WIRIS OM tools: a semantic formula editor

With the increasing reliance on computers for the automatic processing of information a new method is needed for editing mathematical formulae. We are used to WYSIWYG editors that produce beautiful presentations of formulae and store the typesetting primitives rather than the meaning of the formulas. However, new services such as database searching or calculation web-services work best if they have access to the semantic information behind a formula. This can only be done with a new generation of formula editors. In this paper we present WIRIS OM Tools [17], a semantic oriented formula editor which addresses these concerns. It is based on the OpenMath language and a suitable transformation process between OpenMath and MathML ex- pressions. Additionally, this approach adds new features for the users such as error, type and syntax checking. The editor is currently being used in the LeActiveMath and WebALT projects

Integrated semantic math I/O in ActiveMath: an evaluation

The ActiveMath system is a web-based learning environment that integrates static mathematical content and interactive exercises with evaluated mathematical input from learners. Mathematical formulæ in ActiveMath are encoded in OpenMath and presented with regional notations. Users can input formulæ using the same notations via a formula editor or using plain-text input. Input to the editor is assisted by allowing users to copy formulæ from other parts of ActiveMath. In this paper we will describe how all these components are integrated and work within the system. We will then discuss recent evaluations of the formulæ input methods run within the LeActiveMath project in Malaga and Edinburgh. The results indicate that, even though the assisted input methods provided by the Formula Editor and copy-andpaste are appreciated by users the most popular input method remains the plain text input fields. Proposals are made for how direct input of text can be facilitated and assisted in future formulæ input systems

Mathematical interactive content: what, why and how

The real challenge of e-Learning is to produce content that brings a general improvement in the way students learn and teachers teach. For that, “intelligent” interactivity is the single most important feature that such content should have. But the design and production of content with this kind of interactivity has turned out to be harder than expected, the main reason being that it requires the convergence of many kinds of experts in parallel to the convergence of the several technologies involved. In the case of mathematics, the least amount of expertise asks for the presence of professional mathematicians, software engineers, publishers, and perhaps learning theorists, that can productively talk to each other. In this paper we want to examine afresh, with a view to the future, what is (or can be) meant by interactivity; the reasons why interactivity should play a role in optimizing general mathematical learning and in making possible, and viable, that mathematics teachers at large embrace a role that is congruent with their present day mission. Finally we propose a check list for desirable features that advanced mathematical learning systems should have, state some guiding principles for their design, and describe what is involved in their production

WIRIS OM Tools: a Semantic Formula Editor

With the increasing reliance on computers for the automatic processing of information a new method is needed for editing mathematical formulae. We are used to WYSIWYG editors that produce beautiful presentations of formulae and store the typesetting primitives rather than the meaning of the formulas. However, new services such as database searching or calculation web-services work best if they have access to the semantic information behind a formula. This can only be done with a new generation of formula editors. In this paper we present WIRIS OM Tools [17], a semantic oriented formula editor which addresses these concerns. It is based on the OpenMath language and a suitable transformation process between OpenMath and MathML ex- pressions. Additionally, this approach adds new features for the users such as error, type and syntax checking. The editor is currently being used in the LeActiveMath and WebALT projects

Integrated Semantic Math I/O in ActiveMath: an Evaluation

The ActiveMath system is a web-based learning environment that integrates static mathematical content and interactive exercises with evaluated mathematical input from learners. Mathematical formulæ in ActiveMath are encoded in OpenMath and presented with regional notations. Users can input formulæ using the same notations via a formula editor or using plain-text input. Input to the editor is assisted by allowing users to copy formulæ from other parts of ActiveMath. In this paper we will describe how all these components are integrated and work within the system. We will then discuss recent evaluations of the formulæ input methods run within the LeActiveMath project in Malaga and Edinburgh. The results indicate that, even though the assisted input methods provided by the Formula Editor and copy-andpaste are appreciated by users the most popular input method remains the plain text input fields. Proposals are made for how direct input of text can be facilitated and assisted in future formulæ input systems

