Mathematics education is critical

Does critical mathematics education embody an obsolete line of thought? Is it just a leftover from an outdated leftist educational movement? If not, what could critical mathematics education mean today and for the future? I see critical mathematics education as an expression of concerns for what socio-political roles mathematics education might play. Critical mathematics education has many roots, one of which is found in Critical Theory that also nourished critical education in general. Sources of inspiration can, however, also bring about presumptions, which can obstruct further development. I suggest a need for critical mathematics education to become re-conceptualised, and developed with new references. Roots are important, but an uprooting can sometimes be necessary. There is an ongoing discussion in education, especially amongst critical educators, about the relationship between research and practice. One could expect a ‘resonance’ between, on the one hand, theoretical and methodological considerations, and, on the other hand, priorities and approaches within educational practice. Although I might articulate issues with reference, sometimes to research and sometimes to practice, I intend, in what follows, not to address research and practice as separate entities. I want to express some of the concerns of critical mathematics education that have significance for both research and practice, i.e. concerns which could bring about the resonance to which I have just referred.

I have already used the notion ‘critical mathematics education’ several times. It is not clear to what that might refer, in particular when I have a kind of uprooting in mind. In order to provide some initial clarifications I consider the claim that ‘mathematics education is critical’, before I try to clarify the notion of ‘critical mathematics education’. This brings me to the concerns of critical mathematics education, and I want to refer to the following questions: (1) How do processes of globalisation and ghettoising frame mathematics education? (2) What does it mean to go beyond the assumptions of Modernity? (3) How should ‘mathematics in action’, including a mixing of power and mathematics, be interpreted? (4) What forms of suppression can be exercised through mathematics education? (5) How could mathematics education provide empowerment? Finally, I will sum up the basic uncertainty in addressing such concerns by referring to the notion of aporia.

Mathematics education could mean empowerment, but also suppression. It could mean inclusion, but also exclusion and discrimination: “Mathematics is not only an impenetrable mystery to many, but has also, more than any other subject, been cast in the role as an ‘objective’ judge, in order to decide who in the society ‘can’ and who ‘cannot’. It therefore serves as the gate keeper to participation in the decision making processes of society. To deny some access to participation in mathematics is then also to determine, a priori, who will move ahead and who will stay behind.” (Volmink, 1994: 51-52) This statement by John Volmink can be read as a dramatic description of the role of mathematics education in marking a division between those who become included in and those who become excluded from society. (I do not propose that mathematics education, or education in general, provides the main cause for social inclusion and exclusion. Many causes play together, but mathematics classrooms are important sites to consider.)

There is no lack of suggestions of how to interpret mathematics education as serving questionable socio-political roles. Besides operating as a gate keeper, it can ensure the social order in such a ‘smart’ form that ‘rational’ citizens, by using their  own free will, accept an imposed order. Mathematics education can support the development of an ideology of certainty (Borba and Skovsmose, 1997); it can provide an unjustified ‘trust in numbers’ (Porter, 1995). Paul Dowling (1998) has emphasized how mathematics education establishes different curricula for different groups of students, and in this way it influence what opportunities become available (or not available) for different groups of students. Generally speaking, mathematics education and social stratification interact.

However, mathematics education can also serve to empower students. Thus, Renuka Vithal (2003) outlines what mathematics education for empowerment could mean in a South African context, and Eric Gutstein (2003a) discusses empowerment with reference to a Mexican community in the USA. Ethnomathematical studies have discussed what empowerment might mean in different cultural settings (see, for instance, D’Ambrosio, 2001; Knijnik, 1999, 2002; and Ribeiro, Domite and Ferreira (Eds.), 2004); and Arthur Powell (2002) and Marilyn Frankenstein (1989, 1995, 1998) have discussed what empowerment could mean for marginalised adults in a USA metropolis.4 Helle Alrø and I have discussed empowerment, in terms of mathemacy, with reference to students in a Danish context (Alrø and Skovsmose, 2002). All such references indicate that it is possible to relate the learning of mathematics to empowerment, and also that an interpretation of empowerment depends on the particular contexts of the learners. Mathematics education can mean disempowerment or empowerment. 

Mathematics education does not contain any strong ‘spine’, but could collapse into dictatorial forms and support the most problematic features of any social development, exemplified by the adaptation during the 1930s of mathematics education in Germany to Nazi-friendly forms (Mehrtens, 1993). However, mathematics education can also contribute to the creation of a critical citizenship and support democratic ideals. The socio-political roles of mathematics are neither fixed nor determined. Both roles, of being a hero or a scoundrel, are available to be acted out through mathematics education. In this sense I talk about mathematics education as being critical. I do not relate mathematics education to any optimistic position claiming the existence of an intrinsic connection between mathematics education and, say, democratic values. 

Nor do I claim that mathematics education per se will serve anti-democratic interests. Instead, I simply claim that no actual functions of mathematics education represent its essence. There is no such essence. The critical nature of mathematics education represents a great uncertainty. Naturally, it is possible to try to ignore this uncertainty. This can, for instance, be done by assuming that mathematics education somehow can become ‘determined’ to serve some attractive social functions when organised in, say, a national curriculum crowned by some nice-looking aims and objectives. But I find this an illusion. The functions of mathematics education cannot be determined (or redetermined) with some positive guiding principles in the introduction to the curriculum. There are no straightforward procedures for ‘determining’ the functions of mathematics education, as they might depend on many different particulars of the context in which the curriculum is acted out. To acknowledge the critical nature of mathematics education, including all the uncertainties related to this subject, is a characteristic of critical mathematics education.

Critical mathematics education is not to be understood as a special branch of mathematics education. It cannot be identified with a certain classroom methodology, nor can it be constituted by a specific curriculum. Instead, I see critical mathematics education as characterized through concerns emerging from the critical nature of mathematics education. These concerns have to do with both research and practice.