Properties of Exercise Strategies

Alex Gerdes
(Open Universiteit Nederland)
Bastiaan Heeren
(Open Universiteit Nederland)
Johan Jeuring
(Utrecht University)

Mathematical learning environments give domain-specific and immediate feedback to students solving a mathematical exercise. Based on a language for specifying strategies, we have developed a feedback framework that automatically calculates semantically rich feedback. We offer this feedback functionality to mathematical learning environments via a set of web services. Feedback is only effective when it is precise and to the point. The tests we have performed give some confidence about the correctness of our feedback services. To increase confidence in our services, we explicitly specify the properties our feedback services should satisfy, and, if possible, prove them correct. For this, we give a formal description of the concepts used in our feedback framework services. The formalisation allows us to reason about these concepts, and to state a number of desired properties of the concepts. Our feedback services use exercise descriptions for their instances on domains such as logic, algebra, and linear algebra. We formulate requirements these domain descriptions should satisfy for the feedback services to react as expected.

In Hélène Kirchner and César Muñoz: Proceedings International Workshop on Strategies in Rewriting, Proving, and Programming (IWS 2010), Edinburgh, UK, 9th July 2010, Electronic Proceedings in Theoretical Computer Science 44, pp. 21–34.
Published: 24th December 2010.

ArXived at: http://dx.doi.org/10.4204/EPTCS.44.2 bibtex PDF

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