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A semantic wiki for mathematical knowledge management
 Proceedings of the 1st Workshop on Semantic Wikis, European Semantic Web Conference 2006, Budva, Montenegro, 2006. CEUR Workshop Proceedings. To appear, provisional online version at http://www.eswc2006.org/technologies/ usb/proceedingsworkshops/ eswc200
, 2007
"... SWIM is a semantic wiki for collaboratively building, editing and browsing mathematical knowledge represented in the structural markup language OMDOC. It has been designed to enable groups of scientists to develop new mathematical theories in OMDOC and to enable scholars to browse such a corpus. Aft ..."
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SWIM is a semantic wiki for collaboratively building, editing and browsing mathematical knowledge represented in the structural markup language OMDOC. It has been designed to enable groups of scientists to develop new mathematical theories in OMDOC and to enable scholars to browse such a corpus. After a short introduction to semantic wikis and their usefulness for mathematical knowledge, this article presents the architecture and the user interface of the current SWIM prototype and outlines the plans for developing its successor, an ontologybased platform for semantic scientific services that exploit the knowledge and make it accessible to the user. 1
What Do Argument Diagrams Tell Us About Students’ Aptitude Or Experience? A Statistical Analysis In An Ill Defined Domain�
"... Abstract. In illdefined domains, argumentation skills are essential in order to define problems and to present, justify, and evaluate solutions. In welldefined domains there exist accepted methods of characterizing student arguments as good or bad. This is not always possible in illdefined domain ..."
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Abstract. In illdefined domains, argumentation skills are essential in order to define problems and to present, justify, and evaluate solutions. In welldefined domains there exist accepted methods of characterizing student arguments as good or bad. This is not always possible in illdefined domains, where competing arguments are often acceptable. In this paper, we use a set of statistical analysis methods to investigate whether, despite the lack of an “ideal solution,”, studentproduced argument diagrams can be diagnostic in that they can be used to reliably classify students into novices and experts or high and low aptitude. Our analysis, based on data collected during three studies with the LARGO ITS, suggests that indeed, argument graphs created by different student populations differ considerably, particularly with respect to the completeness and “connectedness ” of graphs, and can thus potentially be used to adapt the system to a particular student’s needs.
Adapting Mathematical Domain Reasoners
, 2010
"... Mathematical learning environments help students in mastering mathematical knowledge. Mature environments typically offer thousands of interactive exercises. Providing feedback to students solving interactive exercises requires domain reasoners for doing the exercisespecific calculations. Since a ..."
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Cited by 5 (5 self)
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Mathematical learning environments help students in mastering mathematical knowledge. Mature environments typically offer thousands of interactive exercises. Providing feedback to students solving interactive exercises requires domain reasoners for doing the exercisespecific calculations. Since a domain reasoner has to solve an exercise in the same way a student should solve it, the structure of domain reasoners should follow the layered structure of the mathematical domains. Furthermore, learners, teachers, and environment builders have different requirements for adapting domain reasoners, such as providing more details, disallowing or enforcing certain solutions, and combining multiple mathematical domains in a new domain. In previous work we have shown how domain reasoners for solving interactive exercises can be expressed in terms of rewrite strategies, rewrite rules, and views. This paper shows how users can adapt and configure such domain reasoners to their own needs. This is achieved by enabling users to explicitly communicate the components that are used for solving an exercise.
Interleaving Strategies
, 2011
"... Rewrite strategies are used to specify how mathematical exercises are solved in interactive learning environments, and to provide feedback to students solving such exercises. We have developed a generic strategy language with which we can specify rewrite strategies in many (mathematical) domains. ..."
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Cited by 4 (4 self)
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Rewrite strategies are used to specify how mathematical exercises are solved in interactive learning environments, and to provide feedback to students solving such exercises. We have developed a generic strategy language with which we can specify rewrite strategies in many (mathematical) domains. Although our strategy language is quite powerful, it lacks an essential component for specifying strategies, namely the interleaving of two strategies. Often students have to perform multiple subtasks, but the order in which these tasks are performed is irrelevant, and steps of solutions may be interleaved. We show the need for combinators that support interleaving by means of several examples. We extend our strategy language with different combinators for interleaving, define the semantics of the extension, and show how the interleaving combinators are implemented in the parsing framework we use for recognizing student behavior and providing hints.
Integrating Proof Assistants as Reasoning and Verification Tools into a Scientific WYSIWYG Editor
, 2005
"... A major problem for the acceptance of mathematical proof assistance systems in mathematical practise is the shortcomings of their user interfaces. Often the interfaces are developed bottomup starting from the mathematical proof assistance system. Therefore they usually focus on the individual syste ..."
