Abstract
The idea that mathematics is needed for our mundane everyday activities has raised the question of how people deal with mathematics outside the school walls. Much has been written in mathematics education research about the possibility of transferring knowledge from and into school. Whereas the majority of this literature commends the possibility of transfer, thus assuming both the desirability of transfer and the importance of school mathematics for the professional and mundane lives of individuals, I am interested in developing an ideology critique on the beliefs underpinning the research on this issue. It will be argued that the use-value attributed to school mathematics disavows its value as part of a political and economic structure, which requires school mathematics to perform other roles than the one related with utility. This critique will be illustrated through the exploration of a typical transfer situation between school and workplace.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
The process of “forgetting” the economic cause has been a major feature not only of the postmodern trend but also of what Ozselçuk and Madra (2010) call “the humanist Marxism”, expressed in the work of well-known Marxists of the twentieth century such as Adorno, Lukács and, more recently, Habermas and Lyotard. These works read Marx in ways that contain or even annul the constitutive determinacy of economy. In the case of postmodernism, the Marxist primacy of the economic is watered down into a set of political, cultural and sexual impediments. In the case of so-called post-Marxists, what is in fact a structural problem, endemic to a mode of production, is transformed into an abstract problem of greed, which could be solved by increasing the values of solidarity, trust, sharing and general commitment to improving the quality of human life (Ozselçuk & Madra, 2010). Painted in this way, Marxism has an uncanny resemblance to a catechism, with charity as the main safeguard of humankind. Economic exploitation, the foundation of capitalism, is reduced to political domination, which can be solved through the goodwill of engaged people.
This is also the case with the vast majority of mathematics education research (which not only disavows the economic but also shows a historical tendency to disavow the social and cultural dimensions, by being centred in a psychological approach). As Paola Valero and I found (Pais & Valero, 2012), even socioculturalism and its use of Marxist psychological theories such as those of Lev Vygotsky and Alexei Leontiev, end up focusing on the cultural and historical dimension of learning, thus completely obliterating its economic dimension. Nonetheless my criticism here concerns research that, although seeking to go beyond a “didactical”, “psychological” and “sociocultural” perspective of school mathematics, by means of emphasizing “political” issues, refrains from analysing the relation between school mathematics and the capitalist system.
When Lacan (seminar of 23 April 1974, in Le séminaire, Livre XXI: Les non-dupes errant, unpublished, cited in Fink, 1995, p. 142) says that “[t]he real is what does not depend on my idea of it”, he is pointing to the dimension of human subjectivity that is independent of our knowledge of it—the Freudian unconscious. Such a conceptualization is what allows Žižek to transpose the real qua psychic dimension to social analysis. His argument is that we may very well know that our economic system is unfair, that schools are subjected to economic pressures, but nonetheless its functioning is real, i.e. it does not depend on our knowledge of it. The same point is made by Lundin (2012) apropos of mathematics education: “[m]easurements, grades, and examinations have consequences only inside the system in which they play a central role (…) it should be as obvious that opinions, thoughts and feelings towards this system do not affect its proper functioning” (p. 83).
At stake here is what in contemporary theory is called the performative power of the word (e.g. Butler, 1997; Derrida, 1976): reality as something which is constituted, posited by the subject. When we say that the world is written in mathematical language—the Galilean idea that mathematics is everywhere—we are not asserting some ontological truth about the world or about mathematics; rather, it is by means of our declaring it that the world becomes “written” in mathematics. The truth claim of a statement cannot be authorized by means of its inherent content, but results from the “‘rationalization’, the enumeration of a network of reasons, masking the unbearable fact that the Law is grounded only in its own act of enunciation” (Žižek, 2008b, p. 100).
A remarkable example is given by Jurdak (2006). After concluding that “the activity of situated problem solving in the school context seems to be fundamentally different from decision-making in the real world because of the difference of the activity systems that govern them” (p. 296), and that students “define their own problems, operate under different constraints, and mathematics, if used at all, plays a minor role in their decision making” (p. 296), Jurdak still insists on the importance of confronting students with real-life situations: “simulations of such authentic real life situations as embedded in situated problem solving may provide a plausible option to develop appreciation of the role, power, and limitations of mathematics in real-world decision-making” (p. 296). He adds, “though quite different in real life from that in school, the process of mathematization is essentially the same and having experience in it in a school context may impact on mathematization in real life” (p. 297, my emphasis). Saying that the process of mathematization is the same, no matter what the context, does not sit well with the sociocultural perspective from which Jurdak writes. It is impossible to find support in the research reported in Jurdak’s text for such statements. The belief that the exploration of real-life situations in school will impact on the way in which people use mathematics in real life is based on a “leap of faith”, and thus constitutes ideology at its purest.
