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Specifying Rewrite Strategies for Interactive Exercises

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Abstract

Strategies specify how a wide range of exercises can be solved incrementally, such as bringing a logic proposition to disjunctive normal form, reducing a matrix, or calculating with fractions. In this paper we introduce a language for specifying strategies for solving exercises. This language makes it easier to automatically calculate feedback, for example when a user makes an erroneous step in a calculation. We can automatically generate worked-out examples, track the progress of a student by inspecting submitted intermediate answers, and report back suggestions in case the student deviates from the strategy. Thus it becomes less labor-intensive and less ad-hoc to specify new exercise domains and exercises within that domain. A strategy describes valid sequences of rewrite rules, which turns tracking intermediate steps into a parsing problem. This is a promising view at interactive exercises because it allows us to take advantage of many years of experience in parsing sentences of context-free languages, and transfer this knowledge and technology to the domain of stepwise solving exercises. In this paper we work out the similarities between parsing and solving exercises incrementally, we discuss generating feedback on strategies, and the implementation of a strategy recognizer.

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Acknowledgments

This work was made possible by the support of the SURF Foundation, the higher education and research partnership organization for Information and Communications Technology (ICT). For more information about SURF, please visit http://www.surf.nl. We thank the anonymous reviewers for their constructive comments. Discussions with Hans Cuypers, Josje Lodder, Wouter Pasman, Rick van der Meiden, Erik Jansen, and Arthur van Leeuwen are gratefully acknowledged.

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This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

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Authors and Affiliations

  1. School of Computer Science, Open Universiteit Nederland, P. O. Box 2960, 6401 DL, Heerlen, The Netherlands

    Bastiaan Heeren, Johan Jeuring & Alex Gerdes

  2. Department of Information and Computing Sciences, Universiteit Utrecht, P. O. Box 80.089, 3508 TB, Utrecht, The Netherlands

    Johan Jeuring

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  1. Bastiaan Heeren
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  2. Johan Jeuring
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Correspondence to Johan Jeuring.

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Heeren, B., Jeuring, J. & Gerdes, A. Specifying Rewrite Strategies for Interactive Exercises. Math.Comput.Sci. 3, 349–370 (2010). https://doi.org/10.1007/s11786-010-0027-4

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