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Specifying strategies for exercises
 Suzuki & F. Wiedijk, eds, ‘AISC/Calculemus/MKM 2008’, LNAI 5144, SpringerVerlag
, 2008
"... Abstract. The feedback given by elearning tools that support incrementally solving problems in mathematics, logic, physics, etc. is limited, or laborious to specify. In this paper we introduce a language for specifying strategies for solving exercises. This language makes it easier to automatically ..."
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Cited by 15 (10 self)
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Abstract. The feedback given by elearning tools that support incrementally solving problems in mathematics, logic, physics, etc. is limited, or laborious to specify. In this paper we introduce a language for specifying strategies for solving exercises. This language makes it easier to automatically calculate feedback when users make erroneous steps in a calculation. Although we need the power of a full programming language to specify strategies, we carefully distinguish between contextfree and noncontextfree sublanguages of our strategy language. This separation is the key to automatically calculating all kinds of desirable feedback. 1
Specifying Rewrite Strategies for Interactive Exercises
"... 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 langu ..."
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Cited by 10 (10 self)
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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 workedout 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 laborintensive and less adhoc 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 contextfree 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.
Feedback Services for Exercise Assistants
, 2008
"... Immediate feedback has a positive effect on the performance of a student practising a procedural skill in exercises. Giving feedback to a number of students is labourintensive for a teacher. To alleviate this, many electronic exercise assistants have been developed. However, many of the exercise as ..."
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Cited by 9 (8 self)
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Immediate feedback has a positive effect on the performance of a student practising a procedural skill in exercises. Giving feedback to a number of students is labourintensive for a teacher. To alleviate this, many electronic exercise assistants have been developed. However, many of the exercise assistants have some limitations in the feedback they offer. We have a feedback engine that gives semantically rich feedback for several domains (like logic, linear algebra, arithmetic), and that can be relatively easy extended with new domains. Our feedback engine needs to have knowledge about the domain, how to reason with that knowledge (i.e. a set of rules), and a specified strategy. We offer the following types of feedback: correct/incorrect statements, distance to the solution, rulebased feedback, buggy rules, and strategy feedback. We offer the feedback functionality in the form of lightweight web services. These services are offered using different protocols, for example
Strategy feedback in an elearning tool for mathematical exercises
 Utrecht University
, 2007
"... Abstract Exercises in mathematics are often solved using a standard procedure, such as for example solving a system of linear equations by subtracting equations from top to bottom, and then substituting variables from bottom to top. Students have to practice such procedural skills: they have to lear ..."
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Cited by 1 (1 self)
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Abstract Exercises in mathematics are often solved using a standard procedure, such as for example solving a system of linear equations by subtracting equations from top to bottom, and then substituting variables from bottom to top. Students have to practice such procedural skills: they have to learn how to apply a particular strategy to an exercise. Elearning systems offer excellent possibilities for practicing procedural skills. The first explanations and motivation for a procedure that solves a particular kind of problems are probably best taught in a class room, or studied in a book, but the subsequent practice can often be done behind a computer. There exist many elearning systems or intelligent tutoring systems that support practicing procedural skills. The tools vary widely in breadth, depth, userinterface, etc, but, unfortunately, almost all of them lack sophisticated techniques for providing immediate feedback. If feedback mechanisms are present, they are hard coded in the tools, often even with the exercises. This situation hampers the usage of elearning systems for practicing mathematical skills. This paper introduces a formalism for specifying strategies for solving exercises. It shows how a strategy can be viewed as a language in which sentences consist of transformation steps. Furthermore, it discusses how we can use advanced techniques from computer science, such as term rewriting, strategies, errorcorrecting parsers, and parser combinators to provide feedback at each intermediate step from the start towards the solution of an exercise. Our goal is to obtain elearning systems that give immediate and useful feedback. 1
WRS 2008 Recognizing Strategies
"... We use strategies to 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. With such a strategy, we can automatically generate workedout solutions, track the progress of a ..."
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We use strategies to 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. With such a strategy, we can automatically generate workedout solutions, track the progress of a student by inspecting submitted intermediate answers, and report back suggestions in case the student deviates from the strategy. Because we can calculate all kinds of feedback automatically from a strategy specification, it becomes less laborintensive and less adhoc to specify new exercise domains and exercises within that domain. A strategy describes valid sequences of transformation rules that solve the exercise at hand, which turns tracking intermediate steps into a parsing problem. This is a promising view at the problem because it allows us to take advantage of many years of experience in parsing sentences of contextfree 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, and we discuss the implementation of a recognizer for strategies. We present a full implementation of such a recognizer, and discuss a number of design choices we have made. In particular, we discuss the use of a fixed point combinator to deal with repetition, and labels to mark positions in the strategy.
DOI 10.1007/s1178601000274 Mathematics in Computer Science Specifying Rewrite Strategies for Interactive Exercises
"... 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 langua ..."
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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 workedout 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 laborintensive and less adhoc 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 contextfree 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.