the scope and limits of critical mathematics education
Paul Ernest
p.ernest(at)ex.ac.uk
University of Exeter, UK
University of Oslo, Norway
Liverpool Hope University, UK
Dedicated to Ole Skovsmose on his 65th Birthday.
Introduction
In the past 25 years these is one scholar above others who has brought critical mathematics education (CME) into prominence in our field, and that is Ole Skovsmose. Starting with his 1985 paper he asked why mathematics education (ME) not only ignores critical education but why, at that time, it also seemed incompatible with it (Skovsmose, 1985). Although there were already social, political and social justice issues (especially gender) on the agenda (e.g., Howson & Griffiths, 1974; Bishop, 1988; D’Ambrosio, 1985; Fennema & Sherman, 1977; Mellin-Olsen, 1987; Sells, 1978), no-one had yet explicitly linked Critical Theory (CT) and the Frankfurt school with ME in the Anglophone research literature.
Since then Ole Skovsmose has gone on to develop his ideas of CME in many books and papers. The wide range of connected ideas he treats in these publications is illustrated by a list of some of the key terms in his titles. These include: aporism, applications, citizenship, competence, critical, democracy, dialogical, formattingpower, globalization, knowledge, mathemacy, mathematical archaeology, meaning, modelling, philosophy, political dimensions, project work, reflective, responsibility, society, social functions, technology,theoretical framework, uncertainty. These terms highlight the emphasis on both epistemological issues and social contexts and issues concerning mathematics, with a special emphasis on education and social critique/social justice.
Although CME has a number of godparents like Ubi D’Ambrosio, and in Scandinavia, Bent Christiansen and Stieg Mellin-Olsen, it is not exaggerating too much to call Ole Skovsmose the father of CME.[1] So it is an honour and a pleasure to pay homage to him, and to try to add a few thoughts, following on in his footsteps.
CME is by now well established and recognised worldwide with strong followings in Europe, North America, and countries of the south such as Brazil and South Africa. It is central to the concerns of conferences such as the Political Dimensions of Mathematics Education series, and the continuing series Mathematics Education and Society. It features regularly in lectures and papers in most of the international conferences in our field, such as the International Congress of Mathematical Education, which in 1988 in Budapest featured a whole day devoted to social issues, some of which were pertinent to CME.
Given this history it is now time to take stock of CME and to consider what progress has been made in conceptual terms. What is CME, and what is its scope and limits? Reflexivity is one of the ideas raised by Ole Skovsmose (2004). My aim here, as someone who subscribes to its principles, is to be reflexive about CME, to turn its critical gaze on itself.
The scope of critical mathematics education
The first question to be addressed is: what is the scope of CME? Taking ME as unproblematic for the moment, the question is then, what is critical mathematics education? What work does the adjective ‘critical’ do or add when appended to ME? How does it change, refocus or even enlarge the scope of ME? To address this it is first necessary to consider the meaning of criticality itself.
The word ‘critical’ has several meanings. First, a situation or problem is critical when the situation or problem is at a point of crisis, a turning point where conditions may deteriorate or improve dramatically, or where action is needed to guide events in one direction or another. Secondly, critical remarks or criticism is the expression of adverse, negative or disapproving comments or judgements. Thirdly, to critique is to analyse the merits and faults of something, typically a cultural product, possibly to uncover and evaluate its hidden dimensions of meaning and social and cultural significance. These differing but interconnected meanings can be traced back to Ancient Greece.
Both ‘crisis’ and ‘critique’ are derived from the Greek word krinein, which refers to ‘separating’, ‘judging’ and ‘deciding’. A ‘critical situation’ or a ‘crisis’ brings about a need for action and involvement, i.e., a need for critique. (Skovsmose, 2004, p. 3)
The word ‘critical’ was adopted by the Frankfurt School of social philosophers in naming their philosophical approach CT.[2] This school was originally founded 1923 in Frankfurt, during the crisis in Germany following World War 1 that led to the rise of Hitler and Nazism. There they developed Critical Conflict Theory drawing on the philosophy of Marx and Hegel, and on the psychoanalytic theory of Freud. Their theoretical standpoint was based on a commitment to egalitarian social justice values. It was a utopian perspective that presupposed the perfectibility of human society, and it viewed functionalism as an ideology as opposed to a rational, given ‘truth’, as some perceived it.
Applying these ideas to ME we have first the notion of crisis: that society and the teaching and learning of mathematics within it are at a point of crisis, at a critical point. Ubiratan D’Ambrosio (2008) links the critical state of the world with mathematics and ME in a powerful statement:
Survival with dignity is the most universal problem facing mankind. Mathematics, mathematicians and mathematics educators are deeply involved with all the issues affecting society nowadays. But we learn, through History, that the technological, industrial, military, economic and political complexes have developed thanks to mathematical instruments. And also that mathematics has been relying on these complexes for the material bases for its continuing progress. It is also widely recognized that mathematics is the most universal mode of thought. Are these two universals conflicting or are they complementary? It is sure that mathematicians and math educators, are concerned with the advancement of the most universal mode of thought, that is, mathematics. But it is also sure that, as human beings, they are equally concerned with the most universal problem facing mankind, that is, survival with dignity. (p. 37)
So the critical state of society provides an overarching concern for any CME worthy of its name: how to contribute most effectively to the improvement of the human condition, and how to address the universal problem facing humankind as identified by D’Ambrosio, namely survival with dignity?