As observed by Lundin (2012, p. 8), “[t]he faithful finds a reason why the game is played, seemingly in reality itself, and at the same time identifies a corresponding explanation why ‘it does not work’”. As a faithful adherent, one perceives oneself as the one “who knows, who sees the sorry state of mathematics education in the light of all that it could be, and dutifully shoulders the burden of reform”. As pointed out by Lundin, however, this attitude, instead of leading to an amelioration of school mathematics, maintains the status quo. This happens because, in the well-intentioned action of improving mathematics education, the faithful fail to acknowledge, in the corrupted reality they lament, the ultimate consequences of their own acts.
Elsa Fernandes participates, as does the author of this text, in the project LEARN, which is one of the activities of the Technology, Mathematics and Society Learning Research Group of the Centre for Research in Education at the University of Lisbon. One of the purposes of this project is to analyse, from a different theoretical perspective, data already collected in previous research work done by the participants in the project.
They all passed, despite the obvious difficulties some of them, e.g. Alberto, have with the subject.
But also that in order to pass in mathematics they do not really need to learn mathematics, but only to reproduce in the exam what the teacher performed during class; they learn the correct way to answer their teacher’s questions, and how to appear busy in order to avoid extra work (Fernandes, 2004).
An important distinction should be made between believing and knowing: “I believe through the other, but I cannot know through the other” (Žižek, 2008b, p. 138). When students say they need mathematics, this assertion belongs to the sphere of the (Lacanian) symbolic: what it really means is that students believe that others believe mathematics is important, and the knowledge they have of the useless character of school mathematics in their practice nobody can hold for them: they experience it in the (Lacanian) real. Our everyday ideological attitude consists precisely in the gap between (real) knowledge and symbolic (belief). Ideology structures our belief against something we know to be real.
References
Abreu, G. (1995). Understanding how children experience the relationship between home and school mathematics. Mind, Culture and Activity, 2, 119–142.
Abreu, G., Bishop, A., & Presmeg, N. (2002). Transitions between contexts of mathematical practices. Dordrecht: Kluwer.
Althusser, L. (1994). Ideology and ideological state apparatuses (notes towards an investigation). In S. Žižek (Ed.), Mapping ideology (pp. 100–140). New York and London: Verso.
Atweh, B., Forgasz, H., & Nebres (Eds.). (2001). Sociocultural research on mathematics education: An international perspective. Mahwah, NJ: Lawrence Erlbaum.
Atweh, B., Graven, M., Secada, W., & Valero, P. (Eds.). (2011). Mapping equity and quality in mathematics education. New York: Springer.
Baldino, R. (1998a). Assimilação solidária: Escola, mais-valia e consciência cínica [Solidarity assimilation: School, surplus-value and cynical consciousness]. Educação em Foco, 3(1), 39–65.
Baldino, R. (1998b). School and surplus-value: Contribution from a third-world country. In P. Gates (Ed.), Proceedings of the First International Conference on Mathematics Education and Society (MES1) (pp. 73–81). Nottingham: Centre for the Study of Mathematics Education.
Baldino, R., & Cabral, T. (1998). Lacan and the school’s credit system. In A. Olivier & K. Newstead (Eds.), Proceedings of 22nd Conference of the International Group for the Psychology of Mathematics Education (PME22), vol. 2 (pp. 56–63). Stellenbosch, South Africa: University of Stellenbosch.
Baldino, R., & Cabral, T. (1999). Lacan’s four discourses and mathematics education. In O. Zaslavsky (Ed.), Proceedings of the 23rd International Conference of the Psychology of Mathematics Education Group (PME23), vol. 2 (pp. 57–64). Haifa, Israel: Technion Israel Institute of Technology.
Baldino, R., & Cabral, T. (2006). Inclusion and diversity from Hegel-Lacan point of view: Do we desire our desire for change? International Journal of Science and Mathematics Education, 4, 19–43.
Bishop, A., & Forgasz, H. (2007). Issues in access and equity in mathematics education. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 1145–1168). Charlotte, NC: Information Age.
Blum, W., & Niss, M. (1991). Applied mathematical problem solving, modelling, applications, and links to other subjects—state, trends and issues in mathematics instruction. Educational Studies in Mathematics, 22(1), 37–68.
