Thread by @bjbalas

My students in S&P have their first problem set due at the end of this week, so here's some examples of the kind of stuff I want them to work on this week. First, the goal: Practice with dot-products, vectors, trig, and using formulas. Time to calculate stuff! <1/n>

Many of the problems are quite dull: Here are some dot-products, practice multiplying and adding. Here are some trig functions (and inverses) to calculate. Here are two points - calculate the Euclidean distance between them. Hopefully this is re-awakening old skills. <2/n>

Next, I almost always introduce them to the formula for calculating visual angle in one way or another. The easier way to do this is to give them the formula and ask them to explain why it is what it is. The point is to practice reasoning about math and talking about it. <3/n>

The harder version is to give them a diagram with obj. distance and size labeled and ask them to come up with the formula. This is MUCH harder b/c they don't know if they're "allowed" to do things like add lines. The point of this version is to push them to try things out. <4/n>

With the formula established, I usually ask them to use it in some problems. Example: Use the diagram below to see how well their own hand matches these estimates. The purpose here is to practice using the formula, but also to get used to making observations of real stuff. <5/n>

Finally, I ask them to combine tools from the problem set. An example: Suppose you're on a ferry looking at the Statue of Liberty - if I tell you how far away you are from the base, how tall the statue is, and the visual angle the face subtends, how big is the face? <6/n>

You only have two tasks: (1) Use the Pythagorean theorem to find the distance from you to the statue's face. (2) Plug that and the visual angle into our formula and solve for object size. BUT, that's often enough to get students a little stuck in instructive ways! <7/n>

First, many just won't know where to start. Should they use trig functions to find angles? No, but they might try. Second, even if they can use the formula to find visual angle, they may be stumped about how to find object size if they have the angle already. <8/n>

The goal is to (1) encourage them to think about what they are trying to calculate and how to get it, & (2) To ask for help if/when they need it. Making it clear that I *expect* (2) to happen a lot and I really do welcome it is almost more important then the math practice. <9/n>

So that's this week's problems - things will get more interesting soon, especially after tomorrow's Geometric Optics lab day. More on that soon, so stay tuned if you're interested in #visionscience and #STEMeducation! <end>

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