## Specifying strategies for exercises (2008)

Venue: | Suzuki & F. Wiedijk, eds, ‘AISC/Calculemus/MKM 2008’, LNAI 5144, SpringerVerlag |

Citations: | 13 - 9 self |

### BibTeX

@INPROCEEDINGS{Heeren08specifyingstrategies,

author = {Bastiaan Heeren and Johan Jeuring and Arthur Van Leeuwen and Alex Gerdes and Bastiaan Heeren and Johan Jeuring and Arthur Van Leeuwen and Alex Gerdes},

title = {Specifying strategies for exercises},

booktitle = {Suzuki & F. Wiedijk, eds, ‘AISC/Calculemus/MKM 2008’, LNAI 5144, SpringerVerlag},

year = {2008},

pages = {430--445}

}

### OpenURL

### Abstract

Abstract. The feedback given by e-learning 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 context-free and non-contextfree sublanguages of our strategy language. This separation is the key to automatically calculating all kinds of desirable feedback. 1

### Citations

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Citation Context ...arning materials. The basic idea is that a student profits from having example solutions played for him or her, followed by an exercise in which the student fills out some missing steps in a solution =-=[30]-=-. We can use the strategy for a problem to play a solution for a student, and we can play all but the middle two (three, last two, etc.) steps, and ask the student to complete the exercise. Buggy rule... |

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Citation Context ... skill. A procedure describes how basic steps may be combined to solve a particular problem. A procedure is often called a strategy (or meta-level reasoning, meta-level inference [8], procedural nets =-=[6]-=-, plans, tactics, etc.), and we will use this term in the rest of this paper. Many subjects require a student to learn strategies. At elementary school, students have to learn how to calculate a value... |

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Citation Context ...e combined with program code in a programming language to be able to specify any strategy. The strategy language is formulated as an embedded domain-specific language (EDSL) in a programming language =-=[20]-=- to easily facilitate the combination of program code with a strategy. Here ‘domain-specific’ means specific for the domain of strategies, not specific for the domain of exercises. The separation into... |

109 | A Tolmach. Building program optimizers with rewriting strategies
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Citation Context ...ing the kind of strategies that are needed in interactive exercise assistants that aim at providing advanced feedback. Our language is very similar to strategic programming languages such as Stratego =-=[33, 24]-=-, and very similar languages are used in parser combinator libraries [21, 31], boiler-plate libraries [23], workflow applications [29], theorem proving (tacticals [27]) and data-conversion libraries [... |

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Citation Context ... to offer many advantages, hundreds of tools that support practicing strategies in mathematics, logic, physics, etc. have been developed. Should e-learning systems give feedback? In Rules of the Mind =-=[1]-=-, Anderson discusses the ACT-R principles of tutoring, and the effectiveness of feedback in intelligent tutoring systems. One of the tutoring principles deals with student errors. If a student made a ... |

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Citation Context ... that aim at providing advanced feedback. Our language is very similar to strategic programming languages such as Stratego [33, 24], and very similar languages are used in parser combinator libraries =-=[21, 31]-=-, boiler-plate libraries [23], workflow applications [29], theorem proving (tacticals [27]) and data-conversion libraries [12], which suggests that our library could serve as a firm basis for strategy... |

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Citation Context ...also for e-learning tools [19]. Some work has been done on trying to explain errors made by students on the level of rewrite rules [17, 22, 26, 5]. Already around 1980, but also later, VanLehn et al. =-=[6, 7, 32]-=-, and Anderson and others from the Advanced Computer Tutoring research group at CMU [1, 2] worked on representing procedures or procedural networks. VanLehn et al. already noticed that ‘The representa... |

80 | Repair Theory: A generative theory of bugs in procedural skills
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Citation Context ...also for e-learning tools [19]. Some work has been done on trying to explain errors made by students on the level of rewrite rules [17, 22, 26, 5]. Already around 1980, but also later, VanLehn et al. =-=[6, 7, 32]-=-, and Anderson and others from the Advanced Computer Tutoring research group at CMU [1, 2] worked on representing procedures or procedural networks. VanLehn et al. already noticed that ‘The representa... |

72 |
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Citation Context ...ion concludes and gives directions for future research. 2. Strategies and feedback Whatever aspect of intelligence you attempt to model in a computer program, the same needs arise over and over again =-=[8]-=-: • The need to have knowledge about the domain.Strategies for Exercises 3 • The need to reason with that knowledge. • The need for knowledge about how to direct or guide that reasoning. In the case ... |

55 |
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Citation Context ...to Anderson, an informative error message is better than bug diagnosis. How do we calculate feedback on strategies? The strategy language is defined as an embedded domain-specific language in Haskell =-=[28]-=-. Using the basic constructs from the strategy language, we can create something that resembles a context-free grammar. The sentences of this grammar are sequences of transformation steps (application... |

