In her conclusion, Asher states
Geometric and then algebraic representations of physical systems have been the hallmark of modern science. The linkage is so tight it is hard to conceive of the study of physics without the involvement of mathematical ideas and mathematical descriptors... these discussions have included speculation on whether this is the nature of the universe, or the nature of the human mind, or simply the scientific tradition of Western culture. (pg. 366)This is certainly not the only occurrence where a people without knowledge of western mathematics have performed amazing feats of engineering (ancient structures like Machu Pichu and the Pyramids come to mind). Western mathematics has found many efficient and effective ways of describing phenomenon, but this is really only one 'way of knowing' how the world around us interacts, It's interesting in the reading to understand how an isolated culture has used very intense powers of observation to solve the problem of navigating around complicated waters. It's also interesting to consider how these ways of gaining knowledge result in a different world view.
The Marshall Island stick charts which incorporate math ideas into navigational knowledge are remarkable creations. Because these sticks model and map the physical world with mathematics, I associate them with a person's mind map of math ideas. Just like a stick chart which helps the Marshallese travel around oceans from one point to the next, a mind map allows a math learner to produce many different strategies to guide him/her from the start of a math problem (the starting point of a sailing voyage) to the end (the destination of the voyage).
ReplyDeleteHow a math strategy (like the Marshallese navigational plan) is developed and implemented depends on the individual's cultural characteristics and learning experiences (like the Marshallese cultural traditions and sailing experiences). As the learner implements his/her problem-solving strategy, he/she needs to have an overall mental structure of math concepts (like the structure of data in the stick charts). During the problem-solving process (like a sailing course), he/she may face difficulties (like storms encountered by the Marshallese) and deal with them confidently (like the Marshallese fighting for survival). When the learner sees the relationship between certain concepts (like the Marshallese finding a way to defeat the storms), he/she will arrive at the right strategy for solving the problem (like the Marshallese reaching the destination).
I always love examples like this. It's amazing what people can do, and there certainly are further similar cases that remain largely unexplained. Does the author make any suggestions for how this research might be used? In what other directions it could go? I'd conjecture it could be a compelling case for illustrating to students that there is more than one way of solving a problem. So often students come shackled with the myth that math (or problem solving in general) can only be done one way.
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