Physics Standards

Here are my M&I class’s first standards. We begin the course with a unit on special relativity with readings from a textbook written by Arnold Arons. Each standard has one or more proficiency indicators and a mastery rubric.

I want to emphasize that great thought went into formulating these standards, which included student input. There is a significant emphasis on reasoning and written articulation of that reasoning. I want to try very hard to dispel the illusion that physics is all about equations. I want students to understand that equations are merely abbreviated notation for fully articulate thoughts, principles, and concepts. There is also a bit of an emphasis on history. I want even introductory students to understand where our discipline came from, and as Bruce Sherwood has remarked on many occasions, I want to emphasize that the twentieth century actually happened despite the vast number of introductory textbooks that blatantly ignore it altogether or relegate it to the last few chapters. One student has already dropped the course, complaining to the department chair (but not to me) that we haven’t done any “real physics” yet and this is hurting his chances for doing well on the MCAT. Unfortunately, the chair, who is a chemist and not a physicist, accepted this as a valid complaint and harshly criticized me for it. I will deal with that issue later.

Students do not expect this particular approach. They expect to be hit with equations from day one and they perceive this alternative approach to be more difficult than it really is. They don’t expect to actually read for understanding. They expect to memorize equations. Their collective prior conditioning is one of the most difficult barriers to overcome.

Okay, here I go. I hope I’m doing this right.

Standard: I can apply the elements of thought to special relativity. (NOTE: This refers to the primary tool in the critical thinking framework developed by Richard Paul and Linda Elder. Here is an interactive explanation of this tool. I like it because it is internally consistent and applicable across disciplines. It also embodies many of the pedagogical ideas behind Matter & Interactions.)
Proficiency Indicator(s): Map special relativity into one or more of the eight elements of thought, with each element having a paragraph devoted to it.
Mastery Rubric: Explanations are physically and mathematically correct, including proper grammar, spelling, and terminology.

Standard: I can describe, using both words and algebra, different methods of synchronizing two clocks in the same reference frame.
Proficiency Indicator(s): Draw a diagram illustrating a given synchronization method. Numerically solve a synchronization problem. Predict and describe the effects of a “wind” on synchronization.
Mastery Rubric: Work is organized and easy to follow. Algebraic quantities are explicitly defined. Numerical quantities include units. Explanations are physically and mathematically correct, including proper grammar, spelling, and terminology.

Standard: I can discuss the importance of the Michelson-Morley experiment.
Proficiency Indicator(s): Articulate the purpose of the Michelson-Morley experiment. Articulate the experiment’s outcome. Articulate the outcome’s implications. (NOTE: These indicators spiral back to the elements of thought, an Aronsonian strategy.)
Mastery Rubric: Work is organized and easy to follow. Algebraic quantities are explicitly defined. Numerical quantities include units. Explanations are physically and mathematically correct, including proper grammar, spelling, and terminology.

Standard: I can distinguish among invariants, constants, and conserved quantities.
Proficiency Indicator(s): Given a list of physical quantities, classify each one as invariant, constant, or conserved. (NOTE: This does purposely does not specify Galilean invariance or Einsteinian invariance. I want students to be able to argue that detail if, for example, they state that acceleration is invariant.)
Mastery Rubric: Work is organized and easy to follow. Algebraic quantities are explicitly defined. Numerical quantities include units. Explanations are physically and mathematically correct, including proper grammar, spelling, and terminology.

Standard: I can use the Galilean transformation, articulated in both words and algebra, to describe motion in different reference frames.
Proficiency Indicator(s): Given a particle’s motion in one reference frame, predict its motion in another reference frame.
Mastery Rubric: Work is organized and easy to follow. Algebraic quantities are explicitly defined. Numerical quantities include units. Explanations are physically and mathematically correct, including proper grammar, spelling, and terminology.

Okay, rip ’em up and tell me what I’m doing wrong.


Defining Teaching, Learning, and Taking a Course

I recently decided to attempt to define the concepts of teaching, learning, and taking a course to see how well my definitions match what I have done for the past twenty years. Upon reflection, I have arrived at two important realizations. I realize now that what I spent most of the first ten years of my career doing was not true teaching. I realize now that no one ever taught me how to learn. I can’t honestly say that my definition of taking a course has caused any stunning realizations, but I think it’s necessary because it operationally combines the other two into something students may find useful. On second thought, maybe school administrators may find it useful too. So here are my definitions. They are still very much mutable and I welcome feedback.

