Do the arrows in free body diagrams have to be the right length?

No.

Draw the tail of the arrow starting on the object, pointing away from the object in the direction that the force acts.  Don't worry about the arrow's length.  Label the arrow with a descriptive variable, such as "T" for tension in a rope or "mg" or "Fg" for the gravitational force.  Off to the side, indicate the object providing and experiencing each force, as "T: force of the rope on the cart, and mg: force of the Earth on the cart."

What?  The length of each vector should be proportional to the magnitude of the force represented, as everyone knows, and as the AP exam occasionally requires.  And no one, let alone the AP exam, requires such precise descriptions of each force.  Whatchu talkin' bout, Jacobs?

I'm talkin' pedagogy.

Free body diagrams are one of the first physics skills I teach each year.  They're intended to give students a starting point for a three-step process:

   (1) Draw free body
   (2) Break angled forces into components, if necessary
   (3) Write two equations for newton's second law:
              (up - down) = ma_y
              (left - right) = ma_x

The physics teaching literature abounds with discussions of conquering a student's fear of mistakes.  In the educational culture that our students so often inherit from middle school, a wrong answer equates morally with being a bad boy/girl.  From such a source springs the trope that all physics teachers have observed: student proffers a blank paper, saying "teacher, help me, I don't know what to do."

The free body diagram provides a clear starting point to solve any force problem.  I can - and do - refuse to discuss a problem with a student who has not carried through all three steps in the procedure above.  Usually, once they attempt all three steps, my students suddenly find that they no longer have such an urgent need for "help."  And when they do ask for assistance, we can discuss the details of their problem solving process rather than the waily-waily woe of how impossible the problems are.

Thus, my requirements about free body diagrams must focus only on the elements that will most likely lead to problem solving success when students move on to steps (2) and (3) above.

I don't want students worrying about the length of their arrows.  That's not in any way important to breaking forces into components, or to writing Newton's second law in each direction.  In fact, it's not always clear at the very beginning of a problem which forces are bigger than others - often knowing the relative magnitude of forces requires significant reasoning involving an analysis of an object's motion, or consideration of the values of trigonometric functions.

Such reasoning can not be part of a student's initial approach to a problem - that's exactly how paralysis by analysis takes hold.  If I look at a student's solution and say "that's great, but the pushing force arrow seems longer than the weight arrow, and it turns out that the pushing force is smaller than the weight, so your free body is wrong..."

...then I've played straight into the waily-waily trope.  What the student hears isn't "almost right, missed one wee detail."  What the student hears is BAD BOY.  BAD GIRL.  YOU FAILED.

Similarly, I find it unproductive to think about starting the force vector at the point of application of the force.  (That is, a normal force arrow should start at the contact point between the object and the surface; the weight arrow should start at the object's center of gravity.)  This subtle convention is in no way important to solving Newton's laws problems in the first month of physics class.

I *do* want students thinking about the source of each force.  In order to be successful at steps (2) and (3), the free body has to be close to correct.  By insisting that students write the object applying and experiencing each force, I force* them to focus carefully on each arrow.  Without this focus mechanism, students tend to draw arrows almost at random, then hang their heads (BAD BOY) when they're wrong.  Don't believe me?  Watch your class work sometime.  I see, again and again, someone draw silly arrows (sometimes before even labeling them!).

* hah!

But if I let them struggle through without asking questions, I often see the same student stop as they start to write the source of each force, stare at the ceiling... then erase the incorrect arrow.

Since I started requiring a list of the source of each force in every free body diagram, I hardly ever see silliness like "force of momentum" in the direction of motion, or the "force of push" when an object was given an initial push, but is now moving without that push happening anymore.

But what happens when the AP exam comes?  It does sometimes require correct arrow lengths, correct starting points for arrows, and not any time-wasting list of sources for forces.

Gotcha.  The AP exam is in May.  I'm teaching free-body diagrams in August; I'm not wholly confident in my students' understanding of Newton's laws until we're reviewing in March or April.

At that point, it's simple to explain this added layer of complexity.  If required, draw bigger forces bigger.  If asked, put arrows for weight at the center of gravity, but arrows for contact forces at the point of contact.

