Conceptual Understanding in Introductory Physics XXVII

This question is inspired by my recent ramblings on electric charge and by the elements of thought in the Paul/Elder critical thinking framework.

(a) In first semester physics, you learned that mass is necessary to calculate the gravitational force shared by two interacting entities. What are the physical implications of mass always being positive?

(b) In second semester physics, you just learned that charge is necessary to calculate the electric force shared by two interacting entities. What are the physical implications of charge bring both positive and negative?


What I Think My Students and I Got Right This Semester

I think my students and I finally got some things right this semester. Too bad it only took twenty-five years, but I’ll take it anyway. Rather than wallow in self pity, I’ll just get right to it.

My students and I have finally mainstreamed special relativity as the starting point in introductory calculus-based physics. There are no equations, only significant conceptual understanding that, when you get right down to it, is far simpler than almost all students expect it both could and should be. Sometimes we get as far as the Lorentz transformation, but usually we don’t and that’s fine. As long as students understand that all…ALL…of the perceived “weirdness” of special relativity comes from the realization that light’s speed is invariant, we’re good. This leads directly to both time dilation and length contraction. Understanding that nothing “really” happens to moving clocks or moving rods is far more valuable than manipulating countless equations.

My students and I have deprecated pencil and paper in favor of LaTeX. We still use whiteboards, but for anything that is to be turned in the expectation is now that it will be done using LaTeX. The Overleaf environment negates the need for a local TeX/LaTeX installagion and works on every device with which I’ve tested it and allows students to build a library of problems and solutions. Of course they also use my mandi package, which was designed specifically for student use in mind. Note that I almost always use a version that is more recent than that on CTAN. Anyway, at the end of the semester students leave with a folder/portfolio of problems and solutions they’ve written. That’s something tangible I never really had as a student.

My students and I have deprecated traditional tests, quizzes, and such in favor of an approach I rather publicly stole from a Caltech course taught by Kip Thorne. The idea is to let students choose what to do in order to demonstrate learning and understanding. I mean, I’m continually told that “ALL physics students will ultimately be judged by their ability, or lack thereof, to work textbook problems” (note that I don’t necessarily agree with this but it is indeed a strong status quo opinion) so why not just eliminate the traditional tests and get down to the nitty gritty. I present a list of problems from each chapter, and not trivial problems either, from which students choose the ones they feel most accurately convey and demonstrate their achievement. I’m not entirely happy with this in that it implicitly assumes that the textbook problems are the ultimate endpoint, and they are most certainly not. Therefore, next time I will experiment further directing students to my list of problems and questions on this blog that, hopefully, go deeper than many textbook problems.

My students and I have almost deprecated handheld calculators in favor of Python. My ultimate goal is to completely depricate them and have ALL calculation done with Python/VPython scripts. That way, students can build a library of scripts for various purposes. However, writing scripts requires learning Python and students are hesitant to dig in at first and frequently end up resorting to calculators. I must try harder to reinforce the utility of Python in subsequent semesters over and above computational problems from the textbook.

In my opinion, I still lack the ability to sufficiently motivate students to engage in their education outside of the classroom environment I strive to create for them. However, just this morning I read the blog entry in this tweet and began reflecting on my own practices. Maybe I should loosen up even more (I run a comparitively relaxed classroom as it is) and just let students be the people they are and see what happens. It’s something I need to think about.

I also want to experiment with having students present problems and solutions to the class as part of their assessments. This seems like an efficient way to implement oral examination into the course without it being a logistical nightmare.

As always, feedback is welcomed.

Conceptual Understanding in Introductory Physics XXVI

This question might serve as a final exam for an introductory physics course. It could serve that purpose for my own courses, but it may not be appropriate for your courses so don’t worry if that’s the case. If you do not include system schemas in your course then this question won’t make any sense to you. I recommend this paper by Lou Turner in The Physics Teacher for familiarizing yourself with system schemas.

(a) Consider four entities in the same region of space, each of which interacts with the other three through some interation, the exact nature of which is not important for our purposes. Draw a schema showing four entities and all of their mutual interactions. Label the entities as 1, 2, 3, and 4.

(b) Draw a system boundary around the system consisting of entities 2 and 4. Explicitly label this sytem.

(c) For this system, write the momentum principle, the energy principle, and the angular momentum principle as specifically as you can given what you know about the system and the four entities. You may feel free to make any necessary (thermodynamic) assumptions for certain approximations to be made as long as you explicitly state them.

(d) For this same system, identify any interactions that could be accounted for using interaction energy (a scalar) rather than force (a vector).

(e) Now, draw a system boundary around the system consisting of all four entities. Explicitly label this system.

(f) For this system, write the momentum principle, the energy principle, and the angular momentum principle as specifically as you can given what you know about the system and the four entities. You may feel free to make any necessary (thermodynamic) assumptions for certain approximations to be made as long as you explicitly state them.

(g) For this same system, identify any interactions that could be accounted for using interaction energy (a scalar) rather than force (a vector).

(h) For the two systems defined above, what would make one preferable over the other? Be as specific and as comprehensive as you can be.

(i) Assume nonrelativistic circumstances in both systems. What, if anything, would change in either schema if you were to transform into a new reference frame? 

I will probably add to this list of parts as I think of good items to add. Feedback welcome!



