Mathematics education and relational ethics: dimensions and
sources
Mark Boylan
Sheffield Hallam University
[email protected]
Abstract
There is an increasing interest in issues of value and purpose in mathematics,
education often from a sociopolitcal perspective. However, explicit discussion of ethics
is less common. Considering different ethical dimensions supports the development of
plural relational ethics. Dimensions discussed are the societal and cultural, being with
the other, the ecological and the self. These enmeshed dimensions act as heuristic to
consider awareness of different forms of relationship and arenas for actions. Various
philosophical and theoretical sources are identified in relation to each of these
dimensions, as well as examples of practice. These support the development of
ethically informed mathematics education praxis.
Introduction
Over the last twenty years, there has been an increasing interest in, and discussion of,
values in mathematics education particularly through the focus on its political
dimensions and social justice. The sociopolitical turn (Gutiérrez, 2013) has involved a
number of currents and traditions within mathematics education. Emphasising the
political in mathematics education is most closely associated with the Critical
Mathematics Education tradition in Europe (see Alrø, Ravn, & Valero, 2010; Mellin
Olsen, 1987; Skovsmose, 1994), the radical mathematics and mathematics for social
justice current in the US (Frankenstein, 1989; Gutstein, 2006), and ethnomathematics
developed in the majority world (D'Ambrosio, 1985; Gerdes, 1996; Powell &
Frankenstein, 1997). These have in common a critique of the prevailing forms of
mathematics curricula and pedagogies and that mathematics education, whatever its
form, is political and its practices are value-laden. The contention is not only that
mathematics education should be political but rather that it is political. More
ambiguously, and perhaps less radically, the term 'equity' is used as means to refer to
a concern primarily for outcomes particularly in relation to closing perceived
achievement gaps (Gutiérrez, 2008).
Mathematics education for social justice and equity is necessarily concerned with the
macro (North, 2006) 'big picture' of social inequality and the significant role that
mathematics and mathematics education has in maintaining relationships of
oppression. However, other important currents in the sociopolitical tide are those that
focus or emphasise the 'small picture' - the micro of the relationships and practices as
found in specific mathematics classrooms. This includes the type of classroom
relationships fostered between teachers and students and between students and each
other as well as individual learners' relationship with themselves and mathematics.
Important here are poststructuralist analyses (see for example, Brown & McNamara,
2005; Hardy, 2004; Mendick, 2006; Walshaw, 2004; 2013) that examine the discursive
1
production of such relationships and so provide accounts that link the micro and the
macro. The influence of each with the other is multidirectional (North 2006) and
dynamic (Griffiths, 2003).
Those who highlight the sociopolitical in mathematics education often emphasise
social justice and democracy as providing an axiological imperative. However, even in
literature that is clearly axiological, ethical discourse is found infrequently (Atweh &
Brady 2009). Perhaps this is because of a prevailing view that social justice is
concerned with broader social concerns and less with individual relationships and
interaction (Atweh 2013). More recently the discussion of ethics has been taken up by
some in relation to mathematics education (Atweh, 2013; Atweh & Brady, 2009,
D'Amborisio, 2010; Ernest, 2013, Neyland, 2004; Roth 2013; Walshaw, 2013) with
Paul Ernest (2013) arguing that ethics is the 'first' philosophy of any philosophical
consideration of mathematics education.
Here, I draw on and add to these accounts to by considering a number of different
dimensions of ethical relationship. Considering these dimensions supports the
identification of a range of potential sources in ethical philosophy that can inform
multiple situated relational ethics in mathematics education. They also describe
different arenas in which ethical action takes place.
Some of these dimensions are prominent in the sociopolitical accounts outlined above
-the societal, the cultural and, the global (D'Ambrosio, 2010). Possibilities for ethically
informed action by mathematics educators in the societal and cultural dimension are
well charted even if ethical discourse is often absent. Therefore, below I limit my
discussion to pointing to ethical and axiological sources that might support and inform
thinking in these areas. A further dimension, and one often cited in contributions that
aim to introduce an awareness of ethics to mathematics education, is the relationship
to 'other' (Atweh, 2013; Atweh & Brady, 2009, Ernest, 2013; Neyland, 2004). An
important source here is interpretation and application of the ethics of Levinas although
others point also the dialogical ethics of Bakhtin (Roth, 2013). Summarising these
contributions, I link them to examples of practice in mathematics classrooms that have
foregrounded relationships with others. I then discuss two ethical dimensions that have,
hitherto, received less attention in the mathematics education literature: the ecological
dimension and the self. I conclude by discussing some of the relationships and
tensions between attending to these different dimensions in relation to mathematics
education suggesting that this extends the meaning of praxis.
