An Experiment That Didn’t Quite Work

I don’t always talk about it, but I like to conduct simple experiments in the classroom. This semester, I decided to conduct one in which students kept track of their own assessment progress. Teachers are often expected to do most all of the work in a class, including keeping detailed records of student performance. Keeping such records is important, but since I’ve recently moved the responsibility of learning directly onto students why not also move the responsibility of recording learning progress onto students too? It could be risky. A student might decide to not keep such records. The records might be lost or even destroyed. In case of a grade dispute, I would need to produce evidence for one side or the other.

My request to students was simple. When an assessment is returned, record the performance rating in a notebook or better yet, take a photograph of the entire thing with your phone’s camera. Of course students who don’t have phones equipped with cameras can’t do this and for them, simply recording the ratings for each assessment somewhere safe if a fine option. That was it.

I didn’t reveal to students that I was keeping records on my end. I really wanted them to assume THEY were completely in charge of documenting their progress. Throughout the course, I would tell them they only needed to reassess on standards for which they had not yet demonstrated proficiency. When a student would ask which standards he/she needed to reassess on, I would refer them to their records, sometimes having to remain expressionless as they told me they had been keeping records. I hoped that after a few times of me doing this they would really get the idea. For the most part, I think many students did indeed take on this responsibility and I think those students took it seriously. I did get a few (not necessarily unexpected) surprises though.

One student said he recently got a new phone and lost his photographic records in the transition from the old phone to the new one. Okay, that’s bad but he recovered quickly by going through the archives I’d been keeping all semester. However, more than one student (I’m counting all three sections of introductory astronomy here) indicated that they’d not been keeping records and had no idea of their current standing. A few even tried to convince me that they weren’t aware they were supposed to be keeping track of their progress, which is strange given that we discussed this at length during the first week of the semester.

So here’s my plan for future semesters.  At the first class meeting, I will hand each student a folder containing the obligatory courses documents (syllabus, explanation of standards based grading, learning expectations, etc.). This same folder will be used to make a learning portfolio as the course unfolds. All assessments will be kept in the folder and in order to be eligible for reassessment, a student must present the entire folder to me for inspection. All past assessments must be in the folder. I’ll probably include a printed calendar page and ask that the date, standard(s), and proficiency rating for each assessment be recorded on this page as a quick visual tool. Ultimately, I think it would also be great step in moving away from a transcript-style record of “learning” to clear documentation of what precisely was asked of students and how they measured up. I can even see my calculus-based physics students benefiting from this as they could also perhaps create a catalog of representative problems/projects that accurately reflect what I hope is an innovative and intellectually stimulating course experience.

Do you think this will help students? I’m certainly open to suggestions on effectively implementing this.


Three Semesters With Standards Based Grading

I need to collect and share some thoughts on my experience so far with standards based grading in both introductory calculus-based physics and introductory astronomy. I don’t know that everything, or anything, here will make much sense but it will help me sort some things out. In doing so, I may see things I’ve not yet noticed.

One realization I had last week was to discontinue using the word “mastery” as a description of what I want students to achieve. Many astronomical and physical concepts took thousands of years to accept. Can I realistically expect students to get to that same level of intellectual confidence in one semester? For some things, like straightforward numerical calculations, yes. For other things, like understanding the chain of evidence that led to ideas like the structure of our solar system, I don’t think so. I’m still struggling with this question. Nevertheless, beginning next semester I have decided to replace “mastery” with “proficiency” because I think that more accurately reflects what I want students to achieve, at least with the more sophisticated concepts and ideas.

I suppose the most challenging thing for me has been deciding whether or not the standards we’ve used are rigorous enough. Do they focus on the most important aspects of the course? Yes, I think. Formulating standards really forced me to think about what I wanted students to take away from the course. I can honestly say that I’ve addressed this issue for years before I adopted SBG so I feel I have a good handle on what I want the takeaways to be. That doesn’t mean they never change though. I treat course planning as always being subject to modification as long as that modification leads to improvements for students. Are there too many standards? Yes, at first I had far too many standards. As of this semester, I see that my standards focus on two basic things: things I call “skills” and things that require deeper thought. In physics, for example, calculating a particle’s momentum, energy, or angular momentum (relative to something else) is a skill. It’s an important skill, one that requires error-free proficiency, and certainly one that is essential for later big picture issues (e.g. conservation of momentum), but does it warrant being an individual standard on its own? At first I decided that it did indeed warrant such importance, but this semester I changed my mind. It is now part of a much more coarsely grained standard.

