The goal of this master thesis is to develop a simplified authoring tool that can be easily used by students to: (1) vary a given interactive exercise or exercise template, (2) author an exercise, a text, add links for peer students, (3) add or author explanations to a worked solution of an exercise, (4) add or author feedback in exercises, (5) add useful visualizations and facilities to put the new content into a content collection so that ActiveMath can present it to a group of peers. Each student from the group should be alerted about contribution of peers. Web 2.0 techniques can be used as well as existing components of ActiveMath including the authoring tool Extasy.

Facebook is a rapidly growing social software. Its success results from i) sharing stuff with friends, ii) facebook platform, and iii) strong commercial partners. Recently, facebook sterted to spread to other countries and continents and the question was raised and intensively discussed whether whether facebook outperforms e-portfolios. In this bachelor thesis, the task consists of a) investigation of e-portfolio characteristics on facebook b) explore the facebook platform design and c) to implement a facebook application that is able to import e-portfolios from remote platforms by using the IMS e-portfolio standard.

Implementation of a semantic representation and principled on-click presentation of (1) different explanations for the same concept and (2) hierarchical microstructure of proofs, examples, exercises, explanations in ActiveMath.

Currently, most learning objects are manually annotated with metadata such as difficulty, educational level, required competencies, required knowledge. At the same time we have large log files from users testing and using the ActiveMath system. The Bachelor thesis will use Machine Learning techniques to learn and improve the metadata (of interactive exercises) in ActiveMath, for instance the pair (educational level, difficulty).

Zu entwickeln ist ein Hausaufgabenszenario für das intelligente Lernsystem ActiveMath. Bei diesem werden nach mehreren Kriterien adaptiv Aufgaben für Hausaufgaben in Mathematik zusammengestellt. Dieses soll nach im SFB-Schwerpunt 'Bildungsqualität Schule' erarbeiteten pädagogischen Vorstellungen modelliert werden. Kontakte und Literatur sind gegeben: Mathematik Lehren 140, 2007, Thema Hausaufgaben.

Zu erweitern ist das Lernszenario 'Prüfungsvorbereitung' so dass es nicht nur zu bestimmten Themen/Konzepten adaptiert wird, sondern auch bestimmte Typen von Aufgaben/Kompetenzen vorbereitet sowie auf eine Menge von potentiellen Prüfungsfragen/Aufgaben zugeschnitten werden kann. Dieses Szenario soll in einer Klasse getestet werden gegen das derzeitige nur auf Konzepte adaptierbare Prüfungsszenario.

For monitoring of user actions, ActiveMath uses a server-based event system which already allows fine-grained loggin. For scientific experiments however, it is often required to observe the user more closely: how long does the user take from seeing the content to entering an answer? Is the user really looking at the ActiveMath window, or doing something else?  The goal is to develop a Firefox browser extension that can monitor client events nd feed them into ActiveMath's event system.

The objective is to realize a non-obstrusive text-input tool for semantic mathematical formulæ producing XML output in OpenMath or content-mathml with the following characteristics: web-based, using a simple text-field sturdy to parse incompletely input formulae presenting asymchronously a 2d-rendering of the formula (using, e.g., ActiveMath's presentation from OpenMath) able to report errors and bring user to error location in input able to let user select a location or fragment in the rendering triggering a selection in the text-field, and vice-versa as much as browsers provide access to able to receive drop or paste of XML or URL-to-it and convert it to the input syntax extensible to new input patterns This Bachelor work is stimulated by our experimental results which indicates that the easy access of plain-text-input goes beyond the confort of use of input-palettes. We expect this work to yield an open-source product licensed with a non-viral license (for example under the Apache Public License) and expect demand at cooperating researchers.

A very common methodology of XML documents management is to allow these to contain considerable amounts of data of which only a small fraction, called fragments, is used in reading operations (in particular web-browsing). This is the case of ActiveMath, among others. Various approaches solve this problem, XML-databases being a simple example that is still fairly immature. XPath is the general tool to address the fragments. A most common approach, but known to scale badly, is to parse the document fully in RAM, e.g. using an in-memory representation, then run the XPath queries on this. All XSLT implementations we know of operate this way. This bachelor work should produce a software whose input is a set of (parametrized) XPath expressions and a set of documents and stores to disk (copies of) the documents, and can then be queried for any xpath expressions directly delivering a stream of the XML fragment in question, probably with all ancestor tags (so as to ensure XML-completeness). We may provide expertise in using JDOM and SAX-parsers for this purpose. Such as software has a chance to work even over HTTP using the Range header.