Conceptual Understanding in Introductory Physics XXV

This question emphasizes geometry and should be done without use of a coordinate system. It should also be done using only symbolic manipulation of vectors. Here it is.

Consider a particle moving with a constant, non-relativistic velocity. Starting with a general expression for kinetic energy in terms of either velocity or momentum, prove that the particle need not be under the influence of a non-zero net force. Do not refer to a coordinate system. Your argument must be stated in words as well as mathematically.

I’m not entirely happy with the way I articulated the question. I’m open to suggestions for improvement, but I want the question to have an air of vagueness about it.

Ideas for Next Fall

This week wraps up another academic year and I’m already mulling over some ideas for doing things differently in calculus-based physics next fall. This post is just a brain dump of those ideas. As always, feedback is welcome.

Okay. My students have totally bought into standards based grading. I struggle with my standards and whether or not they’re rigorous enough. I rather think they’re okay, but I also struggle with workflow issues. This semester, I piloted LaTeX (using Overleaf) in my second semester (e&m) course and most of the students say they love it; others haven’t said one way or the other. The biggest benefit is that students can create problem solutions as PDF documents. This, together with a wonderful piece of software called PDF Expert (available for both OS X and iOS), makes for a fantastically efficient workflow for making corrections and returning them to students very quickly. I’ve also recently been deeply influenced by an unusual homework policy I found in a graduate course on gravitational waves taught by Kip Thorne. Instead of assigning problems, students get to selects the ones they find interesting or instructional. Yes, these are graduate students but I think I can make this work in my own courses.

So here’s what I’m thinking about implementing in my courses next academic year. Instead of having a list of standards, I will simply say that students should be able to work representative problems for each broad topic area (perhaps that means a single chapter, perhaps that means a small group of three or four chapters). For each topic area, I will present a list of appropriate problems from the book. From the list, students can choose the problems (haven’t worked out how many that means) they find the most challenging or interesting or instructional, write up their solutions in LaTeX, and submit them for assessment. I can have non-computational problems, computational problems, and experiment problems on the list and specify that one of each must be attempted. I think I would also impose the restriction that once a student has chosen and begun a particular problem, a he/she may not drop it for one that is considered easier. I hope this would encourage motivation to stick with a problem until it is solved. This may even motivate the student to do some research. In case you’re wondering, yes, this approach also allows me to “force” certain problems into students’ minds and I think that’s okay. Students would collect complete proficency-rated solutions into a portfolio presented to me at the end of the semester with copies of all their work from the course. They have something tangible to show and to take with them to show other students and other faculty.

What do you think about this approach? Is it rigorous enough? Is it harmful in any way? Comments and feedback are welcome!


Conceptual Understanding in Introductory Physics XXIV

This question was inspired by chapters 13, 14, and 15 of Matter & Interactions and would, I think, make a good final exam question even in courses where M&I isn’t used. The story line in those chapters makes a wonderful progression through different charge distributions and their fields and interactions with other similar charge distributions. The rather obvious patterns in this progression are worth emphasizing. They seem to be a consequence of superposition, which is one of most conceptually astounding ideas in physics.

Make a table giving at least one charge distribution, or combination of distributions, that gives rise to an electric field or electric interaction (force) that varies as 1/(r^n) where n = 0, 1, 2, …, 9. It may be the case that not all values of n are represented in the table. 

I can think of at least one example where a double digit value of n is needed, but most courses don’t deal with that situation.


Conceptual Understanding in Introductory Physics XXIII

This question came to me while I was planning for this semester’s introductory calculus-based e&m course (using Matter & Interactions of course). My overall desire and plan is to move away from the traditional number crunching type of problems, where all students really do is manipulate coordinate components of vectors or perhaps vector magnitudes, all without any genuine concern for the underlying geometrical implications. I completely understand the importance of this skill, but with computing having become rather ubiquitous I think such number crunching can be relegated to computational activities and labs. To change the status quo, I want to build a library of conceptual questions and problems that go as far beyond number crunching as I can get. I want students to think about the assumptions we make in physics and about how those assumptions are formulated. I want students to be able to, as Cliff Swartz once said, know the answer to a problem before calculating it. (I’ll link to the reference for that paraphrased quote once I dig it up.)

This particular question addresses two things, one that I never questioned as a student and one I only recently thought about as a teacher. It also addresses my continual search for ways to introduce symmetry arguments into introductory physics as early as possible. See what you think. You may find this question intimately related to this post.

(a) Formulate an explanation for why the electric field of a particle, or any other finite charge distribution, must decrease, as opposed to increase or remain constant, as distance from the charge distribution increases. 

(b) Formulate an explanation for why the electric field of an infinite (keeping in mind that true infinite charge distributions don’t exist) charge distribution must remain constant, as opposed to increase or decrease, as distance from the charge distribution increases. (It may help to consider an Aronsonian operational definition of “infinite charge distribution.” In other words, if a charge distribution can’t be truly infinite then what precisely do we really mean by “infinite charge distribution” in the first place?)

By the way, as always these questions are framed within the context of introductory calculus-based physics. I hope I have made correct assumptions about the physics of the situations. If not, please feel free to let me know. Oh, and yes, you could probably use gravitational or magnetic fields instead of electric fields in this question.