Semester 4, Jacobs
Best Practices in e-Learning in Mathematics
panta rhei
In our General Computer Science lecture, which we offer to an international student body, we are challenged with the students' different mathematical backgrounds. The majority of our students believe that these mathematical discrepancies are very problematic; especially in the beginning of a course. Students reported that they had problems to get acquainted with the professor's notation systems; others had the feeling that the pace of the course was determined by the best students, while others students did not face any problems.
We believe that the theory of Communities of Practice can help to understand and countervail these discrepancies. Students do not share the same understanding as the lecturer, they actually form various sub-communities that e.g. differ in their preferred notations, basic mathematical assumptions, and mathematical performance. Instead of enforcing students to become acquainted to the lecturer's practice, we want to take their social context into account and adapt the lecture. We want students to understand that although outsiders may get the impressions that mathematicians form a homogeneous, unified community, they actually form various sub-communities and that exactly these grouping are valuable for deepening knowledge and learning.
We will carried out two experiences using a prototype web application, consisting of an online precourse and online course: The precourse includes a pool of problems on mathematical prerequisites to prepare new students before arriving on campus. Based on the students interaction, we want to identify mathematical CoPs. The online course presents slides and homeworks and provides a course forum and rating facilities for discussions and feedback. The course makes use of the identified CoPs and provides CoP-specific views on the course material. Consequently, students and teachers may access the course from different angles and potentially identify discrepancies and misunderstandings.
More information on the panta rhei project will be presented at 4th Workshop on Mathematical and Scientific e-Content in September
2nd SCooP Workshop
see proceedings
JOMDoc
JOMDoc is a Java API for OMDoc documents, which facilitates the parsing of OMDoc XML documents (either from the filesystem or from OMBase) into a Java data structure, to manipulate them conveniently, and to serialize the result back to XML. JOMDoc basically offers one class per OMDoc XML element, with methods for conveniently accessing attribute values and child elements. The internal structure can be traversed like an ordinary XML tree with the getChild() and getParent() methods which are available for every JOMDoc element. Several consistency checks for constraints that are specified in the OMDoc specification, but which cannot be checked by a simple validation against an XML schema, are performed.
Currently JOMDoc is compatible with OMDoc 1.2. In the next releases the mmlkit functionality is to be integrated into JOMDoc, probably by directly using the JOMDoc internal data structure.
locutor
locutor is a full reimplementation of the Unix SVN client developed at Jacobs University focusing on smart management of change. Whereas Subversion compares text files line by line, locutor is able to use semantic knowledge about the document format to distinguish semantically relevant from irrelevant changes. Semantically irrelevant changes, for example, for LaTeX include whitespacing, comments, newlines, include/ import and URI normalization.
The next release of locutor will be able to perform customized operations before every commit and after every update so that it is possible to filter LaTeX files available for locutor and the SVN database for change management. Thus, only semantically relevant changes would trigger conflicts.
Furthermore, in the presence of our fs-tree model [1] all files may reference other files [2]. If locutor receives a change upon updating a file, it is not only able to determine its semantic relevance. It can also compute the effect of the change and determine the set of files that need to be rechecked.
http://www.kwarc.info/nmueller/publications.html
[1] Fine-Granular Version Control & Redundancy Resolution at http://www.kwarc.info/nmueller/papers/lwa08-fst.pdf
[2] Towards Change Management on Hybrid OMDoc Documents at (not yet uploaded, the link and the title on my webpage are obsolete)
TNTBASE
TNTBase is a project that concerns the development of the database for the documents in OMDoc format. TNTBase will be based on the so-called XML-enabled repository, i.e. the repository which stores XML content natively. It has been decided to modify Subversion server and force it to use also Berkeley Database XML in cooperation with Berkeley DB as a back-end storage. Now Subversion can use internally two types of file system: it's own FS and Berkeley DB. Since Berkeley XML DB was designed to be easily integrated with Berkeley DB, the decision was to use the second option of Subversion back-end and force Subversion to leverage from using Berkeley DB XML for storing fulltext versions of XML documents internally in Subversion. This part is implemented already.
The very next step would be to implement a wrapper which reads the internal structure of stored XML documents in Berkeley XML DB and provides users the functionality that most of the XML-native databases have. When this is done, the next point is to implement a kind of client library or HTTP-interface that works with TNTBase and fulfill the most common user requirements.
Further steps need to be defined depending on what users of TNTBase want to obtain first. For example, math search or query engine, receiving aggregated documents (e.g. all examples from a set of theories), model for distributing knowledge across multiple TNTBases or something else.
SWiM
The development of the semantic wiki SWiM (recent paper, slides, poster; book chapter) into a collaborative editor for OpenMath content dictionaries has been continued. Special attention was paid to defining notations for symbols and to editing formulæ. The first goal has been achieved by developing an ontology for the semantic structures of OpenMath Content Dictionaries and utilising it in SWiM (paper, slides), for the second one we have integrated the Sentido visual (but semantic!) formula editor into the TinyMCE HTML editing component that is used for editing documents in SWiM [1]. In summer 2008 the OpenMath edition of SWiM will be deployed to the content dictionary editors of the OpenMath society as a tool for developing and presenting the content dictionaries of the upcoming OpenMath 3.
Another new feature targets both a knowledge engineering and an educational audience: SWiM now supports discussions about issues (= bugs, problems) with mathematical knowledge items and assists with solving these issues. An issue could be that some definition or theorem is hard to understand, and a possible solution would be to provide an example for it (paper, lightning talk). This is supported by a domain-specifically extended argumentation ontology that makes the argumentative structure of the discourse about a knowledge item explicit. In order to model this ontology, we have conducted a survey about typical issues and solutions in mathematical knowledge management. Besides the above-mentioned OpenMath case study, a use case for this will be supporting the documentation and formalisation of a large mathematical proof (paper, poster).
- Christoph Lange, Alberto González Palomo: Easily Editing and Browsing Complex OpenMath Markup with SWiM (submitted to MathUI Workshop)
Krextor
Krextor is an extensible XSLT-based framework for extracting RDF from XML, supporting multiple input languages as well as multiple output RDF notations. Krextor provides convenience templates that try to do "the right thing"™ in many common cases, as to reduce the need for manually writing repetitive code. Extraction modules for OMDoc and OpenMath content dictionaries are available.
- Versión para impresión
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