Using Bourdieu to examine number sense in young children – a gatekeeper to life’s opportunities?

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By Rebecca Turvill

Bourdieu’s central concern with the way the education system reproduces social class is particularly relevant in the discussion of mathematics education. Academic success in mathematics is seen as a gatekeeper to life’s opportunities (Noyes, 2007). Importantly, such success may be cemented early in a child’s education. The English primary mathematics curriculum is largely concerned with the development of “number sense”. The concept is not universally defined within curriculum documentation, however extrapolation from the National Numeracy Strategy (DfEE, 1999) suggests it amounts to a confidence and flexibility using and calculating with number.

Drawing on Bourdieu’s concepts of habitus and field, I propose that number sense itself acts as a gatekeeper to mathematical success. As such, a child’s life opportunities are restricted very early in their educational career, from their earliest encounters with number sense.

I am using primary mathematics education as the field. This presupposes mathematics can stand discretely and, whilst this may be debated, reflects the position of mathematics teaching almost exclusively in English primary schools. I also conceptualise primary mathematics as separate from secondary (or high school) mathematics as curriculum and pedagogy are distinctly split at this point. It is increasingly important for children to be seen as “secondary ready” placing a strong emphasis on the skills they are expected to master during primary school. By conceptualising primary school mathematics as a field, we can appreciate the opportunities and barriers presented by the system. Importantly, the field of primary mathematics education is not experienced equally by all those in it. Persistently, children from lower socio-economic classes leave school with lower attainment in mathematics. The concept of habitus allows us to consider this inequality.

Habitus, the “taken-for-granted” way in which we act (Bourdieu, 1984) is shaped throughout one’s early socialisation and is well established on entry to education. It is an embodiment of a child’s early experiences and thus directly their social class. Walkerdine (1988) demonstrates how language use in the home is class dependent, with mathematical terminology being heavily value laden in different settings. Even more specific to mathematics, is the work of Peter Bryant (2013) who demonstrates that children from more prosperous homes demonstrate stronger mathematical reasoning skills.

Where a child’s habitus does not align well with the field two consequences are observed. Firstly, a child receives a negative message about themselves. This is disabling as they believe mathematics is not for them. A negative learning spiral from the negative self-image developed is often the result (Ernest, 2011). Secondly, the curriculum is changed to “support” the child. This is often greater rehearsal and practise of failed skills – number sense skills – a limited mathematical diet. Thus children from lower socioeconomic classes are further excluded from learning just the type of mathematics needed to allow them access to the privileges mathematics provides.

Bourdieu’s key concepts of field and habitus thus provide a crucial way to critically examine how number sense skills in primary school are pivotal in reproducing social class.

Rebecca Turvill is a first year PhD student at Brunel University.

References:

Bourdieu, P. (1984) Distinction Cambridge: Harvard University Press

Bryant, P. (2013) Some Reasons for Reasoning, http://mad.ly/df6c83?pact=372119510284083140&fe=1 accessed 6.2.14

DfEE (Department for Education and Employment) (1999) The National Numeracy Strategy Framework for Teaching Mathematics from Reception to Year 6. London:DfEE

Ernest, P. (2011) Mathematics and special educational needs: theories of mathematical ability and effective types of intervention with low and high attainers in mathematics. Saarbrücken : LAP LAMBERT Academic

Noyes, A., (2007) Mathematics Counts…for what? Rethinking the Mathematics Curriculum in England, Philosophy of Mathematics Education Journal No. 21  Philosophy of Mathematics Education Journal ISSN 1465-2978 (Online)

Walkerdine, V. (1998) The Mastery of Reason. London: Routledge

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11 thoughts on “Using Bourdieu to examine number sense in young children – a gatekeeper to life’s opportunities?

