday lunchtime in term–time, buses (often bearing the U of W logo) roll up at Coventry schools to bring their mathematically–talented 6th formers to the University Maths Dept for an afternoon of intense teaching in A–Level Further Mathematics -- the standard A-Level Mathematics syllabus does not really stretch those with a flair for the subject.

Over 100 students from Coventry and Warwickshire are now registered with our Further Maths Centre, which started in a small way some 7 years ago. The success of its 3–year pilot phase was instrumental in persuading the Government to fund the creation of a national Further Mathematics Network which will cover the country. Students in state schools will no longer be deprived of the chance to develop their full mathematical potential simply because their school or college can't find a qualified teacher or because the class is too small to be economic.

So Warwick is changing lives in Coventry and we really are "part of it" after all.

July 19, 2006

Tickeys for Wikis

Follow-up to Explaining the Silence from Computer-aided assessment for sciences

Anyone wondering how effective crossing fingers was for

"the joint proposal on wikis as a teaching–and–learning tool"

might like to know: it worked!

Warwick's Education Innovation Fund has agreed to support a 2–year project to investigate the use of wikis in undergraduate teaching and learning; the lead will be taken in:

  • The Department of Computer Science in Year 1 (a wiki will be established to support a first–year programming module with contributions from students, staff and experts from the computing industry).

  • The Department of Mathematics in Year 2 (final–year students will create their own wiki of module resources built around a given skeleton syllabus; in other words, they will write their own lecture course. Their contributions will form a significant part of the module credit).

Other University departments have expressed an interest in devising their own experiments with teaching wikis.

If you would like to be kept informed of this project's progress, or to join in, please send me an email.

July 10, 2006

More thoughts from 14th March

Follow-up to Looking back to 14th March … from Computer-aided assessment for sciences

In the previous blog we decribed some of the features of Maple TA and WeBWorK presented at the March workshop. Two other CAA software architects introduced their brainchildren at the meeting: Chris Sangwin told us about his System for Teaching and Assessment using a Computer algebra Kernel (STACK) , and Martin Greenhow gave us a roller-coaster ride through his Mathletics program.

This open source software is designed for intelligent assessment of deeper mathematical knowledge in the growing number of subject areas that require it. Although STACK can deliver standard online question types (e.g. MCQs), its real strength is to handle student–provided answers to questions like these:

1. Factorise the following polynomial into a linear and a quadratic factor and hence find its roots:


(where a different equation is generated each time the question is called)

2. Write down a continuous function passing through the points (1,0) and (0,1) with exactly three turning points: a maximum, a minimum and a point of inflexion.

This kind of functionality is made possible by calling a computer algebra system (CAS); currently STACK uses the open–source Maxima system (try it out ). It can not only manipulate students' answers and give responsive feedback but can also help to generate problems randomly from a single template and provide corresponding worked solutions. In his talk Chris gave us some fascinating insights into the challenges that mathematics presents in this area, in particular, how to handle the subtleties of notation in

  • students' submitted answers (fx might mean f times x or the functional value f(x))
  • the CAS (interpreting various positions of minus signs for instance)

STACK tolerates informal entries in student answers (for instance, accepting 3xy instead of 3*x*y) and encourages students to "validate" their answers, in other words, to confirm that the program has correctly interpreted their entry when it displays the formal version.

We are currently exploring the possibility of using STACK for some low–level assessment taken by large numbers of first–year mathematics and statistics students. Its PHP architecture marries well with the Department's learning resources website Mathstuff.

Martin Greenhow and his team of research students have been developing this CAA resource and using it for their teaching and assessment at Brunel University for some years now. Its strengths include

  • well–developed and thoughtful pedagogy
  • large banks of mathematics questions aimed at the A–Level/starting–university zone.

The questions (perhaps better thought of as "question templates") are written in a combination of HTML, MathML, Javascript, SVG script, and can call on a library of functions for such things as displaying a polynomial intelligibly in the conventional way. Responsive feedback is a central feature of Mathletics: question templates include randomised parameters and context-aware alternatives; the feedback of hints and model solutions respects the choice of parameters and context, and responds to student mistakes by using their wrong answers to guess at "mal-rules" or common student misconceptions. Experience at Brunel has shown that this feedback plays a central role in student learning. Although the stand-alone questions can be interpreted in a suitable web browser endowed with the appropriate plug-ins, they are really designed for use with Question Mark Perception, which can deliver sequences of questions, record and analyse students' answers, provide the feedback and so on.

Coding individual questions is a skilled and time–consuming activity, but when the parameters are varied and the context is changed, each template generates thousands of different questions (as many as 1020 for some templates!). Thus the Mathletics framework can create essentially unlimited numbers of different exams on the same set of topics, allowing students to learn by extended practice. Mathletics is responsive to issues of accessibility, gender, and ethnic background.

