Genu(re)flections: Mathematics, democracy and the
arts
Dalene
M. Swanson
Universities
of British Columbia and Alberta
Lest we forget: what it means to be
human
In her address at the November 2009 graduation
ceremony of the University of St. Andrews, Scotland, Principal
and Vice-Chancellor, Dr. Louise Richardson, made the following
rather insightful remark in reference to the role of the
university in the mandate of educating (http://www.st-andrews.ac.uk/news/archive/2009/Title,44179,en.html):
In a somewhat unlikely
statement, the German philosopher, Friedrich Nietzsche,
once said: “The most common form of human stupidity is
forgetting what we were trying to do."
What are we universities trying to do?
As John Stuart Mill memorably said in his inaugural address
as Rector of St Andrews in 1867: "Universities are
not intended to teach the knowledge required to fit men
for some special mode of gaining their livelihood. Their
object is not to make skilful lawyers, or physicians or
engineers, but capable and cultivated human beings." Universities
are not here simply to provide raw materials for the skills
economy. Rather, universities generate understanding of
where we have been, where we are, where we might go, and
what it means to be human. The Arts are essential to that
exploration.
Her comment is equally applicable to contemporary
education and modern society more broadly, most especially
in recognition of our new era of neoliberal economic globalization.
More and more standardized, efficiencies-based
and surveillance-driven modus operandi are prescriptively
defining the interests of the individual and collective
in terms of market-driven imperatives in consonance with
the demands of the nation state competing for resources,
means and power on a global stage. Acting in accordance
with ‘(inter)national’ relations of exchange, this dominant
thinking is reflected in the production of fact factories
for the ‘New Knowledge Economy’ through the increasing
trend towards techno-scientistic corporatist economic utilitarianism
in education[1], or rather, ‘learning’ discourses[2].
This functionalism is concomitant with increasing privatization,
standardization, instrumentality and commodification of
curricula and educational environments. It is in this prevailing
(structural) condition that the (ideological) rules of
the game have been set in terms of the (ironic) assumption
of ‘common/global good’ by (uneven) capitalist relations
of production and ‘market forces.’ It is a normalizing
condition pervading all aspects of our lives and is increasingly
foreclosing the public sphere, in Arendtian terms[3], and leaching (imaginative and practical)
capacity and disaggregating political will for resistance.
It instigates the question: in our incremental accommodation
of this general depoliticized “common sense” hegemony,
our slow capitulation to a diminished public space, and
our relinquishing of freedoms even with greater consumerist
“choice” and networked transnational intercommunicative
access, is this neoliberal spread a form of global “political
evil”[4] as Patrick Hayden (2009) asseverates
in drawing on the political thought of Hannah Arendt, or
is it ‘merely’ stupidity on our parts[5],
in forgetting what we were trying to do?
So what are we trying to do? And whatever
it is, or is not, why might it be important? Who cares?
Why should we care, and why might it be important
not to forget, but rather to witness, recognize and remember,
even as this is complicated and tenuous? And further, what
‘appropriate’ ethical action(s) might we explore or be
called upon to support or participate in? …. And,
why are the Arts, in particular, important to that exploration
as Louise Richardson asserts?
