Conferences on Intelligent Computer Mathematics - Birmingham 2008
CICM '08

Doctoral Programme

Birmingham, UK, 29-31 July 2008

Christine Mueller: Community of Practice in the STEM disciplines

The motivation for my research is that the Science, Technology, Engineering, and Mathematics (STEM) community depends on social factors as any other scientific discipline. I view STEMicians as mathematical practitioners, who understand mathematics as the language of science and as the basis for several disciplines. Although outsiders may get the impressions that mathematical practitioners form a homogeneous, unified community and share the same practice all over the world, they actually form various sub-communities that differ in preferred notations, basic assumptions, and the choice of motivating examples. With my work, I want to emphasize that we need to take the social context of mathematical knowledge into account in order to prepare it for human recipients.

I propose to apply the economic theory of Communities of Practice (CoP) by Jean Lave and Etienne Wenger [LW91] to the domain of mathematics. By analysing documents, I want to identify characteristics that are inscribed into these documents and that can be used to identify and describe CoPs. Assuming that semantic representation formats facilitate the reification and automated processing of characteristics, I aim at providing a theoretic model of how to represent, interrelate, and extract characteristics from documents. In addition to the inscribed characteristics, I am analysing ratings, annotations, and the browsing of documents and aim at eventually enriching a given representation format to encode further practice-relevant information.

I intend to use the reified and semantically marked up characteristics to automatically identify groups of users (CoPs) that share the same mathematical practice. Moreover, I want to describe these communities wrt. to their common perspective. Based on this, I will facilitate CoP-specific views on mathematical content, that is the CoP-specific selection and adaptation of content. Consequently, mathematical content can be seen from different angles: Foreign material can be accessed with a perspective one is accustomed to and, vice versa, a foreign view can be applied to already known content. Whether my approach can improve mathematical knowledge management, e.g. by supporting the communication, exchange, and consumption of mathematics, will be evaluated with several proof-of-concept implementations in educational and scientific scenarios [pan08, MMK08].

References:
[HG07] Brent Hendricks and Adan Galvan. The Connexions Markup Language (CNXML). http://cnx.org/aboutus/technology/cnxml/, 2007. Seen June 2007.
[Koh05] Michael Kohlhase. Semantic markup for TEX/L TEX. Manuscript, available at http://kwarc.info/software/stex, 2005.
[Koh06] Michael Kohlhase. OMDoc – An open markup format for mathematical documents [Version 1.2]. Number 4180 in LNAI. Springer Verlag, 2006.
[LW91] Jean Lave and Etienne Wenger. Situated Learning: Legitimate Peripheral Participation. Cambridge University Press, 1991.
[MMK08] Normen Müller, Christine Müller, and Michael Kohlhase. The math markup language toolkit (mmlkit). http://kwarc.info/projects/mmlkit, seen June 2008.
[pan08] The panta rhei Project. http://kwarc.info/projects/panta-rhei/,