The demanding requirements of authoring have to be set against the huge searchable repository of existing questions: new–style Mathletics (with randomisation) has about 1500 question styles (each realising to thousands/millions of questions) spanning around 120 topics at GCSE/AS and A–level/university levels 1 and 2. They range broadly across algebra, geometry, calculus (incl. Laplace transforms, differential equations and vector calculus), logic, decision maths, numerical methods, economics applications, probability and statistics . New questions are constantly being developed (as part of the Mathematics for Economics: Enhancing Teaching and Learning Project (METAL) for instance), and Martin is keen to encourage others to join in this creative process.

We are planning to try out Mathletics in the Autumn on a small subset of the first-year engineering students without A-Level Maths. If this pilot is successful, we would hope to use it to support the mathematical needs of the whole cohort later on. We have a site licence for QM Perception and are well placed for this. Although my attempts a few months ago to get Mathletics running on the University network were abortive, one of our postgraduate CAA team members, John Hattersley, is now on the case. I hope to report soon of his success, at least on the well-tried version 3.4 of Perception, which will run another year here; another challenge will be to run it on version 4.2, to which we are upgrading next month. Stay tuned.

July 07, 2006

Looking back to 14th March …

Follow-up to Pi in the Sky? from Computer-aided assessment for sciences

… the date of a Computer–Aided Assessment workshop at Warwick showcasing some of the software we are evaluating as part of an in–house CAA Project (for 'in–house' read 'Warwick Science Faculty'). Four software packages were exposed to scrutiny, and I would now like to say a little about each, our experience so far and the plans we have for them. More details will be posted soon on the Project website.

Maple TA (MTA).
This commercial Teaching and Assessment package from the Canadian firm Maplesoft is built on their well-known computer algebra system Maple. This foundation give MTA one of its mains strengths, namely the way it handles mathematics:

  • at the authoring stage — it has a palette of mathematical symbols and a LaTeX facility
  • in its rendering of equations onscreen
  • its ability to include random parameters in question templates
  • its ability to parse mathematically–equivalent answers.

At the workshop, its praises were sung by a representative from Adept Science (who distribute MTA in the United Kingdom) and moderated "Warts and All" by Michael McCabe, who had used it to assess Mathematics students at Portsmouth University a few months earlier.

Five weeks after the workshop, we used MTA, in tandem with Question Mark Perception, for a 50-minute summative test taken by 166 students registered for a second-year module in elementary number theory. The test contained 11 multiple-choice questions (MCQs) and contributed around 6% to the module credit. It was fairly easy to author the questions, the test was reliably delivered on the day by the hosting service, and I found it straightforward to extract and process the students' answer files from its database. On the negative side I found its imposed marking scheme and MCQ format frustratingly restrictive and laboriously had to adjust marks student-by-student to allow 3 for a correct answer, 1 for 'don't know' and zero for a wrong choice, normalising the totals by subtracting 8. In particular, I could not return the students' scores as soon as they clicked the submit button. Here Perception won hands–down on pedagogical flexibility but couldn't compete on the maths.

We were fortunate in getting MTA for an extended trial evaluation period. We tried, without success, to run it locally on a Java server that was configured for other apps. Subsequently we changed to the hosted service. Apart from an unfortunate loss of data two days before the test, this worked robustly and we have now taken out a 500–student departmental licence for the coming academic year, when we hope to go beyond the simple MCQ format and begin to exploit MTA's full mathematical capabilities.

This is a mature open–source assessment package developed with generous NSF funding at the University of Rochester. It has been around for over a decade and is currently used by over 80 (mainly North American) universities. When Jim Robinson of the Warwick Physics Department started looking for a suitable CAA package to improve and reinforce the mathematical abilities of his department's first–year students, he listed the following criteria. The software should preferably be:

  • Capable of rendering mathematics
  • Free
  • Client–independent and available off site using web–based technology

It should also offer:

  • A good bank of problems at right level
  • Easy authoring, customizable question formats and individualised problems
  • Instant feedback — hints, right/wrong, model solutions

WeBWorK has all these desirable features. Earlier this year, Jim installed WeBWorK on a Linux box, an old 500MHz PC. He needed some Linux systems admin experience – plus a few hours (no installation wizard) to install the WeBWorK software and problem libraries; it needs Perl, Apache, SQL server (MySQL), LaTeX, dvipng plus a few other apps (all free). Thereafter all course administration is web based.

Since Christmas, we have been running a pilot using volunteer Physics students taking the first–year Maths for Scientists module. Initially we plundered the very large collection of question banks to create a sample assigment based on the first term's material (mainly calculus) and subsequently provided a second assignment of home-made questions on the second-term's content (including linear algebra).The student feedback is currently being analysed, and we have begun to create assignments to be used by the whole cohort of Physics students taking the Maths for Scientists module next term.

As this entry is growing rather long, I will take a break now and discuss STACK and Mathletics later.

July 2006

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  • The LaTeX equations are a little wobbly in their baselines That's because they use mimeTeX. I am try… by Steve Mayer on this entry
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