This brings up another question in my mind, namely the question of whether or not there could be different sets of standards. I can envision having one set of “training” standards whose purpose is to ease students into this strange new way of assessment with goals that are more easily obtainable early in the course. These standards may address “skills” as described above and may serve as a gateway to accessing future standards. Staying with the example of calculating a particle’s momentum, how many attempts are necessary to demonstrate proficiency? Is one successful attempt sufficient? Should I require, say, three consecutive successful attempts before awarding permanent proficiency? Should I mandate that after, say, two unsuccessful attempts to demonstrate proficiency with the same question related to a given standard that a new question must be given? I rather like that idea because it prevents the gaming of one particular question. By the way, some students seemed surprised to discover that the questions that I use to check for proficiency on a given standard will be different from one attempt to another. Somewhere along the line they were led to think that the same questions/assessments would be used over and over. I don’t know how or why that happened, but I need to make sure that doesn’t crop up again.

When students request individual assessments, am I treating all students the same in judging their proficiency? Am I subconsciously holding some to higher or lower criteria for some reason? This is always in the back of my mind.

Is it okay for some standards to be more difficult to achieve than others? I think it’s probably okay for standards to get progressively more challenging as a course unfolds. In fact, I’m almost convinced that this is a necessity. I think to make this work, I need to make sure the questions/assessments I use to judge proficiency need to grow more challenging during the course. I have a large collection (hundreds) of astronomy and critical thinking science questions that I developed in working on the LCTTA materials. I need to go through these questions and see how they reflect, if at all, the course standards. These questions were developed over several years before I moved to standards based grading so it is possible that some of them need to be modified.

Is it okay for students to collaborate during assessments? I conclude that it is. My main reason to not allow collaboration is to discourage cheating. How would I recognize cheating? Well, I think if two or more students turn in identical responses, and I mean down to the letter, to an assessment then I am conditioned to suspect cheating. One way I have to guard against this is to immediately turn the assessment into an oral one. I begin asking each person with the same response different targeted questions, giving them an opportunity to demonstrate that they didn’t just copy someone else’s thoughts in writing. This has led me to see the power of oral assessments in general. I don’t know that requiring some assessments to be oral is practical, but I would like to experiment more with this idea because I think the confidence with which one explains reasoning is directly proportional to one’s understanding of that reasoning, but I may be wrong. As I write this in my office, I have one student outside in the hallway attempting an assessment. That student is accessing Google, hoping to find something useful. I’ve tried all semester to convince my astronomy students that Google isn’t of much use to them in this course because we don’t focus on “Googleable” (is that a word?) things. I provide them with numerous activities with the expectation that they have to complete them outside of class. Unfortunately, to my knowledge not a single student has recognized that some of the assessment questions appeared in the activities. Many, okay most, of them do not do that and do not realize till the semester’s end nears that I wasn’t kidding. I don’t know how much nagging should be necessary at this level (freshman/sophomore undergraduate level) to get this point across to them. Some colleagues tell me that because this is a community college I should nag more than I would need to at a four year college, but I don’t accept this. Our transfer courses are supposed to have the same expectations of our students that they would be subjected to at a four year school. At what point do I say that this is not my problem as an instructor, but a problem of time management and organization for the students? I don’t have a good answer to that question.

What if in the course of assessment, a student displays deficient writing skills? What should I do? Should I not award proficiency for this reason alone? Should I overlook atrocious grammar? Should I overlook consistent misspelling of common words (e.g. “celestrial” instead of “celestial”)? Should I overlook the inability to write a coherent, complete sentence? My response thus far has been to try to correct these problems within the context of my own courses. I tell students that it’s not enough to understand something, but that it’s also necessary to effective and correctly communicate understanding both orally and in writing. Word choice matters. Clarity matters.