53 |
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Citation Context ...eedback. Our language is very similar to strategic programming languages such as Stratego [33, 24], and very similar languages are used in parser combinator libraries [21, 31], boiler-plate libraries =-=[23]-=-, workflow applications [29], theorem proving (tacticals [27]) and data-conversion libraries [12], which suggests that our library could serve as a firm basis for strategy specifications. Our strategy... |

22 |
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Citation Context ... In particular, we discuss the use of a fixed point combinator to deal with repetition, and labels to mark positions in the strategy. 1. Introduction Tools like Aplusix [9], ActiveMath [15], MathPert =-=[4]-=-, and our own tool for rewriting logic expressions [25] support solving mathematical exercises incrementally. Ideally a tool gives detailed feedback on several levels. For example, when a student rewr... |

22 |
ML for the Working Programmer, 2nd edition
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Citation Context ...g languages such as Stratego [33, 24], and very similar languages are used in parser combinator libraries [21, 31], boiler-plate libraries [23], workflow applications [29], theorem proving (tacticals =-=[27]-=-) and data-conversion libraries [12], which suggests that our library could serve as a firm basis for strategy specifications. Our strategy language can be used to model strategies in multiple mathema... |

21 |
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Citation Context ...dvanced exercises. We will collect more data from the experiments, and analyze and report on the results. Also, we want to apply our ideas to domains with less structure, such as computer programming =-=[3]-=-, software modeling, and maybe even serious games in which students have to cooperate to achieve a certain goal. A final area that requires further investigation is how to make strategies more accessi... |

17 |
Authoring interactive exercises in ActiveMath
- Goguadze, Tsigler
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(Show Context)
Citation Context ...s 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. 1. Introduction Tools like Aplusix [9], ActiveMath =-=[15]-=-, MathPert [4], and our own tool for rewriting logic expressions [25] support solving mathematical exercises incrementally. Ideally a tool gives detailed feedback on several levels. For example, when ... |

17 | iTasks: executable specifications of interactive work flow systems for the web
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(Show Context)
Citation Context ...y similar to strategic programming languages such as Stratego [33, 24], and very similar languages are used in parser combinator libraries [21, 31], boiler-plate libraries [23], workflow applications =-=[29]-=-, theorem proving (tacticals [27]) and data-conversion libraries [12], which suggests that our library could serve as a firm basis for strategy specifications. Our strategy language can be used to mod... |

14 | Comparing approaches to generic programming in haskell
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- 2007
(Show Context)
Citation Context ...uld contain the following definitions: once s (p ∧ q) = {p ′ ∧ q | p ′ ← run s p } ∪ {p ∧ q ′ | q ′ ← run s q } once s (¬p) = {¬p ′ | p ′ ← run s p } once s T = ∅ Using generic programming techniques =-=[18]-=-, we can define this function once and for all, and use it for every domain. With the once function, we can define some powerful traversal combinators. The strategy somewhere s applies s to one subter... |

12 | Strongly typed rewriting for coupled software transformation
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Citation Context ...], and very similar languages are used in parser combinator libraries [21, 31], boiler-plate libraries [23], workflow applications [29], theorem proving (tacticals [27]) and data-conversion libraries =-=[12]-=-, which suggests that our library could serve as a firm basis for strategy specifications. Our strategy language can be used to model strategies in multiple mathematical domains. In the technical repo... |

10 | MathDox : mathematical documents on the web
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Citation Context ... show this information in a progress bar. Each time a student performs a correct step, the progress bar is updated. Strategy unfolding. We have constructed an OpenMath binding with the MathDox system =-=[11]-=-, in which a student enters a final answer to a question. If the answer is incorrect, we return a new exercise, which is part of the initial exercise. For example, if a student does not return a corre... |

9 |
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Citation Context ...mbinator to deal with repetition, and labels to mark positions in the strategy. 1. Introduction Tools like Aplusix [9], ActiveMath [15], MathPert [4], and our own tool for rewriting logic expressions =-=[25]-=- 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... |

9 | Feedback in an interactive equation solver
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(Show Context)
Citation Context ...in several contexts, most notably in compiler construction [31], but also for e-learning tools [19]. Some work has been done on trying to explain errors made by students on the level of rewrite rules =-=[17, 22, 26, 5]-=-. Already around 1980, but also later, VanLehn et al. [6, 7, 32], and Anderson and others from the Advanced Computer Tutoring research group at CMU [1, 2] worked on representing procedures or procedur... |

8 | Feedback services for exercise assistants
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- 2008
(Show Context)
Citation Context ... use the strategy language, as introduced in the previous sections, to give feedback to users of our e-learning systems, or to users of other e-learning systems that make use of our feedback services =-=[14]-=-. We have implemented several kinds of feedback. Most of these categories of feedback appear in the tutoring principles of Anderson [1], or in existing tools supporting the stepwise construction of a ... |

