Abstract
The last chapter considered examples of mathematical objects embodied in the spatial environment. This chapter contemplates how the cultural environment confers particular images on mathematics that further shape how it is perceived, and how it evolves. To begin this discussion I want to consider the notion of objects from a different perspective towards setting the scene for a preliminary consideration of how specifically mathematical objects derive from cultural contexts in everyday life. In the first instance I take, as an example, an art object, not so much as thing in itself, but to consider its provenance as an object. Could an analogy with the apprehension of artistic objects help us to think a little differently about the apprehension and provenance of mathematical objects? How do humans relate variously to mathematical or artistic objects? How are objects situated or created in relations? I shall argue that the objectivity of the piece is a function of its social location.
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Dreyfus and Eisenberg (1996).
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Brown and McNamara (2011).
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Mumford, Series, and Wright (2002).
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For example, Sharp (2002).
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If these finger movements on a keyboard and mouse were to be seen as “gestures” this popular area of mathematics education research would extend to a rather different conception of the human subject, less centred in a physical body.
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Department for Education (2010).
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Žižek (2001b, pp. 215–216).
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Pampaka, Williams, Hutcheson, Wake, Black, Davis, and Hernanadez-Martinez (in press).
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Barwell (2010) has discussed the role of mathematics in confronting issues of climate change. He argues that we only really know anything about climate change because of mathematics. The changes, he suggests, are at too large a scale for humans to discern them individually for the most part. We need mathematics to understand and (maybe) respond to a huge threat. I see a number of analogies between climate change and the financial crisis in terms of the demands placed on mathematics. The certainty of mathematics is always with respect to some motivated choice of axiomatic field, and often, false analogies are drawn between axiomatic fields and real life. The economy is governed by psychology and by exact calculations, and in the case of climate change there is also a psychological dimension to the reading of mathematical models that feed directly in to any mediatised account, such as the ones that Barwell presents. Populations respond to various stimuli. We are perhaps destroying our world and our children’s world, and if we really knew that we might act differently. But the stories that govern our actions are not yet quite enough to convince us that we could change. Or rather they do not convince us that we might have the capacity to act collectively in a different way. There is not an objective picture because it is only possible to understand the world in terms of how it might be possible to change it, and that requires people to change – and media plays a part in how they change. People do not typically obey mathematical models. There is a psychological dimension that needs to be integrated. For mathematics to be true we have to select the correct story in which it appears.
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Brown, T. (2011). Cultural Mediation of Mathematics. In: Mathematics Education and Subjectivity. Mathematics Education Library, vol 51. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-1739-8_3
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DOI: https://doi.org/10.1007/978-94-007-1739-8_3
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