Implications and implicatedness: mathematics,
science and society
The sciences, and in particular, the mathematical
sciences have a long history of claiming universal Truth
through perpetuating the myths of precision, objectivity
and certainty. This claim to truth and epistemological
‘purity’ has in the past taken on (almost) theological
significance in its clinical repulsion of the taintedness
and messiness of subjectivity, political bias and the unpredictability
of the human condition. Implicit in this claim to Truth
is the dangerous “dream of the universality of a single
logic” (Smith, 2006). Inevitably as I write this here,
I am caught up, myself, in the very discourse that speaks
of science and mathematics as if they were coherent and
discrete bodies of knowledge, for this non-neutral point
of view disregards the multiplicities of epistemologies
that can be constituted (although perhaps need not be constituted)[6] as mathematical or scientific
through the lived experience of their ontological emergence
in numerous indigenous, contemporary or localized cultures
or contexts geopolitically (See Swanson, 2009). It is the
product of Enlightenment thinking that allows as normal
the constitution of ‘mathematics’ as synonymous with Western
mathematics, and which permits the principles of its recognition
to be deployed in terms of Western orthodoxies[7]. But the problem is even
greater, for such claims to pure, universal Truth and objectivity
have masked cultural and socio-historical bias and laid
claim to epistemological authority through the very process
of such effacement of its human and therefore subjective
roots. This would be an interesting point to note for its
own sake, except that it is a very dangerous narrative
of truth-making because its interest is one of power
and position.
Long considered the “Queen of the Sciences,”
Western Mathematics is deferentially constituted as pre-eminent
in the “social division of labour of discourses” (Bernstein,
2000) in the social domain. Reasons for this are historical
and rooted in the rationalist enterprise of the Enlightenment.
Its epistemological authority amongst the sciences and
other knowledge domains has afforded it the privilege
to speak on behalf of Others, epistemological ‘others’
as well as human ones, silencing voices and behaving
divisively in paying homage to the hierarchy of capitalist
relations as a ‘natural’ condition of being with the
rise of civil libertarianism. In other words, who can
and who cannot have access to mathematics, how it is
interpreted, used, and in whose name it speaks, are both
ideological and invested in power. The verticalization
of discourses in the social domain where the mathematical
sciences assert more ‘credibility,’ voice and power than
say, indigenous perspectives (see Swanson, 2007) or the
Arts is an arbitrary condition invested in agency and
a particular world history, but has become a naturalized
condition, from dominant perspectives, of the doxic order
of the everyday world. In this sense, mathematics and
its associated sciences have participated in the normalization
of unjust eco-social conditions and are implicated in
racism, ableism, gender and ethnic discrimination, and
prejudice of almost every kind (see Swanson, 1998, 2004,
2005, 2006, 2008), yet hidden behind a veil of political
neutrality and universal objectivity: a powerful public
relations front. Thus, it can be interpreted that its
relationship is most often one of “intrinsic dissonance
with democracy” (Skovsmose & Valero, 2001).
In these ways, it can be understood as committing a universalized
symbolic violence (Bourdieu and Wacquant, 1992) on the
marginalized, underrepresented, impoverished and ‘localized’
in contexts glocally, participating in dividing the world
and normalizing these unequal divisions[8].
Yet, global social institutions, or international
policies—whether these reference global or national conflict,
development issues or climate change—genuflect towards
the sciences, especially in the name of the guru of technology.
The accompanying incantations often purpose ‘saving the
world’ or advancing the acceptance of a ‘progressive,’
‘modern’ future as a settled promise of universal ‘rightness’
and global ‘hope,’ conflating the aspirations of individuals
or situated collectives with those of the nation state.
But, the reflections of this state of
affairs can be seen in the education system internationally.
Perhaps more than any other subject on the school curriculum,
mathematics has appealed to notions of a ‘universal language’
in the education of which triumphs technocentric economic
utilitarianism, and in whose differentiated access individuals
are defined in terms of nationalist, and now global, ‘citizenship.’
To be a ‘good’ economically-contributing and successful
citizen for the nation state (and now globally ‘relevant’),
is to be ‘mathematically literate.’ Mathematical illiteracy
is most often constituted as concomitant with ‘failed citizenship,’
vagabondism, a burden on the state, resulting in denied
access to academic advancement and life opportunities for
alienated individuals and marginalized groups within the
nation state. Increasingly standardized mathematics education
curricula across the world, despite ‘learner-centered,’
‘constructivist,’ seemingly-democratic curricular language
that is appropriated and accommodated by this economic
exchange-relations model, propels global neoliberal spread
and rational imaginaries of new iterations of empire, justified
under the banner of ‘upliftment,’ ‘progress’ and ‘modernization.’
