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ABLEISM IN MATHEMATICS EDUCATION: IDEOLOGY,
RESISTANCE AND SOLIDARITY
Rossi D’souza
Homi Bhabha Centre for Science Education
I attempt to sketch out a comprehensive view of how Ableism functions in
Mathematics Education. Ableism is not simply the injustice faced by disabled people
but is also the privileges enjoyed by non-disabled people. While Ableism constructs
some students as having “learning disabilities”, most students as “normal”, it also
constructs students as “gifted”. Ableism functions as an Ideology where “inclusive
education” serves as its “sublime object” that restricts possibilities for introspecting
contradictions within mathematics education. As a mathematics teacher in a school
for blind children I observed that oppressed people including school students are
quite politically aware and conscious about the forms of oppression they live
through.
INTRODUCTION
Ableism is often described as though being synonymous with the discrimination
faced by people with disabilities. At MES8, I (D’Souza, 2015) had also spoken about
Ableism as a form of oppression faced by people with disabilities. I had then
advocated then advocated the definition of Ableism as presented by Campbell (2001):
“A network of beliefs, processes and practices that produces a particular kind of
self and body (the corporeal standard) that is projected as the perfect, speciestypical and therefore essential and fully human. Disability then is cast as a
diminished state of being human.” (pp. 44)
Such a conception of Ableism is similar to the idea of deficiencialism coined by
Renato (2015) in his thesis titled “Deficiencialism: an invention of deficiency by
normality” in which he cites as an example of, “normal people defining abnormal
people”.
But there’s more to Ableism that most discourses do not sufficiently convey. For
example, although “deficiencialism” aptly connotes having less (than “normal”), it
says little about what “having more” could entail. The concept, “Gifted” carries this
connotation of “having more”, but is unfortunately celebrated as an individual feat,
even though giftedness (being blessed with more) can exist only in relation to
deficiency (being cursed with less). So if we speak of giftedness as being inherent
(not a socially constructed problem), we imply that so is deficiency (D’Souza 2016b).
Skovsmose (2016) discusses how “difficulties (that) arise from the relationship
between Braille and mathematical symbols” (p. 3). However, we should relate these
difficulties to our privileges, that arise from the relationship between dominant
languages like English and mathematical symbols. “Mathematical symbols” does not
mean visual-English symbols.
In relation to caste, Somwanshi (2015), argues how, that “caste is a structure that
includes ‘everyone […] (and) oppression can’t exist without someone getting undue
privilege”. In a similar sense, Ableism is a structure that includes everyone, not just
the disabled people. It is not just the oppression of disability, but it is also privilege.
Finkelstein (1998) argues how “Human beings are by nature, frail animals.” and that
unlike the natural world, “In the social world, however, experience in managing
human frailty has provided us with an amazing cornucopia of interventions that make
possible the susrvival of those possessing the greatest physical and mental
deficits.”(pp. 29)
I would actually problematize the term “able-bodied” and replace it with “enabled
bodied”, since “ability” among human beings is as social as disability!
In education and cognition, it is quite acceptable to state and rationalize the claim that
blind children also “visualize”. Arcavi (2003) argues how “Vision is central to our
biological and socio-cultural being.” and locates the experiences of even blind people
as a visual experience by stating that “visualization may go far beyond the
unimpaired (physiological) sense of vision.” Making vision central to learning
mathematics, he states as though it is a good thing that, “the centrality of
visualization in learning and doing mathematics seems to become widely
acknowledged. Visualization is no longer related to the illustrative purposes only, but
is also being recognized as a key component of reasoning (deeply engaging with the
conceptual and not the merely perceptual), problem solving, and even proving.”
Thus is becomes rather evident that, similar to the idea of deficiencialism, sighted
people define the visually imparied. But further, they (we) also describe the
experiences of blind people through the perspective of sight.
Such narratives have severe implications especially for blind students learning
mathematics. When the discourses surrounding mathematics define it as a visual
activity, one the hand it constructs blind students as naturally and biologically less
capable of pursuing mathematics, but on the other hand, it constructs (and privileges)
sighted students capable of visual reasoning, as being more capable of doing
mathematics.
In such discourses, although there isn’t a direct defining of deficiency by normality,
there underlies an assumption of what constitutes “normal” thus implying, as a
corollary, the definition of the deficient. The object of the definition is thus in the
absence.