Relational ethics in mathematics education
The ethical stance that frames my discussion draws on relational postmodern ethics1.
Bauman (1993) contends that humans are morally ambivalent and not essentially good
or bad. This suggests that in mathematics education the development of democratic
citizens or the nurturance of ethical and moral beings (Noddings,1998) is not about
fostering or creating environments that will simply support the development of the
naturally good moral actor. Ethical phenomena and situations are non-rational as they
are not regular and predictable and morality is not universalizable. This entails
1
Here I refer to and discuss Bakhtin's axiological thought. I leave aside the question of whether the label
postmodern is fully appropriate.
2
rejecting utilitarian and rule based ethics. Ethical action is, like the self itself, relational
and dialogical (Bakhtin, 1993). Moral responsibility arises as part of subjectivity
(Bakhtin 1993; Erdinast-Vulcan, 2008; Levinas, 1982) in its relationality: "being for the
Other before one can be with the other - is the first reality of the self" (Bauman, 1993,
p.13)2. Each ethical actor is unique - " a once-occurrent participation in being" (Bakhtin,
1993, p.58) who cannot be replaced and who has a non-transferable responsibility
(Levinas, 1982; Erdinast-Vulcan, 2008).
Alongside the emergence of ethics as topic of concern in mathematics education is a
parallel interest in the importance of affect in axiological questions (see for example,
Angier and Povey, 1998; Walshaw and Brown, 2012, Mendick 2006). Discussions of
emotionality support, and are supported by, postmodern ethical thought that disputes
the separation of rationality from emotion with "human valuation grounded in bodily
feelings and volitions which underlie and accompany acts" (Anton, 2001, p. 220).
Actors are not free floating (Bauman, 1993) or universal beings but exist in concrete
situations (Bakhtin, 1993). Elsewhere I have argued that emotionality and issues of
social justice variously intersect, interrelate and are intertwined (Boylan, 2009),
describing different strengths of relationship. The last - 'intertwined' - inferring that the
experience of emotion and affective discourse are inscribed with power and social
position (Abu-Lughod & Lutz, 1990; Zembylas, 2005).
Because the ethical self is an embodied historical entity, a unitary ethics of
mathematics education that fits all situations and circumstances is not possible.
Bauman (1993) argues that this does not necessarily lead to moral relativism, if this is
understood as a comparison between different ethical codes that are culturally
applicable. However, others writing from a post-modern perspective are more
comfortable with embracing a qualified relativism (Shildrick, 1997). An alternative, and
the position I take here, is to respect an ethical pluralism (Anton, 2001) that is entailed
not so much by different cultural norms or contexts a by the uniqueness of the ethical
actor in each concrete situation (Anton, 2001; Bakhtin, 1993). Whatever standpoint is
taken on the issue of relativism, the deconstruction of ethical codes shifts the focus to
relationship, practice and action as the sites for ethical reflection.
Most choices involve, in ethical terms, contradictory consequences; they may have
both desirable and undesirable outcomes. Thus they are morally ambiguous and
ambivalent: "virtually every moral impulse, if acted upon in full, leads to immoral
consequences" (Bauman, 1993, p.11). For example, there is a tension between caring
for the other, which, if taken to the extreme, removes autonomy and leads to
oppression. Similarly, in mathematics education, we know that qualifications in
mathematics affect learners' life chances. Mathematics is key gatekeeper to further
study, so supporting learners to attain mathematics qualifications is worthwhile.
Moreover, because patterns of socioeconomic and cultural disadvantage are refleced
in patterns of mathematical attainment, supporting those who are currently
disadvantaged to attain mathematically may support changes in such patterns in the
longer term. Therefore, a desire to promote equity supports actions to maximise
student attainment outcomes.
2
The meaning of 'other' is discussed below.
3
However, doing so, may inculcate in students a focus on learning for results, leading to
alienation, self-abnegation, distress and restrictions on available identities (Reay &
Williams, 1999). At a social level, it may serve to support and preserve a dominant
ideology in which attainment outcomes are the measure of educational worth, thus
helping to maintain a wider, alienating, performativity culture. There are alternatives
that appear ethically preferable, for example, a pedagogy that involves a slower
relationship to learning mathematics which emphasises the 'whileness' that makes
something worthwhile (Jardine, 2012). However, these too have possible negative
ethical implication given the currency of mathematics qualifications in industrial
commodity societies that are rewarded, in part, for speed and curriculum coverage.