  1. Nick Allum February 7, 2014 at 11:49 am Reply

    Clearly there is a social class gradient to educational achievement that starts very early. I’m not sure what using the word ‘habitus’ adds to the story, though. Disadvantaged families are typically less well-educated and do not have the educational and economic resources to help their children. They may also be less motivated, partly because there is less concern about loss of status compared to middle class families (see Breen & Goldthorpe etc). We know that if disadvantaged children attend pre-school, their outcomes are better later on. So it is not as if there is something completely unavailable to these children just by dint of the wrong ‘habitus’. How would the empirical evidence on class and academic achievement differ if ‘habitus’ and not the more readily identifiable features of experience I mention above were really the causal factor? It just looks like a pointless neologism to me I have to say. But I could be wrong!

    • bsabourdieu2011 February 7, 2014 at 1:42 pm Reply

      Hi Nick, thank you for your comment. We have passed this on to the author. We would just add that the disagreement between you and the author may come down to the question of structuralism versus poststructuralism. Habitus is not a quantifiable entity. It is a heuristic device to enable our sociological understanding to accommodate the self-understandings of their situations of the people analysed in detachment by professional economists, sociologists etc. The question then becomes, as Bourdieu saw, to what extent do the ‘detached’ analyses acquire symbolic power and modify the aspirations, expectations of ordinary people, e.g. university choice in relation to the supposed objectivity of hierarchical league tables which then become self-fulfilling. When you realise that much scientific objectivity is the euphemised subjectivity of the dominant, you have to transform the relation between science and the public so as to generate egalitarian encounter.

  2. Nicola Ingram February 7, 2014 at 2:38 pm Reply

    The word habitus is not interchangeable with the word experience. Habitus incorporates an understanding of experience but rather than simply being a neologism for experience it is a theoretical tool for considering the ways in which experiences come to be internalised and shape perception, conception and action. It would appear to me that it is highly relevant to use it in this context. It sounds like very interesting research.

  3. Nick Allum February 9, 2014 at 12:27 pm Reply

    The author says that habitus is the embodiment of a child’s early experience. This seems like a theoretical tool or heuristic insofar as it defines a construct to refer to a collection of real beliefs, ways of thinking and behaving in relation to , in this case, mathematical thinking. The author suggests that the presence or absence of particular types of habitus (where it aligns or does not align well) can explain differential educational attainment. This seems perfectly straightforward quantitative reasoning. It also implies that habitus has real referents or components that can be observed or at least inferred from some empirical data. This is I assume the rationale behind doing an empirical project, such as this is. Otherwise, why not dispense with data altogether? To me, the general argument, that educational inequality starts early on and is transmitted through taken for granted ways of thinking that vary according to class background seems totally plausible, if not a bit obvious. But I don’t see why one needs to cloud it with obscurantism. It is rather too important for that, IMHO. On the other hand, if the basis of our disagreement is that science is nothing more than the euphemised subjectivity of the dominant then is scientific reasoning ruled out of court? If so, what is the critical rational basis for assessing the validity of anyone’s inferences here? Genuinely puzzled.

  4. bsabourdieu2011 February 10, 2014 at 10:30 am Reply

    Dear Professor Allum,

    Thank you for your interest in this PhD research and taking the time to give your feedback on it. The student who is new to academia has said she finds the comments very useful and has learnt from the response.

  5. Bernhard Wagner February 10, 2014 at 3:26 pm Reply

    I would just like to add that habitus should not be used in mainly descriptive way. Bourdieu is very careful not to essentialise or naturalise a specific “working class habitus” (or any other habitus). Doing so would probably reverse his intention. Habitus is meant to be a tool to explore suppression and the reproduction of inequality. Interpreting it as a description of a somewhat deficient set of attitudes (Nick for instance speaks of a lack of motivation) would reverse cause and effect of inequality.

    • Nick Allum February 10, 2014 at 7:11 pm Reply

      There was no normative component to my comments, except the assumption that equal access to education and its benefits is a good thing. I fail to see how trying to identify causal pathways to unequal outcomes brings about more inequality. I was precisely arguing against unnecessary essentialising, preferring to consider separate components of beliefs behaviour etc as contingent and not rolled into one thing called habitus, which cannot in any case be adequately defined as to be any use, so it seems. Just saying that habitus is a tool to explore something does not get us very far if one cannot say what it is and what it is not in any given situation. I fear that Bourdieu’s being careful not to essentialise any kind of habitus is simply the way in which such ‘theorists’ ensure that they can never be proved wrong. As a thought experiment, try to think of what evidence would convince you that a) habitus did not exist or b) habitus was not the cause of educational inequality? If that is impossible to do, then one must severely question the utility of such a concept for social science.