The assumed rightness of the current global economic development
agenda is facilitated through the universalisms and technocisms
of dominant mathematics, and mathematics education, practices. In
this sense, current hegemonic mathematics practices have
a poor record of contributing to democratic fora. For the
most part, despite moves in several quarters towards more
‘progressive’ or democratic ideals, the narrowness of mathematics
curricula’s (state-centered) objectives—such as, mathematical
literacy for citizenship towards global competitiveness
and national economic growth; national prestige and global
advantage through scientific advancement; and modernization
and (post)industrial development of the state—in effect,
increase our (political) ignorance and aid our stupidity
in forgetting what other purposes might be worthy of/towards
our (post)humanity. In examining our ethical commitments
towards those purposes, perhaps we may recall what we might
have been trying to do, or what we might do (differently).
At least in the educational arena, as an awakening from
our lethean languor, perhaps this might be in fact to generate
pluralist understanding(s) of where we have been,
where we are, where we might go, and what it means to be
human.
Performing interconnections as a performance
of democracy
Finding a set of paths back
to the purposes that Louise Richardson reminds us of
might well lie in relationships. In the case of Mathematics,
this may lie in its relationship to the Arts (including
Social Sciences and Humanities), to indigenous perspectives,
to society, to history and culture, to language, to ideology.
This may include its relationships to political purpose,
to principles of democracy, to histories, to social justice,
to geo/(bio)politics, to ecological ways of knowing,
to spirituality, … relationships to the interconnectedness
between these, the nodes and interstices, and relationships
to itself and its own defining principles and mandates—reflexivity
in mathematics discourse and practice [9]. I believe,
as a starting point, this means unraveling the discursive
knots while embracing the difficulties and complexities
of these relationships. Beginning to understand implies
a searching—critically, studiously, precisely—through
the sodden rhizomes hidden beneath the heavy soil of
assumptions. It also means never guaranteeing meaning
or settling on a hegemonic singularity of logic[10].
Coming to understand generatively is seeking poetic ecologies
of knowing and filigreed hope. It is about discomfortingly
searching for liminality and the (in)between of things.
It is fostered through pondering, looking awry (Žižek,
1992), embracing difficult knowledge (Britzman, 1998)
and being receptive to the unexpected. It is about claiming
rather than repulsing paradox and ambiguity. It is enabled
through (de)liberating (on) ways of (re)imagining other
pathways, other purposes, other pluralities, and
other ways of being/becoming human[11].
These connections, such as the ones between
mathematics, democracy and the arts, cannot be understood
as natural. They are constituted tenuously
and are the substance of the discursive constitution of
the boundaries of mathematics, of democracy, of the arts.
This is a function of how they are defined and maintained
from dominant perspectives. Mathematics and the sciences,
upholding their authority, police their own boundaries.
It is the strength of the “insulations between discourses”
(Bernstein, 2000) that inhere in power and create silences,
acting to diminish other discourses and weaken voices,
generally common characteristics of mathematics practices.
What constitutes and does not constitute mathematics or
science is a function of agency—savoir and pouvoir, knowledge and power, in the Foucaultian sense.
Mathematics, a saturated discursive practice
(Dowling, 1998) and pre-eminent in the social division
of labour of discourses in the hierarchical
social domain (Bernstein, ibid.) casts a gaze upon other
discourses, fields, and practices and recontextualizes
(Bernstein, ibid.) these practices into its own (Dowling,
ibid.). In this way, mathematics’ connection with the arts
is often a consumptive one, one of appropriation, so that
the uneven relationship is maintained rather than contested.
This is a critical concern for advocating interdisciplinarity,
which often does not address the inequality and contest
the agency in the ‘new’ relationships. In advocating for
connectedness between the arts and mathematics, the relationship
often maintains the patronage towards the arts, which
have been peripheralized by the “strong voice” of the sciences[12].