There is not a 'right' or universal answer to these conflicting ethical considerations.
Further, this ambiguity deepens given that "what we and other people do may have
profound, far-reaching and long lasting consequences, which we can neither see
directly nor predict with precision" (Bauman, 1993, p.17). Although, in usual
circumstances, the actions of each teacher and the practices in each classroom do not,
on their own, have a significant influence on wider dimensions, the consequences of
actions extend beyond the immediate. In mathematics education research, accounts of
adult reflecting on their experience of learning mathematics indicate how mathematical
experiences impact on individuals' relationships to themselves that extend into the
future (Black et al. 2009; Bibby, 2002; Boaler, 2005; Boylan & Povey, 2009).
Ethical dimensions
The ethical dimensions that are my focus in this paper, in order of decreasing
magnitude, are3: the ecological, the societal and cultural, the other, and the self. This is
not an exhaustive list and other categorisations are possible. For example, I
conceptually embed the economic - an important concern in issues of social justice
and equity - as part of the societal and cultural. However a classical Marxist might
substitute the economic for cultural and subsume the latter as the superstructural
expression of an economic base. A dimension not considered here is the temporal that
recognises mathematics as a cultural product of our ancestors and positions humans
as 'participants in the great, age-old human conversations that sustains and extends
our common knowledge and cultural heritage (Ernest, 2013, p. 11) such a recognition
entails "acknowledging that the conversation is greater than yourself" (ibid).
These dimensions are all social and political as well as ethical. In addition, the choice
of dimensions to consider, the distinctions between them and even the order in which
they are discussed are value laden. The categorisation acts as a heuristic and a tool
for reflection. The dimensions are enmeshed in each other and are not distinct or
separate. Considering different dimensions is a means of realising an ethical pluralism.
Such pluralism extends Bakhtin's polyphonic epistemology into ethics. This
epistemology proposes that truth arises momentarily, and cannot be expressed in a
single statement but only in simultaneous and contradictory statements that involve
interaction between position holders (Sidorkin, 2002).
3
'Magnitude' here refers to a relative size and type of being involved.
4
Three meanings of ethical dimension are particularly relevant. One meaning is as a
dimension of awareness. This echoes Spinoza's concept of planes (Spinoza, 2000
cited in Walshaw and Brown, 2012). Existing in webs of relationality, it appears
impossible to hold in our awareness the complexity of all the different patterns of
relationship "that cannot in principle be fitted into the bounds of a single
consciousness" (Bakhtin, 1984). Yet these types of relationship are not of the same
sort. Our ethical awareness can shift focus on to different forms of relationship.
Awareness expands and contracts either involuntarily or through conscious focus. This
does not mean that the forms of knowing in different dimensions are necessarily the
same. This entails the need for an epistemological or existential pragmatism (Boylan,
2004).
The second meaning is that each dimension is an arena for action. Ethical action of
mathematics educators involves paying attention to the quality of actions and
relationship in each of the dimensions and the interrelationships between dimensions.
One important aspect of such action is to pay attention to how to create, instigate or
foster spaces in which learners of mathematics can also develop as ethical actors in
relation to each of the ethical dimensions. Thirdly, considering different dimensions
encourages an examination of multiple sources in the philosophy of ethics.
The societal and cultural dimension
The societal and cultural dimensions have been the main focus for those concerned
with equity in mathematics and of critical mathematics education and mathematics
education for social justice. An important focus here is seeking to research and
develop practices that support more equitable attainment outcomes in mathematics as
a means of addressing social oppression and inequity (Gutiérrez, 2002; Gutstein,
2006). Depending on the context, different contributors to these traditions have
foregrounded different pedagogies for a counter-hegemonic mathematics education.
