2013 June

By Dr. Nicholas Parker.

a. Introduction

Since 2008 the School of Mathematics and Statistics has incorporated computer-based assessments (CBAs) into its summative, continuous assessment of undergraduate courses, alongside conventional written assignments. These CBAs present mathematical questions, which usually feature equations with randomized coefficients, and then receive and assess a user-input answer, which may be in the form of a numerical or algebraic expression. Feedback in the form of a model solution is then provided to the student.

From 2006 until the last academic year (2011/2012), the School employed the commercial i-assess CBA software. However, this year (2012/2013) the School rolled out a CBA package developed in-house, Numbas, to its stage 1 undergraduate cohort. This software offers greater control and flexibility than its predecessor to optimize student learning and assessment. As such, this was an opportune time to gather the first formal student feedback on CBAs within the School. This feedback, gathered from the stage 1 cohort over two consecutive years, would provide insight into the student experience and perception of CBAs, assess the introduction of the new Numbas package, and stimulate ideas for further improving this tool.

After an overview of CBAs in Section b and their role in mathematics pedagogy in Section c, their use in the School of Mathematics and Statistics is summarized in Section d. In Section e the gathering of feedback via questionnaire is outlined and the results presented. In Section f we proceed to analyze the results in terms of learning, student experience, and areas for further improvement. Finally, in Section g, some general conclusions are presented.

b. A Background to CBAs

Computer-based assessment (CBA) is the use of a computer to present an exercise, receive responses from the student, collate outcomes/marks and present feedback [10]. Their use has grown rapidly in recent years, often as part of computer-based learning [3]. Possible question styles include multiple choice and true/false questions, multimedia-based questions, and algebraic and numerical “gap fill” questions. Merits of CBAs are that, once set up, they provides economical and efficient assessment, instant feedback to students, flexibility over location and timing, and impartial marking. But CBAs have many restrictions. Perhaps their over-riding limitation is their lack of intelligence capable of assessing methodology (rather CBAs simply assess a right or wrong answer). Other issues relating to CBAs are the high cost to set-up, difficulty in awarding of method marks, and a requirement for computer literacy [4].

In the early 1990s, CBAs were pioneered in university mathematics education through the CALM [6] and Mathwise computer-based learning projects [7]. At a similar time, commercial CBA software became available, e.g. the Question Mark Designer software [8]. These early platforms featured rudimentary question types such as multiple choice, true/false and input of real number answers. Motivated by the need to assess wider mathematical information, the facility to input and assess algebraic answers emerged by the mid 1990s via computer-algebra packages. First was Maple’s AIM system [5, 14], followed by, e.g. CalMath [8], STACK [12], Maple T. A. [13], WebWork [14], and i-assess [15]. This current generation of mathematics CBA suites share the same technical capabilities, summarized in Box 1.
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We’re giving a day-long workshop titled “Building online maths assessments using Numbas” at the University of York on the 4th of July. It’ll be an introduction to using Numbas, from logging on to the mathcentre editor, through selecting questions to make a test, to eventually writing your own questions.

The workshop is provided by the Sigma North East network for excellence in mathematics and statistics support, and attendance is free.

There’s more information, and a booking form, on the Sigma NE event page.

I’ve just released v1.5 of Numbas on Github. While there have been loads of changes since the last time I remembered to bump the version number up, the biggest change recently is that I have rewritten the default theme to use the knockout.js framework. It makes the underlying code a lot simpler, and allows us to do a few new things that would have been very complicated. In particular, there is now a Review mode which is made available when you have finished an exam – you can click on any question on the feedback page to go back to it and compare your answers with the expected answers, as well as seeing any marking feedback and the model solution in the Advice section.

The version numbers in the Numbas source code repository don’t mean too much since we push updates to the stable branch as soon as they’ve been tested instead of lumping them together, but it’s good to mark progress every now and then.

The mathcentre editor tracks the stable branch, so you can try the new features there now.

The Review mode was something we had in the previous system we used at Newcastle, and it was the one thing that many of the students asked for in a survey conducted at the end of the first semester by Dr. Nick Parker. I’m glad it’s finally in Numbas!

When you finish an exam, you can click on any question to review it.

Marking feedback and the correct answers are shown for each part.

And the model solution given in the Advice section is also revealed.

I’ve just deployed an update to the Numbas editor which makes searching a bit easier, and gives everyone a user profile.

I’ve replaced the old question/exam index pages with a new system which is a lot quicker when the database contains a lot of items (for example, the mathcentre database, which currently contains over 600 questions).

It’s now possible to filter questions by tag, which should make organising and finding questions you’re working on a bit easier. The tags on the question editing page are now clickable, so you can easily find related questions.

Every user has a profile page where they can provide a bio, along with links to their exams, questions, and the tags they’ve used. You can edit your bio by clicking on the “edit your profile” link on your profile page.

Thanks to Joshua Beals for giving me a prod to sort out the searching interface – it was beginning to creak a bit!

You can try out the new features at the mathcentre Numbas editor.