In a recent problem, we talk a lot about frames of reference. It’s something we hear people say (usually, it sounds something like “Well, from my frame of reference…”), but probably don’t think a ton about, until confronted with a problem like this. At this point, I think it’s useful to start with a definition. If you define “frame of reference” you get the following (from Merriam-Webster): “a set of ideas, conditions, or assumptions that determine how something will be approached, perceived, or understood.” What’s really important in this problem is both perception and understanding - learners perceive this problem initially in one way, and then by considering their frame of reference, are able to understand it and find a solution.
The real question, then, is why does it matter to encounter a problem that challenges you to talk about frames of reference? For me, as a parent, and as a teacher (of children and adults), there are a couple of reasons. First, part of the nature of children is that they tend to work from a single frame of reference. It is not easy for a young child, a middle schooler, or even a high schooler to shift their frame of reference, to account for more than one perspective. In fact, many times they may not realize that a different viewpoint or frame of reference even exists. For me, anything that asks us to practice shifting our perspective is a good thing. In this case, the learner has to shift their perspective to see the problem from a different physical vantage point. I have seen, over my years teaching, that this is something that often doesn’t occur to people to do - they’ll consider a problem from one view, get stuck and say ‘‘It can’t be done!’’ when, in fact, it can… you just have to come at it in a different way.
The second reason that this matters is that frames of reference are something that we grapple with, without really knowing it, all the time. Just the other day, my 6 year old asked me why the sun moves around the sky during the day. And I really struggled to find a way to explain (while driving…) that this is just one way to look at it. Generally we think of the way planets move from the perspective of being on the sun, which means that the sun isn’t the one moving, we are, which is pretty tough to explain to a 6 year old. This is a matter of frame of reference. From her perspective, we’re staying still, and the sun is moving, yet, that’s not the only possible frame of reference. Her frame of reference is based in her experience about the world, but isn’t fully accurate, in terms of how science generally talks about planetary motion. I’m still working on a way to help her change her frame of reference to see things from the sun’s vantage point, and us as moving, without all of the props I would have used to teach this to 7th graders.
The problem this plays a part in, for us, is about the motion of a tank, and really boils down to physics, which is rooted in math. But frames of reference aren’t just something that matter in math and physics; they matter everywhere. Frames of reference matter in engineering; can you imagine how bridges or buildings would turn out if the architects and engineers only considered them from one vantage point? Probably not so safe. Frames of reference matter in art too. Artists of every kind try to convey their point of view to their audience, and how you view a piece of art and the reaction you have to it, all depends on your (you know what’s coming, right?) frame of reference. Your frame of reference matters in how you interpret what you read; when children read literature in school, teachers often introduce information about the time period, the author, the world around the story. All of this is in an effort to help children understand the frame of reference of the author or the story and begin to be able to read and think with that perspective in mind. Having experiences that relate to considering the frame of reference, and to trying to understand something by trying a different frame, is a worthwhile experience because it is useful in all areas of life, not just math!
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