Interim report: ‘Development and integration of computer-aided assessment of discrete mathematics’

Dr. Martin Greenhow from Brunel University has submitted the following interim report for his project.

The principal aims of this project are to extend and exploit computer-aided assessments in elementary discrete mathematics (sets, logic, graph theory). These questions were written in Questionmark’s Perception version 3 and exploit random parameters throughout, including very full feedback and diagrams, thereby generating thousands of rich questions that form an effective learning resource. The present project builds on this by covering existing topic gaps, translating some of the resource into Perception 5 (this has a significantly different architecture) and evaluating the products.

The first main aim of editing and extending the database for questions spanning elementary sets and logic has been largely achieved, as have the underlying functions needed to produce graphs and adjacency matrices. Current work is focussing on algorithms on graphs and will be finished within a month, ready for student use, see below.

Translation into Perception 5 has now been achieved for one or two trial questions involving both equations (in MathML) and diagrams (in Scalable Vector Graphics – SVG), see figure. This is currently in a pre-release version but tests will be published to a server in the next month. This will give us greater confidence that we have resolved all of the technical issues and can indeed exploit the Perception 3 database of questions within Perception 5. We have been in close contact with the software vendors, Question Mark Computing, throughout this process. The open source question coding will then be properly documented and made future-proofed and portable to other CAA systems and ordinary web pages.

The final part of the project will be to evaluate the products; this will take the form of formal trials (for marks) and the sets and logic questions have already been run with one cohort of students, and will be run with another in a few weeks time alongside the questions on algorithms on graphs for both cohorts. In addition, informal testing on the questions published under Perception 5 but delivered via mobile devices will be carried out.

screenshot of question in Perception 5

Figure: the adjacency matrices are produced by an external function returning a MathML string, whilst the graph diagram is similarly produced, the function returning an SVG string. The number of vertices and edges changes with each question producing thousands of realisations.

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