ConvergeDiverge

Today in non-major, algebra-based physics we went over the fairly classic problem of determining which will win a race down a hill, a sliding block or a hoop, cylinder, or solid sphere? I like working through this problem because it’s a great way to show students the value of not plugging in numbers too early, but rather let the equations play out so that you whittle the problem down into what really affects the difference in answers between all the options. It’s also a nice example of thinking about a distribution of initial energy; in this case, the object will go slower when some of its potential energy gets converted into rotational kinetic energy. The object that has the least amount of energy going into rotation (or none, in the case of the sliding block) will have the most available to go into its translational kinetic energy. And that will be determined by the objects’ moments of inertia.

Everything was proceeding like it has in years past when I’ve taught this section, but then a question came up: should we account for friction? One student in particular noted that he thought that there had to be friction present in the rolling objects’ case, even if you said the sliding part was frictionless. And for the conservation of energy equation to play out, you really did need to include it.

I’ve got some ideas, but I want to ask  you all – what do you think? Part of me feels that this is connected to an oddity I see in a lot of my non-majors, in that they are always wanting to think about friction, air resistance, etc. (Compare that to my physics majors, who in today’s Matlab class were very pleased to not account for air resistance in a model we coded for hitting a baseball a certain distance.) I’ve been thinking a lot about why my non-major students are so attached to the ideas of friction and drag. In class we talk a lot about setting up models, adding in additional factors as we get more and more specific with the model. But this year’s class especially isn’t happy with the discussion. They ask, “if we live in a world with friction, why would we even bother to ignore it?” I was talking with a colleague in the health sciences, and he said that the students (many of them the same ones I have in my class) ask essentially the same thing for some models he talks about. So at the very least, their questions like this aren’t limited to physics.

But to get back to the original question, do we need to include rolling friction in the analysis of which rotating object will go down the ramp the fastest?

*”hup” is how my college physics professor pronounced “hoop” when we covered this. He said, memorably, “what is that, a hup?” and I almost always dissolve into giggles thinking about it even now. I guess you had to be there.

[Image Creative Commons licensed / Flickr user phonogalerie.com]

In my last post, I talked about how students were drawing very complicated free body diagrams (FBDs) in class. Not even stick figures, they were drawing extremely complicated figures with gears on pulleys, wheels on cars, etc.

This is all fine and dandy in that part of the learning process is understanding that we simplify down a scenario into dots and circles (as seen in the beloved physics joke “consider a spherical cow (or chicken)…”). But what worries me about these drawings popping up in class is that is the sort of information I would have hoped the students would have absorbed by reading the textbook ahead of time.

This conundrum deserves a fresh look at goals and methods. Why do I want students to read the textbook ahead of time? I want them to come to class with a working knowledge of the material. I don’t expect them to be able to crank out problem after problem in class, but I want them to come with familiarity with terminology and ways of thinking that apply to what we’re studying. As I tell my students, my strength is not in regurgitating the textbook. My strength is bringing to them verbal or active explanations about ways of knowing. Classtime is about putting the book knowledge into action.

What have I been doing to spur that kind of in-depth reading? I’ve played around with strategies over the past few years, including having students write one-paragraph summaries of what they’ve read. Last fall I administered reading quizzes that were due before each class period.  Student feedback, both mid-semester and end-of-semester, asked to have these kinds of quizzes due all at one time for a given chapter, so I switched to that for the spring semester and have continued to do the same thing (this year on Mastering Physics, instead of Blackboard). And I’ve got about half a page’s worth of explanation in the syllabus about what I mean by “read before class.”

But my sense is that it’s still not working quite right. Students are still coming to class with some very basic questions (such as, “what exactly is mu [the coefficient of friction] again?”) They also have been looking at me (forgive this insertion of a southern idiom) like a calf looking at a new gate when I start different analysis types, like objects on inclined planes.  (“Why are we working with a tilted Cartesian plane?”)

