Among many others goals, I do want to teach physics as a coherent set of ideas, principles, and models, not as a set of equations to be memorized, selected, and manipulated.
So, here’s what I’m working with now.
So with the above goal in mind, I think these directions are working against me. To me, this sounds I’m explicitly asking students to engage in “recursive plug-in-chug” with maybe a sketch to make sure they get the signs right. So, how would I go about improving this?
Here’s my first attempt at writing what I’d want it to be:
I’ve borrowed a lot of this from you modelers out there… you know who you are. And I don’t think these directions are necessarily linear, although maybe I do think that representing the situation early makes more sense, because it guides you to what models or ideas might be useful. I also think the average velocity idea is one of the most important ideas about there, even though I’m not sure it’s a model. Of course, sometimes representing or applying models will lead you to new questions. And asking if a model applies is a question itself. And sometimes you can jump to (3) pretty quickly and end up needing a representation to be your abacus. But the gist is this: Be interested in something, construct representations that will let you see that interesting thing a new way, apply ideas and try to break models. So maybe that’s what the directions should be.
Now, sure, being careful about signs is important (and having equations at your finger tips helps), but it’s not something you “machine” into students. I feel comfortable letting student work (especially with interesting problems, representations, and ideas) be the place where the necessity for and an interest in being careful arise together. See, the first set of directions above pretty much dictates that a “sketch and a coordinate system” will be their representation and that an algebraic manipulation of some equation will be their machinery. There are even some rules to help them figure out which equation(s) they might use (i.e., put questions marks next to unknowns). I think the implicit idea behind such directions is this one: “If we just get students to follow these steps, they’ll be less likely to make mistakes and more likely to arrive at the right answer.” Perhaps a more charitable interpretation is an explicit concern that students need clear directions and scaffolding to learn. This confuses learning and understanding with the capacity to follow directions and be careful.
Lastly, to me, the engagement-distance between “listing and solving for unknowns” and “deciding what’s interesting” is huge, and asking students to “decide what’s interesting” demands of me that I bring them perplexing problems.