Tony Brown

definitive (di-fin’i-tiv) defining or limiting: positive: final: authoritative. n. (gram.) an adjective used to limit the extent of signification of a noun. - adv. defin’itively. - defin’itiveness; defin’itude [L. definire, -itum, to set bounds to - de, finis, a limit.] (Chambers, 1989, p. 371). A response to Paul Ernest

In the book I relay an anecdote concerning Derrida attending a conference dedicated to his work. Having sat through countless papers discussing his work it finally became his turn to appear on stage. Whilst flattered by the level of interest in his work he declared that in listening to all the papers he had experienced a sense of being "already dead". It seemed that in his view the nature of the event led to an emphasis on summing up the past, bringing things to a close and focusing away from the present. This sort of feeling is behind my bewilderment as to why Paul Ernest should want a definitive account. What motivates such an aspiration and how would one reconcile this with the notoriously slippery world of post-structuralism? Later on in the book I include this quote from Derrida himself which may illustrate for us now the problem as I see it.

If writing is inaugural it is not so much because it creates, but because of a certain absolute freedom of speech, because of the freedom to bring about the already there as a sign of the freedom to augur. A freedom of response which acknowledges as its horizon the world as history and the speech which can only say: Being has already begun.....(Writing) creates meaning by enregistering it, by entrusting it to an engraving, a groove, a relief, to a surface whose essential characteristic is to be infinitely transmissible. Not that this characteristic is always desired, nor has it been; and writing as the origin of pure historicity, pure traditionality, is only the telos for a history of writing whose philosophy is always to come.

I am intrigued by the notion of treating this sort of phrase systematically and moving to a definitive stand. What would this look like? In the book I proceed cautiously:

"I take Derrida to mean, crudely, that inscription in writing functions closely in relation to the psychological phenomena it locates and, indeed, becomes part of it. In reading Derrida one never gets to what he means but rather one experiences the on-going sensation of being moved on before you are ready. His words never frame the final version of his "present" thinking. ... Derrida’s refusal to allow any anchorage in truth makes his work quite distinctive and more radical in its ability to reject orientation around universal structures."

My own attempt is inevitably crude and personal. Derrida has expressed himself in a particular way and it seems strange to seek a literary transformation of it. The individual reader uses it as he or she will. As an academic working with Derrida’s writing one is confronted by a number of conflicting agendas. It appears that Derrida himself has no desire to be summed up, preferring his readership to engage in deconstruction themselves rather than tell people what it is. Much of the power of what he says derives from this cutting across academic norms which demand definition. In addressing the mathematics education community such norms are very powerful, such as in the current interminable wearying debate regarding the distinctions between radical and social constructivism. At the level of the philosopher it seems one can choose either to play the old game of definition, or, alternatively, modify this, as do post-structuralist writers, and simultaneously play the game of resisting it. However, at the level of practitioner, concerns seem to be a little different. Within mathematics education research for example we can oscillate between describing "how things are" and "how things work for us". As an individual practitioner, whilst valuing the former and probably believing that I am right in my own version, I, nevertheless, privilege the latter. And so philosophy for the practitioner becomes a fairly messy business with various bits cut and pasted over the diverse range of professional and intellectual pursuits I am engaged in, not least publishing writing where conventional styles serve to filter work though recognisable structures. Although, maybe, I have aimed too high in the book, I do not aspire, like some others, to creating "a" or even "the" philosophy of mathematics education (that has come and gone). With Paul Ernest’s style of review I feel as though I am being forced into an exchange as might occur between a persistent news journalist seeking to point out inconsistency in a politician’s account while the politician seeks to deny this. It seems to me that any quest for a definitive work is a philosophically centred demand rooted in the old school; an attempt to package, to sterilise, to kill off the material it examines. Thus it was with some horror that I found my book being misrecognised as an application for the post of "grim reaper", and it is with some relief that I find my references have not been taken up.

I was intrigued by Paul Ernest’s suggestion that I have failed in my bid to be a philosopher whilst succeeding in getting a consolation prize for engaging with issues of practice. I can live with that, that is, if I indulge myself with a little nostalgia for the days when theory and practice were separate. He is quite right in suggesting that I am privileging practice over watertight philosophy. Indeed I am flattered by this suggestion. Paul Ernest observes that "a number of the deep philosophical sources drawn upon are either misunderstood or described in such oversimplified terms as to be problematic". It would not surprise me if much of what I say about these sources is shot full of holes but a rather bewildering reviewing technique is deployed in engaging with this issue. Paul Ernest picks up on Peirce to whom I devote just five sentences where I acknowledge use of secondary sources, which misguidedly I saw as better than not mentioning him at all. Whilst I have learnt the lesson of not using secondary sources this is a very curious choice in seeking to pinpoint my style of referral to philosophical writings. Peirce was English speaking and writing in the last century whereas nearly all of the philosophers I discuss are from the continent and writing this century, mainly in the last fifty years. My detailed discussions of Ricoeur, Derrida and Schutz, for example, which are based on original sources and stretch to a dozen pages each, would have benefited more from this sort of critique.