The dominance of visual representations of mathematical ideas should not be taken
for granted as the norm, but rather as contradictory to the claim of mathematics as
being about ideals and abstractions.
Ableism and Ideology
Conservative approaches towards addressing social, political or educational crises
often ignore systemic contradictions, and present a stereotypical narrative that locates
the source of the problem on a group of people.
In mathematics education research too, we ignore contradictions within what we
understand as mathematics education, and tend to blame, for example, “teachers who
passively follow the traditional rote learning method”, “students with special needs in
mainstream schools”, etc.
Lundin (2012) presents two characteristics of, what he calls as, the standard critique
of mathematics education. The first characteristic involves, taking for granted what
mathematics knowledge is, how it is formed, and how it can benefit its bearers. He
further states how such knowledge could be actively discovered or constructed by
learners through meaningful and realistic problems. And such knowledge is assumed
to be beneficial for self and society. The second characteristic of the standard critique
involves describing school mathematics as boring, mechanical and based on
memorization of facts and algorithms.
The standard critiques generally imply that with better teaching methods, and with
assistive tools and technologies, the problem will be solved and mathematics will be
accessible for all. It thus calls for a reform in the same direction.
However, by ignoring the contradictions within mathematics education, the mere
focusing on better teaching approaches is doomed to failure. Lundin thus concludes
that such “a path is a dead end and we need to look for other ways forward.”
While presupposing a nature of mathematics from a visuonormative perspective, even
(teaching-learning) experiments on visually challenged students become problematic.
Inclusive mathematics education has often been not about real students. The
understanding of mathematics and blindness by sighted educationists are rarely
developed through authentic engagement with blind people. And even if it is, it is
often to teach them mathematics or to test the feasibility of their technologies. Their
learning is often derived from their own experiences in learning mathematics in a
visual manner, enjoying the visual mathematics, but projecting it as accessible for all
by attempting to fix the “symptoms” of mathematics by developing technologies and
pedagogies for “the blind student”. But this too does not “fix” the problem.
Visuonormativity in mathematics, which serves to (in)validate what counts as
mathematics operates to prevent mathematization even before the students come into
the picture. And even when students are encouraged to construct their own
mathematical ideas they are actually made to construct the acceptable mathematics.
Mukhopadhyay and Roth (2012) point out that:
Even though constructivist theory emphasizes the personal construction of knowledge,
actual mathematics education practices generally aim at making students construct the
“right”, that is, the canonical practices of mathematics—not realizing that for many, this
may mean symbolic violence to the forms of mathematical knowledge they are familiar
with, and that the standard processes typical of mathematics education contribute to the
reproduction of social inequities. (p. vii)
“The blind student” thus serves as an ideological figure created in an attempt to fix
the contradictions in the ideology of curricular mathematics education that is on one
hand abstract and idealist in discourse, but “visual” or rather, occularcentric in
practice. Thus, every attempted solution to the problem if constructed through the
lens of vision cannot solve these, as Lundin mentions, “malfunctions ...ultimately
created by mathematics education research itself.”
However, as mathematics is very much linked to schooling and education, such
contradictions are easily dismissed through the narrative of “education for all” and
“ICT for teaching mathematics to blind children”.
Building up from Žižek's (2008) ideology critique, Pais and Valero (2012) show “how
“mathematical learning” has become the sublime object of the field's ideology and, as
such, a stumbling block in the process of reflexivity”
The exclusion of blind children legitimized through the process of failing (verb), are
generally addressed through making better teaching methods. But this exclusion is in
fact a “symptom” of the ideology. In the words of Pais and Valero (2012), we need to
“posit them as a window into the entire contradiction of schooling” and curricular
mathematics.
Ableism in conscientization?
Another aspect of Ableism is in addressing disability with the assumption that
oppressed (disabled) people have a false consciousness about their lived reality and
need the help of politically conscious sighted educationists to help them liberate
themselves. For example, Freire (2005) speaks about the oppressed people in the
following manner:
Submerged in reality, the oppressed cannot perceive clearly the “order” which serves the
interests of the oppressors whose image they have internalized.
While there is a lot of truth of the statement, it often translates into a call for a certain
kind of intervention that locates the people as lacking a political consciousness. This
is generally coupled with the researcher’s taking mathematics knowledge for granted.