The same applies to connections with democracy.
Skovsmose and Valero (2001) discuss how in mathematics education
research in general, assumptions are most often made by
researchers that their research objectives are automatically
democratic in principle. This is without any critical interrogation
of whether this holds true or even addresses principles
of democracy directly. Often, assumptions about democracy
are made based on a facile understanding of what classifies
something as democratic even as this is a debated term.
Further, the connections are often superficial where they
exist and may even work counter-logically to the deeper
underpinnings of democracy as a result. An example of this
is some of the ways in which mathematics is used towards
‘democratic citizenship,’ where it is nothing more than
addressing issues of the electoral process—democracy equals
voting, nothing more, nothing less, according to this premise [13]. The deeper ideological and philosophical
meanings of democracy as a political and social condition
are disregarded. Another related issue is that of mathematics’
relationship with social justice. Often, certain initiatives
are taken towards a ‘Mathematics for Social Justice’ approach,
which while most useful in directly addressing social justice
issues through problem-solving, sometimes leave unattended
the structural conditions of injustice in which mathematics
itself is implicated. Its divisive power in the social
domain is left intact. For example, in some instances,
those who do not have access to mathematics paradoxically
do not have access to social justice mathematics, so that
it remains a privileged position for those with the means
to choose to be ‘global citizens’ or social justice-oriented.
(See Swanson (2008), response to Gutstein). Problematic
is the structural conditions of poverty, oppression, ecological
degradation, social inequality, constructed disadvantage
via ‘difference’ discourses (see Swanson, 2004, 2005, 2006,
2008, 2009, 2010a, 2010b) in which mathematics discourse
and practice is implicated in socio-political context.
The ‘postmodern’ trend,
in which the ‘narrative’ and ‘social justice’ turns have
found their moments, have in many instances enabled an
inclusive interdisciplinarity that has opened up options
for considering relationships and interconnections—such
as those between the mathematical sciences, the arts
and aesthetics, and democracy discourses—with more paradigmatic
credibility and freedom. Arts-infused discourses and
arts-based practices have been at the forefront of this
movement. As well, with popular emphases on identity,
otherness, culture, citizenship, posthumanism, postcolonialism
and transnationalism, the new discourses on ‘border-crossing’
and ‘bridging of boundaries’ (see Swanson, 1998) offer
vital approaches to critical engagement with multiple
perspectives, hegemony and power, intersubjectivity,
liminality, and the ‘inbetween-ness’ of things. Greater
focus lies in the agency invested in demarcations and
relationships, centres and margins, dominance and alterity.
The poststructural consideration of how things might
come to be understood as true, rather than whether they
are in fact true or not, honours this shift in focus,
and permits questions about how discourses, events, operations,
disciplines, and so forth, come to be constituted in
one way as opposed to others. Testing the boundaries
of mathematics, a discipline whose borders traditionally
have been rigorously policed, is no straightforward task.
There are always investments and interests in such a
supremacist status quo. Probing for porousness along
its edges through which the unruliness of ‘the margins’
in the form of the arts, for example, or indigenous and
other ways of knowing may find play, or encouraging conversations
about and between them, might be the intention of (post)humanizing
and democratizing a discipline that has formally claimed
objective distance from such subjectivizing. The jury
is still out on whether such commitments serve the interests
of a greater human ethic, but whether this is the case
or not, it is the Arts (in which I am including the Humanities
and Social Sciences) that serve the important purpose
of critiquing the conceits and hegemonies of mathematics
practices and its technoscientistic and economic utilitarianism.
It is the Arts that live in human institutions. It is
the Arts that claim the hope of decolonizing it. As Giovanni
Battista Vico, who lived from 1668 to 1744, Italian philosopher,
lawyer and classicist, once noted:
Mathematics is created in the self-alienation
of the human spirit. The spirit cannot discover itself
in mathematics. The human spirit lives in human institutions.