  6. Bernhard Wagner February 10, 2014 at 9:17 pm Reply

    Theorist in inverted commas – not a big fan I take it. 🙂
    I personally find habitus a very helpful way of exploring how inequalities are being reproduced, how structure gets internalised.
    Habitus certainly is a rather broad and maybe a somewhat elusive concept. I see it as a way of thinking (method) as well as a description of internalised social reality. I would however also argue that Bourdieu is anything but elusive when applying his theory to empirical research. Putting the habitus concept into (research) practice is certainly a challenge, but there are a number of pieces of research that manage to do that quite brilliantly. The often cited Formations of Class and Gender by Beverley Skeggs for instance manages to apply the concept in its complexity and in my opinion demonstrates the relevance and the usefulness of the idea without psychologising / essentialising class consciousness.

  7. Nick Allum February 10, 2014 at 10:36 pm Reply

    Haha! Well, I do like what Bourdieu wrote about surveys, although he could have followed up his criticisms a bit more explicitly. And he was definitely an empiricist of some kind, and not only a theorist. Which is a good thing. But I tend to agree with Goldthorpe and others that while Bourdieu might have made a passable description of the situation in early 1960s France, (although not an original one – there were others in Britain and the US making precisely the same observations without the use of obfuscatory and flowery language) subsequent educational expansion has occurred without the widening of class differentials that Bourdieu’s notion of habitus and cultural capital implies. Far from sustaining inequality by locking out children without the necessary cultural resources derived from adequate domestic learning environments, schools, universities and, by extension, the state, have instead brought about a huge increase in educational opportunity and with it the expansion of middle class occupations. This macro-level disconfirmation of the main implication of Bourdieusian thinking is even borne out in the micro-level evidence that shows, as I mentioned earlier, that the effect of pre-school care for children from homes with poor learning environments is more beneficial than for those lucky enough to have more congenial resources at their disposal.

    I think the most one can say is that Bourdieu had some ideas that weren’t particularly original but that did a job of explaining the situation 50 years ago. Empirically they just don’t hold up well now.

    A heartfelt plea: If admirers of Bourdieu were to be intellectually honest enough not to rush to meet rational criticism with the usual slipperiness and wilful ambiguity (as above), we might actually get somewhere and render sociology useful as an emancipatory influence on public policy. At the moment we leave that to social policy people, and labour economists, even psychologists – who by and large eschew fancy-pants linguistic gymnastics and get on with trying to explain empirical regularities. British sociology, I fear. finds this terribly naive and thus continues its downward spiral to the margins of public and intellectual life.

    Sorry if this sounds rather depressing but that is what I have concluded over a number of years. However: the new generation of PhDs have it in their hands to do something about it.. so go for it!

  8. Joe Baxter-Webb (@joewebbuk) February 19, 2014 at 12:24 pm Reply

    Hey all,

    No maths expert but marginally interested in Bourdieu. One thing I did notice when I was supporting maths lessons at a secondary school was that maths curricula tend to be structured around first learning abstract rules, and then only applying them to “concrete” real-world scenarios in the “advanced” questions. This was all back-to-front for a lot of the working class kids I was working with, and I often found that if I, for example, skipped measuring area in the abstract and went straight onto the supposedly more difficult real-world applications (questions revolving around measuring turf or cutting carpet) they got it much quicker.

    It’s anecdotal, but I’d suggest that either the curriculum is ass-backwards for some kids. That’s either a social background thing, an individual psychology thing (although as far as I know habitus is a confluence of both – in this case it affects a persons’ relationship to abstracted, theoretical knowledge) or maybe it’s just ass-backwards for all kids to some degree, because educators are still inclined to value theory over practice (something Bourdieu might agree with).

  9. 德州撲克 October 13, 2014 at 6:06 pm Reply

    Wonderful content, thanks a lot !!

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