As an aside, while I’ve been writing this post off and on over the past three hours I’ve been working with one student in particular who cannot read or write at a college level. Three hours! Is that justified? In these days of slashed budgets and loss of positions, I’m told that such efforts are essential. I don’t know…would YOU spend three hours with a student who clearly isn’t prepared to be in your environment? It’s not that I mind doing it, because doing so does allow for some actual learning to take place, but I obviously cannot do this with every single student.

Unfortunately I must also address certain questions that are taboo in my environment. I’m not allowed to ask how students who can’t read and write at high school level get into college courses. I’m not allowed to ask about the negative impact of a 20+ contact hour teaching load on my ability to spend as much time on assessment as I probably should due to the amount of paperwork it can generate. I’m not allowed to cite students’ refusal to sometimes do work outside of class as having anything to do with my performance. In fact, there seems to be an asymmetry in that students can cite my deficiencies as reason for their underperformance but I’m not allowed to cite their deficiencies as reason for my (lack of) effectiveness or for their inability to succeed. I’m supposed to pretend that students who can’t read or write at grade level can be successful in my environment. I’m not sure how to deal with these issues, so I’ll just keep pretending they don’t exist while knowing that they really do.

Another thing I have to consider is my grade distribution. My classes are capped at twenty-four and while it’s rare for the calculus-based physics to fill, it’s not uncommon for two out of three sections of first semester astronomy to fill in the fall semester. I come under scrutiny if too many students earn an A and if too few students earn an A. My chair seems to think that an A should be difficult to obtain yet also thinks that physics “is just F=ma” and so I’m not sure what to make of this. I feel that while some standards should probably be more challenging to tackle, proficiency should be attainable. I just can’t accept setting standards for which students have no hope of demonstrating proficiency. On the other hand, am I obligated to take into account things like insufficient reading or writing proficiency that seems present in many of our students? I don’t know.

On the first day of class, I show students my definitions of teaching, learning, and taking a class. Am I succeeding in adhering to these definitions? Am I right to do so?

I’ve raised a lot of question. Some are relatively straightforward to answer but others will take time to figure out.

Students: Putting My Transcripts Where My Mouth Is

For years, I’ve told students that in the grand scheme thing grades don’t matter. I firmly believe that traditional grades are no more an indication of what someone knows than is eye color. Yet, we’ve all been judged as people by these letters on our transcripts. They’ve kept us from being permitted to accomplish certain objectives, all the while with the judges knowing, but not admitting, that grades are in no way standardized and essentially mean nothing. They act as a filter from having to dig deeper into our individual competences, strengths, and weaknesses. After twenty-one years of teaching, I still feel this way and until I adopted standards-based grading I always kept the arbitrariness of traditional grades in mind. Professional accreditation agencies insist on having our transcripts on file, which to me merely amplifies the notion that despite the ideal that higher education is the same everywhere, as it should be, it really isn’t. A letter, an A for example, on a community college transcript carries no consideration next to that very same A on a Harvard transcript and we all know this. It’s one of the many dirty little secrets of higher education. Higher education is as much about politics, arbitrary rankings, and aggrandizement as it is about providing a learning environment. Okay, I’m jaded but people who know me already know that. Anyway, I have also threatened over the years to post my own undergraduate and graduate transcripts online and I have finally decided to do just that, right here. I have removed certain personal information but have otherwise not edited anything.

Undergraduate Transcript 1/2

Undergraduate Transcript 1/2

Undergraduate Transcript 2/2

Undergraduate Transcript 2/2

Graduate Transcript

Graduate Transcript

I want students to understand a few things about transcripts.

