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yММK.ТrТyrУхTHE TENSION BETWEEN WHAT MATHEMATICS EDUCATION SHOULD BE FOR AND WHAT IT IS ACTUALLY FOR
Alexandre Pais
Technology Mathematics and Society Learning Research Group
Centre for Research in Education, University of Lisbon
One of the introductory questions in this discussion group is "What is mathematics education for?" In this contribution we would like to explore the fact that there are no global answers to this question. If we position ourselves as mathematics educators then the reasons to teach mathematics appear very obvious, but if we think in the broad society and its characteristics we may question those reasons, and highlight others related with issues of corporification and governance. Then the tension between what we think math education should be for and what is the real role performed by math education in our society emerges and should be a matter of concern.
School and education
In our time, education has became disciplinarized, scholarized, academicized. As mentioned by Stoer et al. (2001), scholarization has become the only legitimacy modality of thinking education. In school, education is a disciplinary device (Foucault, 2003), which fabricates the individual. Following Foucault's thought, school has became one of the bigger modern disciplinary centres of the body. Obligatory in the modern societies, in school we are introduced to the disciplinary society, via academically recognized knowledge, by the way we submit our bodies and minds to the training devices (in school there is a huge load of corporal discipline, whether is in the organization of space, or in rules as norms about what is considered to be good and bad behaviour). It is in school that the human being, no longer a person but a student, starts to understand the hierarchy of behaviours and knowledge, by means of the creation of classificatory systems that limit, integrate. and exclude them. School plays the role of an apparatus to govern the population by fabricating the kinds of subjects that hegemonic society stipulates as normal, from the dissemination of norms that function as calibration devices. So, school is far from being the place of education. On the contrary, it has developed the function of reducing, dominating, and suffocating education by the ways of re-inscribing it within the structure of the state. Knowledge in school can be understood as an alibi; an alibi to the formation of the subject needed to the modern society.
The purpose of mathematics in school
In official documents it is easy to understand the normally explicit arguments that justify mathematics teaching in school: because it is useful to the student in her/his daily life; because is an important cultural heritage that must be preserved; the argument that the study of mathematics develops psychological skills; and final, the most propagated in the recent years, because it contributes to the development of participative citizens in a socio-political perspective. All those arguments are a decoy. It is easy to deconstruct them and show how fragile and incoherent they are, specially (especial) the socio-political argument (Pais, 2005). Mathematics appears in school with other surreptitious functions.
In recent years there have appeared in the mathematics education scenario studies that abandoned the traditional psychological approach and engage in a more sociological view (Lerman 2000; Valero, 2003). Some of those studies, that are very different from each other, have pointed out other roles taken by mathematics education. For instance, studies justifying how school mathematics works as a gatekeeper in the assessment to further studies or to a profession; how it could generate situations of social exclusion according to issues of gender, race, language, social class; how the failure in mathematics tends to be more traumatic to the student, because she or he feels the importance that mathematics has in curriculum, to her/his future, and also to his or her social image (not knowing mathematics is not know how to think rationally); not to achieve success in mathematics catalogues the student as incompetent, unsuited to the demands of a society more and more technological.
The power of school mathematics is immense, in the sense that it shapes us to something, formats us, alters our conduct and behaviours, changes our life aspirations, causes emotional harassment and familial conflicts. Here we need a very important notion from the work of Foucault (2003): school mathematics acts like a device that makes behaviour elements to be reinforced or punished, as they adhere to the rule or not. Using Foucaults terminology, like a normalization device. As stated by Popkewitz (2002), who takes into account the work of Foucault on education:
[the mathematical curriculum] is an inscription devise that makes the child legible and administrable. The mathematics curriculum embodies rules and standards of reason that order how judgments are made, conclusions drawn, rectification proposed, and the fields of existence made manageable and predictable. (p. 36)
From these lines emerge another purpose for the teaching of mathematics. An implicit and tolerated argument but, because of that, very powerful: teaching mathematics to approximate the student to the norm, to normalize, by putting in motion mechanisms that penetrate the bodies, the gestures and the behaviour. Normalizing is associated with the governance of people, by "controlling their multiplicities, using them at maximum, maximizing the utility of their work and activity, thanks to a system of power susceptible of control them" (Foucault, 2004, p. 105). Basically, making grow at the same time the docility and the utility of all elements of the system (p. 180).
The tension between what we want and what it is
As researchers, we want mathematics education to be an important school subject to students lives. We convey the idea of mathematics education as a central discipline in a more and more mathematical knowledge based society to teachers and public opinion. In some sense, we reinforce the importance of mathematics education, and by doing that, we contribute to the role of governance and corporification taking place at school.
Should our focus of research be not only what we imagine that mathematics education should be for, but also what role is asked from mathematics to carry out in schools? How is the teaching of mathematics contributing, in a disguised way, to the fabrication of the kind of people that our society needs?
So, our wish, as researchers, to develop a mathematics education that allows the young student to be an active, critical and participative citizen in our society is one thing. But it is another matter what our society understands as being active and participative: what does it means to educate people to be participative in a more and more market-orientated society? How are we researchers concerned with the development of an idea of citizenship, and encouraging a mathematics education that makes accessible powerful tools to analyze, critique, and act upon, social and political issues, problematizing the role of school in our society?
References
Foucault, M. (2003). Vigiar e punir. (27Њ ed.). Petrѓpolis: Editora Vozes.
Foucault, M. (2004). Microfэsica do Poder (20Њ ed.). Rio de Janeiro: Ediчѕes Graal.
Lerman. S. (2000). The social turn in mathematics education research. In J. Boaler (Ed.), Multiple perspectives in mathematics teaching and learning (pp. 19-44). Westport: Ablex Publishing.
Pais, A. (2005). Uma abordagem crэtica das relaчѕes entre sociedade, ciъncia e matemсtica num contexto educacional (tese de mestrado). Lisboa: DEFCUL.
Popkewitz, T. S. (2002). Whose heaven and whose redemption? The alchemy of the mathematics curriculum to save. Prodeedings of the Third International Mathematics Education and Society Conference (pp.34-57). Aalborg: Centre for Research in Learning Mathematics.
Stoer, S. et al. (2001). Transnacionalizaчуo da Educaчуo: Da crise da Educaчуo р ЋEducaчуoЛ da Crise. Porto: Afrontamento.
Valero, P. (2003). Socio-political perspectives on mathematics education. In P. Valero & R. Zevenbergen (Eds.), Researching the socio-political dimensions of mathematics education: issues of power in theory and methodology (pp. 1-17). Dordrecht: Kluwer.
This paper was prepared within the activities of Project LEARN: Technology, Mathematics and Society (funded by Fundaчуo Ciъncia e Tecnologia (FCT), contract no. PTDC/CED/65800/2006. A bigger version of the ideas discussed here is presented at HYPERLINK "http://www.mes5.learning.aau.dk/Papers/Pais_Mesquita.pdf" http://www.mes5.learning.aau.dk/Papers/Pais_Mesquita.pdf.
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