based on the critique of the ideological nature of mathematics in society and schools
(Ernest, 1991; Mellin Olsen, 1987; Skovsmose, 1994). As an alternative to the
dominant form of mathematics, the ethnomathematics tradition has emphasised the
importance of the inclusion of informal and culturally based mathematical practices
(D'Ambrosio 1985; Gerdes ,1996; Powell & Frankenstein, 1997). Ethnomathematics is
one approach to support the social and cultural identity of oppressed and
disadvantaged groups through and as part of learning mathematics (Gutstein, 2006;
Shan & Bailey, 1991). A related concern, and one supported by the pedagogical
thought of Paulo Friere, is to connect mathematics to the lived experience of learners
(Frankenstein, 1989; Gutstein, 2006; Mellin Olsen, 1987). An aspect of this is the
inclusion of curriculum content that is focused on issues of social justice and that
supports learners to "read the world" (Gutstein, 2006) critically through mathematics
(see also, Frankenstein, 1989; Skovsmose, 1994). One aim of such approaches and
itself an important aim of critical mathematics education, is to empower learners to
participate as democratic citizens (Christiansen, 2000; Skovsmose & Nielsen, 1996;
Vithal, 2003). Further, a significant concern for social justice in mathematics education
is the ideological support that mathematics, as presently constructed in society and in
schools, gives to dominant groups' representations of knowledge as beyond dispute
(Restivo, 1992;) and that knowledge and knowing mathematics are solely rational
(Walkerdine, 1988).
5
The critical tradition, then, offers both a critique of mathematics education and
alternative practices across a range of issues and concerns. As noted in the
introduction, generally, axiological commitments are implicit rather than explicit. Here. it
may be worthwhile to engage with general discussions of social justice in education,
Particularly, those that draw on both distributive and relational theories of social justice
and in so doing emphasise the importance of recognition and respect for diversity
(Gewirtz, 1998; Griffiths, 2003; Fraser 1997; Fraser and Honneth 2003; North, 2006,
2008). Such accounts can provide useful tools for reflection on critical mathematics
education.
Being with others
As stated earlier, the ethical thought of Levinas has been influential in the development
of relational ethics (Bauman, 1993) and in the call for ethics to be explicitly considered
within mathematics education (Ernest, 2013, Atweh, 2013; Atweh & Brady, 2009,
Neyland, 2004; Roth 2013). Jim Neyland (2004) invokes the philosophy of Levinas
when reviewing the neo-liberal agenda in mathematics education to argue that ethical
responsibility is properly the starting point for engagement with others. This
responsibility does not arise from exchange and is not dependent on reciprocity; it
arises as part of subjectivity within encounters that are 'face to face'. Relationship to
other is, or should be, the original ethical form from which societal and institutional
relationships are developed.
The primary model for relationship, for Levinas, is the face-to-face encounter. Bakhtin's
dialogical description of relationality stresses not only the encounter with the image of
the other but also the act of speaking and answering - dialogue and the voice
(Erdinast-Vulcan, 2008)4. Roth (2013) applies these concepts to a close reading of a
pedagogical encounter in a mathematics context that highlights the exposure of both
teacher and learner to each other and the role of affect - including not only those of
care and positive regard but of frustration and exasperation. In addition, he locates the
source of ethical responsibility in answerability and the dialogical nature of learning
relationships.
Various implications for practice of an ethics that takes relationship with the other as
primary have been proposed. Neyland (2004) proposes a 're-enchantment' of
mathematics education, that takes, as its starting point, a collective ethical review by
teachers of mathematics of their practices and seeks to develop or restore a sense of
purpose and spontaneity and encourages surprise and joy. Roth (2013) stresses the
importance of fostering dialogue and dialogic relationships in education that extend
beyond the curriculum to forms of organisation and leadership in educational
institutions. Further, Atweh and Brady (2009), also draw on Levinas to develop the
notion and importance of responsibility and propose a socially 'response-able' (Puka
2005) mathematics education. Features of this are examining the place and nature of
mathematics in education as whole, developing students' response-ability through the
curriculum and that of teachers' through pedagogy. From a different ethical starting
4
There are many parallels between Levinas and Baktin's ethical philosophy (see Erdinast-Vulcan, 2008;
Roth, 2013). Dialogue is also important for Levinas with 'saying' and 'said' as central concepts (see Roth,
2013).
6
point suggestions for practice, in their detail, are similar to those found in the critical
mathematics tradition with an increased emphasis on the form of interactions.
The insertion of these ethical considerations into mathematics education is relatively
recent. Thus, it is perhaps unsurprising that, so far, discussions of the implications for
mathematics education of ethics that emphasise alterity have been somewhat abstract.
