Thesis Title: Community of Practice in Mathematics
Please note, I am currently in the progress of structuring and narrowing down my research interest.
Communities of Practice: Using the metaphor for all the subsequent research interests …
- e.g. for extending document mark-up formats with social and collaborative components
- e.g. for understanding mathematical practice
- e.g. for the discussion on adaptation/ user modelling/ community modelling
Document Management
- Semantic mark-up of mathematical documents and mathematical practice
- Logical structure of mathematical knowledge (theories and interrelations)
- Narrative (didactic/ rhetorical) structure of mathematical documents (see mathui paper)
- Mark-up of mathematical notations and notation context (see small survey, see mathui paper, mkm 2008)
Accessibility of Mathematical Knowledge
- Adaptation of mathematical knowledge: Selection, Sequencing, and Presentation of mathematical knowledge (see ABIS, FGWM)
- Adaptation of mathematical notations
- Intelligent selection and recommendation of mathematical examples and exercises
- User modelling and community modelling (see ABIS, FGWM)
Semantic Packaging Format: Integrating Semantic Tools (WSKS paper)
Integrating Semantic Web and Social Web
- Enriching (semantically marked-up) mathematical documents with social contexts: ratings, semantic tagging
- Discussion and social interaction with (semantically enriched) mathematical contents
Case study: proof-of-concept prototype for mathematical E-Learning
[...] was!” KWARC research group’s blog « Proving and Programming My Research Areas and Focus [...]
With our mathematical format we provide a mark-up of mathematical theories and interrelations, i.e. we can model theory morphism and views.
This aspect of our format is not my work, but was mainly done by Michael Kohlhase and Florian Rabe, which are in charge for the theoretical (mathematical) foundations in our group. I am trying to understand and interpret their infrastructure, e.g. to understand (and if possible model) mathematical practice — here this would be the practice of structuring knowledge, reusing knowledge, …
My tasks is it to (if needed) extend our approach with a social component reflecting the preference and practice of mathematicians: For example, we have added such a social component to model notation preferences.
However, writing documents in our format requires additional efforts, as authors have to mark-up theories and interrelation, i.e. explicate the concepts they re-use and create. In order to motivate authors to write it, we want to provide as many services as possible for this format (and this is also part of my job): For example, in the field of E-Learning we could use our theory-infrastructure to generate course material that leads from theory to theory, …