Abstract
This collection of papers is the principal outcome of a network project funded by the UK Arts and Humanities Research Council and the London Mathematical Society. This editorial introduction sketches the state of research into mathematical cultures and assesses the achievements of the network project with respect to its stated aims.
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Notes
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See Larvor review of The Philosophy of Mathematical Practice Paolo Mancosu (ed.) OUP 2008 in Philosophia Mathematica (2010) 18(3): 350–360 for a representative list.
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See Larvor “What are Cultures?” in Cultures of Mathematics and Logic Selected papers from the conference in Guangzhou, China, 9–12 November 2012. Shier Ju, Benedikt Loewe, Thomas Mueller, Yun Xie (eds.) Birkhäuser, Basel (2016) for a partial list.
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Wilder offered this definition of culture: “We use [the term ‘culture’] in the general anthropological sense… In this sense, a culture is the collection of customs, beliefs, rituals, tools, traditions, etc., of a group of people…” Introduction to the Foundations of Mathematics (John Wiley; second ed. 1965 (first published 1952) p. 282).
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Pergamon Press, 1981.
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And therefore, this observation is no criticism of Mancosu’s editorial work. Oxford University Press, 2008.
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For the origin of this term, see Lerman, S. (2000). The social turn in mathematics education research. In J. Boaler (ed.), Multiple perspectives on mathematics teaching and learning (pp. 19–44). Westport, CT: Ablex. For a recent overview, see Karen Francois’ video presentation to the cultures of logic and mathematics conference in Guangzhou https://youtu.be/umuKvJFR_7U (2012). See also François, K. & Stathopoulou, C. (2012). ‘In-Between Critical Mathematics Education and Ethnomathematics. A Philosophical Reflection and an Empirical Case of a Romany Students’ group Mathematics Education.’ Journal for Critical Education Policy Studies, 10(1), 234-247 ISSN 1740-2743.
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Michael Harris, one of the contributors to the series, has written an entire book on this tension: Mathematics without Apologies: Portrait of a Problematic Vocation (Princeton University Press, 2015). He presented Chapter eight of this book at the third meeting of the mathematical cultures network.
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See Sørensen in this volume and Larvor (2016) in Shier Ju, Benedikt Loewe, Thomas Mueller, Yun Xie (eds.) for further detail.
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There is plenty of research on pupils’ feelings about mathematics; less on their cultural perception of mathematics. There is some interesting material on learning and teaching cultures in Hersh & John-Steiner (2011) Loving and Hating Mathematics, especially pp. 273–300 & 312–315.
References
Arts and humanities research council science in culture theme website. http://www.sciculture.ac.uk/.
Association for the philosophy of mathematical practice website. http://www.philmathpractice.org/.
Francois, K. (2012). Video presentation to the cultures of logic and mathematics conference in Guangzhou. https://youtu.be/umuKvJFR_7U.
François, K. & Stathopoulou, C. (2012). In-Between critical mathematics education and ethnomathematics. A philosophical reflection and an empirical case of a Romany students’ group mathematics education. Journal for Critical Education Policy Studies, 10(1), 234–247. ISSN 1740-2743.
Harris, M. (2015). Mathematics without apologies: Portrait of a problematic vocation. Princeton University Press.
Hersh, R. (2006). 18 Unconventional essays on the nature of mathematics. Springer.
Hersh, R. & John-Steiner, V. (2011). Loving and hating mathematics. Princeton University Press.
Larvor, B. (2010). The philosophy of mathematical practice. P. Mancosu (Ed.) OUP 2008, Philosophia Mathematica, 18(3), 350–360.
Larvor, B. (2016). What are Cultures? In S. Ju, B. Loewe, T. Mueller & Y. Xie (Eds.), Cultures of mathematics and logic selected papers from the conference in Guangzhou, China 9–12 November 2012. Basel: Birkhäuser.
Larvor, B. Mathematical cultures. https://sites.google.com/site/mathematicalcultures/.
Lerman, S. (2000). The social turn in mathematics education research. In J. Boaler (Ed.) Multiple perspectives on mathematics teaching and learning (pp. 19–44). Westport, CT: Ablex.
Mancosu, P. (2008). The philosophy of mathematical practice. Oxford University Press.
Wilder Raymond L. (1965). Introduction to the foundations of mathematics (2nd ed.). John Wiley.
Wilder Raymond L. (1981). Mathematics as a cultural system. Pergamon Press.
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Larvor, B. (2016). Editorial Introduction. In: Larvor, B. (eds) Mathematical Cultures. Trends in the History of Science. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-28582-5_1
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