  • Transcripts are a reflection only of the past, and do not represent what you may or may not know (whatever that means) now or in the future. I would also argue that they also probably didn’t accurately reflect what you did or didn’t know then, only how you performed on some arbitrary tasks.
  • Just because your transcripts say you may not be competent, they have no way of showing how you’ve changed, grown, or learned since they were recorded.
  • Accreditatin agencies and many employers reqire transcripts to be on file and open to inspection by any number of people who are not qualified to evaluate them. Why keep transcripts secret? They’re nothing to be ashamed of.
  • When I look at a transcript that shows all As and a perfect 4.0 GPA, I immediately think, “This person didn’t have to work for it.” I know that’s a blanket generalization, but it’s what comes to mind for me. Remember that people are not born knowing anything about physics or anything else. Everything academic is learned, and learning requires struggle, something I have only recently seen publicly admitted among colleagues. I was always told that learning is easy for talented people. What crap!
  • As a student now, I would much rather take a course from someone who really struggled to understand the material instead of from someone who whizzed right through it. Only the former instructor can empathize with the learning process as it exists for the vast majority of students who experience it.
  • For me peronally, every course on my transcripts is part of the story of my life at that time. I can remember every class I took and every professor (maybe not the name, but definitely how the course was facilitated and how I felt about the course at the time. The “at the time” part is important, because I misjudged a few things back then.
  • Certain courses are of personal value to me. My obsession during high school and undergraduate was celestial mechanics. The only, and I emphasize ONLY, reason I chose to attend UNC-CH was that at the time, it was the only college in the state that offered a separate major in astronomy (as opposed to a minor in astronomy) and was the only college that offered a course in celestial mechaincs taught by one of the “celebrities” in the field. Morris Davis had just officially retired when AST131 was finally put on the schedule, and I was determined to ace that course. Dr. Davis was one of the professors I met when I came to UNC-CH to look around early in my senior year of high school. He was also one of the few who took my interests seriously and encouraged them. He even arranged for me to visit the U.S. Naval Observatory during the summer of 1987 so I could meet my (at the time) heroes in the Nautical Almanac Office. As you can see, I met that goal and no one can ever take that away from me. To my knowledge, that was also the last time AST131 was ever offered at UNC-CH. What an honor to have taken my most cherished course from a player in the field for his last class! It almost makes me cry to think about it. Oh, and by the way, one of the reasons I got an A- in the course was that I’d studied much of the material on my own as an obsession. There wasn’t much in the course that I’d not seen before. I’d studied Gaussian and Laplacian orbit determination, elementary celestial mechanics, and the creation of ephemerides for comets and asteroids. This, I suspect, is what many student in physics mistake for learning in the classroom. In other words, I think most of the people who effortlessly breeze through do so because of prior experience with the content. Woe to those who are seeing it for the first time, but those are the students I think we should be targeting because they are the majority.
  • My calculus grades are interesting. At the time, UNC-CH required four semesters of calculus. I got an A in the first semester because it was nearly a word for word repeat of my high school calculus course, same textbook (Tomas) and all. I got a D in each of the following three semesters, the first of which was taught by a a then graduate student who is now employed by the UNC-CH math department as a course coordinator. The third and fourth semesters were taught by fully tenured professors, but the courses did not contain the material described in the course catalog, at least not to the extent that they were helpful to me as an astronomy major. In one of them, the professor used the languate of differential forms to  present the material. Whis is very cool, and something I find personally interesting, but he did to with no discussion of why he was doing it and with no connection whatsoever with other areas like, you know, physics. The fourth semester is a blur now because I can’t remember one single thing I learned from the course or from the professor. Incidentally, we used the same text (Thomas) for the first two semesters and another text (Schenk) for the second two semesters. I still have them of course.
  • Flash forward to my first year of graduate school. I’d not taken a course in ordinary differential equations  at UNC-CH because it wasn’t required for astronomy majors and my experiences with the math department had soured my desire to interact with them any more. So I registered for MAT390, ODEs, at UNCG. I was the only grad student in the class and of course got no graduate credit for it, but that didn’t matter to me. As you can see, I got an A. It wasn’t just an A to me, it was a sign that I really did have a brain and that I could use it in the proper environment. This was the first time in my life I aced tests in a college math course! There’s no feeling like that. The professor (Jerry Vaughan) provided meaningful explanations of the course content and for the first time, I literally saw where most undergraduate classical physics equations came from. But it also meant that something had probably been amiss while I was at UNC-CH because I had not changed enough myself to make any of this happen.
So students, I ask you to think about the reaction you would get from asking your teachers, instructors, or professors to see their undergraduate and graduate transcripts. Some would flat out refuse. Some would boastfully hand them over (well, copies of them anyway). Remember that we as faculty have unfettered access to your transcripts, and we do look at them for time to time to see if, for example, prerequesites have been met or to evaluate transfer course credit. Neither of this is in any realy way an evaluation of what you know about anything, and it certainly isn’t an evaluation of your inherent worth as a person. I like symmetry, and symmetry dictates that you be allowed to see our transcripts with no excuses from us.
I will admit that these transcripts have kept me out of doctoral programs. UNC-CH told me point blank that I would be wasting time applying to their graduate school becuase they would not accept me. (Now, I firmly believe that if a department graduates students it deems unprepared for its own graduate program, that department is acting hypocritically and should refund the student’s tuition. Yes, I know…but still.) UNC-CH also told me that the don’t allow new graduate students to take undergraduate courses a refreshers when I knew of at least one of two doing that very thing (I know their names…). I was also told that none of my graduate course work would apply to any doctoral program to which I might be admitted. Only one institution, Wake Forest University, told me that my undergraduate transcript is the one that doesn’t matter and that my graduate transcript was all that mattered to them. However, I decided not to pursue study there. I have come to the realization that despite the privilege having a PhD offers, I would have been miserable in a PhD program. These incidents were my awakening to the political aspectes of doctoral level physics in this country (some of it, not all of it…). Apparently, it’s not this way in other disciplines from what I have seen and heard.
Finally students, I leave you with the assurance that your transcripts aren’t the ultimate assessment of anything about you. They barely matter, and matter in no significant way. Look at me. I’m where I want to be, doing what I want to do, and enjoying every minute of it. I’m not ashamed of anything, and you shouldn’t be either.