As for the list of sources for forces... these are still worth writing, even on the AP exam, I think.  An ambiguous label like "F1" might not earn credit; but if F1 is clearly defined as "the force of person 1 on the ball", then that could hardly be clearer and will certainly earn credit.  More importantly, even on the AP exam, even after lots of prep, students tend to panic and revert to making novice mistakes.  By disciplining themselves to write the sources of forces - as they have been doing all year - they're more likely to find their groove, letting their knowledge flow.

Dealing with the inauthenticity of formal teacher evaluations

Prologue: It seems I need to be clear that the issues I describe below are NOT happening to me at my current school, Woodberry Forest.  No, the vast majority of my administrators here have had my back regarding anything in the classroom, and I appreciate it.  That - and the honor system - are why I continue to teach at Woodberry.  And while I have indeed experienced some of these issues at previous schools, the post below is not  intended to be autobiographical.  

I talk to probably a dozen physics teachers each year who are dealing with some subset of the story below.  These teachers aren't always perfect, but they are invariably working hard to improve their skills in a difficult profession.  This post is for them.  They need to know they are not alone in their struggles; they need support from those of us who have overcome similar situations.

If you're an administrator reading this... it's likely that you're not part of the problem, because, well, you're taking the time to read this.  But know that being the administrator for a physics teacher is too often similar to adopting a shelter dog. Whatever happened to the dog previously is in no way your fault, and you want nothing but the best for the dog now.  Yet, you are a person, and it's possible - even likely - that the dog has negative associations with some of the things people do.  It's not productive to blame the dog for her skittishness.  All you can do is work every day to build trust.


How many times have I heard the story?

1) Physics teacher doesn't hand out high grades for poor work

2) Students complain to parents and other teachers on ridiculous grounds*

3) Parents fight blindly for their children

4) Administrators either believe the parents uncritically, or set up a "he said, she said" false equivalence between the parents' complaints and the teacher's defense

5) Administrators give teacher a formal list of things to improve, most of which are unrelated to good physics teaching

6) Teacher follows administrator instructions to the letter

6a) Sometimes, administrator moves goalposts, demanding more "items for improvement" that are even more unrelated to good pedagogy

7) Teacher is informed that his or her contract will not be renewed.

* "He makes people sing a song if they forget their homework. How can the school support a teacher who embarrasses his students like this?" There are bigger hills to die on, kid.  Even if your complaint were, well, true.

Physics is different from most other subjects.  For one thing, physics has right and wrong answers; there's no way to BS a physics test by writing an essay with advanced vocabulary and a few buzzwords sprinkled in.  For another, good physics teachers don't play the "game of school" the same way that others do.  Like all good teachers, we expect more from our students than spitting back memorized facts and algorithms.  Yet, experience (and stats from the College Board's exams) show that it's much more difficult to pass a physics class than it is to pass in history, math, English, or language.  Thus, for parents and students it's too often easier to try to fight us politically than to intellectually engage with the subject.

In your first year at a school, or in your first year teaching an advanced class, you cannot do much about items 1) to 3) above.  Expect these to happen to you.  The only antidote is culture building, such that those who advance these complaints become social pariahs.  That takes years - and the timescale of the effect of the complaints is weeks or months. Be prepared.

We can start our riposte with item 4).  Assume - at least until you have serious evidence to the contrary - that your administrators are well-meaning.  In fact, that's usually the case.  Yet, it's overwhelmingly likely that your administrators are benignly ignorant about physics teaching.  So, develop a collegial relationship with them.  Copy them on email updates to your class's parents.  Warn them ahead of time if you know or suspect that a ridiculous complaint might come to them: "Hey, I'm giving my first AP test tomorrow.  Know that my students will all think they failed (they won't have), and they'll work themselves into a state about their grades, because I'm giving authentic AP-style questions.  Please don't respond to any complaints for a few days!  By week's end the students will have done their corrections and seen more clearly how well they did.  If you'd like to talk Friday after school, I'll be around."

