Abstract
We explore the social context of mathematical knowledge: Even though, the community of mathematicians may look homogeneous from the outside, it is actually structured into various sub-communities that differ in preferred notations, the choice of basic assumptions, or e.g. in the choice of motivating examples. We contend that we cannot manage mathematical knowledge for human recipients if we do not take these factors into account. As a basis for a future extension of MKM systems, we analyze the social context of information in terms of Communities of Practice (CoP; a concept from learning theory) and present a concrete extensional model for CoPs in mathematics.
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References
Barrow, J.D.: Ein Himmel voller Zahlen. Auf den Spuren mathematischer Wahrheiten. In: Rowohlt (2002) (Original publication 1992 Pi in the Sky)
Brown, J.S., Duguid, P.: The Social Life of Information. Harvard Business School Press (2000)
Brown, J.S.: Learning in the Digital Age. online (2005) (seen on 2006-02-07), at: http://www.johnseelybrown.com/learning_in_digital_age-aspen.pdf
CiteSeer.ist scientific literature digital library (viewed March 2006), web page at: http://citeseer.ist.psu.edu
Connexions. Project home page at (seen January 2005), http://cnx.rice.edu/
Connexions: Sharing knowledge and building communities (February 2006), White paper at: http://cnx.org/aboutus/publications/ConnexionsWhitePaper.pdf
Dourish, P.: Where the Action Is: The Foundations of Embodied Interaction. MIT Press, Cambridge (2003)
Davenport, T.H., Prusak, L.: Working Knowledge, 2000 edn. Harvard Business School Press (1998)
Farmer, W.: Mkm: A new interdisciplinary field of research. Bulletin of the ACM Special Interest Group on Symbolic and Automated Mathematics (SIGSAM) 38, 47–52 (2004)
scholar, G.: (seen January 2005), web page at: http://scholar.google.com ,
Heintz, B.: Die Herrschaft der Regel: Zur Grundlagengeschichte des Computers. Campus Verlag (1993)
Heintz, B.: Die Innenwelt der Mathematik. Zur Kultur und Praxis einer beweisenden Disziplin. Springer, Wien (2000)
Kohlhase, A., Kohlhase, M.: CPoint: Dissolving the author’s dilemma. In: Asperti, A., Bancerek, G., Trybulec, A. (eds.) MKM 2004. LNCS, vol. 3119, pp. 175–189. Springer, Heidelberg (2004)
Kohlhase, A., Kohlhase, M.: An exploration in the space of mathematical knowledge. In: Kohlhase [koh05], pp. 17–32
Kohlhase, M. (ed.) MKM 2005. LNCS (LNAI), vol. 3863, Springer, Heidelberg (2006)
Kohlhase, M.: OMDoc An open markup format for mathematical documents (Version 1.2). LNCS (LNAI). Springer, Heidelberg (to appear, 2006), http://www.mathweb.org/omdoc/pubs/omdoc1.2.pdf
Melis, E., Buedenbender, J., Andres, E., Frischauf, A., Goguadze, G., Libbrecht, P., Pollet, M., Ullrich, C.: The activemath learning environment. Artificial Intelligence and Education 12(4) (winter 2001)
Manzoor, S., Libbrecht, P., Ullrich, C., Ma, E.M.: Authoring presentation for openmath. In: Kohlhase [koh05], pp. 33–48
Naylor, W.: Mappings between presentation markup and semantic markup for variable-sized objects. In: Second International Conference on MathML and Technologies for Math on the Web, Chicago, USA (2002)
Osterlund, C., Carlile, P.: How Practice Matters: A Relational View of Knowledge Sharing. In: Huysmann, M., Wenger, E., Wulf, V. (eds.) Communities and Technologies, Kluwer Academic Publishers, Dordrecht (2003)
Probst, G., Raub, S., Romhardt, K.: Wissen managen (2003) edn., vol. 4. Gabler Verlag (1997)
Schloen, T.: Expertennetzwerke als Innovationsschmiede - das Konzept der Communities of Innovation. In: Ernst, S., Warwas, J., Kirsch-Auwärter, E. (eds.) wissenstransform, pp. 40–53. LIT Verlag (2005)
Weinberger, D.: Tagging and Why it Matters. 2006-05-22 (May 2005), online at: http://cyber.law.harvard.edu/home/uploads/507/07-WhyTaggingMatters.pdf
Wenger, E.: Communities of Practice: Learning, Meaning, and Identiy. Cambridge University Press, Cambridge (1999)
Zadeh, L.A.: Fuzzy sets. Information and Control 8, 338–353 (1965)
Zinn, C.: UnderstandingInformalMathematicalDiscourse, Arbeitsberichte des Instituts für Informatik. Universitä Erlangen-Nürnberg, Institut für Informatik, vol. 37 (September 2004)
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Kohlhase, A., Kohlhase, M. (2006). Communities of Practice in MKM: An Extensional Model. In: Borwein, J.M., Farmer, W.M. (eds) Mathematical Knowledge Management. MKM 2006. Lecture Notes in Computer Science(), vol 4108. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11812289_15
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DOI: https://doi.org/10.1007/11812289_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-37104-5
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