Teaching is creating an environment in which students can freely immerse themselves in the process of gaining proficiency in, or mastering, a discipline by all possible means, using all provided resources, and by finding other resources. The environment will be free of barriers, intimidation, and outside distractions, and provides opportunity for exploration of intellectual endeavors without fear of failure, reprisal, abuse, intimidation, or punishment. Barriers, in this context, are things we use to relieve us of the responsibility for learning. Some barriers are unavoidable, but many are entirely avoidable, and it is the avoidable ones that teaching must minimize. Hopefully, this definition includes both scholarly classroom teaching and research.

Learning is the willingness to take advantage of your freedom to fully immerse yourself, free of distractions, in gaining proficiency in, or mastering, a discipline without fear of failure, reprisal, abuse, intimidation, or punishment. Learning can happen without knowing what your newly discovered knowledge may be used for in the future. Learning must happen without giving in to feelings of (intellectual) uncomfortableness. Learning never ends, but intermingles with periodic reflection. Hopefully, this definition includes both scholarly classroom learning and research.

Taking a course from an educational institution is an opportunity, indeed a guarantee for an opportunity, to (a) learn under the supervision of an expert in a discipline and/or (b) to earn a credential certifying that you have demonstrated proficiency in a skill or discipline. The expert creates the environment and students do the learning, and that includes deciding what is and is not relevant to the course contents. One depends on the presence of the other. This expert also provides constructive feedback throughout the process and provides a final professional, data driven assessment of a student’s performance. Learning can happen without taking a course, but taking a course guarantees you will have the requisite environment and increases your chance of success.


Letter of Apology to the Vector Cross Product

Dear Cross Product,

I know I’ve said some pretty nasty things about you in the past. I won’t rehash the entire list here, but I will try to explain the feelings that brought about my unjustified words.

My frustration began when I first learned the name given to you by Josiah Willard Gibbs. He named you a “product” and that naturally made me think of the concept of multiplicative product. After considerable thought, I’ve concluded that you’re not actually a product at all. You’re a geometrical construct that has nothing to do with multiplication. For years, I’ve been glossing over this detail with my students, not that they caught onto the problem. If they did, they never let on. Nevertheless, it bothers the heck out of me now. I’ve been accused of being needlessly pedantic, but I’d rather be accurate than sloppy when terminology is involved. Just think how we (physics teachers) screw with students’ minds with “massless rope” or “frictionless pulley” or “infinitely far away.” These are all well intended terms, but none is physically accurate. I think I’m going to call you by a new pet name, like maybe just “vector cross.” Honestly, it’s a term of endearment, and one that removes all hints of multiplication. Yeah…it fits. Like it? Oh by the way, I’m going to start calling your sibling “vector dot” instead of “vector dot product” too.

My frustration continued when I realized that you exhibit a geometrical paradox, or so I thought. The two vectors out of which you’re constructed define a plane, but somehow out of that combination we get something that is perpendicular to that plane! Ridiculous! When a see-saw rotates one way or the other under the influence of a net torque, the rotation happens in the plane defined by the moment arm and the applied force. The physics happens in a plane, not in a direction perpendicular to that plane. If that were really true, then there would be no legitimate way to talk about torque or angular momentum in two dimensional problems. This really bugged me until I finally figured out where you’re coming from. It dawned on me that your direction is defined to coincide with the axis around which rotation happens. I get that now, but it would help if this were explicitly documented somewhere, especially in the introductory literature. This whole “how you get something from a plane that’s perpendicular to that plane” thing really got to me and made me say you should “die a quick death.” I’m really sorry I said that, but it’s what I felt at the time.

WAIT! DON’T GO! HEAR ME OUT….PLEASE!

Anyway, all that’s in the past now. I’ve grown. I’ve matured. I now realize that you are wise beyond your years. I’ve changed, I want to tell you why. See, I have this weird fantasy that introductory calculus-based physics should include elementary (VERY elementary) aspects of tensor analysis, at least enough to give students an understanding of the inertia tensor in certain simple geometries. Well, you’re the secret ingredient to making that happen. Your ability to be written as both a vector and an anti-symmetric tensor, along with a review of elementary linear algebra students have already seen in previous classes, is the bridge from vectors to tensors. You ARE a tensor, in a weird sort of way.

But there’s something else about you that I never appreciated before. You’re necessary to discuss a vector’s derivative. You’re the best way to describe the change in a vector when the vector’s magnitude is constant. I was aware of this years ago, but the underlying logic escaped me until very recently. Now I see it all.

I guess that’s all I wanted to say. I hope you can forgive me.

Sincerely,

Joe