Math.Comput.Sci. (2010) 3:349–370 DOI 10.1007/s11786-010-0027-4 Mathematics in Computer Science Specifying Rewrite Strategies for Interactive Exercises Bastiaan Heeren · Johan Jeuring · Alex Gerdes Received: 26 January 2009 / Revised: 30 July 2009 / Accepted: 10 December 2009 / Published online: 10 March 2010 © The Author(s) 2010. This article is published with open access at Springerlink.com 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 calcu- late 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. Keywords Strategy language · Interactive exercises · Feedback · Recognizer · Context-free grammar 1 Introduction Tools like Aplusix [12], Active-Math [21], MathPert [4], the Freudenthal Digital Mathematics Environment (DWO) [5, 18], and our own tool for rewriting logic expressions [32] support solving mathematical exercises incrementally. Ideally a tool gives detailed feedback on several levels. For example, when a student rewrites p → (r ↔ p) into ¬ p ∨ (r ↔ p, our tool will tell the student that there is a missing parenthesis. If the same expression is rewritten into ¬ p ∧ (r ↔ p), it will tell the student that an error has been made when applying the definition of implication: B. Heeren · J. Jeuring · A. Gerdes School of Computer Science, Open Universiteit Nederland, P. O. Box 2960, 6401 DL Heerlen, The Netherlands e-mail: bhr@ou.nl A. Gerdes e-mail: age@ou.nl J. Jeuring (B) Department of Information and Computing Sciences, Universiteit Utrecht, P. O. Box 80.089, 3508 TB Utrecht, The Netherlands e-mail: johanj@cs.uu.nl; jje@ou.nl