Mathematics: a Form of Hegemony
We’ve all been there: flunking at math.
We’ve all been there: flunking at math. Well, except if you’re “naturally” good at math since you were a child then I guess it is a different story. But, I’m sure that most people could relate to getting a bad grade at math, being frustrated at math, forgetting the formula, being stuck on one question that makes your head think about it all week, and other good stuff.
2+2 is 4 quick math
It is what drives me to choose social science major in high school — from where I came from, you have to choose between natural science or social science to be your major during high school. My sister was a natural science major in high school. I looked at her courses and assignments which are full of math — there are even 2 courses on math! Then, I think to myself: “I think it’s better to stick to history, geography, sociology, and economy”.
I still remember what I said to one of my friends when being asked why I chose social science as my major. In regards to math, I asked her rhetorically “when will I use all of these formulas anyway?”.
Though ironically, it is during my time in high school that I “fell in love” with math. I’m not good at math but if you ask me whether I like math or not, my answer would be: hell yea.
I always believed that math is universal. It is the language that we could use to communicate with aliens.
Those numbers, formulas, finding x and y, figuring out coordinates in cartesian coordinates, proofing why a triangle is a triangle, and many more look and certainly feel so abstract. It feels that it exists in our minds. But, even though it feels so abstract, it feels good because it gets your brain going. Therefore, secretly, I used to look down on people that don’t like math, especially for the reason that it is useless and not pragmatic. I used to think that those people are missing the point. Math is supposed to hone your mind, not solve everyday problems.
However, I encountered one article — an anthropological article. An article by Everett (2017) explained that there is a language without a number system. Those people are having a difficulty in counting even small numbers
Even though I’ve been in college as an anthropology major for a semester, it really shocks me. It makes me rethink the epistemology of mathematical knowledge. The generally accepted belief is that mathematical knowledge is rational — epistemologically speaking. Simply stated, rationality in epistemology refers to the idea that knowledge stems from reason — not empirical observation/experience (Kleinman, 2013). Kleinman (2013) gave an example that you intuitively know that 5 is less than 6 or that 2+2=4. You don’t need external validity to ensure that you know 2+2=4. However, that is simplifying things.
As stated by Everett (2017), children are actually having a hard time understanding numbers. It is not in our biological nature to be a “numerical creature”, we require culture in order to understand numbers (Everett, 2017). Our capability in understanding numbers would stem from language. It is the numerical system in a language that would allow humans to think numerically. Linguistically, language and human thought are intertwined as stated by the Whorfian hypothesis which is a hypothesis that is generally accepted in linguistic anthropology (Barton, 1996). In short, because of language, we can do math.
Language does not exist in a vacuum. They don’t suddenly appear with their grammar, alphabet, etc. Humans — collectively — constructed them. We agree that the word ‘table’ for example, refers to an object constructed usually from wood, having feet, having a function to place our belongings, and many more. Ontologically, the word or concept of ‘table’ would be dependent on the socio-cultural-historical context of society — especially viewed from the perspective of nominalism (Neuman, 2014). In other words, a language couldn’t be separated from its social and cultural context. Wittgenstein also asserts a relatively same thing that language exists in a social context, hence, the learning of language would be dependent on — fundamentally — social context (that’s why he proposed the idea of a language game) (Kleinman, 2013).
Therefore, because our numerical capabilities are dependent on language and language couldn’t be separated from social context, mathematics — as a discipline and as an understanding — also couldn’t be separated from social context. However, as stated in the beginning, math is usually understood as a universal thing. Math is also usually thought to give a rigid answer, unlike science. Mathematics, especially in the academic circle, stands in this position very strongly — that math is universal, separated from social context, and value-free (Borba, 1990; Fasheh, 1982, Gerdes, 1994; Pinxten, 1994).
However, to think that mathematics exists “in its own world” while mathematics is fundamentally related to social and cultural context would be a form of hegemony and politics (Barton, 1996; Borofsky, 1994).
The study of ethnomathematics — the study of how mathematics is practiced and understood by a particular group of people or, in other words, mathematics in social and cultural context (Barton, 1996; Borba, 1990; Fasheh, 1982, Gerdes, 1994) — have shown that mathematics couldn’t be separated from people. Although mathematics shows things that could be agreed upon, phenomenologically, mathematics serves different purposes, functions, and meanings for different people (Borba, 1990; Fasheh, 1982).
Ethnomathematics differentiates between Mathematics (with the capital M) and mathematics (with lowercase m). Mathematics is the math we traditionally understand — objective, universal, free from culture and value. Therefore, the teaching of math as we know it adheres to the principle of Mathematics. mathematics, on the other hand, is math in a more cultural way. We see math in its relation to society and culture.