Course generation as a hierarchical task network planning problem

This thesis presents course generation based on Hierarchical Task Network planning (HTN planning). This course generation framework enables the formalization and application of complex and realistic pedagogical knowledge. Compared to previous course generation, this approach generates structured courses that are adapted to a variety of different learning goals and to the learners\u27; competencies. The thesis describes basic techniques for course generation, which are used to formalize seven different types of courses (for instance introducing the learner to previously unknown concepts and supporting him during rehearsal) and several elementary learning goals (e. g., selecting an appropriate example or exercise). The course generator developed in this thesis is service-oriented thus allowing the integration of learning supporting services into the generated course in a generic and pedagogically sensible way. Furthermore, learning environments can access the functionality of the course generator using a Web-service interface. Repositories are treated as services that can register at the course generator and make their content available for course generation. The registration is based on an ontology of instructional objects. Its classes allow categorizing learning objects according to their pedagogical purpose in a more precise way than existing metadata specifications; hence it can be used for intelligent pedagogical functionalities other than course generation. Course generation based on HTN planning is implemented in Paigos and was evaluated by technical, formative and summative evaluations. The technical evaluation primarily investigated the performance to Paigos; the formative and summative evaluations targeted the users\u27; acceptance of Paigos and of the generated courses.Diese Arbeit stellt Kursgenerierung vor, die auf Hierarchical Task Network Planung (HTN Planung) basiert. Der gewählte Rahmen erlaubt die Formalisierung von komplexem und realistischem pädagogischem Wissen und ermöglicht im Vergleich zu bisherigen Techniken die Generierung von strukturierten Kursen, die an eine Vielzahl von Lernzielen angepasst sind. Aufbauend auf allgemeinen Techniken zur Kursgenerierung wird das pädagogische Wissen für sieben verschiedene Kurstypen und für eine Reihe von elementaren Lernzielen formalisiert. Die in dieser Arbeit vorgestellte Kursgenerierung ist service-orientiert. Dadurch steht ein generischer Rahmen zu Verfügung, in dem externe Lernsysteme in die generierten Kurse eingebunden werden und dem Lernenden zur Verfügung gestellt werden können, wenn es pädagogisch sinnvoll ist. Weiterhin können andere Lernsysteme über eine Web-Service Schnittstelle auf die Funktionalitäten des Kursgenerators zugreifen: Datenbanken werden als Services betrachtet, die an dem Kursgenerator registriert werden können, und auf die während der Kurserstellung zugegriffen wird. Die Registrierung verwendet eine Ontologie, die verschiedene instruktionale Typen von Lernobjekten repräsentiert und es erlaubt, Lernobjekte nach ihrem pädagogischen Verwendungszweck zu klassifizieren. Sie geht dabei über existierende Metadatenspezifikationen hinaus und ermöglicht pädagogische komplexe Funktionalitäten, so wie beispielsweise Kursgenerierung und weitere. Die vorgestellte Kursgenerierung ist implementiert in Paigos und wurde durch technische, formative und summative Evaluationen untersucht. Die technische Evaluation analysierte in erster Linie die Performanz von Paigos; die formative und summative Evaluationen widmeten sich der Frage der Akzeptanz und Verständlichkeit der von Paigos erzeugten Kurse aus Benutzersicht

Web Application for Learning Mathematics

Web application which assists in the process of learning mathematics is presented in the paper. The application and its functionalities will be explained in detail. Also, there will be presented parts from the web application using diagrams such as the E-R diagrams and the UML diagram

The freedom to extend OpenMath and its utility

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Students´ language in computer-assisted tutoring of mathematical proofs

Truth and proof are central to mathematics. Proving (or disproving) seemingly simple statements often turns out to be one of the hardest mathematical tasks. Yet, doing proofs is rarely taught in the classroom. Studies on cognitive difficulties in learning to do proofs have shown that pupils and students not only often do not understand or cannot apply basic formal reasoning techniques and do not know how to use formal mathematical language, but, at a far more fundamental level, they also do not understand what it means to prove a statement or even do not see the purpose of proof at all. Since insight into the importance of proof and doing proofs as such cannot be learnt other than by practice, learning support through individualised tutoring is in demand. This volume presents a part of an interdisciplinary project, set at the intersection of pedagogical science, artificial intelligence, and (computational) linguistics, which investigated issues involved in provisioning computer-based tutoring of mathematical proofs through dialogue in natural language. The ultimate goal in this context, addressing the above-mentioned need for learning support, is to build intelligent automated tutoring systems for mathematical proofs. The research presented here has been focused on the language that students use while interacting with such a system: its linguistic propeties and computational modelling. Contribution is made at three levels: first, an analysis of language phenomena found in students´ input to a (simulated) proof tutoring system is conducted and the variety of students´ verbalisations is quantitatively assessed, second, a general computational processing strategy for informal mathematical language and methods of modelling prominent language phenomena are proposed, and third, the prospects for natural language as an input modality for proof tutoring systems is evaluated based on collected corpora