Authoring of Semantic Mathematical Content for Learning on the Web

Authoring of Semantic Mathematical Content for Learning on the Web Paul Libbrecht Doctoral thesis at the faculty of computer-science of the Saarland University under the supervision of Prof. Jörg Siekmann and Dr Erica Melis,† and under the expertise of Prof. Gerhardt Weikum and Prof. James Davenport. Dissertation zur Erlangung des Grades des Doktors der Ingenieurwissenschaften der Naturwissenschaftlich- Technischen Fakultäten der Universität des Saarlandes. Saarbrücken, Germany – 2012 This doctoral thesis has been defended on July 30th 2012 at the University of Saarland under the supervision of a committee appointed by the faculty dean, Prof. Mark Groves: Prof. Jörg Siekmann (reporting chairman), Prof. James Davenport (reporter), Prof. Gerhard Weikum (reporter), Prof. Anselm Lambert (chairman), and Dr. George Goguadze (faculty member). Colophon This doctoral thesis is typeset using the pdflatex programme, a contemporary part of classical TeX distributions (see http://tug.org/). This programme is run through TeXshop, an application for TeX on MacOSX (see http://pages.uoregon.edu/koch/texshop/). The source of the thesis has been partially written in TeX sources (chapters 2, 5, and 9, as well as the chapters without numbers) and partially using OmniGroup’s OmniOutliner, an outliner for MacOSX (see http://www.omnigroup.com/omnioutliner), followed by a hand-made XSLT stylesheet to convert an almost visual source to its TeX counterpart. This thesis is typeset using the font urw-classico, a clone of the font Optima realized by Bob Tennent for the TeX users; see http://www.ctan.org/tex-archive/fonts/urw/ classico/. The main body of the text is typeset in 10 pt size. About the Cover-Page Graphics This picture, made of a collage of photographs by myself, Carsten Ullrich, and Edgar Kessler, expresses the projection relationship between the author at work with his authoring tools and the various learning situations. Ownership and License The text in this thesis has been entirely written by me. At times, I cite research of other persons using the normal citation mechanism: in this thesis, I am using a short key made of the initial part of the author names in square brackets followed by the year, as in [ML71]. The key refers to the bibliography appendix where all the details of the publication are given and, as much as possible, a URL to access the publication. Eidesstattliche Versicherung Hiermit versichere ich an Eides statt, dass ich die vorliegende Arbeit selbst- ständig und ohne Benutzung anderer als der angegebenen Hilfsmittel angefertigt habe. Die aus anderen Quellen oder indirekt übernommenen Daten und Konzepte sind unter Angabe der Quelle gekennzeichnet. Die Arbeit wurde bisher weder im In- noch im Ausland in gleicher oder ähnlicher Form in einem Verfahren zur Erlangung eines akademischen Grades vorgelegt. I hereby grant the recipient of this text a license to copy and redistribute the content of this thesis under the license Creative Commons Attribution Germany. See http:// creativecommons.org/licenses/by/3.0/. This license allows free redistribution, modi- fication, and inclusion. 3 Abstract This thesis explores how a mathematician can create content which lets students learn via ActiveMath. This software runs on the web, and employs semantics mathematical technologies and artificial intelligence to support the student. The thesis describes not only a tool to edit content but also studies the workflows of authors when creating content. An important authoring paradigm introduced here is called WYCIWYG – What You Check is What You Get. This places the target learning environment as the central concern. Indeed, the learning environment, which is the assembly of content and software, represents the final product of the authoring work. This thesis exploits and develops classical paradigms: copy-and-paste, search, and collaborative authoring. To support the authoring workflows, several software pieces have been implemented and tested: within an editing tool and the ActiveMath software. The following work describes their usages, their technical facets, and case studies of how current authors have used them in their day-to-day activities. Zusammenfassung In dieser Dissertation untersuchen wir Möglichkeiten, die einem Mathematiker zur Verfügung stehen, um Lerninhalte für ActiveMath zu gestalten. Diese intelligent-adaptive Lernumgebung nutzt semantisch-mathematische Technologien und Methoden der künstliche Intelligenz, um den Lernenden zu unterstützen. Diese Dissertation beschreibt nicht nur ein Werkzeug zur Bearbeitung des Inhaltes, sondern auch typische Abläufe und Prozesse bei der Inhaltsgestaltung. Ein wichtiges Paradigma für die Autorierung nennt sich WYCIWYG (für What You Check is What You Get: Was Sie prüfen, ist [das,] was Sie erhalten). Es rückt die Lernumgebung in den Mittelpunkt, denn letztlich ist diese als Zusammenspiel der Software und der erstellten Inhalte das Endprodukt, mit dem der Lernende arbeitet. Kopieren und Einfügen, Suche sowie kollaboratives Autorieren sind andere klassische Paradigmen, die in dieser Arbeit aufgegriffen und weiterentwickelt werden. Zur Unterstützung des Autorierungsprozesses wurden mehrere Programme, sowohl in der Lernumgebung ActiveMath als auch in einem Texteditor, entwickelt und getestet. Diese Doktorarbeit beschreibt deren Gebrauch, technische Aspekte, sowie Fallstudien von Autoren, die sie in ihrer täglichen Arbeit verwendet haben. Résumé Dans cette thèse, nous explorons les différentes voies qu’a un mathématicien pour créer un contenu permettant d’apprendre avec ActiveMath: apprendre les mathématiques avec un logiciel du web qui emploie les technologies des mathématiques sémantiques et de l’intelligence artificielle pour assister l’étudiant. Un des paradigmes important de la création de contenu s’appelle WYCIWYG (What You Check is What You Get: ce que vous révisez est ce que vous obtenez), il met l’environnement d’apprentissage au centre. En effet, cet environnement, assemblage du contenu du système, est l’objectif final de la création. D’autres paradigmes classiques sont exploités: le copier-coller, la fonction de recherche et la création collaborative. Pour contribuer au processus de création, plusieurs logiciels ont été réalisés et testés, tant dans un outil d’édition que dans ActiveMath. Dans cette thèse, nous décrivons leur usage et leurs aspects techniques. En outre, un chapitre est consacré aux études de cas de plusieurs auteurs qui les ont utilisés dans leur quotidien professionel. Acknowledgements I would like to thank my thesis advisers, Erica Melisy and Jörg Siekmann, who always tried to push the advancement of this research and have given it a frame towards its reality. I am particularly thankful to Erica Melis for her permanent opening to my questioning and inclination to debate, and the professional replies she always made to them; I am particularly thankful to Jörg Siekmann for his impressive enthusiasm about the subject. The team where this research has happened was intrumental to this thesis: the many authors that patiently tried and accepted or rejected authoring methods, as we report in the chapter9 as well as the team at the ActiveMath group. I would like to particularly thank Eric Andrès and Michael Dietrich, for having taken over the duty of teaching authoring. Thanks to Carsten Ullrich, Stefan Winterstein, George Goguadze, Martin Homik, Michael Kohlhase, and Vladimir Breznev for active and fruitful discussions around ActiveMath. Thanks to all our students for their curious and brave implementation attempts, in particular Shahid Manzoor and Yecheng Gu. The detailed list of software contributions is described in the appendixA. I’m indepted to my committee for their reviews. I would like to particularly thank James Davenport for his proactive suggestions which have uncovered the depth of the challenges several times. I would like to thank my parents and family at large for their impulse into this intellectual entreprise. They have contributed to create the curiosity and tenacity needed to attack and discover such research. This thesis is largely due to the patience of my family which saw me spend long nights and week-ends on the topic while the weeks were busy with more business- oriented works (such as research projects). My wife Corinne, in particular, has supported each advance by encouragements and acclamations. They have even brought my kids to pique me on a regular basis to ensure that the thesis was the focus of work! Thanks for their patience while it has taken much longer than one would have wished or planned. yErica Melis has directed this thesis until 2008. She passed away in 2011. 4 Contents Introduction7 I Context 13 1 Authoring an E-Learning System 15 1.1 Introduction.............................. 15 1.2 Expectations of the Authoring Work................. 18 1.3 Sample Authoring Tools........................ 20 1.4 How is Content Accessed....................... 21 1.5 Conclusions.............................. 32 2 ActiveMath and Semantic Mathematical Documents 33 2.1 Semantic Mathematical Formulæ................... 34 2.2 Semantic Mathematical Documents................. 35 2.3 Concepts in the ActiveMath Learning Environment......... 41 2.4 The Components of the ActiveMath Server............. 43 2.5 Learner Tools............................. 50 2.6 Conclusions.............................. 53 II Authoring for ActiveMath 55 3 WYCIWYG: Authoring with jEditOQMath 57 3.1 Mission................................ 57 3.2 Set-up for jEditOQMath.......................

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