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Cited by 3 (1 self)
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A major problem for the acceptance of mathematical proof assistance systems in mathematical practise is the shortcomings of their user interfaces. Often the interfaces are developed bottomup starting from the mathematical proof assistance system. Therefore they usually focus on the individual system and its proof development paradigm and neglect traditional forms to communicate proofs as used by mathematicians. To address this problem we propose a topdown approach where we start from an existing scientific WYSIWYG text editor which supports the preparation of mathematical publications in high quality typesetting and integrate a mathematical proof assistance system to support proof development and validation. Concretely, we extend the document format of the text editor by semantic markup to encode formal mathematical content and to communicate with the formal system. Additionally we provide interaction markup defining contextsensitive means to control the mathematical proof assistance system through the text editor.
ContextAware Adaption. A Case Study on Mathematical Notations
, 2008
"... In the last two decades, the World Wide Web has become the universal, and — for many users — main information source. Search engines can efficiently serve daily life information needs due to the enormous redundancy of relevant resources on the web. For educational — and even more so for scientific i ..."
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Cited by 1 (1 self)
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In the last two decades, the World Wide Web has become the universal, and — for many users — main information source. Search engines can efficiently serve daily life information needs due to the enormous redundancy of relevant resources on the web. For educational — and even more so for scientific information needs, the web functions much less efficiently: Scientific publishing is built on a culture of unique reference publications, and moreover abounds with specialized structures, such as technical nomenclature, notational conventions, references, tables, or graphs. Moreover, many of these structures are peculiar to specialized communities determined by nationality, research group membership, or adherence to a special school of thought. To keep the muchlamented “digital divide ” from becoming a “cultural divide”, we have to make online material more accessible and adaptable to individual users. In this paper we attack this goal for the field of mathematics where knowledge is abstract, highly structured, and extraordinarily interlinked. Modern, contentbased representation formats like OpenMath or content MathML allow us to capture, model, relate, and represent mathematical knowledge objects and thus make them contextaware and machineadaptable to the respective user contexts. Building on previous work which can make mathematical notations adaptable we employ user modeling techniques to make them adaptive to relieve the reader of configuration tasks. We present a comprehensive framework for adaptive notation management and evaluate it on an implementation integrated in the elearning platform panta rhei.
A Review on Artificial Intelligence in Special Education
"... Abstract. Innovative educational technologies have started to open new ways of interacting with students with special educational needs (SEN). Amongst the most effective approaches during the last decade (20012010) are those based on Artificial Intelligence (A.I.) techniques. The effective applicat ..."
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Abstract. Innovative educational technologies have started to open new ways of interacting with students with special educational needs (SEN). Amongst the most effective approaches during the last decade (20012010) are those based on Artificial Intelligence (A.I.) techniques. The effective application of A.I. methods is seen as a means of improving the quality of life of SEN learners. Hence, a need for introducing A.I. techniques arises in order to develop both diagnosis and intervention processes. This paper presents a brief overview of the most representative studies of the past ten years, used for the above purposes.
Communities of Practice in Mathematical ELearning
, 2008
"... With the globalization in education, bridging cultural differences by making course material more accessible and adaptable to individual user needs becomes an important goal. In this paper we attack this goal for the field of mathematics where knowledge is abstract, highly structured, and extraordin ..."
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With the globalization in education, bridging cultural differences by making course material more accessible and adaptable to individual user needs becomes an important goal. In this paper we attack this goal for the field of mathematics where knowledge is abstract, highly structured, and extraordinary interlinked. Modern representation formats like our OMDOC format allow us to capture, model, relate, and represent mathematical learning objects and thus make them contextaware and machineadaptable to the respective learning contexts. But to make mathematical knowledge accessible to learners of diverse cultural backgrounds we also need to model mathematical practice. In this paper, we show that many practices of mathematical communities can already be modeled in OMDOC and outline extensions to support further ones. We have implemented a collection of services that allow applications to interpret and manage OMDOC and its practice representations as well as to adapt OMDOC for users and communities. These services have been integrated into our prototype ELearning platform panta rhei to demonstrate how systems can improve the accessibility of mathematical ELearning materials.
UTILIZING DIAGNOSING PROBLEMS IN A PROBABILISTIC DOMAIN TO BUILD STUDENT MODELS
"... In this paper we aim to estimate the differential student knowledge model in a probabilistic domain within an intelligent tutoring system. The student answers to questions requiring diagnosing skills are used to estimate the actual student model. Updating and verification of the model are conducted ..."
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In this paper we aim to estimate the differential student knowledge model in a probabilistic domain within an intelligent tutoring system. The student answers to questions requiring diagnosing skills are used to estimate the actual student model. Updating and verification of the model are conducted based on the matching between the student's and model answers. Two different approaches to updating are suggested, i) coarse and ii) refined model updating. Moreover, the effect of the order of which questions are presented to the student is investigated. Results suggest that the refined model, although takes more computational resources, provides a slightly better approximation of the student model. In addition, the accuracy of the algorithm is highly insensitive to the order of which the questions are presented, more so when using the refined model updating approach..
Enriching the Student Model in an Intelligent Tutoring System
, 2014
"... The course of study for this award was developed jointly by ..."