So I’m going to gently change up the reading quiz method to (1) have at least one question due before every class and (2) have at least one question of each set be an actual problem to solve, hoping to move this pre-reading into workable knowledge territory. This isn’t revolutionary by any means, but I think is illustrative of a major point of teaching: you’ve got to be flexible. Truly, I’m working with a best-case scenario of students here at Wheaton: they are extremely capable. Freshmen come in with an average 3.7 GPA and the middle 50% of them have ACT scores between 27-32.  Of all the students I’ve ever worked with, these should be “getting it,” in the naive sense of that phrase. But if they’re not, it’s time to change up tactics. There’s a lot of research out there about how to get your students to read before class. But I’m starting to feel as though it depends upon a very wide variety of factors that can change from year-to-year, even at the same school. Not to mention the fact that the act of “reading” means very different things to different people.

I speak to my students about the syllabus being a “living document.” Policies and procedures are not set in stone. I do a mid-term anonymous evaluation in which I ask students to comment on what they’d like to be started, stopped, or continued in our course. I usually end up changing up some things after that point. But it’s totally worth changing up things earlier if need be. We’ll see how this experiment goes.

[Image Creative Commons licensed / Flickr user The Bees]

*See The Big Bang Theory

This year marks the fourth I am teaching some form of introductory physics. Some factors have changed (institution, textbooks, student ability level) but I’m finding that some things remain the same. I’m getting a better handle on the common misconceptions my students have.

A big one revealed itself this week regarding free body diagrams (FBDs) and Newton’s third law (or N3, as I abbreviate it.) Randall Knight’s College Physics textbook, which we’re using, spends a whole chapter on just understanding what forces are and practicing drawing FBDs. I appreciate this approach, especially for intro physics for non-majors, because it helps students face their misconceptions about what forces are and helps them understand that the drawing of the scenario often motivates the solution.

This Wednesday in class I broke out for the first time this semester our mini-whiteboards,* passed out markers, and got the students into groups of three. We practiced drawing FBDs straight from drawings and translating FBDs from word problems. Each group switched drawers for each successive problem so that everyone had some practice while the other members of the group advised.

This procedure was really revealing: FBDs AND action-reaction pairs were all over the place. Below is an example of what I’d draw if I were working one of these problems (Rachael and Jon are pushing on a box, which is moving at a constant speed in the direction Rachael is pushing), and what the students typically drew (sans hands actually gripping a box, feet with toes on the floor; they got quite detailed with their drawings!). Note that the vector lengths are not in their proper scale in either drawing (they should be; I was just a bit lazy in drawing this for this post.)

Note that the students have drawn the action-reaction pairs for all the forces, instead of just the ones acting on the box. As they were drawing, questions started popping up, largely along the lines of  ”if everything has an action-reaction pair, how does any movement happen at all? Isn’t everything just in a deadlock?”

What to take away from this? First of all, getting students to draw in class and getting a look at their work can be very revealing. If I were to have just drawn the figures for them in class and they copied along, we would not have had this chance to confront the misconception. They might have gone on from this point just doing their drawings “because Dr. Whitney drew them this way” and not understanding the utility of a FBD. They might not have even gotten the drawings right from this point on, which would then affect the work they would do as we approach future topics like torque.

Secondly, I’m not sure I’ve ever seen a textbook that clearly articulates that identifying action-reaction pairs for N3 and drawing FBDs are separate analyses (that sometimes work together)  with different purposes. Admittedly, my sample size is small; when I was in college we used Serway. I once taught as an adjunct using Young/Freeman. My first year of college teaching we used Giambattista and I switched to Knight the next year. Knight does go through the practice of drawing two FBDs for two objects and then drawing a connecting line between the action-reaction pairs, an approach I appreciate. But not all problems use two objects with clearly identifiable N3 pairs. Sometimes we’re just interested in one object sitting on an inclined plane. The weight does of course have an action-reaction pair (with the earth), but we don’t draw it in. And so when students are left with something not having an obvious N3 pair they are sometimes  conflicted about what to do.

From this situation, takeaways for me are to (1) get the students to be active in class, (2) give yourself opportunities to see their minds working so that you can facilitate corrections, and (3) always be on the lookout for ways of knowing that are obvious to physicists but should be stated clearly for students.

Preview for my next post: I’ve got a strong policy of reading the textbook very deeply and carefully before class begins. Why did my students draw such complicated drawings of FBDs, instead of in the simplified form as directed in the textbook?

*Our intro room has been designed to have whiteboards all around the classroom to facilitate work like this, but because enrollment has grown in my class we’re meeting in a room in a different department.