(x, in Davis &
Hersh, 1986)
The rhizosemiotic (Gough, 2006,
2009) links between mathematics, democracy, and the arts,
are often tenuous, moving and weak ones. But this ‘weakness’
is an opportunity. Rather than cementing and foreclosing
on what those linkages are to mean in a globalized world,
they offer spaces of opportunity for imagining multiple
alternatives, resistances, diverse understandings
and pluralities of possibility.
From Dust to dust: a narrative
In teaching a mathematics methods course
in an arts-based elementary and middle school level
Teacher Education cohort at the University of British Columbia,
I collaborated with the Arts-methods teacher and artist-in-resident,
Dr. Alex de Cosson, in a joint Visual Art—Mathematics project
with our 36 students. As an Art-Mathematics installation,
we aspired to the creation of a Sierpinski Triangle[14], a fascinating fractal geometrical
form in which is embedded wonderful imbricated and self-similar
patterns of patterns, Fibonacci sequences found everywhere
in nature and the cosmos, and magical concepts that play
with ambiguous and anti-intuitive ideas on infinity. Embedded
in the Sierpinski are the reflections of conceptual patterns
from what is often referred to as Cantor’s Dust, exposing
Cantor’s fascination with an ‘infinity of absence.’ Integrating
eco-sustainability concerns, visual art, embodiment, social
and mathematical history, and exposure to non-standard
mathematics curricular ideas, we set out to collaboratively
collect literally hundreds of used, recyclable ‘pop’ cans [15] with which to build
our installation. We planned our construction over several
classes, studying the concepts and collaborating in small
groups over design and implementation. We collaboratively
collected, washed and dried the used pop cans. We acquired
the bottles of glue and glue guns. The project had parallels
in the design of large colourful cardboard tetrahedra that
were constructed alongside the installation of the tin-can
Sierpinski Triangle. Our plan was to put the tin-can Art-Mathematics
installation and adjoining cardboard tetrahedra on display
for all to enjoy in various places around the foyer of
our Faculty of Education building. The huge tin-can installation
was carefully installed near the entrance to the Faculty
of Education for all to see on entry and suitably photographed
for posterity. The student teachers and teachers were delighted
and the Sierpinski installation was striking and satisfying.
There was much discussion about the artistic and mathematical
merits of the project and about issues of creativity, embodiment
and eco-sustainability in pedagogic practice. Discussions
ensued about integrating mathematics and the arts, as well
as about how, through the integrated project, mathematics
might become reconceptualized and (re)constituted as more
accessible, exciting and intriguing through such a project,
especially for students alienated by the often disinterestedness,
disembodiedness and rigidity of traditional approaches
to the teaching and learning of mathematics. Issues of
democracy came into focus in the discussions. From our
perspectives as teachers of mathematics and art methods,
and as expressed by the students to us, the joint collaborative
project was felt to be a wonderful success.
The next day, I received
an early morning e-mail from Alex to the effect that
the Sierpinski installation had disappeared… It was gone….
There were no remains. We were both aghast and set out
to investigate who might be responsible. Whatever could
have happened to it?.... A student working late in the
library had come out into the foyer on leaving to go
home and caught on camera the event. A ‘homeless person’
looking for recycling material to sell at a recycling
depot had wandered through the foyer of the building,
seen the installation, and in recognizing the monetary
value of the tin cans, had systematically deconstructed
the entire installation, leaving with many huge bags
full of recyclable cans. From Cantor’s Dust, to the everyday
dust of the street. The everyday realities of poverty
and injustice in a local community had crept into the
edifices of the ivory-towered academy and had disrupted
any sense of neutrality of education possible. The
lived injustices, entrenched in our societies, articulated
politically with a collaborative project to integrate
visual art and mathematics. The unexpected dismantled
the expected outcomes of curriculum. It evoked questions
about what happens when the dust of the street and the
everyday infuses itself within the dusty corners of the
school mathematics curriculum. For the pre-service education
candidates, the unexpected deconstruction of the installation
that they had constructed in the foyer of the university’s
education building led to pedagogic discoveries about
the political implications of teaching—amongst other
points, that education is always ever a political act.