The second meaning of critical concerns criticism, the expression of adverse, negative or disapproving comments or judgements. This then enters into CME in its responsibility to offer values-based criticisms of society, mathematics and the social practices of ME, most notably the teaching and learning of mathematics. This cannot be separated from the function of critique, which in analysing the strengths and weaknesses of mathematics, society, ME and their complex inter-relationships must necessarily offer criticism. This then raises the specific question, what problems or areas of concern do CME address, or more broadly, what problems should it address?
In my view there are four main domains to consider. First, if CME is to offer a values-based critique it needs to clarify the assumed or base values from which it begins its critique. What values or ranges of values are presupposed by CME? Second, if CME is to critique mathematics itself it needs to address epistemological issues about philosophies, theories and perceptions of mathematics. What is mathematics, what philosophies of mathematics are there, and what presuppositions underlie these views and philosophies of mathematics?[3] Third, in some ways the central force of the critique of CME is directed at society and social problems and issues, so a critique of society and of the role of mathematics in society is necessary. Fourthly CME is ultimately directed at ME. Thus CME is concerned with critiquing the practices of the teaching and learning of mathematics, including the central institutions in which the teaching and learning take place, but not neglecting the informal and culturally distributed practices by means of which mathematics is taught and learned outside of formal institutions. However, as well as these primary areas of study of ME comprising the practices involved in the teaching and learning of mathematics, ME is also a field of study, an academic discipline, and it is the business of CME to critique this secondary object of study as well (Ernest, 1998a). What is the present state of the ideas, theories, research and publications in ME and what should it be?
Do the four domains of values, epistemology, social theory, and ME exhaust the scope of CME? Not necessarily; this is just a first listing of the most obvious domains involved. It might be that ontology, for example, is significant enough to require separate critical attention from CME. Another candidate might be economics, given the deep implication of mathematics in the economic perspective of the world and indeed in the contribution of Marx’s philosophy to CT, not to mention the international credit and banking crisis beginning in 2008-09. However I shall be satisfied with the four domains outlined above for this chapter. But my analyses must always remain tentative in case the domains listed prove inadequate for accommodating all of the problems of and issues for CME.
According to this analysis CME has four main domains of operation and application. These are values (ethics), epistemology, social theory and education, but not surprisingly there is overlap between them. It might be seen as arbitrary whether to treat the societal place of mathematics as one of epistemology or social theory, especially if social constructivism is advanced as a philosophy of mathematics, with its emphasis on the social construction and warranting of mathematical knowledge (Ernest, 1998b). Within each of these domains and any issues identified within them, there is a need for critical examination, especially of received views, ideologies, power hierarchies, institutions, social-structures, and the combination and interplay between them, along what Foucault terms the knowledge-power-money axis.
A further step in this analysis would be to identify particular questions, problems and issues that fall within these four domains. However, I shall leave this project for another occasion and move on to exploring the limits of CME.
The limits of critical mathematics education
In the spirit of reflexivity I want to push CME to the limit. It is clear that CME depends on critique, on a critical attitude. So what does this mean when applied to CME itself? In the spirit of reflexivity I want to offer this critique of CME focussing on the first two parts of its name as headings: namely critical and mathematics. Doubtless the third term, education could also be foregrounded in such a critique, but I shall leave that for a future paper, although I make a few remarks to this end in my conclusion.
Criticality
There is a long and honourable tradition of criticality in philosophy. There was very relevant work on reason, dialogue, dialectics and criticism by the Ancient Greeks. Later, in initiating modernism in philosophy, Descartes’ use of doubt puts critique centre stage in epistemological methodology. Criticality was first explicitly headlined in philosophy in Kant’s major works ACritique of Pure Reason / Practical Reason / Judgement. The most influential of these is the Critique of Pure Reason, an investigation into the structure and limitations of reason, which attacks traditional metaphysics and epistemology. However, the main targets of these books and the earlier work mentioned are philosophy and philosophical theory itself. Clearly the idea of discussion, proposing ideas and claims, followed by argument, rebuttal and critique, is as old as philosophy itself. However, CT does not just depend on the use of criticality, but its deployment in a wide ranging philosophical critique of society and social structures. Although there are anticipations, this project was given pride of place in the work of Karl Marx, the grandfather of CT, and of course fully developed in CT itself.
The criticality I wish to discuss here is not the general broad sense as evidenced throughout philosophy, but the modern political project within philosophy that critiques society on an ethical basis in terms of democracy, social justice and freedom. According to Foucault (1992) this project is motivated by an attitude or ethos which places importance on exploring and going beyond whatever it is that limits our freedom, however that freedom is defined (Osberg, 2008).