With an already preconceived notion that the oppressed people have a false
consciousness, we tend to overlook and disregard their political tools and political
consciousness. And if it is necessary to further conscientize the people, it is necessary
to begin from, and maybe even learn to use their political tools from whence a
solidarity can develop.
Although, to a large extent false-consciousness does operate among oppressed
people, approaching oppressed people with the lens of false-consciousness, is
problematic.
While we have critical mathematics, Freirean pedagogy and Giroux as political tools,
the oppressed people too have a political theories of resistance and empowerment.
While initially the oppressed may come across as having a false-consciousness, it is
possible that they do so only in the presence of the privileged researcher, who is from
the group of oppressors.
For example, in my course of my teaching mathematics in the blind school, it was
only after three years did a teacher from a marginalized background speak about
being discriminated by some school authorities due to her caste. The fact that I was
personally quite close to the school authorities (owing to my privileged location)
definitely contributed to her not feeling like talking about caste to me. But when she
did speak about caste, she would cite Ambedkar in her narrative about knowledge and
empowerment. She too would say how she would not criticize the school authorities
since doing that could threaten the space (which was achieved after a long struggle)
where the children interact with each other. Some students too were rather politically
conscious about their location. But would of course not be open about it in front of
rich visitors who were potential donors.
In the context of mathematics education, for example, in MES8 I had cited examples
of one of my blind students raising the question, “If mathematics is all in the head
then why is there an emphasis on the paper and pencil?” Another incident I had cited
was of when I asked my students what was their most difficult topic in mathematics
to which they replied, “Steps”. They could solve mathematical problems, but had to
show all the in-between steps on paper.
I had presented these and other incidents as examples of the injustice faced by
students. However, it was wrong on my part to locate these episodes within the
framework of only injustice. The students were in fact asserting themselves as
mathematics doers who were conscious of having their form of mathematics
invalidated were aware that their right to self-determination in mathematics was
being denied.
I share more recent incidents. I began a discussion on numbers with a group of 10
(visually challenged) students (ages 11-19), seated in a circle on the floor. Through
the course of discussion the concept of odd and even numbers came up. So I asked
how to characterise numbers as odd or even. In the beginning, a number of students
agreed that those numbers which could be evenly divided by 2 should be categorized
as even (eg. 2, 4, 6,...) while those that could not, as odd (eg. 1, 3, 5,...). When asked
about the number zero, all seemed to arrive at a consensus that zero is both odd as
well as even. The justification was that zero leaves no remainder when divided by 2,
hence it is even; however, we cannot divide zero by two since we have nothing to
divide. Hence, zero is odd. During further discussion, one student named Faizan
raised his discomfort with including zero as an odd number. He argued, that numbers
have the property that “odd + odd = even”; “even + even = even”; “odd + even =
odd” and “even + odd = odd”, for all natural numbers. Based on these properties he
defined odd and even numbers. During a further course of our discussion, the number
-4 turned up. On asking whether -4 is an odd or even number, Faizan stated that
“before deciding that, we need to know where did these numbers like -1, -2 come
from? i.e. there has to be a reason. For example, when we found numbers that could
be divided by two, we called them even and those that could not be divided, as odd.”
As we would continue the session, he interrupted, saying that “when we visited the
mall, the lift had numbers -1 and -2 to indicate the upper and lower basement.”
The discussion that followed surrounded the need to conceptualize negative numbers.
In between, Faizan interrupted stating that the idea of having negative numbers is
very old, while malls with basements are comparatively new. He later on
hypothesized that maybe during the Harappan civilization building structures which
had some sort of basements could have given rise to the concept of negative numbers.
The discussions continued with other hypotheses and examples that led them to
conclude that it makes more sense to categorize -2, -4, … as even numbers so that it
fits into a continuous pattern of alternating even and odd numbers whether read
backwards or forwards. I wrote about the above incident in a publication D’Souza
(2016a).
But a few days later the students would again choose to dismiss zero as an even
number, since zero had a property different from other even numbers - “If you kept
dividing an even number by 2, you’d reach an odd number. This does not work if zero
is categorized as even.” This contradicted my claim of zero being just another even
number. (D’Souza 2016b)
This incident needs to be located within a context. The NCERT[1] Class VI
Mathematics textbook introduces the concepts of odd and even numbers in the
following manner:
“Even and odd numbers
Do you observe any pattern in the numbers 2, 4, 6, 8, 10, 12, 14, ...? You will find that
each of them is a multiple of 2.
