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Mathematics Education for ‘All’—As If Children with Disabilities Count

By Jayasree Subramanian 

It was sometime in 2007, when I was traveling in a village in the district of Hoshangabad, that I first felt a sense of alienation as a mathematics educator. The village and its concerns struck me as so far removed from my concerns as a mathematics educator that, for once, I felt an acute sense of irrelevance. I could just not imagine how to begin a conversation about ‘important mathematics’ with anyone in the village. If mathematics is for all, why did I feel a strong disconnect in discussing, for example, how many solutions a polynomial equation would or could have or why Pythagoras theorem is true or irrational numbers exist? Why did I feel totally out of place there? This existential crisis did not arise out of my attempt and failure to communicate ‘meaningful’ mathematics to young adults in the village. Rather, it came out of an instinctive recognition of the fact that in case a young person in the village was drawn to mathematics, his/her only hope would be to get out of the village. Clearly, so much else had to happen to the village – the terrain, the people and their sensibilities had to be transformed – before one could realize the vision of mathematics for ‘all’. This would be the case even for the wealthy farmers in the village. It is not often that one has an opportunity to experience the disconnect between school mathematics and prospective learners as starkly as I did in this case.

Mathematics as a school subject is notorious for being a gate keeper. It is inaccessible to various sections of learners. More than four decades of research has tried to understand the gender difference in aptitude for and achievement in mathematics. There is also a lot of literature on the difficulty that first generation school goers and students belonging to marginalized communities, such as Latinos and African-Americans in the US context, face in coping with school mathematics.  Mathematics, however, has a slightly different relationship with disability. First of all, there is a learning disability associated with mathematics referred to as ‘dyscalculia’ in the literature on teaching and learning of mathematics. Secondly, some percentage of children with disabilities, such as high functioning autism, have been found to be gifted in mathematics (Chiang & Lin, 2007). Some researchers also claim that there is an association between creativity and a predisposition to some form of mental illness (Nettle, 2005). Similarly, there are a few famous mathematicians who turned blind at an early age or later and it is believed that blindness may not be an obstacle for doing mathematics as mathematics is abstract (Jackson, 2002). In other words, a few people with some specific kind of disability could be mathematically ‘gifted’ enough to make significant contributions to mathematics while children with dyscalculia will be marked as having a form of disability precisely because of mathematics figuring as a compulsory subject in school. However, when the state seeks to provide mathematics for ALL, the implication is that mathematics education has the potential to make a significant contribution to the life of the learners. In the context of inclusive education, clearly the belief extends to include those with some form of disability as well.

What mathematics for children with disabilities?

In the context of children with disabilities, the National Focus Group on Teaching Mathematics says,

Inclusion is a fundamental principle. Children with special needs, especially children with physical and mental disabilities, have as much right as every other child to learn mathematics and their needs (in terms of pedagogy, learning material etc.) have to be addressed seriously. The conceptual world of mathematics can bring great joy to these children, and it is our responsibility not to deprive them of such education (NCERT, 2005, pp. 12)

Children with disabilities are expected to join mainstream schools as inclusive education demands that schools should not discriminate against any child on the basis of physical or mental ability. That said, children with disabilities can join special schools if there are any. To understand how children with disabilities configure in our minds as students learning mathematics, let us do a thought experiment. Suppose one enters a special school as a mathematics educator. Is one’s reaction likely to be as dramatic as my experience of visiting a remote village? Is one likely to feel a sense of alienation as a mathematics educator? If one does not, is it because special schools afford more hope for ‘meaningful’ mathematical interaction than schools in remote villages? Or is it because, given that it is a special school, one does not expect to communicate much mathematics? In general, do mathematics educators hope to communicate much mathematics to children with disabilities, whether they are in mainstream schools or in special schools? An honest answer would be a resounding ‘NO’, though one does not expect to hear it.

