Academic journal article The Mathematics Enthusiast

Beyond Postmodernity in Mathematics Education?

Academic journal article The Mathematics Enthusiast

Beyond Postmodernity in Mathematics Education?

Article excerpt

Abstract:

A radical form of postmodernity is presented with reference to Nietzsche's ideas with respect to truth, knowledge, sciences, progress, democracy, and ethical values in general. Thereafter is presented Foucault's archaeology of knowledge. This brings us forward to the notion of genealogy, which is a defining idea for the postmodern conception of critique. However, it is emphasised that a critique can address the generativity of mathematical rationality by considering mathematics-based fabrications. Finally, imagination is presented as yet another feature of a critical enterprise. It is illustrated how such a three dimensional critical enterprise is relevant for both mathematics and mathematics education. In this way the paper suggests moving beyond the postmodern outlook.

Key-words: critique, genealogy, generativity, fabrication, imagination, postmodernity, mathematics, mathematics education.

Whilst postmodernity has brought new profoundness to critical activities, it has also formed some limitations. I find it important to address both aspects and in that way try to move beyond postmodernity. I am going to discuss this possible move with reference to mathematics and mathematics education.

The label postmodernity has been used widely with reference to new trends in architecture, art, and literature which break with modernist principles; it has been used with reference to new conditions for knowledge production; and it has been used in social theorising to refer to new social and cultural phenomena. I am going to use postmodernity as a reference to a critique of Modernity, and I will concentrate on philosophical aspects of this critique.

Modernity itself can be associated with some general conceptions of science: that natural sciences will be able to reveal the secrets of nature, and that science in general can be both objective and neutral. An integral feature of Modernity is the recognition of the importance of science, knowledge and education, and the whole Enlightenment project makes integral these aspects of the modern outlook. Furthermore, Modernity can be associated with the emergence of ideas about democracy, freedom, and equality. Clusters of such different ideas are brought together by the notion of progress: self-improvement is a human possibility.2

Taking a closer look at the modern period we find that very different socio-political phenomena developed together with the scientific discoveries, the formulation for democratic ideals, and the preoccupations about enlightenment and progress. Colonialism and exploitation took many forms, racism as well. During Modernity one finds laborious attempts at providing a scientific underpinning of racist classifications of human beings as being more of less developed. Similar classifications were applied to languages: some were identified as being more developed and complex than others. Such ethnic and linguistic classifications were weaved together with notions of progress and development and theorised into grand discourses that could legitimate colonialism and suppression.3 Zigmunt Bauman made a gloomy addition to such observations by emphasising that even the holocaust can be seen as being made possible through discourses established within modernity.4 With such observations we have entered a fierce critique of Modernity, and this is what postmodernity is about.

Let me try to summarise how we are going to proceed. I will present the most radical form of postmodernity by outlining some of Nietzsche's ideas about truth, knowledge, science, progress, democracy, and ethical values in general. Then I will present an example of the archaeology of knowledge by referring to studies by Foucault. This brings us forward to the notion of genealogy, which is defining for the postmodern conception of critique. I will discuss genealogy with respect to mathematics education and emphasise the extreme importance of this line of critique. However, I will then emphasise that a critique addressing fabrications that can be related to mathematical rationality is crucial as well. …

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