These are called even numbers. The rest of the numbers 1, 3, 5, 7, 9, 11, ... are called odd
numbers.
...
Fill in the blanks:
The smallest even number is _______.”
Mathematical ideas are presented as facts. Even though questions are posed, the
“correct answer” is decided by the book. The need for talking about standard, current,
accepted definitions never comes out. This essential fact that definitions are modified
by people depending upon their need for mathematical ideas, is hidden. Such a form
of introducing mathematical ideas may lead a researcher to hypothesize (and
consequently find evidences) that such a textbook would lead students to passively
accept the content as fixed and unquestionable, which are to be memorized and
applied, and which justifiably decides their fate. And this would be true in a
significant number of cases. But despite the fact that mathematical concepts are
presented in such a canonical manner, the students would, to some extent, freely
redefine concepts. And in doing so would resist the ideologies.
Final words
My argument is not to mean that our role as sighted privileged people is to do
nothing. I think that our role is to acknowledge how we are privileged by structural
oppression and that the oppressed too have their means of resistance. As mathematics
educationists we should look at teachers, students as activists and comrades rather
than mere receivers of political consciousness, in a joint struggle against structural
oppression. They are activists. Their activism just needs to be nurtured “and that the
educator must [sic] himself be educated”.
I am currently exploring whether Ideology is an appropriate framework to analyse
Mathematics education from the perspective of Ableism, and what could that entail.
Ableism which needs to be distinguished from Disability requires a deeper theoretical
understanding from a perspective of both philosophy and social justice. Without
addressing the philosophical aspect, our social justice approach may just be futile.
But the resistance will continue with or without us. And we need to be open to the
possibilities that the oppressed are in fact resisting us as well, and quite justifiably so.
If mathematics education does not lead to a direction towards liberation then we need
rethink why we teach mathematics in the first place. We need to ask whether we use
mathematics to arrive at a more just society? Or are we using the narrative of social
justice to sell our mathematics?
NOTES
1. National Council of Educational Research and Training is a governmental body that provides consultation the the
Indian Government in academic matters related to school education.
REFERENCES
Arcavi, A. (2002). The Role of Visual Representations in the Learning of
Mathematics Educational Studies in Mathematics 52(3), pp. 215-241
Campbell, F. (2001). Inciting legal fictions: Disability’s date with ontology and the
ableist body of the law. Griffith Law Review, 10(1), (pp. 42-62)
D'Souza, R. (2015). Challenging Ableism in High School Mathematics. Proceedings
of the Eight International Mathematics Education & Society Conference, Portland
State University, Oregon 21-26 June 2015 (pp. 427-440)
D'Souza, R. (2016a). Where do/did mathematical concepts come from. For the
Learning of Mathematics 36(1), 25-27.
D'Souza, R. (2016). Ableism and the Ideology of Merit. For the Learning of
Mathematics 36(3), [in process].
Finkelstein, V. (1998). Emancipating Disability Studies. The Disability Reader. NY:
Continuum International Publishing Group
Freire, P. (2005)[1970] Pedagogy of the Oppressed, 30 th Anniversary Edition. NY:
Continuum International Publishing Group
Lundin, S. (2012) Hating school, loving mathematics: On the ideological function of
critique and reform in mathematics education. Educational Studies in Mathematics
80(1), pp. 73-85
Marcone, R. (2015). Deficiencialismo: a invenção da deficiência pela normalidade.
[Deficiencialism: An invention of disability by normality.] Unpublished doctoral
dissertation, Universidade Estadual Paulista, Rio Claro, Brazil.
Pais, A., Valero, P. (2012) Researching research: mathematics education in the
Political. Educational Studies in Mathematics 80(1), pp. 9-24
Skovsmose, O. (2016). What could Critical Mathematics mean for Different Groups
of Students? For the Learning of Mathematics 36(1), 2-7.
Somwanshi, G. (2015). How can we exclude the storyteller from the story being told?
Round Table India. Retrieved from: http://roundtableindia.co.in/index.php?
option=com_content&view=article&id=8135%3Ahow-can-we-exclude-thestoryteller-from-the-story-being-told on 25th September 2016
Žižek, S. (2008) [1989] The Sublime Object of Ideology. NY: Verso