Abstract
In thinking mathematically, how does mathematics itself become something different? And how do we ourselves change? To unsettle the ground a little for later chapters, I commence with an exploration of these issues through considering extracts from a personal reflective diary work by a former student, Krista Bradford. The diary was created as a part of a research masters’ degree programme. The enquiry attended to the cross-cultural perception of mathematical concepts during some classroom research. Formerly a primary teacher in the United Kingdom, Krista was teaching mathematics to teenagers for Voluntary Services Overseas in Uganda. The research was carried out within a practitioner enquiry frame as part of a distance education course that I had initiated within a charity-funded project. As Krista had not worked on mathematics at this level since the end of her own schooling, she experienced a steep learning curve. This curve was made steeper as she became more aware of how mathematics was constructed in Ugandan schools. Its derivation from Western curricula compounded difficulties for the students she was teaching. Krista’s raised awareness of the cultural issues also brought into question her own agency within this development context. As a white person from the west she faced the challenge of mediating the externally defined demands of the western inspired curriculum and the more immediate educational needs of her students.
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- 1.
Radford (2003).
- 2.
Žižek (2007).
- 3.
Lacan (1988, p. 53).
- 4.
In his later work Lacan suggests that “the displacement of the signifier determines the subjects in their acts, in their destiny, in their refusal, in their blindnesses, in their end and in their fate, their innate gifts and social acquisitions notwithstanding, without regard for character of sex, and that, willingly or not, everything that might be considered the stuff of psychology, kit and caboodle, will follow the path of the signifier” (1988, pp. 43–44).
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Luke (2003, p. 336).
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Bartolini-Bussi & Boni (2003) describe the circle not as “an abstraction from the perception of round shapes” but as reconstructions, by memory of “a library of trajectories and gestures” (p. 17). (Quoted by deFreitas and Sinclair, forthcoming.)
- 8.
Mathematics is initially experienced intuitively prior to its later encapsulation in symbolic form, where there is also some later evolution of the symbolic forms. For example, Spyrou, Moutsios-Rentzos and Triantafyllou (2009) discuss some experimental work with 14-year-old children where “embodied verticality” was linked through gravity with “perpendicularity”, which led “to the conquest of the “first level of objectification” (through numbers) of the Pythagorean Theorem, showing also evidence of appropriate “fore-conceptions” of the second level of objectification’ (through proof) of the theorem” (cf. Radford, 2003).
- 9.
- 10.
This work had been first developed elsewhere: Parker and Heywood (1998); Heywood and Parker (2010); Brown and Heywood (2010).
- 11.
Aspects of this activity were inspired by the opening scene of a Hungarian film called Werckmeister harmonies, in which a bar of drunken men are encouraged to perform planetary movements. This can be viewed at http://www.youtube.com/watch?v=VFmu7BYbthY
- 12.
- 13.
Barthes (1972); Gabriel and Žižek (2009, pp. 50–81).
- 14.
Ricoeur (1984).
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- 16.
Elsewhere I have written about instances of depleted pedagogical technology being all that remained of past learning experiences. A student could remember the phrase Silly Old Harry Caught A Herring Trawling Off America (SOHCAHTOA) having something to do with trigonometry. Yet the student was unable to recover the associated trigonometrical relations (Brown & McNamara, 2011). I was arguing that our mathematical selves are built through caricatures of earlier experiences.
- 17.
Michael Green is a string theorist now occupying the chair previously held by Newton and Hawking. Woit (2006) provides a contrary view.
- 18.
Quoted in Edemariam (2009, p. 34).
- 19.
Frege’s attempt to find a common ground for all mathematics by using the set theory collapsed when Russell provided his famous barber paradox, and when Gödel proved that such an attempt is impossible.
- 20.
Badiou (2009a).
- 21.
- 22.
Trends in Mathematics and Science Study.
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Brown, T. (2011). The Regulation of Spatial Perception. In: Mathematics Education and Subjectivity. Mathematics Education Library, vol 51. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-1739-8_2
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