Communities of Practice in MKM: An Extensional Model

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. People don’t learn to become [... mathematicians] by memorizing formulas; rather it’s the implicit practices that matter most. Indeed, knowing only the explicit, mouthing the formulas, is exactly what gives an outsider away. Insiders know more. By coming to inhabit the relevant community, they get to know not just the “standard” answers, but the real questions, sensibilities, and aesthetics, and why they matter. John Seely Brown in [Bro05]