Boaler, J. (1993). Encouraging the transfer of ‘school’ mathematics to the ‘real world’ through the integration of process and content, context and culture. Educational Studies in Mathematics, 25, 341–373.
Boaler, J. (1999). Participation, knowledge and beliefs: A community perspective on mathematics learning. Educational Studies in Mathematics, 40(3), 259–281.
Boaler, J. (2009). The elephant in the classroom: Helping children learn and love maths. London: Souvenir Press.
Brenner, M. (1998). Meaning and money. Educational Studies in Mathematics, 36, 123–155.
Brown, W. (1995). States of injury. Princeton, NJ: Princeton University Press.
Brown, T. (2008). Lacan, subjectivity, and the task of mathematics education research. Educational Studies in Mathematics, 68(3), 227–245.
Brown, T. (2011). Mathematics education and subjectivity: Cultures and cultural renewal. Dordrecht: Springer.
Brown, T., & McNamara, O. (2011). Becoming a mathematics teacher: Identity and identifications. Dordrecht: Springer.
Brown, T., & Walshaw, M. (2012). Mathematics education and contemporary theory: Guest editorial. Educational Studies in Mathematics, 80(1–2), 1–8.
Butler, J. (1997). The psychic life of power. Stanford, CA: Stanford University Press.
Butler, J., Laclau, E., & Žižek, S. (2000). Contingency, hegemony, universality. London: Verso.
Chapman, O. (2006). Classroom practices for context of mathematics word problems. Educational Studies in Mathematics, 62(2), 211–230.
Cole, M. (2003). Might it be in practice that it fails to succeed? A Marxist critique of claims for postmodernism and poststructuralist as forces for social change and social justice. British Journal of Sociology of Education, 24(4), 487–500.
De Lange, J. (1996). Using and applying mathematics in education. In A. Bishop, M. Clements, C. Keitel, J. Kilpatrick, & C. Laborde (Eds.), International handbook of mathematics education (pp. 49–97). Dordrecht: Kluwer.
Derrida, J. (1976). Of grammatology. Baltimore, MD: The Johns Hopkins University Press.
Dowling, P. (1998). The sociology of mathematics education: Mathematical myths, pedagogic texts. London: Falmer.
Eagleton, T. (2001). Ideology, discourse, and the problems of ‘post-marxism’. In S. Malpas (Ed.), Postmodern debates (pp. 79–92). Basingstoke: Palgrave.
Engels, F. (1968). Marx and Engels Correspondence (Letter to Franz Mehring, London, July 14, 1863). International Publishers. Retrieved from http://www.marxists.org/archive/marx/works/1893/letters/93_07_14.htm, 25 December 2012.
Ernest, P. (2007). Epistemological issues in the internationalization and globalization of mathematics education. In B. Atweh, A. Calabrese, B. Barton, M. Borba, N. Gough, C. Keitel, C. Vistro-Yu, & R. Vithal (Eds.), Internationalisation and globalisation in mathematics and science education (pp. 19–38). New York: Springer.
Evans, J. (1999). Building bridges: Reflections on the problem of transfer of learning in mathematics. Educational Studies in Mathematics, 39, 23–44.
Fernandes, E. (2004) Aprender matemática para viver e trabalhar no nosso mundo [Learning mathematics to live and work in our world]. PhD thesis. University of Lisbon.
Fernandes, E. (2008). Rethinking success and failure in mathematics learning: The role of participation. In J. F. Matos, P. Valero, & K. Yasukawa (Eds.), Proceedings of the Fifth International Mathematics and Society Conference [MES5] (pp. 237–247). Lisbon: Centro de Investigação em Educação, Universidade de Lisboa.
Fink, B. (1995). The Lacanian subject: Between language and jouissance. Princeton, NJ: Princeton University Press.
Frankenstein, M. (1983). Critical mathematics education: An application of Paulo Freire’s epistemology. Journal of Education, 165(4), 315–339.
Freudenthal, H. (1973). Mathematics as an educational task. Dordrecht: Reidel.
Gerofsky, S. (2010). The impossibility of ‘real-life’ word problems (according to Bakhtin, Lacan, Žižek and Baudrillard). Discourse: Studies in the Cultural Politics of Education, 31(1), 61–73.
Gravemeijer, K. (1994). Developing realistic mathematics education. Utrecht: CDbeta.