This work will contribute to the exercise system of the web-based learning environment ActiveMath. In word problems not only mathematical formulas have to be computed but also the metric measures of the solutions. Since learners make metric errors more often than not, these errors have to be diagnosed by independent but integrated diagnosis engines. Tasks: Introduce metric content into ActiveMath content Develop general but context-dependent diagnosis engines Use computer algebra system in the diagnosis Generate feedback to learner according to diagnosis

OpenMath is a standard for semantic encoding of formal expressions. It defines symbols for mathematical operations, mathematical and physical constants, units and dimensions and other formal constructions. This project aims to develop a type checking engine for OpenMath Simple Type System (STS). The type checker can have a wide range of users such as the whole OpenMath community, and particularly ActiveMath system will profit from it in it's various components. For example, exercise subsystem will partially use type checker for evaluating user's answers in interactive exercises.

Implement the use of Latent Semantic Analysis into the LeActiveMath search (usage of the Lucene library, information retrieval, LSA).

Starting with an existing content-storage for OMDoc, refactor the code in order to create an instance storage per content-collection while still providing consistency checks as is done currently.

The ActiveMath search engine has now a good Lucene-based index. It offers search for text, characteristics, and formulae. Navigation through the search results, however, could be much enhanced. Among the enhancements, graph-approaches to navigate the content are wished. Examples include kartoo.com or thesaurus.maths.org. This bachelor work is expected to deliver an fully tested component that is usable by non-techie learners within the ActiveMath learning environment. User-testing and analysis thereof expected as well.

ActiveMath presents mathematical content to a browser from a semantically encoded content. Among others, this allows the mathematical formulae to be presented with tooltips, click-to-explain-the-symbol, or copy-and-paste, all from the simple fact of enconding semantically the formulae (using OQMath, OMDoc, and OpenMath). We wish to extend this ``value-added presentation of formulae'' by considering supplementary input of the author. An example would be annotations about the variables in a well-defined context (e.g. ``m is a the mass of the ball''), another avenue might be the usage of type-information about the symbols. The bachelor work should include the enrichment of a 10-15 pages ``book'' in order to convince mathematicians of the well-foundedness of the approach.

ActiveMath is a web-application for mathematics on the web, it presents both static and interactive documents in contemporary web-browsers with high-quality rendering of formulæ in either HTML+CSS, XHTML+MathML, or PDF (through TeX). The Bachelor work will separate the rendering engine into a tool-set following a document processing paradigm where an author would simply 'run the ActiveMath processor' in order to get the many possible documents formats rendered.

ActiveMath is a web-application providing intelligent support to learn mathematics. ActiveMath is currently interfaced to a few web- services but we expect a growing number of such services. These web-services use both server to server calls as well as specialized links. Using XML-Schema and WSDL documentation technologies (which partially exist in open-source form), the bachelor work consists on writing a full featured documentation of the web-interfaces of ActiveMath. Documentation should include all datatypes used in ActiveMath's URLs and server-to-server calls. We expect extensions to current WSDL and XML-Schema documentation producers to be realized (and contributed back), for example xsddoc. Expertise in XML is expected and... a sense of communication and writing. A capability to read java is also expected.

The current selection mechanism for MathML elements in Mozilla is text-like and is full of inconsistencnies. This bachelor should provide, within the Mozilla community support and contribution system, a first implementation of mathematical selection for MathML under the conditions of MathML's parallel markup.

The goal is to use existing tools such as WebEQ, HELM's and many others to provide the automated conversion of presentation-encoded mathematical documents, typically easily convertible to MathML- presentation or TeX, to the semantic format of OMDoc, including OpenMath for mathematical expressions. The breadth and generalizability of this conversion defines the grade: In the case of a master's thesis, it would be expected that most of the wikipedia content is convertible. Alternatively, thorough coverage of thematic segments of the abstracts of Zentralblatt Math should be convertible (the latter being the biggest and oldest mathematical research litterature review service). n the case of a bachelor thesis, a subset of this is expected, for example a thematic part of wikipedia.

The goal is to valorize a web-site made mostly of static web-pages by the addition of blocks that could be called 'what the web says' which relays what other pages, blog, feeds, forum-posts, ... are 'saying' about the given page. The work should be deployed within the highly visible OpenMath.org website which is served by a simple Apache server. It should be based on regular monitoring of the logs (e.g. for the referrer header), of identified rss streams or even web-search-engines-results and should only quote content from trusted sources. It should be sufficient to provide a 'news' channel to such a site as http://www.openmath.org/ (in its home page or at individual content-dictionaries). Part of this work will also be deployed by the EU project Intergeo for interactive geometry tracking what the web says about individual constructions or collections thereof.