A Handbook for Teaching and Learning in Higher Education Enhancing academic and Practice

Mathematics and statistics
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Further developments have occurred more recently in relation to assessment, where the
power of computer algebra systems has been employed to ease issues of both question
setting and marking. There are now a number of alternatives, including AIM (Alice
Interactive Mathematics) and its related development STACK (System for Teaching and
Assessment using a Computer Algebra Kernel), which we focus on in Case study 2.
STACK offers advantages over AIM, which is no longer being developed, in that it
employs the open-source computer algebra system Maxima instead of Maple.
Case study 2: Stack
STACK exploits the full power of a computer algebra system to offer significant
flexibility in authoring tasks for students (see Sangwin and Grove, 2006). One
may create random problems based on a given structure, provide worked
solutions and assess student responses. Answers may involve arbitrary
mathematical expressions couched in syntax employed for Maxima, allowing one
to determine the mathematical properties of the answers that students provide.
Feedback can also be linked to the student responses.
The software thus addresses many of the issues raised in the initial part of this
section, and has been widely adopted in the USA, UK, Australia, Canada and
Norway. STACK incorporates a range of features that are of particular relevance:
• free availability – STACK is owned by the academic community, there is no
licence and the package can be freely downloaded (see http://stack.
bham.ac.uk/);
• ease and flexibility of use – STACK can be easily customised to reflect the
particular style of approach of the individual lecturer;
• ease of access for students – STACK allows for integration into the virtual
learning environment Moodle.
(The Authors)
Sangwin (2002) considers the power of such software to help develop higher mathematical
skills. This signals a major new role for technology in learning mathematics. In
particular, it is now possible to challenge students to produce ‘instances’ (as Sangwin
calls them), which is a task that has always probed more deeply into students’
understanding, but has been seen to be very demanding on staff (for example, it is very
instructive for a student to construct an example of a 4 by 4 singular matrix, with no two
entries the same – but who wants to mark 200 when they can all be different and all still
correct!). Other contributions to the role of technology (some with special reference to
higher skills) in computer-aided assessment may be found at www.mathstore.ac.uk.