Gutiérrez, R. (2010). The sociopolitical turn in mathematics education. Journal for Research in Mathematics Education, 41, 1–32.
Hoyles, C., Noss, R., Kent, P., & Baker, A. (2010). Improving mathematics at work. New York: Routledge.
Hudson, B. (2008). Learning mathematically as social practice in a workplace setting. In A. Watson & P. Winbourne (Eds.), New directions for situated cognition in mathematics education (pp. 287–302). New York: Springer.
Jameson, F. (1991). Postmodernism or, the cultural logic of late capitalism. Durham, NC: Duke University Press.
Jurdak, M. (2006). Contrasting perspectives and performance of high school students on problem solving in real world situated and school contexts. Educational Studies in Mathematics, 63, 283–301.
Klette, K. (2004). Classroom business as usual? (What) do policymakers and researchers learn from classroom research? In M. Høine & A. Fuglestad (Eds.) Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education [PME28], (Vol. 1, pp. 3–16). Bergen, Norway.
Lacan, J. (2007). The other side of psychoanalysis: The seminar of Jacques Lacan book XVII [1991] (1st ed.). New York: Norton & Company.
Lave, J. (1988). Cognition in practice: Mind, mathematics, and culture in everyday life. Cambridge: Cambridge University Press.
Lave, J., & McDermott, R. (2002). Estranged learning. Outlines, 1, 19–48.
Lerman, S. (2000). The social turn in mathematics education research. In J. Boaler (Ed.), Multiple perspectives on mathematics teaching and learning (pp. 19–44). Westport, USA: Ablex.
Lundin, S. (2012). Hating school, loving mathematics: On the ideological function of critique and reform in mathematics education. Educational Studies in Mathematics, 80(1), 73–85.
Lyotard, J.-F. (1984). The postmodern condition: A report on knowledge [1979] (1st ed.). Minneapolis: University of Minnesota Press.
Martin, D. B. (2011). What does quality mean in the context of white institutional space? In B. Atweh, M. Graven, W. Secada, & P. Valero (Eds.), Mapping equity and quality in mathematics education (pp. 437–450). New York: Springer.
NCTM. (2000). Principles and standards for school mathematics. Reston: NCTM.
Niss, M. (2007). Reflections in the state and trends in research on mathematics teaching and learning: From here to utopia. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 1293–1312). Charlotte, NC: Information Age Publishing.
Niss, M., Blum, W., & Huntley, I. (Eds.). (1991). Teaching of mathematical modelling and applications. Chichester: Ellis Horwood.
Nunes, T., Schliemann, A., & Carraher, D. (1993). Street mathematics and school mathematics. New York: Cambridge University Press.
OECD. (1999). Measuring student knowledge and skills: A new framework for assessment. Paris: OECD.
Ozselçuk, C., & Madra, Y. (2010). Enjoyment as an economic factor: Reading Marx with Lacan. Subjectivity, 3(3), 323–347.
Pais, A. (2011a). Criticisms and contradictions of ethnomathematics. Educational Studies in Mathematics, 76(2), 209–230.
Pais, A. (2011b). Mathematics education and the political: An ideology critique of an educational research field. PhD Thesis. Denmark: Aalborg University.
Pais, A. (2012). A critical approach to equity in mathematics education. In O. Skovsmose & B. Greer (Eds.), Opening the cage: Critique and politics of mathematics education (pp. 49–92). Rotterdam: Sense Publishers.
Pais, A., Fernandes, E., Matos, J., & Alves, A. (2012). Recovering the meaning of “critique” in critical mathematics education. For the Learning of Mathematics, 32(1), 29–34.
Pais, A., & Valero, P. (2012). Researching research: Mathematics education in the political. Educational Studies in Mathematics, 80(1–2), 9–24.
Peters, A., & Burbules, N. (2004). Poststructuralist and educational research. Lanham, MD: Lowman and Littlefield.
Popkewitz, T. S. (2004). The alchemy of the mathematics curriculum: Inscriptions and the fabrication of the child. American Educational Research Journal, 41(1), 3–34.
Presmeg, N. (2010). Editorial. Educational Studies in Mathematics, 73(1), 1–2.
Radford, L. (2012). Education and the illusions of emancipation. Educational Studies in Mathematics, 80(1–2), 101–118.
Riall, R., & Burghes, D. (2000). Mathematical needs of young employees. Teaching mathematics and its applications, 19(3), 104–113.
Saxe, G. (1991). Culture and cognitive development. Mahwah, NJ: Erlbaum.
