Philosophy of Ethnomathematics - Barton (2012)
The philosophical standpoint of ethnomathematics seems to be very dissonant. That is, Barton presents several points of view on the philosophy of ethnomathematics, some of which have very different perspectives. In Barton’s paper (2012), he mentioned that a premise of ethnomathematics is that it rests on the concept that there can be more than one form of mathematics. For example, one belief that is that mathematics is a circle of self-justification. That is, mathematicians believe that math is true since bridges can be built without falling down. Since it works, it must be right. As such, Barton argues that describing the perception of its usefulness as a justification, does not make mathematics true (Barton, 2012).
Another philosophical position, as outlined by Barton (2012), is the idea that throughout history there must exist a time at which mathematics is true at that particular moment. In addition, if that mathematics is true, then it too must explain previous views. As such, mathematics is continually changing and historically relative. As history is culturally bound, so too must be mathematics. However, there exists a problem in this philosophy: if it is true that each historical time frame exists true mathematics that explains prior mathematical theories, then it implies that there is one direction that mathematics is heading – towards an objective conception. However, as mentioned above, ethnomathematics states that there exists many progressions occurring at the same time in different directions (Barton, 2012).
Barton also discusses Neo-realism as another perspective. This theory implies that the existence of mathematics exists outside of culture. As such, whenever different conceptions arise, they must be heading towards something that is “pure and culture-free” (Barton, 2012). This implies that mathematics within a culture is a “shadow of the ‘real’ mathematics”. In other words, cultural mathematics is a “false” math, only mirroring something that is truer that exists outside of the culture. As such, when cultures have differing views on mathematics, only one culture will have a more “true” sense of what mathematics is (Barton, 2012).
A few past philosophical perspectives as mentioned by Barton (2012) debate the issue of mathematics being true versus being discovered. Barton mentions Wittgenstein’s perspective in which mathematics exists only because people talk about it. For example, negative numbers did not exist until they were discussed. This begs the question: were negative numbers invented to make prior mathematics true or were they merely discovered? Another problem is the usefulness of mathematics. That is, if mathematics is a “human creation, then how is it that mathematics corresponds to our world so well, and so useful in it?” (2012). Barton parallels this with evolution in the sense that mathematics grows, changes, and supersedes other ideas. Thus people all over the world use it for its convenience. It then passed on from generation to generation, changing to adapt what is most useful.
Barton offers an “alternative perspective” in his article. In this perspective, he provides an analogy of two cultures working on a model separately. When they come together, their models are different. They try working with their respective models as long as they can, until they either, create a new system altogether, or use a model that is relies on one more heavily than the other. Barton claims this as an “internal process, a human process, a cultural process” (2012). As such, this perspective demonstrates the cultural building of mathematics as one culture in collaboration with another to developed a better, easier, and faster method than working alone.
Overall, the philosophical perspectives mentioned by Barton (2012) demonstrated a wide range of views. Each perspective illustrated its own meaning of ethnomathematics and how it came to be. In terms of equity, this paper demonstrates how each culture provides their own form of mathematics. While working together, we can develop a more succinct, effective, and efficient method of mathematics. As mentioned by Barton (2012), in his alternative perspective, working together is where we can hope to grow.
Another philosophical position, as outlined by Barton (2012), is the idea that throughout history there must exist a time at which mathematics is true at that particular moment. In addition, if that mathematics is true, then it too must explain previous views. As such, mathematics is continually changing and historically relative. As history is culturally bound, so too must be mathematics. However, there exists a problem in this philosophy: if it is true that each historical time frame exists true mathematics that explains prior mathematical theories, then it implies that there is one direction that mathematics is heading – towards an objective conception. However, as mentioned above, ethnomathematics states that there exists many progressions occurring at the same time in different directions (Barton, 2012).
Barton also discusses Neo-realism as another perspective. This theory implies that the existence of mathematics exists outside of culture. As such, whenever different conceptions arise, they must be heading towards something that is “pure and culture-free” (Barton, 2012). This implies that mathematics within a culture is a “shadow of the ‘real’ mathematics”. In other words, cultural mathematics is a “false” math, only mirroring something that is truer that exists outside of the culture. As such, when cultures have differing views on mathematics, only one culture will have a more “true” sense of what mathematics is (Barton, 2012).
A few past philosophical perspectives as mentioned by Barton (2012) debate the issue of mathematics being true versus being discovered. Barton mentions Wittgenstein’s perspective in which mathematics exists only because people talk about it. For example, negative numbers did not exist until they were discussed. This begs the question: were negative numbers invented to make prior mathematics true or were they merely discovered? Another problem is the usefulness of mathematics. That is, if mathematics is a “human creation, then how is it that mathematics corresponds to our world so well, and so useful in it?” (2012). Barton parallels this with evolution in the sense that mathematics grows, changes, and supersedes other ideas. Thus people all over the world use it for its convenience. It then passed on from generation to generation, changing to adapt what is most useful.
Barton offers an “alternative perspective” in his article. In this perspective, he provides an analogy of two cultures working on a model separately. When they come together, their models are different. They try working with their respective models as long as they can, until they either, create a new system altogether, or use a model that is relies on one more heavily than the other. Barton claims this as an “internal process, a human process, a cultural process” (2012). As such, this perspective demonstrates the cultural building of mathematics as one culture in collaboration with another to developed a better, easier, and faster method than working alone.
Overall, the philosophical perspectives mentioned by Barton (2012) demonstrated a wide range of views. Each perspective illustrated its own meaning of ethnomathematics and how it came to be. In terms of equity, this paper demonstrates how each culture provides their own form of mathematics. While working together, we can develop a more succinct, effective, and efficient method of mathematics. As mentioned by Barton (2012), in his alternative perspective, working together is where we can hope to grow.