24 SES 06 B, Issues of Mathematics Learning
Where school mathematics is taught by modelling and applications, by context tasks and mathematics in everyday context, a mathematical gaze is thrown on reality. This particular gaze brings about a requirement for recognition of some selected elements of reality and a suppression of all others. Experiences of life very seldom provide adequate means for such recognition. In this way, the gaze decontextualises reality and recontextualises its selected elements in pedagogic practice. As Bernstein (2000) argues, the recontextualising principle as a key organizer of school mathematics practice is hardly known to all those learners of school mathematics whose orientation to meaning can be described as contextual rather than as decontextual, as concrete rather than as abstract, as embedded in horizontal discourse rather than in vertical discourse. When learners of mathematics do not recognize that –in the classroom– reality is always a reality under a mathematical gaze, they are in danger to misunderstand the didactical function of reality for the learning of mathematics and, thus, not able to produce legitimate text (e.g. Gorgorió, Planas and Vilella 2002). In this way, context problems bear the danger of a) marginalizing students’ experiences of life, of b) mythologizing the relation between mathematics and life, and of c) jeopardizing disciplinary mathematical learning (Dowling 1998). Therefore, it has been argued (e.g. Bourne 2004, Jablonka and Gellert 2012, Cooper and Dunne 2000) that it is necessary –and possible– to make the recontextualising principle, to some extent, explicit also for those learners, who do not enter schools already equipped with the prevalent recognition rules. But how can this be achieved? We are inspired by the work of de Freitas (2008) who introduced future mathematics teachers to an activity of re-writing textbook problems, making future teachers aware of and critical about the ‘real’ as it was presented in the problems, by shifting contexts of context tasks while maintaining the mathematical structure unchanged. De Freitas’ (2008) focus is on the potential of this activity for fostering critical awareness.
In a professional development workshop, we involved mathematics teachers of underprivileged learners in an activity of context variation. The focus of the activity was not on a socio-critical perspective on mathematical application, but on the emerging distortions of reality and on ways in which these distortions can be made productive for the students. By providing students with an experience of context variation, the aim is to de-mythologize the relation between mathematics and life. In this way it is hoped that within the mathematics classroom, spaces can be opened, in which both experiences of life as well as disciplinary mathematical learning can genuinely be productive. Our research questions are: How do the teachers transfer the context variation activity to their teaching and how do their students react?
Bernstein, B. (2000). Pedagogy, symbolic control and identity: theory, research, critique. Lanham: Rowman and Littlefield. Bourne, J. (2004). Framing talk: towards a ‘radical visible pedagogy’. In J. Muller, B. Davies & A. Morais (Eds.), Reading Bernstein, researching Bernstein (pp. 61–74). London: RoutledgeFalmer. Cooper, B., & Dunne, M. (2000). Assessing children’s mathematical knowledge: social class, sex and problem-solving. Buckingham: Open University Press. Dowling, P. (1998). The sociology of mathematics education: mathematical myths/pedagogic texts. London: RoutledgeFalmer. De Freitas, E. (2008). Critical mathematics education: recognizing the ethical dimension of problem solving. International Electronic Journal of Mathematics Education, 3(2), 79–95. Gorgorió, N., Planas, N., & Vilella, X. (2002). Immigrant children learning mathematics in mainstream schools. In G. de Abreu, A.J. Bishop & N.C. Presmeg (Eds.), Transitions between contexts of mathematical practices (pp. 23–52). Dordrecht: Kluwer. Jablonka, E., & Gellert, U. (2012). Potential, pitfalls, and discriminations: curriculum conceptions revisited. In O. Skovsmose & B. Greer (Eds.), Opening the cage: critique and politics of mathematics education (pp. 287–307). Rotterdam: Sense. Kroon, S., & Sturm, J. (2000). Comparative case study research in education. Zeitschrift für Erziehungswissenschaft, 3(4), 559–576.
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