If your administrator still brings silly complaints to you uncritically, don't defend yourself.  Point out the ridiculousness of the complaint.  I was recently talking to a teacher whose administrator came to her yet again with something stupid... for example, "Parents are telling me that your class timer ends with a cartoon dynamite explosion, and the students feel uncomfortable because of all the terrorism in the news."  On one hand, sure, it's not a big deal to change timers.

But my response to this administrator would be polite yet aggressive: "For the sake of peace, I'm happy to change the timer.  But I want you to consider your approach here.  Do you truly believe that I'm promoting terrorism, or that I'm bullying students into feeling uncomfortable?  Because if you do, you need to fire me right now - that's not acceptable in this or any school.  Or, do you think that students and parents are finding any little thing they can think of to discredit a new teacher who teaches rigorously?   The next time you hear something silly like this, would you please support me by shutting it down?"

If your administrator is competent, they'll see your point, and listen.  Sure, they may feel obliged to bring a few more of these silly things to you, but they'll do so with a wink; and, hopefully, they'll be more aggressive about shutting down parents.  By calling attention to the lack of intellectual basis for these sorts of complaints, you're forcing the administrator to recognize and acknowledge the falseness of the false equivalence.

And what if the administrator isn't competent?  What if they say something huffy like, "Our parents and students are our customers.  We must always take their concerns seriously.  I'm disappointed that you would dismiss their thoughts as invalid.  Remember, perception is reality."

Then you're on to 5), 6), and 7) above.  But now you know not to take your administrator seriously.

What to do, then, when the administrator responds to complaints with a checklist of elements of your teaching to improve?

Do nothing.  Don't engage a vacuous argument on its merits; don't play a rigged game by the rules.

Understand that a formal evaluation of teaching means nothing.  Yeah, sure, you can make checklists that sound objective, with goals that are black-and-white achieved or not achieved.  It still means nothing.

If the head of the school - the one who decides who is hired and fired - knows your value and wants to keep you, (s)he will do so.  If you don't meet some of the black-and-white evaluation objectives, this school head will suggest that you're improving on those items, or that they don't apply to your class, or that your overall value to the students and the school outweighs the few "deficiencies" in your teaching.  Just keep doing what you think is right for your students, and outlast whichever administrative flunky is giving you trouble.

If the head of school wants you gone, there's nothing you can or should do - (s)he will find a way.  As you meet checklist objectives, more will suddenly appear.  Or, as you seem to meet a black-and-white objective, the school head will suggest that you didn't actually meet it.  (Perhaps they will instead merely rubber stamp the judgment of a subordinate who wants to get rid of you.  That's the same thing.)  You'll be gaslit, undermined, Huckabee-Sandersed, and, eventually, let go.  Nothing you say about meeting your improvement objectives will matter. 

(Imagine that, as Lando lay down his winning hand to take Han's ship, Han had pulled out the thick Sabacc rulebook.  "No," Han told the braying crowd as they reveled in Lando's smackdown.  "Rule 23.1a, section viii allows the opponent to call for an Imperial tournament director to inspect the cards, if the opponent has adhered scrupulously to sections i, ii, and iv-vii inclusive."  Don't you think the Rancor would have shown up five movies early?  That's what we sound like when disputing teacher evaluations - even, especially, if we are right.)

If you're being gaslit, stop trying to please those who are unpleaseable.  Let it go.  Polish your resume, talk frankly to whatever allies you have, and figure out what is best for you in the long term.  A good physics teacher can usually find a job without trouble.  If you absolutely need this particular job for the sake of your family's finances, well, hunker down and live like Syme in 1984 until you don't need the job, or until the revolution comes.  All reigns end eventually.

Your sanity and self respect is important.  Move on to the next job.  Learn from the one you left - but don't try to learn how to please a boss who refuses to be pleased, nor how to better meet teacher evaluation standards.  Learn instead how to get out ahead of whiny parents.  Learn how to judge which colleagues and administrators to trust, and which not to.  Learn how the (often silent) majority of students at your old school are uncomfortable or even angry that you're gone.

And throw yourself into knowing, challenging, and caring for the students at the new place.  Somewhere, you'll find a school who appreciates expertise, and allows room for you to develop even more expertise.