Ethnomathematics challenges the arrogant view of Mathematics. Why is it called arrogant? From this perspective, math is reduced to a mere yes or no question. A dichotomy of right and wrong. Another type of math such as indigenous mathematics (mathematics and its meaning for a particular group of people) would be seen as wrong or, at the very least, an imperfect form of mathematics (Gerdes, 1994). Gerdes (1994) also identifies the impact of the Mathematics perspective such as oppressed mathematics which is a phenomenon where there is a mathematical concept but is not considered mathematics because it doesn’t fit with the Mathematics framework.
Epistemologically, the perspective of Mathematics also reduced in which people acquire knowledge. Because math is seen as an objective, cold, and free from context discipline, there’s only one way to acquire mathematical knowledge which is a boring abstract lecture on mathematical formulas and proofing (Fasheh, 1982). However, culture plays an important role in how people can gain knowledge. As Pinxten (2016) suggests that the instrument of people to gain knowledge is varied and the structuralist view has been challenged constantly, especially with the idea that every group has its own worldview that serves as its “software” or “lenses” in seeing the world.
To put it into perspective, Grabiner (1993) shows that the people of Warlpiri in Australia, though don’t have a rigid conception and understanding of mathematics, use numerical patterns in their kinship system. Those numerical patterns would influence how inheritance work in their society. In this case, “math” is used in social and cultural contexts. In addition, Fasheh (1982) adds that in Palestine, there are some mathematics modules created by UNESCO. However, the catch is that those math modules are not created by the people that understand the culture of people in Palestine and Fashes emphasizes that it leads to yet another boring lecture with no purpose and meaning, and worst it does not foster the student’s understanding. Not to mention, the way to understand math (that was explained previously) is also pressured by authority (Fasheh, 1982) and it feels natural, fostering the effect of hegemony more.
Let’s be honest here. The way we are generally being taught about math — which is predominantly those boring lectures — feels natural. It feels that this is how math is supposed to be. We took for granted that math does not serve any pragmatical value. However, it is important to realize that math does serve pragmatical value and more importantly meaning if it’s put in social and cultural context. I think this is why most students feared math.
It is being feared because students face something abstract and cold without any additional information. Mathematics doesn’t serve students to face their problems. Borba (1990) thinks of ‘problems’ as struggles that are in line with students’ interests. It is not struggling in the sense that students are struggling with calculus problems for example. Those are what Borba (1990) called pseudo-problems. Borba (1990) suggests that putting mathematics back in its social and cultural context would help students face their ‘problems’. To help students face their ‘problems’, a dialogue would be needed. Borba (1990) stated that dialogue — which boils down to mutual and active listening — would help teachers to recognize the ‘problems’ of their students. Making education in general and mathematics, in particular, more democratic (Fasheh, 1982). This is also in line with Freire's (2005) conception of education which denies the top-down or what he called the “bank model” of education. By this, mathematics would be seen as not only relevant but also helpful and joyful.
One might ask, how do we come to this state? One answer would be colonialism or a eurocentric approach to mathematics (Barton, 1996; Gerdes, 1994). The Mathematics perspective generally comes from the European tradition of math. Utilizing colonialism and globalization, the European thinking of mathematics is formalized, particularly in Third World countries (Prinxton, 2016). The European approach to mathematics view math as objective, but, ironically, from an anthropological perspective in general and an ethnomathematical perspective, in particular, the European approach to mathematics is also cultural and contextual (Pinxten, 1994).
However, because this contextual view is universalized, it became a problem because it blocked out different perspectives. Fasheh (1982) sees this phenomenon as ironic because mathematics is supposed to help people to think in a diverse way and help them see different perspectives. But the reality shows that mathematics goes in the opposite direction — becoming cold, exclusive, and distant from people.
No wonder people in Third World Countries perform poorly in mathematics. They are being alienated from the discipline, don’t understand the meaning of mathematics, how mathematics could help them, and so much more. Mathematics is a really powerful tool because it helps people to question and doubt. Looking at Gramsci’s hegemony (Borofsky, 1994), in order to maintain the status quo, it makes sense to reduce mathematics to be a banal, cold, and meaningless discipline.
So, do we need to disregard Mathematics altogether and replaced it with mathematics? No. As Barton (1996) suggests, detaching mathematics from its context (Mathematics) does have its merit which speeds up mathematical progression. However, to suggest that mathematics has to be or is supposed to be in that manner, especially in regards to mathematical education, would be a reduction of the essence of mathematics itself.
Blocking out different perspectives of mathematics would not speed up mathematical progression. Anthropology always emphasizes the importance of diversity as an asset (Borofsky, 1994) and diversity of thoughts would definitely help the progress of a discipline, including mathematics. Applying an ethnomathematical perspective to mathematics would foster a contextual approach to mathematics, give mathematics a sense of purpose and relevancy, and give a chance for a more democratic attitude in mathematics (Borba, 1990). I believe, with this, mathematics could be fun and not feared, either by students or by the general public.
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