7 |
Online Diagnose in intelligenten mathematischen Lehr-LernSystemen (in German
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Citation Context ...at supporting detailed feedback for each exercise is very laborious, providing a comprehensive set of possible bugs for a particular domain requires a lot of research (see for example Hennecke’s work =-=[17]-=- on student bugs in calculating fractions), and automatically calculating feedback for a given exercise, strategy, and student input is very difficult. Feedback should be calculated automatically. We ... |

7 | Interactive learning and mathematical calculus
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(Show Context)
Citation Context ...ll occurrences of T and F in the logical expression. After completing this part of the exercise, we ask to solve the remaining part of the exercise. This kind of feedback is also used by Cohen et al. =-=[10]-=- in an exercise assistant for calculus. Hint. A student can ask for a hint. Given an exercise and a strategy for solving the exercise, we calculate the ‘best’ next step. The best next step is an eleme... |

7 | Supporting tutorial feedback to student help requests and errors in symbolic differentiation
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Citation Context ...rocedures, and the possibility to define recursive procedures. As far as we can see, neither VanLehn nor Anderson use parsing for the language for procedures to automatically calculate feedback. Zinn =-=[34]-=- writes strategies as Prolog programs, in which rules and strategies (‘task models’) are intertwined. 3. Three example strategies In this section we present three strategies for rewriting a classical ... |

6 |
Doaitse Swierstra and Luc Duponcheel. Deterministic, error-correcting combinator parsers
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Citation Context ...-repairing parsers, which we can use to improve feedback on the level of strategies. Related work. Explaining syntax errors has been studied in several contexts, most notably in compiler construction =-=[31]-=-, but also for e-learning tools [19]. Some work has been done on trying to explain errors made by students on the level of rewrite rules [17, 22, 26, 5]. Already around 1980, but also later, VanLehn e... |

4 |
et al. Aplusix, a learning environment for algebra, actual use and benefits
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Citation Context ...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. 1. Introduction Tools like Aplusix =-=[9]-=-, ActiveMath [15], MathPert [4], and our own tool for rewriting logic expressions [25] support solving mathematical exercises incrementally. Ideally a tool gives detailed feedback on several levels. F... |

4 |
The Essence of Strategic Programming. 18 p.; Draft; Available at http://www.cwi.nl/~ralf
- Lämmel, Visser, et al.
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(Show Context)
Citation Context ...ing the kind of strategies that are needed in interactive exercise assistants that aim at providing advanced feedback. Our language is very similar to strategic programming languages such as Stratego =-=[33, 24]-=-, and very similar languages are used in parser combinator libraries [21, 31], boiler-plate libraries [23], workflow applications [29], theorem proving (tacticals [27]) and data-conversion libraries [... |

3 |
Handling Errors in Mathematical Formulas
- Horacek, Wolska
- 2006
(Show Context)
Citation Context ... to improve feedback on the level of strategies. Related work. Explaining syntax errors has been studied in several contexts, most notably in compiler construction [31], but also for e-learning tools =-=[19]-=-. Some work has been done on trying to explain errors made by students on the level of rewrite rules [17, 22, 26, 5]. Already around 1980, but also later, VanLehn et al. [6, 7, 32], and Anderson and o... |

2 |
Solving of linear equations, linear inequalities and systems of linear equations in interactive learning environment
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(Show Context)
Citation Context ...in several contexts, most notably in compiler construction [31], but also for e-learning tools [19]. Some work has been done on trying to explain errors made by students on the level of rewrite rules =-=[17, 22, 26, 5]-=-. Already around 1980, but also later, VanLehn et al. [6, 7, 32], and Anderson and others from the Advanced Computer Tutoring research group at CMU [1, 2] worked on representing procedures or procedur... |

2 |
On the effect of immediate feedback
- Erev, Luria, et al.
- 2006
(Show Context)
Citation Context ... still debated. Anderson observed no positive effects in learning with4 Bastiaan Heeren, Johan Jeuring and Alex Gerdes deferred feedback, but observed a decline in learning rate instead. Erev et al. =-=[13]-=- also claim that immediate feedback is often to be preferred. Feedback in e-learning systems supporting incrementally solving exercises. There are only very few tools that mimic the incremental pen-an... |

1 | Seely Brown and Kurt VanLehn. Repair theory: A generative theory of bugs in procedural skills - John - 1980 |

1 | Chaachoua et al. Aplusix, a learning environment for algebra, actual use and benefits - unknown authors - 2004 |

1 | Erev Ido Erev, Adi Luria. On the effect of immediate feedback - Anan - 2006 |

1 | Passier and Johan Jeuring. Feedback in an interactive equation solver - Harrie - 2006 |