Exploring the potential, limitations and use of objective questions in advanced calculus
conference contributionposted on 2009-04-02, 13:19 authored by N. 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.
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