Interactive Learning and Mathematical Calculus

Cohen, Arjeh M.; Cuypers, Hans; Jibetean, Dorina; Spanbroek, Mark

doi:10.1007/11618027_22

Cited by 5 publications

(5 citation statements)

References 4 publications

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“…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 [13] in an exercise assistant for calculus.…”

Section: Strategy Unfoldingmentioning

confidence: 99%

Specifying Rewrite Strategies for Interactive Exercises

2010

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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 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 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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Section: Strategy Unfoldingmentioning

confidence: 99%

Specifying Rewrite Strategies for Interactive Exercises

2010

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“…Sometimes it is cumbersome to use a domain reasoner to give feedback to students, or there is no domain reasoner available. The DME [19], MathDox [14,15], and Math-Bridge [52] offer the possibility to hardcode custom feedback in an exercise. For a typical multi-step exercise, this sometimes increases the size of the exercise measured in lines of text by a large factor.…”

Section: Design Considerationsmentioning

confidence: 99%

“…The environment provides some reusable components for specifying goals etc., but still requires a substantial amount of programming for developing a domain reasoner. For most domains, developing a domain reasoner is a challenging task and requires learning environments -DME [19] web-based learning environment by the Freudenthal Institute for secondary math education -Math-Bridge [52] e-learning platform for online bridging courses in mathematics, the successor of ActiveMath [38] -MathDox [14,15] software tools for creating interactive mathematical documents by Eindhoven University of Technology prototypes -Logic tool [36,35] bringing propositions into disjunctive normal form, and proving equivalences between logical formulae -Ask-Elle [23] stepwise development of simple functional programs …”

Section: Design Considerationsmentioning

confidence: 99%

“…For example, in a learning environment for mathematics that supports solving an exercise stepwise, an exercise about quadratic equations might be solved as in Figure 1. Stepwise exercises are particularly popular in learning environments for mathematics, such as MathDox [14,15], the Digital Mathematical Environment (DME) of the Freudenthal Institute [19], Math-Bridge [52] (based on ActiveMath [38]), APlusIx [13], the Carnegie Learning Algebra tutor, etc. Environments such as the DME and Math-Bridge offer thousands of stepwise exercises to a student.…”

Section: Introductionmentioning

confidence: 99%

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Feedback services for stepwise exercises

Heeren

Jeuring

2014

Science of Computer Programming

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Advanced learning environments such as intelligent tutoring systems for algebra, logic, programming, physics, etc. let a student practice with stepwise exercises, and support a student solving such exercises by providing feedback. These environments usually provide various types of feedback, for example about the correctness of a step, common errors, hints about how to proceed, or complete worked-out solutions. Calculating feedback is generally delegated to a dedicated expert knowledge module, also known as a domain reasoner. Existing architectural descriptions of learning environments do not precisely specify the interaction between this module and the rest of the learning system. We propose a design based on the stateless client-server architecture that clearly decouples the expert knowledge module from the learning environment. We describe a set of feedback services that support the inner (interactions within an exercise) and outer (over a collection of exercises) loops of a learning system, and that provide meta-information about a class of exercises, such as solving quadratic equations, or performing Gaussian elimination. The feedback services do not depend on a particular domain and are based on the various feedback types described in the literature.The paper analyzes which domain-specific knowledge about an exercise class is needed for implementing the feedback services. Based on this analysis, we developed a framework for implementing domain reasoners that offers generic functionality such as rewriting, simplifying, and comparing terms. We have implemented several domain reasoners in this framework, both for external learning environments and for simple prototypes. The proposed design is evaluated with these implementations, and we reflect on our experience with developing domain reasoners.

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“…Filtered by requiring support for Content MathML, the list still includes many interesting projects, e.g., the semantically oriented formula editor WIRIS OM Tools [5], Integre MathML Equation Editor [6], MathDox [10], and new attempts to bring an interactive editing process to the web, like the Connexions MathML Editor [7].…”

Section: Challenges Of Content Mathml Supportmentioning

confidence: 99%

The Formulator MathML Editor Project: User-Friendly Authoring of Content Markup Documents

Kovalchuk

Levitsky

Samolyuk

et al. 2010

Lecture Notes in Computer Science

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Implementation of an editing process for Content MathML formulas in common visual style is a real challenge for a software developer who does not really want the user to have to understand the structure of Content MathML in order to edit an expression, since it is expected that users are often not that technically minded. In this paper, we demonstrate how this aim is achieved in the context of the Formulator project and discuss features of this MathML editor, which provides a user with a WYSIWYG editing style while authoring MathML documents with Content or mixed markup. We also present the approach taken to enhance availability of the MathML editor to end-users, demonstrating an online version of the editor that runs inside a Web browser.

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Interactive Learning and Mathematical Calculus

Cited by 5 publications

References 4 publications

Specifying Rewrite Strategies for Interactive Exercises

Specifying Rewrite Strategies for Interactive Exercises

Feedback services for stepwise exercises

The Formulator MathML Editor Project: User-Friendly Authoring of Content Markup Documents

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