## MATHEMATICS AND THEIR EPISTEMOLOGIES -- AND THE LEARNING OF MATHEMATICS

Citations: | 2 - 0 self |

### BibTeX

@MISC{Burton_mathematicsand,

author = {Leone Burton},

title = {MATHEMATICS AND THEIR EPISTEMOLOGIES -- AND THE LEARNING OF MATHEMATICS},

year = {}

}

### OpenURL

### Abstract

This paper reports on the results of a study of the epistemologies of seventy research mathematicians utilising a model containing five categories, socio-cultural relatedness, aesthetics, intuition, thinking style and connectivities. The perspectives of the mathematicians demonstrate extreme variability from one to another but certain persistent themes carry important messages for mathematics education. In particular, although mathematicians research very differently, their pervasive absolutist view of mathematical knowledge is not matched by their stories of how they come to know, nor of how they think about mathematics.

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Citation Context ... inexorable process which is independent of those mathematicians who pursue it and of the time and place where it is pursued. There is a literature (for example, see Bloor, 1991, Davis & Hersh, 1983, =-=Lakatos, 1976-=-) which critiques philosophical and epistemological perspectives on the ‘objectivity’ of mathematics, rejects absolutism (Ernest, 1991) and attempts to build links between the socio-cultural positioni... |

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Citation Context ...ossible product of an inexorable process which is independent of those mathematicians who pursue it and of the time and place where it is pursued. There is a literature (for example, see Bloor, 1991, =-=Davis & Hersh, 1983-=-, Lakatos, 1976) which critiques philosophical and epistemological perspectives on the ‘objectivity’ of mathematics, rejects absolutism (Ernest, 1991) and attempts to build links between the socio-cul... |

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(Show Context)
Citation Context ...a literature (for example, see Bloor, 1991, Davis & Hersh, 1983, Lakatos, 1976) which critiques philosophical and epistemological perspectives on the ‘objectivity’ of mathematics, rejects absolutism (=-=Ernest, 1991-=-) and attempts to build links between the socio-cultural positioning of a subject as powerful as mathematics and its epistemological stance (for example, see Lerman, 1994, Restivo et al., 1993, Skovsm... |

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(Show Context)
Citation Context ..., 1991) and attempts to build links between the socio-cultural positioning of a subject as powerful as mathematics and its epistemological stance (for example, see Lerman, 1994, Restivo et al., 1993, =-=Skovsmose, 1994-=-). In many ways, this literature matches similar critiques made by philosophers and sociologists of science (for example, Harding, 1991, Rose, 1994) of reductionism and claims of value-free ‘objectivi... |

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(Show Context)
Citation Context ...l stance (for example, see Lerman, 1994, Restivo et al., 1993, Skovsmose, 1994). In many ways, this literature matches similar critiques made by philosophers and sociologists of science (for example, =-=Harding, 1991-=-, Rose, 1994) of reductionism and claims of value-free ‘objectivity’. In Burton, 1995, I used the critical literature to derive an epistemological model built upon five categories. I conjectured that ... |

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Citation Context ...le and only possible product of an inexorable process which is independent of those mathematicians who pursue it and of the time and place where it is pursued. There is a literature (for example, see =-=Bloor, 1991-=-, Davis & Hersh, 1983, Lakatos, 1976) which critiques philosophical and epistemological perspectives on the ‘objectivity’ of mathematics, rejects absolutism (Ernest, 1991) and attempts to build links ... |

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Citation Context ...angles is crucial.” This seems to me to be a devastating comment on the teaching style experienced by students. If intuition, or insight, is as important to mathematics as many claimed to me (and see =-=Hersh, 1998-=-), and as important to mathematics education as is claimed by Efraim Fischbein (1987), why do teachers do so little to acknowledge and nurture it? 5. Styles of thinking I set out on the study with two... |

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(Show Context)
Citation Context ...xample, see Lerman, 1994, Restivo et al., 1993, Skovsmose, 1994). In many ways, this literature matches similar critiques made by philosophers and sociologists of science (for example, Harding, 1991, =-=Rose, 1994-=-) of reductionism and claims of value-free ‘objectivity’. In Burton, 1995, I used the critical literature to derive an epistemological model built upon five categories. I conjectured that this model c... |

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Citation Context ...ny ways, this literature matches similar critiques made by philosophers and sociologists of science (for example, Harding, 1991, Rose, 1994) of reductionism and claims of value-free ‘objectivity’. In =-=Burton, 1995-=-, I used the critical literature to derive an epistemological model built upon five categories. I conjectured that this model could offer a framework for exploring and possibly explaining links betwee... |