The need for survival that compelled the ‘street person’
to deconstruct the installation in order to access the
recycled material for monetary gain for his own survival
surpassed the need for preservation of ‘the mathematics’
or ‘the art’ which imbued the structure, from our privileged
perspectives, with ‘value’ outside of a purely economic
one. Ironically, it served as a challenge for the pre-service
teachers to look beyond the pedagogy of the school curriculum
to the political pedagogic curriculum of everyday social
injustice. Through rhizosemiotic play and the pedagogic
experiences of this collaborative Art-Mathematics project,
mathematics, democracy and the arts laid claim to each
other in constituting learning opportunities, but also
in their integral relationship in this project, to meanings
for pedagogy and curriculum beyond the confines of disciplines.
It did so, while bringing to the fore the need for critical
fora to debate and challenge the interests of education
and society, to look deeply and democratically into society
and our vision(s) of the world. It is these critical
fora for which the Arts offer dialogical space and promise
support to sustain public debates and engage political,
human and ecological challenges that demand our attention.
Debates that may help us reclaim the public, the political,
and the human. Ones that help us to witness and remember,
albeit with ambiguity and difficulty. Debates and challenges
that in education go beyond content and curricular specifics,
but that instead help us generate pluralist understanding(s)
of where we have been, where we are, where we might go,
and what it means to be human.
Notes
[1] Ironically, Louise Richardson draws on Nietzsche’s
comment about stupidity while bringing forward her
argument that universities are not there to provide
fodder for the skills economy. The correlation between
stupidity or ignorance and educational functionalism
is strong when we are reminded of Hobart’s (1993)
remark that as standardized, managerial, functionalist
and “technical superiority grows, so does the growth
of ignorance” (10).
[2] Gert Biesta (2005) differentiates ‘learning’
from ‘education,’ bemoaning the fact that the ‘new
language of learning’ heralds a trend towards education
as a marketable commodity invested in economic relations
of exchange rather than something whose purpose and
value may be deeply and intellectually debated in
terms of democratic principles, where trust, violence
and human relationships are necessary features of
such a debate and of education itself.
[3] Chet Bowers (2006) refers similarly
to this effect as “enclosing the (cultural) commons.”
[4] Patrick Hayden (2009), working in the
field of International Relations, and drawing on
the political theory of Hannah Arendt, notes:
Even as globalization shapes the
horizon of current political thought and action, it
does so at the risk of drawing that horizon ever tighter;
it is less certain that the concept of ‘globalization’
continues to express transformative potentials rather
than functioning as a token of the very effacement
of the political. Globalization has become not only
the political foundation of the present, but also the
suspect guardian of the future of the political itself.
… I argue that neoliberal economic globalization is
a form of political evil. (92)
[5] This stupidity is itself an effect and
offset of the political evil of neoliberalism, a
production of ignorance that contributes to a symptomatic
erasure of history, a making unnecessary the historical
in the constitution and vitalization of the human
condition. The apolitical, ahistorical comportment
of modernization permits the ‘forgetting’ and the
stupidity of such forgetting is thus tolerable, hence
an ignore-ing/ance of the necessity of our political/
historical condition in understanding what it means
to be human. I believe that this ignoring and forgetting
is an attributable structuring of neoliberalism rather
than just a side-effect. In conversation with Graham
Giles, he reminded me that Hannah Arendt had commented
that there was no cure for stupidity, referring to
the absence of the kernel of judgment, and that “following
Heidegger, the ‘forgetting’ is precisely what is
forgotten in the ethos of liberal conceit!” (E-mail
communication: April 7, 2010)
[6] I add the important caveat that these
localized, contextualized or indigenous emergences
of lived experience and contributions might not need
to be constituted as ‘mathematical’ or ‘scientific.’