Physics Standards, M&I Chapters 1-3

Here are my M&I class’s standards for chapters 1-3. Students had considerable input into the formulation of these standards.

Standard: I can use consistent and correct vector notation.
Proficiency Indicator(s): Correct vector notation is used consistently throughout a problem or explanation.
Mastery Rubric: Vectors are indicated with arrows. Vector components are indicated with appropriate subscripts or indices. Vector magnitudes are indicated with single or double bars.

Standard: I can recognize the signs of an interaction.
Proficiency Indicator(s): Given a system’s behavior, I can state whether or not an interaction is present.
Mastery Rubric: List or otherwise articulate which signs of an interaction are present or absent.

Standard: I can correctly write and apply the momentum principle for a chosen system.
Proficiency Indicator(s): Given a system, I can write the momentum principle as it applies to the system, including terms for the individual momentum contributions to the total momentum and for all external interactions affecting the system.
Mastery Rubric: All parts of the system, and their contributions to the total momentum, are accounted for. All external interactions affecting the system are accounted for.

Standard: I can infer physical consequences from the momentum principle for a chosen system.
Proficiency Indicator(s): I can determine whether or not the system’s total momentum is conserved. I can choose my system to make certain calculations mathematically simpler.
Mastery Rubric: Inferences must be directly drawn from the momentum principle.

Standard: I can draw a correct schema for a chosen system.
Proficiency Indicator(s): Given a problem, I can draw a schema that includes all relevant entities, the interactions among those entities, and a choice of system.
Mastery Rubric: Persistent interactions are drawn with solid arrows. Temporary interactions are drawn with dotted or dashed arrows. Arrows representing interactions must be labeled.

Standard: I can draw a correct free body diagram for a chosen system.
Proficiency Indicator(s): Given a system, draw the free body diagram for that system within the current context.
Mastery Rubric: The system must be represented as a solid dot. Interactions must be represented with correctly labeled arrows. Arrows’ magnitudes and directions must be correct relative to each other. The diagram must correctly represent the physical content of the problem.