The recommendations of the experts in the Focus Group is based on a particular belief about what they understand as mathematics and school mathematics in particular; a belief that is shared by all of us whether we are mathematicians, mathematics educators, teachers, or the common public. We believe that mathematics is universal, that it is the language of nature, it is abstract and logical, it can bring great joy to everyone, and that it has applications everywhere. The assertion in the Focus Group report quoted above – “the conceptual world of mathematics can bring great joy” to children with disabilities – is premised on this belief about mathematics and not on any empirical evidence supporting it. Our image of mathematics is almost god like – unique, abstract, omnipresent, and omnipotent. We see school mathematics as a selection from this unique body of knowledge and believe that with appropriate pedagogy and learning materials, everyone can and should learn mathematics. Multiplication, division, percentages, ratio, proportion, fractions, rational and irrational numbers, algebraic equations, factorization of polynomials, measurement and geometry – all these for all children, without discrimination; the only challenge is to figure out how to teach and manage an inclusive classroom. Yet as a mathematics educator, one experiences an existential crisis in one context and in the other, namely in the context of children with disabilities, one faces the invisible student or an absent classroom. Does this have anything to do with our understanding of mathematics?

Traditionally, feminists have provided a systematic critique of disciplinary knowledge. Feminist critique of science is a well established domain now with rich literature spanning over a period of three decades. However, there is very little critique of mathematics from a feminist perspective. Critiques of mathematics as a discipline and, more importantly, mathematics education come from research in mathematics education. These critiques challenge the notion of mathematics as a universal body of knowledge. They argue that different contexts for engaging with mathematics result in different kinds of mathematics. Thus, mathematics produced in the context of work such as carpentry, carpet weaving, architecture etc., mathematics used in everyday life such as marketing, mathematics that figures as a source of pleasure in games and puzzles and mathematics as a pure pursuit of truth are not the same, even though they may have something in common. Moreover, there are different traditions of pursuing mathematics as a discipline.  Many mathematics educators have argued that to ignore this diversity and to treat every other form of mathematics as special and limited instances of the discipline of mathematics, as practiced today in the universities, is an act of appropriation, erasure and misrepresentation of the multiplicity of mathematics. They argue that like music, mathematics is also diverse and evolving. These critiques enable us to recognize that mathematics curriculum development involves values and serves the interest of certain sections of learners more than others. They allow us to raise questions such as ‘whose interest does the existing mathematics curriculum serve in the name of mathematics for all?’, ‘if mathematics education were to serve the interests of learners who are differently abled what kind of mathematics should be taught?’, and ‘if equity concerns are central to mathematics education, could a uniform mathematics curriculum meet the needs of diverse set of learners?’ (Subramanian, 2016).

In order to develop a mathematics curriculum that will be of interest to children with disabilities, the first step is to suspend the belief that all children can learn the same mathematics and encourage research on mathematics education that meets some specific ends for children with specific kinds of disabilities.

References:
Jackson, A. (2002) The World of Blind MathematiciansNotices of the American Mathematical Society, Vol 49, No 7, pp 1246-1251
Nettel, D (2005). Schizotypy and mental health amongst poets, visual artists, and mathematician. Journal of Research in Personality 40 (2006) 876–890
Chiang, H.M & Lin, Y.H (2007). Mathematical ability of students with Asperger syndrome and high-functioning autism A review of literature. Autism Vol. 11 no. 6 547-556
NCERT (2005). Position Paper, National Focus Group on Teaching of Mathematics. Retrieved on August 1st, 2016.
Subramanian, J. (2016). ‘One Mathematics for All: Can it be realized in a Multicultural and Multilingual country?’ in Intercultural Education Special Issue: Intercultural Mathematics Education (Ed) Brian Greer and Swapna Mukhopadyay. Routledge Taylor & Francis Group.  pp266-277

Bio:
Jayasree Subramanian is an Associate Professor in the Azim Premji School of Education, TISS (Hyderabad).  Her PhD is in the area of Algebraic Number Theory in Mathematics from University of Hyderabad. She has been deeply interested in gender, caste and other social justice issues. Her research interest is in the area of Mathematics Education and Social Justice Concerns. Before joining TISS Hyderabad, she was a Fellow at Eklavya (Madhya Pradesh) for seven years and worked in the area of Mathematics Curriculum and Material Development.

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For more stories, read Café Dissensus Everyday, the blog of Café Dissensus Magazine.

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