Of course, the performance of the words mathematics
and science carry their own assumptions, and the
principles of recognition that constitute them as
such lie within Western discourses and are viewed
through a particular colonizing lens. The fact that
the activities of many cultures in the past are now
constituted (often, but not always, dichotomously)
as art or mathematics, when no word for art or mathematics
was used to describe them as such in their time and
culture, testifies to the normalizing governmentality
(Foucault, 1991) of Western scientific discourses.
[7] In one sense of this, as Smith (2006)
avers: “What distinguishes the tension in current
circumstances especially for teaching is the fact
that the very question of what constitutes knowledge,
its nature and character, has been posed and answered
for today’s world almost exclusively by Western powers.
This has been the case since the 18th century,
when so-called European Enlightenment philosophers
sought the universal conditions of knowledge in human
reason, thereby conflating and confusing their own
determinations of what is reasonable with the determinations
of everyone else” (xxiii).
[8] In respect of its extrapolation to the
North-South debate, as a normalized and legitimized
logic, dependency on modes of global knowledge that
have been verticalized over local, indigenous or
situated ways of knowing and being, educational systems
in many ‘developing’ country contexts afford little
opportunities for creating traction to assist in
resisting and redirecting the development agendas
set out for them by international agencies, partnerships
and institutions that have an investment in the existing
set of paternalistic social relations.
[9] In reference to what he refers to as
a “political and epistemological crisis” (16), Smith
(2006) avers:
The consequence is that a profound
rupture is evolving between a new, deep social awareness
of the human world’s interconnectedness (and its interconnectedness
to the natural world) while hard-line economistic interpretations
of life are insisting on an older rationality that
relies on exactly the opposite—on the split between
the subject and object, on a conception of radical
personal autonomy, and most disastrously, on a split
between politics (now conflated with economics) and
history. (Ibid.)
[10] This refers to the danger of the dream
of a single logic, as Smith (2006) asserts.
[11] Or perhaps this might
entail rediscovering earlier, indigenous
or localized ways of knowing.
[12] I have often addressed this in discussions
with teacher education candidates in mathematics
methods courses I have taught. I believe that in
our enthusiasm to incorporate art into mathematical
practices in the classroom, towards the asserted
commitment of greater ‘social justice,’ we need to
be careful that it doesn’t become tokenism, or that
the effect isn’t simplistic. It is what I refer to
as ‘bunnies on the borders’ pedagogy, one which makes
mathematics ‘look pretty’ with colourful handouts
that hide the dry instrumentality of the practice,
as with a sugar-coated pill. This practice is often
a manifestation of the teacher’s own fear or dislike
of the subject (more prevalent than what you’d imagine
in elementary and middle school teachers), and unable
to engage with it in any alternative or positive
way, the teacher attempts to hide mathematics’ perceived
‘distastefulness’ from her students by incorporating
‘art’ as a peripheral pretty-making or ‘fun-making’
process.
[13] This is only the case in certain instances.
There is a lot of work being done to democratize
mathematics education practice in schools—street
mathematics, Ethnomathematics, and culturally responsive
mathematics pedagogy are all examples (See Swanson,
2009).
[14] This is a similar initiative to the
one Darren Stanley and Wayne Tousignant describe
in their paper in this special issue, although this
construction is a 3D triangle as opposed to the tetrahedron.
We did construct different sized tetrahedra from
coloured cardboard with different size triangles
cut out and placed on the main tetrahedra. We were
not aware of each others initiatives at the time
of engaging in these projects.
[15] Fizzy drink tin cans, such as Coca
Cola, Sprite, Pepsi. Pop drinks and pop cans are
North American terminology.
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