Sunday, 8 February 2015

For February 8 - Response - Gerdes

The Gerdes article investigates the politics around mathematics literacy of persons in Mozambique and deals with issues around colonization and the eradication of “indigenous mathematics” (p 138), where an implicit mathematics was disregarded and replaced with rote learning and memorization in schools. Gerdes’ use of cultural methods for teaching geometry involves imposing European mathematics over top of cultural interpretations of geometry (i.e. the use of mathematics in everyday life).

            As a White mathematics educator of the dominant culture, I know I must tread carefully when discussing issues of colonization. Although it is critical to retain aspects of culture in teaching, it would be as oppressive to maintain only a form of indigenous mathematics, as it would be to teach the colonized mathematics curriculum. By this, I mean that reducing persons to indigenous mathematical knowledge and restricting what other mathematics they learn sustains a colonial dominance in the opposite direction. Gerdes’ suggestion is just as problematic, as his imposition of European mathematics to build “cultural-mathematical confidence” (p. 144), as he calls it, colonializes the everyday mathematics and shows that, “See, your mathematics is acceptable and correct in the way WE (White) do mathematics!” I will nod in Gerdes’ directions for briefly mentioning an in-class question that could be used to generate discussion around the choice in use of mathematics, “Which method has to be preferred for our primary schools? Why?” (p 149). This provides the opportunity to explore the ownership of knowledge, which is at the heart of creating change.

By exposing persons to mathematical ideas in “European” mathematics (that is, the current mathematical structure in which gender, culture, race are normatively White), if university education is truly to be the focus (again, White institutions), then we must prepare students for this institution. Building bridges, as Gay and Cole suggest, is also problematic, as the bridge-builder in the connection between indigenous and White mathematics establishes that there, indeed, exists a rift between the two, and hence also owns the divide between the two; I am sure those in Mozambique did not decide that their mathematics were “different” from the White form of mathematics.


But what, then, is the point of teaching ethnomathematics, if we are just to Whiten individuals in their respective institutions? It is then, my opinion that the institution must change. For if the expectations maintained in the institution are dominant and remain unchanged, then teachers will always hesitate to teach traditional ways of knowing. The defensive reason will be, “But you need to know this method for university mathematics”.  The types of mathematics that are decided to be “valid” and “invalid” in a university, as Burton (1995) writes, remains pre-decided and has social and cultural implications that remain ignored due to the “objective” characteristic of mathematics. This falsely marries the content with the interpretation, the latter of which is not objective.

2 comments:

  1. The issue of colonization and how it affects indigenous education has long been discussed, mainly for the numerous negative consequences that are associated with it. Indeed, most often when a land is taken over by a civilization, it is not just the physical land that is lost, but much of the culture as well.

    I immediately thought of the age of Jacques Cartier, John Cabot, Samuel de Champlain and the other European explorers who traveled the lands that are now Quebec and Ontario. While there are many atrocities associated with the contact between Europeans and the Aboriginal people of what is now Eastern Canada, there are some interesting ethnographic events that took place. For example, when Jacques Cartier first met the chief Donnaconna, in order to communicate and trade with the First Nations of the area, Donnaconna and his sons went to France to learn the language/customs, while people from Cartier's company stayed and lived with the Aboriginal groups. They were often referred to as the "coureur des bois". By no means were both parties whole-heartedly in agreement with this arrangement, but it allowed both cultures to learn from each other in a way that, for the time, didn't result in the loss of indigenous knowledge, mathematical or otherwise.

    Unfortunately, this small act was not representative of what has happened across Canada, or the world for that matter. With new education curriculum being introduced, governments are attempting to recognize indigenous cultures, however any knowledge that we learn is still within the modern education system, which does not necessarily reflect that values of Aboriginal groups. While it is impossible to change the past, hopefully we can learn from it. As different cultures work together, we must recognize that there is no single education system, or way of teaching that works best for all people. In order for societies to advance, we must put aside petty differences, and be willing to accept that our traditional way of learning and teaching may not always be the best way.

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  2. Is the primary purpose of elementary and secondary schools to prepare students for a university degree? About 6% of the world's population hold a university degree. In 2012, about 20% of Canadians over the age of 15 had a university degree. I have the mindset that the purpose of public schooling is to help build a society of critical thinkers. I agree that it is valuable to recognize the mathematics of indigenous cultures, but I also agree that taking a total shift to indigenous mathematics is just as detrimental as only considering European mathematics. Suppose that a student from a particular indigenous culture wishes to pursue a university degree which he or she cannot pursue in their home country. If they do not have the experience in the European mathematics studied at the university, it would be an even more challenging transition than it initially was. Education should give students the opportunity to pursue whatever endeavor they wish to choose, and there are as many types of students as there are endeavors in the world.

    I'm brought to moving away from mathematics and considering globalization; a topic we discussed last class. The evolution of a global business model called for a "global language." Although French almost won the race, English ended up being chosen as the "language of business." Do I believe this was the best choice? Probably not. Spanish and French are much more beautiful languages to read and listen to in my opinion, but that is just aesthetics. I suppose that European mathematics could be considered the analogue. What is unfortunate though is the loss of the "native" mathematical language. There needs to be a balance; without balance, we as educators may loose opportunities to engage in rich mathematical conversations with our students.

    I question the last quote of this paper regarding an "objective" nature to mathematics. What is exactly meant by the word "objective"? I certainly do not believe mathematics to be an objective discipline at its core, but I do think that it is taught in an objective manner in schools. There is a belief in many students that mathematics cannot be a creative process, something which I hope to look into in future research. There is a correspondence with creativity and human efforts, something I think is lost in mathematics classroom. If the objective nature of mathematics could be reduced (but not eliminated!), perhaps we could see creativity make its way in.

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