Nevertheless, they provide an ethical weight to existing critiques of dominant forms of
current mathematics education practices. Further, they connect to accounts of
practices that contend that social justice in mathematics education should be enthused
and informed by a concern for the centrality of classroom practices that support just
relationships between teacher and students and students and their peers (for example,
Allexsaht-Snider and Hart, 2001; Angier & Povey, 1997; Boaler, 2007; Noddings, 1993;
Povey, Burton, Angier, & Boylan 1999). Jo Boaler, in a significant study, proposed the
notion of "relational equity" to describe “equitable relations in the classrooms; relations
that include students treating each other with respect and consider different viewpoints
fairly’” (Boaler, 2008). As well as creating just relationships, such practices tend to
overcome the differential access to the mathematics curriculum that different groups of
learners face and tend to ameliorate the effects of a damaging and disconnected
curriculum. Boaler's study in an ethnically diverse school demonstrates how more open,
connected and problem-solving approaches to learning mathematics, embedded in
structured group work can lead not only to overcoming social and cultural inequalities
but also to developing the respect of learners for each other across social differences.
Whilst an ethics that emphasises the importance of relationship to others can inform
pedagogical and curriculum frameworks perhaps more important is the development of
an ethical sensibility. Such a sensibility can inform moment-to-moment interactions and
the creation of pedagogical spaces in which ethical relationships can be fostered.
The ecological dimension
D'Ambrosio (2010) extends concerns with social and cultural issues and relationship to
consider the global situation. He critiques an unreflective, rationalist and technicist
mathematics education that does not contribute to the most universal problem facing
humanity: survival with dignity. In doing this, he echoes the emergence of critical
theory in response to the economic, social and military conflicts of the middle of the
twentieth century. He proposes that values must be inserted into rationalist and
technicist reasoning of mathematics education (Ernest, 2013): "It is important to
question the role of mathematics and mathematics education in arriving at the present
global predicaments of humankind" (D'Ambrosio, 2010, p.51) as mathematics provides
the foundation for global systems and relies on these systems.
D'Ambrosio summarises the range of crisis, and threat and frames this in terms of the
following dimensions of peace: inner peace, social peace, environmental peace,
military peace. He proposes a primordial ethics that "recognizes the fundamental
necessity of the mutual relation between the individual, the other and nature" (2010 p.
59). Such relationships are marked by a quality of reciprocity between these three
which is necessary for both individual and species survival. This ecological dimension
has two notable aspects in relation to mathematics and mathematics education. The
first of these is the role mathematics plays in the current environmental crisis and in
7
responses to it. The second is in relation to the values implicit in how humans, or at
least those in the capitalist rich majority world, conceive and enact their relationships
with other existences on the planet. I will consider each of these in turn.
In the current international financial and economic crisis mathematics and
mathematical processes have been significant causes of social destruction and
devastation (Ernest, Greer & Sriraman, 2009). Further, the role of mathematics in
formatting our world (Skovmose 1994) is an important part of the critical mathematics
education analysis. Richard Barwell (2013) examines the mathematical formatting of
climate change, noting how the descriptive, predictive and communicative aspects of
climate science involve the use of mathematics and mathematical literacy. Climate
change is a "realised abstraction" (Barwell, 2013 p. 10) that, through mathematics,
formats the world. In particular, it formats our relation with the climate as measurable,
and potentially controllable, but:
This construction of the climate does not include the stories of our
ancestors about how the weather has changed or the anguish of people
whose way of life has been disrupted by drought or floods or melting of ice
(p.11).
The narrowness of such constructions are contested, for example, by those who
campaign with the slogan of 'climate justice' to attempt to counter the abstraction of
climate change by introducing the discourse of values, emotion, meaning and
embodied life. However, such contestations are often anthropocentric and other- thanhuman interests may not be considered or valued. The alternative is to generate
spokespersons for the interests of a wider constituency of human and non-humans
(Latour, 2004; Macy & Brown, 1998).
A significant capitalist response to the current environmental crisis has been to enlist
mathematics and mathematical tools in the search for market solutions. Under the
banner of green capitalism mathematics is being used a means to extend the
commodification of natural resources in new ways (Sullivan, 2010). One response to
the ecological crisis is to see in it an opportunity for the extension of the enclosure of
land and resources that occurred and occurs during the phase of primitive
accumulation of capital during periods of the development of industrial capitalist
economies (Delueze & Guattari, 2004). The development of carbon credit markets and
markets in 'ecosystem services', are reconfiguring the earth as akin to a corporation
providing products to humanity that can be broken down into quantifiable categories
that are ascribed a financial value (Sullivan, 2010). Mathematics is central to this
endeavour:
those numerate in the labyrinthine abstractions accompanying the creation of
new ecological commodities and markets – accountants, brokers, bankers, and
assisting ecological scientists – become the expert mediators and managers of
monetary value of both (Sullivan 2009, p. 23)
The value and worth of the natural world and our relationship to it is transmuted into
valorisation - everything - water, trees, clean air, biodiversity, ecosystems - can be
given a price:
8
The quantification skills of ecological science, economics and finance are
combined to assign prices to these ecological 'services', thereby bringing
them forth as new, albeit fictional, commodities (Sullivan, 2010, p.117).
