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Hendricks / Jeschke / Thomsen / Weinzierl Mumie eLearning Environment and Authoring Tool for a Modern Education in Mathematics Online Educa Berlin 2005 Workshop 16: Implementing Large-Scale Blended Learning at Universities TU Berlin - Main Building Dipl.-Inform. Uwe Sinha TU Berlin, Institute of Mathematics 30 November 2005

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Uwe Sinha Online Educa Berlin November 2005 Contents: 1.Background 2.Mumie: Ideas & Concept 3.MmTeX & Mmcdk: eLearning Content for Mathematics 4.Outlook

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Uwe Sinha Online Educa Berlin November 2005 Background

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Uwe Sinha Online Educa Berlin 2005 Generations of eLTR technologies: First Generation : distribution of information document management passive static objects simple training scenarios isolated communication applications electronic presentation environments dynamical content management granular flexible knowledge atoms highly interactive and adaptive complex training szenarios integrated cooperation environments support of active & explorative learning modern human computer interfaces Next Generation: Object of current research and development Used in many national and international universities WebCT & Co. Virtuelle Labore Mumie Cinde- rella Applet Factory

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Uwe Sinha Online Educa Berlin 2005 Change in mathematical Power Results in : Changes within Mathematics itself: Changes within mathematical education: Development of new research areas Expansion of research methodology Diversification of users of mathematics Expansion of mathematical competencies Develop new learning and teaching methods

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Uwe Sinha Online Educa Berlin 2005 Intelligent Assistive Technologies in eLearning environments for Mathematics: precisely formalized language naturally given entities strictly encapsulated entities internal structure of entities clear dependencies betw. entities high continuity of knowlegde Highly structured field: 1.(Pure) mathematical research 2.Mathematics := key technology for many applied sciences high level of adaptivity required, new competencies demanded Broad audience:

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Uwe Sinha Online Educa Berlin 2005 Pedagogical Concepts Support explorative, nonlinear learning styles Offer flexible scenarios Develop Visualizations for complex mathematical objects & concepts eLearning Concepts Comprehension – Oriented Independent and Individual Learning Interdisciplinary & Soft Skills

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Uwe Sinha Online Educa Berlin 2005 eLearning/Knowledge Systems in Mathematics: Content Area: Granular knowledge atoms with interactive components, allowing composition of different courses adaption to different target groups Semantic Retrieval Area: User-specific retrieval of information and visualization of relations answers to individual requests knowledge nets Intelligent Training Area: Granular training material, highly interactive, using intelligent validation: adaptation to learning goals support self-directed learning Virtual Laboratories Area : Self-directed learning environment, supporting explorative learning individualized learning

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Uwe Sinha Online Educa Berlin November Mumie: Ideas & Concept

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Uwe Sinha Online Educa Berlin 2005 Mumie: eLearning Categories Courses from granular elements of knowledge Composition with the CourseCreator tool Interactive multimedia elements Non- linear navigation Excercises, combined into to Exercise paths Interactive, constructive environment Embedded in an exercise network Intelligent input & control mechanisms User driven information retrieval system Knowledge networks User defined constructions includes an encyclopedia VirtLabs Combinable experiments Explorative learning and research Experiments integrating CAS & Num. Tools Intelligent input & control mechanisms Retrieval Training Content

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Uwe Sinha Online Educa Berlin 2005 Mumie Design Concepts: Support multiple learning scenarios Support classroom-style teaching General Design Concepts: Pedagogical Concept: Concept for contents: Technical Concept: Visualize mathematical contexts Non-linear navigation Visualize mathematical concepts & objects Support experimental scenarios Support explorative learning Adapt to individual learning styles Modularity – Granularity Mathematical precision Split Teacher - Author Split Content – Use DB based on field-specific ontology XML-Technology Dynamic, on-the-fly, generation of pages Strict separation of content and layout Theme concept for user-adaptive presentation MathML used for presentation of mathematical symbols OpenSource

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Uwe Sinha Online Educa Berlin 2005 Mumie: Architecture PostgreSQL Database (Contents, Stylesheets,…) Java Application Server (Processes requests, delivers documents) Browser

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Uwe Sinha Online Educa Berlin 2005 Mumie Screenshots:

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Uwe Sinha Online Educa Berlin 2005 CourseCreator: Course without content assigned Course with content assigned

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Uwe Sinha Online Educa Berlin MmTeX & Mmcdk: eLearning Contents for Mathematics

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Uwe Sinha Online Educa Berlin 2005 General Demands: Based on authoring standards of community – Mathematics: LaTeX Support development of interactive, multimedial elements – good mathematician / teacher good programmer / designer Allow reusability of contents – Granularity Support variety of pedagogical concepts Support existing standards as far as possible

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Uwe Sinha Online Educa Berlin 2005 MmTeX: Create mathematical contents Converter based on LaTeX – Supports MumieTeX and parts of normal LaTeX – MumieTeX designed for pedagogical concepts of Mumie – supports integration of interactive, multimedia contents (pictures, applets)

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Uwe Sinha Online Educa Berlin 2005 MmTeX: Mumie-TeX Code Example \documentclass[sloppy]{japs.subelement.remark} %Metadaten \begin{content} \title{Example} Part of Laplace's formula for determinants: $\text{det}A = \sum_{k=1}^n A_{ik} (-1)^{i+k} \text{det} S_{ik}(A) \quad \forall i \in \{1, \ldots, n\} \quad$ A matrix: \[A= \begin{pmatrix} 3 & 19 & 27 & 22,5 \\ 45 & 1 & x & \lambda \end{pmatrix} \] \end{content}

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Uwe Sinha Online Educa Berlin 2005 Result

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Uwe Sinha Online Educa Berlin 2005 Mmcdk: Concept Java-based shell environment for Mumie – Authors Offers explorer-like overview of all existing content, including a preview Provides templates for recurring elements Allows to search and navigate within the contents

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Uwe Sinha Online Educa Berlin Outlook Mumie: Version Control & Management of MumieTeX- Sources MmTeX: Support semantical encoding Mmcdk: talk with Mumie DB, get a GUI

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Uwe Sinha Online Educa Berlin 2005 Thank You!

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