Secada, W., Fennema, E., & Byrd, L. (Eds.). (1995). New directions for equity in mathematics education. Cambridge: Cambridge University Press.
Seidman, S. (Ed.). (1994). The postmodern turn: New perspectives on social theory. Cambridge: Cambridge University Press.
Sierpinska, A., & Kilpatrick, J. (Eds.). (1998). Mathematics education as a research domain: A search for identity. Dordrecht: Kluwer.
Skovsmose, O. (1994). Towards a philosophy of critical mathematics education. Dordrecht: Kluwer.
Sriraman, B., & English, L. (2010). Surveying theories and philosophies of mathematics education. In B. Sriraman & L. English (Eds.), Theories of mathematics education: Seeking new frontiers (pp. 7–32). Heidelberg, DL: Springer.
Sriraman, B., Roscoe, M., & English, L. (2010). Politicizing mathematics education: Has politics gone too far? Or not far enough? In B. Sriraman & L. English (Eds.), Theories of mathematics education: Seeking new frontiers (pp. 621–638). Heidelberg: Springer.
Stech, S. (2008). School mathematics as a developmental activity. In A. Watson & P. Winbourne (Eds.), New directions for situated cognition in mathematics education (pp. 13–30). New York: Springer.
Stinson, D. (2004). Mathematics as “gate-keeper”(?): Three theoretical perspectives that aim toward empowering all children with a key to the gate. The Mathematics Educator, 14(1), 8–18.
Valero, P. (2004). Socio-political perspectives on mathematics education. In P. Valero & R. Zevenbergen (Eds.), Researching the socio-political dimensions of mathematics education (pp. 5–24). Boston: Kluwer.
Valero, P., & Stentoft, D. (2010). The ‘post’ move of critical mathematics education. In H. Alrø, O. Ravn, & P. Valero (Eds.), Critical mathematics education: Past, present and future (pp. 183–196). Rotterdam: Sense Publishers.
Verschaffel, L., Greer, B., & De Corte, E. (2000). Making sense of word problems. Lisse: Swets & Zeitlinger.
Verschaffel, L., Greer, B., Van Dooren, W., & Mukhopadhyay, S. (2009). Words and worlds: Modelling verbal descriptions of situations. Rotterdam: Sense Publishers.
Vighi, F., & Feldner, H. (2007). Ideology or discourse analysis? Žižek against Foucault. European Journal of Political Theory, 6(1), 141–159.
Vinner, S. (1997). From intuition to inhibition—mathematics education and other endangered species. In E. Pehkonen (Ed.), Proceedings of the 21th conference of the International Group for Psychology of Mathematics Education, vol. 1 (pp. 63–78). Helsinki: Lahti Research and Training Centre, University of Helsinki.
Vinner, S. (2000). Mathematics education: Procedures, rituals and man’s search for meaning. Regular lecture given at the Ninth International Congress of Mathematics Education (ICME9), Japan. Retrieved from http://www.fi.uu.nl/nwd/nwd2003/handouts/vinner.pdf, 20 February 20012.
Walshaw, M. (2004). The pedagogical relation in postmodern times: Learning with Lacan. In M. Walshaw (Ed.), Mathematics education within the postmodern (pp. 121–140). Charlotte, NC: Information Age Publishing.
Williams, J. (2011). Towards a political economic theory of education: Use and exchange values of enhanced labor and power. Mind, Culture and Society, 18, 276–292.
Williams, J., & Wake, G. (2007). Black boxes in workplace mathematics. Educational Studies in Mathematics, 64, 317–343.
Žižek, S. (1993). Tarrying with the negative. Durham: Duke University Press.
Žižek, S. (1994). The spectre of ideology. In S. Žižek (Ed.), Mapping ideology (pp. 1–33). London and New York: Verso.
Žižek, S. (1995). The metastases of enjoyment. London: Verso.
Žižek, S. (2004). Organs without bodies: Deleuze and consequences. London: Routledge.
Žižek, S. (2008a). The sublime object of ideology [1989] (1st ed.). London: Verso.
Žižek, S. (2008b). The plague of fantasies [1997] (1st ed.). London: Verso.
Žižek, S. (2012). Less than nothing. London: Verso.
Acknowledgments
This article is part of my PhD project, supported by the Foundation for Science and Technology of Portugal, grant SFRH/BD/38231/2007. It is also part of the Project LEARN, funded by the same foundation (contract PTDC/CED/65800/2006).