Mathematics is necessary for this process of commodification and so formats the
world and our scope for action:
mathematics intervenes in reality by creating a 'second nature' around us,
by giving not only descriptions of phenomena, but also by giving models for
changed behaviour. We not only 'see' according to mathematics but we
also 'do' according to mathematics (Skovsmose, 1994, p.55).
Holmes Rolston (2007) suggests that we are at a turning point where the technosphere,
previously constructed within the biosphere, could become the realm in which natural
history is located. In which case, in the terms Skovsmose uses, the mathematical and
technologically formatted second nature would be not a 'second nature' but 'nature'. An
environmental ethics that is based on appeals to ecological care as good for humans
as well as ecosystems, has little purchase against calls for geo-engineering as a
response to climate change, or the commodification processes pointed to above. An
alternative is the development and promulgation of an 'earth ethics' that does not value
other existences as a human resource but valuing the earth as:
a superb planet, the most valuable entity of all, because it is the entity able
to produce and sustain all the Earthbound values. At this scale of vision, if
we ask what is principally to be valued, the value of life arising as a creative
process on Earth seems a better description and a more comprehensive
category then to speak of careful management of planetary natural
resources that we humans own (Rolston, 2007, p. 21).
Through its involvement in these processes mathematics serves to extend the
separation and alienation of humanity from the rest of the biosphere that has been an
aspect of recent times. This represents perhaps the final triumph of a disembodied
rationality - the mastery of reason (Walkerdine, 1988) - in which mathematics and
mathematical processes take primacy over and interrupt visceral relationships with the
world. David Jardine (1994) calls for an alternative mathematics that does not take
human existence and mathematics as prior to encounter with the world but as
embedded in it and an aid to appreciation of being:
Mathematics is not something we have to look up to. It is right in front of us,
at our fingertips, caught in the whorl patterns of the skin, in the symmetries
of the hands, and in the rhythms of blood and breath (p. 112).
The mathematics of 'kinship' (Jardine, 1994) can be a means of enhancing our
relationship with the world, particularly the natural world and imbuing this relationship
with generativity and life. This contrasts with the algorithms that sustain 'necrocapitalism' (Bannerjee, 2008; Sullivan, 2010). These algorithms through a process of
valorisation suck value from the the world leaving empty cyphers standing for complex
webs of relationship. An ecological ethics calls not only for an environmentally
informed critical mathematics education but also for a critique of the social
construction of mathematics itself as separate and disconnected from the earth. Such
9
a mathematics education would take seriously the call to redevelop or develop a sense
of responsibility for not only humanities own survival but for the future life on the planet
(Guattari, 2000).
The self
It may appear strange, initially at least, to turn from a concern with the ecological
dimension that focuses on the biosphere and the totality of living relationships to the
self. From a phenomenological ecological perspective any part of existence is
intimately bound into webs of relationship that mean it is meaningless to speak of 'the
self' if by that is meant a bounded entity that exists separately and independently of
these webs (Jardine 2002). The self is intrinsically relational (Levinas 1998; Bakhtin,
1993). I is possible to extend the meaning of 'other' in Bakhtin's architecture of
relationally - 'I for myself", "the-other-for-me", and "I-for-the-the-other" (1993, p.54), to
include existences other than humans.
