“KWARC was!”

In November 2007, I ask the members of the KWARC group to fill out questionnaires to get a better intuition about the social and scientific practice of the KWARC community. The detailed results have not been published due to data privacy issues, but the general findings are provided in evaluation.pdf.

After reading the book How to solve it by Polya [Pol73], I decided to analyze different ways of problem solving based on how my colleagues and students (altogether 10 volunteers) proved the following simple lemmas: (1) For all prime numbers p≥5 prove that z=p2-1 is divisible by 24 and (2) Proof that the center of gravity of a polygon equals the average of all points of the polygon. Although no representative survey was carried out, the case study brought up some interesting findings: For (1), some person wrote a lot of explanatory text for almost every step of their proof; while others skipped several steps they found obvious. The level of formality varied among the test persons: some wrote their proofs very close to a form that could be verified by e.g. theorem provers, while others stick to a rather informal writing of their proofs. Moreover, the test persons took different approaches of how to proof the lemma: Some could easily write down a formal proof, while others started with examples and counter examples to get a better idea of how to solve the given problem. For (2), some test persons used drawings to get a better idea whether they had to proof or refute the given geometric problem.

In his blog, Normen Müller recently posted a comment on Only humans are capable of understanding and making necessary intelligent choices. I agree that the structural semantic techniques allow for relieving humans from tedious choices or analysis. Accordingly, I apply semantic techniques to extract COP relevant information from documents in order to instantiate a mathematical COP model. If documents on their own are not sufficient to model COPs, I will also consider web2.0 techniques to gather further COP-relevant information.

Given that semantic techniques are the most suited approach for automatic extraction of COP data, a specific semantic representation technique/ format needs to be found. Since my work applies COP to the domain of mathematics, these should be suited for this domain. Looking at the mathematical representation format such as MATHML, OPENMATH , and OMDOC , OMDOC seems the most suited one for mathematics.

OMDOC’s advantage lies in its three layers: the object layer, the statement layer, and the theory layer. MATHML and OPENMATH are standards that provide semantics on the object layer, i.e. on the level of formulae. For example, thanks to their mark up, software can distinguish operations such as ’+’ , which represents the arithmetic ‘addition’ operation as well as the logical ‘OR’ operation. The statement layer allows for typing of document fragments, e.g. definitions, examples, or lemmas. The theory provides the context of the mathematical concept. The strength of OMDOC also lies in its implementation. For example, an assertion element with types such as ’lemma’ is used instead of elements for every mathematical object.

The usage of OMDOC will allow me to verify, whether semantic mark-up facilitates the automatic description COPs. I will point out whether OMDOC supports COP-information extraction or whether the format needs to be extended. Since OMDOC has been invented and is continuously developed by our research group, I will not only be facilitated to understand the syntax and mark-up but, moreover, will be able to suggest extensions and contribute to the further development of OMDOC.

To observe the mathematical practice, I currently see two methods: (1) An interactive approach in which I contact members of my group to question them about the understanding and view on mathematical practice, and (2) an document-based approach, in which I analyze their publications and lecture notes in order to describe the mathematical practice based on documents. The latter approach, continues the discussion in Andrea and Michael Kohlhase’s paper at the MKM06, in which they assume that mathematical practice is inscribed into documents and that an analysis of document collections allows for identifying communities of practice.

I assume that the combination of both approaches allows for (1) verifying whether a mathematical COP exists, i.e. whether the mathematical practice instantiates the model of a general COP, and (2) describing mathematical practice (e.g. based on interviews and documents) and comparing it with the model; and (2) verifying the assumption of whether or not documents are suited to identify mathematical practice at all and/ or on their own (without additional consideration of e.g. social networks between the authors).
(3) If no mathematical COP exists, I could verify whether and how such a COP can be established (e.g. by comparing the current state with the required conditions in the COP model).

Another application refers to the usage of COP models to support the requirements gathering: The client has a problem, based on that the engineer extracts requirements. The COP-supported requirements gathering tool, then verifies these requirements by comparing them with the client’s COP’s requirements: either approving, extending them or indicating conflicts between them. For example, the client does not specify the language but his COP prefers German and English. Or the client requires French, which conflicts with his COP’s requirements. Related work in this field is currently achieved by the Frauenhofer Institute, Instute Experimentelles Software Engineering.

In their paper at the Mensch und Computer conference on the Sen-sation System , C. Beckmann et al. suggest an approach to model stages of team based on the economic research of team dynamics (e.g. Group Dynamics by Tuckman and Drexler et al. or Change Theory (unfreezing,transition, refreezing) by Kurt Lewin). This idea could also be transferred onto the modeling of COP life cycles and would enable software to identify the current stage of a COP and to e.g. support the establishment COPs.

In contrast to designing software to support a social system, the social system could also be used to improve the software design, e.g. by enabling the software to automatically understand and identify the practice of the social system it supports. Enabling a machine to understand the concept of a COP can be achieved by semantics, either by means of symbolic semantics (e.g. logic) or statistical methods.

From this perspective, my research could aim to design a methodology of how to enable software to identify/ know about/ take into account the practice of a mathematical social system (e.g. the MKM community) using semantics technologies and, based on this, offer functionalities that deploy the internal COP model to e.g. improve the systems search or recommendations.

During the doctoral seminar of the Conference on Mensch und Computer, Volker Wulf introduced us to the community of conferences in the field of Human Computer Interaction (HCI) and Computer Supported Collaborative Work (CSCW) . He explained that most research in this community aims at developing software that has an effect on an existing social system, i.e. a specific community in the real world. Most commonly, three steps are taken: (1) a pre-study to observe the social system and to gather requirements, (2) the design of a system that solves the existing problems, (3) an evaluation of the effect of the developed system on the social system.

Accordingly, my research could focus on the development of software that supports an existing social system, e.g. the community of the Conference on Mathematical Knowledge Management (MKM). In respect to the suggestion by Wulf, this would require a pre-study, i.e. an observation of the MKM community, to identify the participants’ current problems and needs, and to conclude requirements for a respective software solution. Afterwards, this would imply the design of the software which functionalities solve the current problems. Finally, I would evaluate the effect of the software on the MKM community and the success of the implementation.