The Frankfurt school chose the term ‘critical’ as the central descriptor of its philosophical approach because they wanted to critique society on an ethical basis, and use the new insights granted by Freud’s theories. Criticality used in this way implies the facility of being able to discriminate between good and bad in society, being able to identify what Marx termed ‘false consciousness’. The use of this formulation immediately places the critic in a superior position as a person with the ability to tell truth from falsehood, right from wrong, what is beneficial from what is detrimental. In other words this posture presupposes that the speaker has an epistemologically or ethically privileged standpoint and judgement. When critical theorists and Marxists speak of ‘false consciousness’ they are presupposing that their own consciousness is correct and their models of reality are true representations. This is both epistemologically and socially problematic. As Osberg puts it:
Within this framework, the only way in which the subaltern classes can come to recognize the “true” workings of power is through outside intervention, e.g., through some form of education. This is the motivation behind critical pedagogy (see, e.g., Freire, 1996). An insurmountable problem with critical pedagogy, however, is that it is paternalistic. The “father figure” (i.e., the “all knowing” educator) has to somehow get the “children” (i.e., working class adults) to “see” what is “really” going on, a relationship which is itself hegemonic. (Osberg, 2008, p. 138)
This sits ill with postmodern epistemological humility, according to which all of our knowledge is tentative and according to which there is no royal road or privileged access to truth. Who is entitled to say their vision is the true one? Certain sections of society through their power legitimate particular historically formed discursive formations and discursive practices, creating a ‘regime of truth’, but these are contingent and not logically necessary or empirically true (Foucault, 1972). So one of the outstanding problems of CT is the assumption of an Archimedean fixed point, a ‘God’s eye view’ from which epistemological and ethical certainties can be determined.
Does this make the language of criticality a meta-narrative that imposes a new rationality, at best a rationality of ‘questioning with a conscience’, at worst, a holier than thou critique within philosophy and social theory? Is criticality reinstalled as the replacement for rationality, despite the postmodern critique of reason from the enlightenment through to modernism? This is one of the dangers attached to the over-valuation of criticality.
Beyond philosophy, criticality is a much prized feature of academic writing. All journal papers and chapters in the sciences, humanities, arts, as well as social science research, including ME, are expected to display criticality. I am expected to write in the ‘critical style’ in this chapter. Criticality is also the sine qua non of higher level study in our field at undergraduate, masters and doctoral degree levels, and I would not expect to award higher grades to students who did not display it in their work. .
Not all in academia accept the automatic privileging of criticality as Cohen (1993, p. x) argues:
I propose to withdraw the automatic ‘cognitive advantage’ of university critical writing, on the grounds that no such advantage is warranted: our writings are outfitted for the grooves of ‘reason’, ‘society’, ‘need’ —each of which is a cosmos of mythology unto itself. In making this withdrawal, I am more or less expressing ‘no confidence’ in the essential activities of the modern university.
The elevation of criticality to the highest level cognitive skill has a theoretical basis in psychology and assessment theory. Bloom’s (1956) taxonomy of educational objectives of the cognitive domain places evaluation at the highest cognitive level above the creative functions of analysis and synthesis. Evaluation is primarily about judgements of quality and worth, including, as it is defined, the abilities of discrimination between different concepts and ideas, and the assessment of the value of theories and representations. These are the functions of being able to think critically, showing that criticality is positioned at the highest level in terms intellectual demand and complexity of judgement, within this framework.
Thus there is a dominant meta-narrative of criticality in academia. One might even say the criticality is fetishized. It is part of our morally self-justified perspective in CME. We in CME are after all the ‘good guys’, the committed ones who care, who are not deceived by the instrumentalism of some of our colleagues. It is us in CME who are fighting for social truth and social justice. The criticality in our position, in our CME, is our shield against being deceived in our work. Is it not the essential capacity that enables us to discern the manipulations, deceptions and exploitation around us in society? But to be a critical academic often means to stand above, beyond or outside of the social problems and issues we judge. It can mean to be dispassionate and disconnected, lacking commitment to the struggles we advocate or endorse.
Despite its elevation and fetishization, or perhaps because of it, there is a tradition of thought that rejects criticality as being of the highest intellectual level. The role of the intellectual whose role is to exercise criticality, that of the critic, is seen by some to be parasitic in the arenas of music, theatre, painting, and other creative arts. For in these pursuits, the practice is one of engaged creation, made up of artists pursuing their creative vision. On their backs sit parasitic critics who are judgmental without being creative, and through these activities making and breaking careers according to their own whims.
Such a perspective does not see criticality as the highest form of intellectual functioning. It does not accord the high status to criticality that much of modern thought does. One of Bloom’s closest associates Krathwohl, repudiates criticality in favour of creativity. Anderson & Krathwohl (2001) challenge the positioning of evaluation as the highest level of cognitive thought. Instead they suggest a revised taxonomy of the cognitive domain which is the same as Bloom’s (1956) original except for the addition of a new top category ‘creating’, which is about being able to create new knowledge within the domain. This echoes artists’ views of the role of critic as secondary, following on from committed creation in the arts.