Further, the choice of what sort of ecological relationships to enact are at root choices
about what sort of a person, what sort of self we wish to strive to become. In the
cultures in which mathematics education is embedded, the self is experienced often as
disconnected from the rest of existence. This is not a hypothetical possibility but one
that was and is part of the everyday experience in other cultures. Sullivan (2009)
contrasts the types of "multilayered and multifaceted reciprocal relationship"
indigenous people have with other beings in their cosmologies including with other
species. Such relationships are not only cultural. Rather they are rooted in material and
energetic exchanges that "affirm reciprocal moral obligations as well as make moral
sense of phenomena that cannot be completely knowable or ultimately controlled"
(p.25). Listening, communication, sharing, encounter, answerability then are not only
found in human-to-human relationships but potentially in all relationships (Sullivan,
2010; Deleuze & Guattari, 1987). The self in such relationships is embodied and
sensuous (Abram, 1997). Yet such relationships are not abstract or universal, the
subject of each is, as discussed earlier, both a unique and once-occurrence (Bakhtin,
1993) and an expression of the totality of relationships. Thus, each self is the universe
knowing itself. The construction of the subject that prevails in mathematics education,
of the sort of selves that are possible or permitted, is disconnected from such
possibilities.
Subjectivity in mathematics education has been the focus of much analysis, particularly
from a poststructuralist perspective (see for example, Brown & McNamara, 2005;
Hardy, 2004; Walkerdine, 1988; Walshaw, 2004). These analyses provide accounts of
the regulated and restricted subjects often produced through the practices of
mathematics education. Implicit in such accounts is an ethical critique of the
consequences of such practices. Here, I consider possible ethically preferable
alternatives. Above, I pointed to the role of affect in relation to ethics. A full discussion
of this is not possible here. Instead, I focus in particular on passion and pleasure in
relation to mathematics education and, secondly, the possibility of creating spaces for
and fostering the ethical self. In relation to both these areas, the work of Foucault is
significant.
10
Passion and pleasure
It is part of the 'common knowledge' of mathematics education that the experience of
mathematics is far from enjoyable for many (cf Bibby, 2002; Boaler, 1997; Nardi &
Steward 2003). Perhaps this has been a significant spur to the development of a
specific sub-discipline in mathematics education research focused on mathematics and
affect. The values of instrumentalist, outcome orientated mathematics education are
utilitarian. Disaffect with mathematics is something not considered important or an
unfortunate burden to be borne in the pursuit of personal goals of gatekeeper
qualifications or school and societal goals of improving or maintaining position with
comparators. Value here is found in outcomes that are separate and disconnected
from the experience of engaging in mathematics itself.
Foucault offers an ethics based on passion and pleasure. He seeks to reclaim passion
from its rejection, in 'civilized' discourses, because of its association with the body and
a mark and potential gateway to madness (Foucault, 1988; Zembylas, 2007). Foucault
sees in passion and affective intensity the possibility of the disruption of regulated and
normalised self (Zembylas, 2007). Although the desire to counter or avoid negative
affect is evident in mathematics education, embracing Foucault's standpoint suggests
putting passion and pleasure at the heart of mathematics education. Such an approach
is found in Heather Mendick's (2006) examination of the gendered experience of
mathematics which draws on queer theory (Britzman 1995) to propose queering
gender and mathematics with the aim of disturbing and provoking pleasure.
Nevertheless, what pleasure might mean in mathematics needs problemetising and
some unpacking. There are already different forms of pleasure found in the
mathematics classroom. Some of these are intentional, for example, the attempt to
sweeten the bitter medicine of mathematics with activities that are intended to be 'fun'
(Moyer, 2001). Alternatively, as Nel Noddings (2005) notes students may feel positive
about grades that they have worked hard for or feel a reciprocal pleasure when they
feel they have pleased their teachers. However, this is different from Foucault's notion
of pleasure as a force compelling action (Zembylas, 2007). Noddings (2005) suggests
that a focus on what students consider they need is not adequate. She emphasises the
importance of the pleasure that comes from learning for its own sake. Where this takes
place collaboratively the pleasure of at least some learners is enhanced (Nardi &
Steward, 2003). However, if mathematics education is to embrace ethics then it must
embrace the importance of learners pursuing their own passions. This may well mean
some not embracing mathematics at all. A concern for pleasure challenges the idea
that mathematics and learning mathematics is necessarily a worthwhile activity (Ernest,
2010).
Ethical self-care
The practices of mathematics education that tend to produce regulated and restricted
forms of subjectivity are instances of, and embedded in, prevailing practice regimes.
Part of Foucault's response to this condition is to promote the practice of freedom
through ethical self-care (Foucault, 1994a) that resists social forces that otherwise
would define subjectivity. Two aspects of this resistance are important in relation to
education. The first is the development of critical faculties:
11
A system of education aimed at preserving and promoting democratic freedom
ought to prepare individuals to recognize such infractions upon personal
liberty as well as to promote the capacity for self-design. This role for
education turns out to be pre-emptive in that the best method for resisting
normalized identities is self-formation (Infinito, 2003. p.58)
The starting point for critique is to recognise the limits of our situation (Infinito, 2003).