Standard: I can correctly calculate gravitational, electric, and spring forces.
Proficiency Indicator(s): Given particles or entities that can be approximated as particles, calculate either relevant force (magnitude and direction) on any one of the entities.
Master Rubric: Calculations must include relevant units. Magnitudes and directions must be correct and must be explicitly accounted for. The relevant arithmetic and algebra must be correct.

Standard: I can predict motion using iterative calculations.
Proficiency Indicator(s): Given a particle and all relevant interactions affecting that particle, correctly predict the particle’s future motion using the momentum principle.
Mastery Rubric: The update form of the momentum principle must be used. Momentum must be updated to reflect relativistic velocity if necessary.

Astronomy Standards

Here are my astronomy class’s first standards. These standards come directly from the first seven inquiry activities done mostly in class. Collectively, these activities form a coherent unit on critical thinking framed so as to form the foundation for astronomy or any other science.

The biggest problem I have, and have had for well over a decade, is that students fail to see how any of this “stuff” has anything to do with astronomy. They, like most young students, have been conditioned to see science as a set of memorizable facts and figures and equations rather than as a process that relies on questioning, reflection, and reasoning. They frequently complain to my chair that I’m wasting their time. Fortunately, my chair almost always defends me. I’ll say more about changing classroom culture in a future post.

Standard: I can articulate a justification for working in groups like scientists do.
Proficiency Indicator(s): 
Write either a sentence or a paragraph explaining the benefits of working in groups compared to working individually.
Mastery Rubric: Each sentence is a complete sentence. There are no spelling, grammar, punctuation, or other errors. My meaning is clear without the reader having to guess at it.

Standard: I can use scientific terms correctly even if those terms are used differently
in non-scientific applications.
Proficiency Indicator(s): Recognize when and if a scientific term is used correctly or incorrectly. If it is used incorrectly, correct the wording so that the usage is correct.
Mastery Rubric: All writing is done in standard English with correct spelling, grammar, syntax, punctuation, and meaning.

Standard: I can create an operational definition of a physical, geometric, or mathematical concept in either list form (as a series of enumerated steps) or in paragraph form (in complete sentences).
Performance Indicator(s): Create an operational definition, in the specified form, for any concept previously encountered in this course.
Mastery Rubric: All writing is done in standard English with correct spelling, grammar, syntax, punctuation, and meaning. The end point must conclusively define the concept involved. The reader must not have to guess at how steps flow. The reader must not have any questions about the concept being defined.

Standard: I can trace a piece of scientific knowledge all the way back to its observational origin.
Performance Indicator(s): Given a scientific fact, I can cite what observational evidence supports that fact. I can also distinguish between evidence that does and does not support a given fact.
Mastery Rubric: All writing is done in standard English with correct spelling, grammar, syntax, punctuation, and meaning.

Standard: I can analyze a concept, passage, document, or any other conceptual unit by mapping it into the elements of thought.
Performance Indicator(s): Write one sentence or one paragraph, depending on instructions, applying each element of thought to the conceptual unit under analysis.
Mastery Rubric: All writing is done in standard English with correct spelling, grammar, syntax, punctuation, and meaning.

Standard: Given a natural phenomenon encountered in this course, I can create a framework that accounts for the phenomenon’s observed characteristics.
Performance Indicator(s): Given a natural phenomenon encountered in this course, I can create a framework that accounts for the phenomenon’s observed characteristics.
Mastery Rubric: All writing is done in standard English with correct spelling, grammar, syntax, punctuation, and meaning. The framework must account for all observational aspects of the phenomenon. The reader must be able to reconstruct the phenomenon from the framework.

Standard: I can recognize the fallacies and distraction techniques described in this activity and I can properly point them out to the person or source using them.
Performance Indicator(s): Identify and rebut a logical fallacy or distraction technique used by another source.
Mastery Rubric: All writing is done in standard English with correct spelling, grammar, syntax, punctuation, and meaning.

Standard: I can assess whether or not an explanation is testable and falsifiable.
Performance Indicator(s): Given an explanation for a phenomenon, explain whether or not it is testable and falsifiable and provide supporting reasoning.
Mastery Rubric: All writing is done in standard English with correct spelling, grammar, syntax, punctuation, and meaning.

Feedback is welcome!

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.