A particular issue that I continue work on is how we can treat the individual. Paul Ernest suggests my account implies "isolated and self-contained individuals". A long standing philosophical controversy continues around the apparent incommensurability of the insider perspective of Cartesian oriented phenomenology and the discursivity of post-structuralism. Nevertheless, I employ both but in distinct parts of my task. I seek to reconcile this in the book in my discussion of insider perspective as follows:

the notion "personal space" leans firmly on Cartesian notions as developed by Husserl. A unified subject is implied; a thinking subject who therefore is (Descartes’ "cogito ergo sum"). This is an idea treated with a certain disdain by post-structuralist writers insofar as it supposes any "completed and finished identity, knowing always where it is going" (Coward and Ellis, 1977, pp. 108-109). As I have indicated Derrida would reject the binary opposition between individual and social perspectives. Lacan (1977, pp. 1-7), meanwhile, stresses the importance of Descartes’ notion, but places much more emphasis on the formation of the thinking subject in the reflexivity of the thinking done. Nevertheless, the thinking subject may not be aware of this theoretical perspective on his actions and so assumes he has more control over his own destiny than may be supposed in post-structuralist formulations. It is this personal perspective I wish to examine... (emphasis added for this present discussion)

In the book, my discussions of how children or teachers "experience" the classroom situation privilege a phenomenological approach. In this I assume there are limits to the individual’s ability to be constantly aware or all the discourses acting through them. As a naive individual I act with intention and believe I have some control over the situation I inhabit. This contrasts with my extended discussion in the final chapter where I give my own views most expression, another dimension of the book curiously not benefiting from Paul Ernest’s attention. In this final chapter, I offer a more detailed account of how society intervenes in an individual’s consciousness. Firstly, using Derrida’s work, I attempt to demonstrate how even personal mathematical insight and intuition are historically generated through social processes. Secondly, I deploy a Habermasian perspective on how the cultural framing of mathematics as experienced in schools problematises any notion of constructing mathematics as part of a political process. Thirdly, I employ the work of Bill Brookes in discussing the difficulties policy makers experience in making any assumption that policy initiatives can adopt a behaviourist relation to the outcomes they envisage. Thus I am curious as to how Paul Ernest reaches the conclusion that I am guilty of "sentimentalising an over-individualistic knowing subject".

It is in the second of these three sections in the final chapter that I discuss Skovsmose. For all the merits of his book, which I enjoy immensely, I was a little surprised that Habermas, whose work clearly underlies his project in a very substantial way, gets less than two short paragraphs of explicit discussion in the book which comprises Skovsmose’s main work to date. My principle point, however, in discussing Skovsmose’s work centres around his penchant for thematising mathematics. I will not repeat my arguments here but suggest in my book that his attempt at integrating mathematics within a practical agenda results in compromises for both mathematics and the practical (or political) agendas themselves. Thematising, I suggest, can shield off as well as enliven mathematical skills. But in the background to this sort of discussion is the difficulty of defining any sort of emancipatory agenda. To take an example, I have a colleague working part time in an deprived inner city primary school, who is conducting PhD enquiries into ways we might define a critical education for nursery children at the beginning of their school careers. Does she carry on as normal, providing them with the standard skills which initiate them into their pre-ordained place at the bottom of the heap, or, alternatively, focus her attention elsewhere and thus neglect the basic skills the children need for participation in society? Her post-structuralist analysis of this situation resists such simplistically defined political projects, governed by attempts at progress. I myself remain torn between the apparent hopelessness of constructing political projects whilst still knowing that I have to try harder.

But to return to my central point in this response. Paul Ernest seems to be suggesting the possibility of a curiously detached, final, authoritative version of philosophy that defies anchorage in any experienced notion of practice; his own work rarely refers to his own insider perspective as a practitioner, or indeed examples of anyone else’s practice. Meanwhile extended sections of my book make inevitably imperfect (autobiographical?) attempts at describing my own lessons and lessons given by my students, set against some discussion of what we, as teachers, might learn from some major contemporary philosophers - a "solution" is not intended. It is indeed an hermeneutic task to reconcile such oppositions in understanding how philosophy serves us.

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Last Modified: 13th November 1997