Once we have a sense of who we are, what is constructing us, there creates the
"possiblity of no longer being doing, or thinking what we are, do or think (Foucault
1994b, p. 311).
Within mathematics education, the critical mathematics and
ethnomathematics traditions, discussed earlier, identify practices that support the
development of critical faculties and examine mathematics as the product and
producer of social constructions.
Infinito suggests such critiques need modelling by teachers. One way of doing this is
by teachers allowing themselves to be seen as "purposefully incomplete" (Infinito,
p.170). In the mathematics classroom, this supports the practice of de-centering
mathematical authority and for, at least some of the time, teachers and students
working collaboratively together on problems which neither students nor teacher know
the answers to.
The second aspect of resistance is engaging in the practice of self-construction. The
concept of self that Foucault employs is at variance with that proposed by Levinas or
Bakhtin who whilst recognising the importance of the uniqueness of the individual
subjectivity, ground their epistemology and ethics in relation to others. Foucault
emphasises care of the self over the care of others. However, in the practices of selfcare the importance of the role each has in the self-construction of others is recognised.
Infinito (2003) proposes that in education this necessitates the need for appropriate
spaces:
within which to try out alternative modes of being a self-that is a, the type of
safe, experimental environment where individuals can participate in the ongoing production of themselves with and in front of others where they can
be both witness to and resources for the experiments of other selves (p.
168)
Again, as in the discussion of the dimension of the other, the quality of pedagogical
space is important in care of ethical selves. Mathematics pedagogies in which there is
only one or a very limited way to be a learner or to participate in mathematics deny the
possibility of such spaces. More positively, descriptions of mathematics classrooms in
which relationality is attended to, echo the importance of space. Corinne Angier and
Hilary Povey, (1990) posit the concept of "spacious" mathematics to describe not only
a relationship to mathematics - explorative and orientated on enquiry - but also to the
nature of relationships in the classroom. More personable or spacious personal
relationships also change the relationship of everyone in the classroom, teacher and
student alike to mathematics. In particular, they support relationships to mathematics
where there is space for both provisionality and for emotionality.
12
Similarly, Victoria Hand (2012) in a study of the practices of teachers engage in
'equitable mathematics instruction' drew on teacher's description of their practices to
identity the concept of 'taking up space'. Taking up space refers both to space in the
classroom - participation, contributing but also beyond the classroom- quoting one
teacher we hear echoes of Foucault:
it's like, being able to have the tools to say, "If I could do this, I will become
anything, I will get other there and take up my space" p. 238
Jo Boaler (2005) provides a vivid description of what happens where learners are not
permitted or have opportunities to 'take up their space'. Jo Boaler (2005) followed up
adults who had participated, as school students, into her earlier research on school
grouping practices. She found that those who had been taught in sets and through
transmissive closed practices at school tended to be working in jobs that paid less and
requiring lower skills than those of similar socio-economic backgrounds who had been
taught in all attainment groups. One of her interviewees who experienced setting
described the effect as putting psychological prison around them.
Conclusion
The sociopolitical turn (Gutiérrez, 2010) in mathematics education necessitates also a
turn towards ethics. Thinking in terms of different ethical dimensions suggests a range
of sources for mathematics education ethics. Clearly, there are tensions between these
sources. This in turn is a reflection of the different ontological and epistemological
qualities of the dimensions. Nevertheless, considering different ethical dimensions is a
way to simplify the "infinitely complex condition of the moral self" (Bauman, 1993, p.14)
The implications of particular moments in this complex condition for different types of
relationship may be examined. It also supports an ethical praxis that, by distinguishing
different relationships and responsibilities, can help to find paths through the type of
ambiguities discussed earlier. The ambiguity and ambivalence of action and the
distance between action and outcomes mean that praxis involves continual adjustment
and change. Mathematics education that is informed by a postmodern ethical
sensibility will involve less the implementation of a programme for social justice or
equity than of a dance between and within different ethical demands within particular
dimensions and between them. This approach resonates with Foucault's (1994a)
emphasis on ethics as practice, or those who contend that social justice is not a state
of affairs to arrive at but rather a verb, an action and a process (Griffiths, 2003; Roth,
2013).
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