posted on 2009-04-02, 13:19authored byN. Baruah, Martin Greenhow
This paper describes our experiences with authoring and trialling questions in
advanced calculus topics, namely ordinary differential equations, Laplace
transforms and Fourier series. These topics are generally taught at the end of
the first year or during the second year of a mathematics or engineering
undergraduate degree. We expect that many of the lessons learned here will
apply to other conceptually-advanced mathematical and scientific content.
Typically, what is significant for such content is that many skills are needed
from previous exposure to calculus and algebra, and that paper-based
questions at this level tend to be more abstract, holistic and open-ended,
requiring the sort of flexibility in marking generally associated with human
markers. For objective, and therefore more constrained questions, we do not
know what is feasible and whether or not questions on advanced topics will
actually test the skills they are designed to test. For example, a student may
carry out e.g. a Laplace transform correctly, but make an elementary
algebraic mistake near the end; this would be easily recognised by a human
marker, but simply marked wrong by any current CAA system which cannot
assess the (generally handwritten) intermediate steps in a student’s solution.
Conversely, any question that can be marked by a CAA system is likely to be
structured or scaffolded (e.g. by asking for intermediate steps explicitly) so
that the original requirement on the student to devise a solution strategy is
lost. This paper explores what can be asked effectively: facility with such
questions is a necessary (but not sufficient) condition for students to master
more advanced topics, so some sort of blended assessment (with human
markers) may still be needed for higher-level skills. We describe the process
of authoring higher-level objective and report of the experience of running the
questions with our second year cohort, including an analysis of the answer
files produced. Our evidence suggests that the assessments were useful to
students in establishing a solid foundation of skills, mainly by being
encouraged, or even forced, to engage with the extensive feedback screens.
History
School
University Academic and Administrative Support
Department
Professional Development
Research Unit
CAA Conference
Citation
BARUAH, N. and GREENHOW, M., 2007. Exploring the potential, limitations and use of objective questions in advanced calculus. IN: Khandia, F. (ed.). 11th CAA International Computer Assisted Conference: Proceedings of the Conference on 10th & 11th July 2007 at Loughborough University, Loughborough, pp. 47-54.