Image source: http://dorothystewart.net/2010/11/26/pipelines-through-paradise/ |
I personally have never been a strong enforcer of learning the proper terminology for mathematical ideas. If a student wants to call it "flipping" instead of "reciprocating," I won't fight it because they're explaining the idea to me in a way that makes sense to them and I feel that terminology just bogs down this thinking process. That being said, terminology has benefits such as saving time and frustration. For example, a student might search, "The little number beside the big number," and spend a fair bit of time locating the word "exponent" before locating the answer to their question about the concept. Terminology is also more useful when we teach the rationale behind it or why a certain convention is used. For example, x ∈ ℝhas a significance if you understand set notation but is a confusing idea out of context. The problem is that the origins to all terms are not always short stories. Instead, I think it's more useful to focus on usage rather than names. For example, it's great if someone knows the words "percentage" and "fraction" but more useful if they are able to apply those concepts in the real world, such as calculating sales tax or dividing a recipe in half. This is a simplistic case but I think it applies more broadly to teaching math as a whole.
I appreciate what Dr. Robin Wall Kimmerer says about the difference in language structure between English and Indigenous languages. As she states in her article, she is not advocating that everyone learn a new language, but instead to shift our focus to respect things in nature instead of taking an arrogant, human-centred view on everything. I think just introducing that idea of considering the animacy of "beings" within our world and speaking in terms of "someone" instead of "something" is a good start in Indigenizing my classroom. This of course would only speak to some students and each person would likely make a personal choice one way or the other, but just by introducing that idea, it opens the students' minds to that perspective. Although I spoke above to how I personally don't emphasize names and focus on ideas in math, Dr. Kimmerer's experiences and the Indigenous perspective of speaking about "beings that are imbued with spirit"(p. 55) using vocabulary for animated beings resonated with me because it reminded me of my culture. For example, my grandmother would be angry with us if we handled books in a rough manner. Books, particularly those that contain some form of instruction, are seen as objects worthy of our respect so while we don't view them as alive, we still acknowledge their importance and are careful when handling them. Therefore, if I actively try to acknowledge of the animacy of beings in my classroom, I believe there will be some students who will resonate with the idea as well or at least understand it, even if they don't fully agree with it.
Very interesting ideas here, Karishma! I agree with you that insistence on standard terminology can get in the way of student understanding -- but that it is also very handy to be able to know the shared terminology in communicating and researching topics. I love your story about respecting books *almost* as if they were animate! It does make a difference in attitude if learners think about other living beings as objects ('what is here') rather than subjects ('who is here'). This does contradict some of the older norms of science (for example, experimentation on animals), but Wall Kimmerer and I would argue that it is time for a rethinking of those aspects of science, for the survival of humans and the ecosystems we rely upon.
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