Jacobs Physics Podcast S2 e1: 2018 AP Physics 1 #5, block on a spring

In this year's first podcast, I discuss the paragraph response problem from the 2018 AP Physics 1 exam, plus I digress about

* evil prosecutors and how students emulate them

* energy bar charts for different systems

* using annotated calculations to teach the paragraph response technique

* multiple ways of looking at collision/energy problems

* applying the paragraph response rubric

Go ahead - listen here.  Let me know what questions you have, and what you'd like me to discuss in a future podcast.

greg

The "factor of change" method for semiquantitative reasoning - AKA Bertha's Rule of Ones

Bertha (pictured) is a
very smart elephant 

[Note: Bertha, who is a very smart elephant, uses this "factor of change" approach all the time.  Since about 2020, I've named this method after her: Bertha's Rule of Ones."]

"Semiquantitative reasoning" means problems asking things like "We double the amplitude of an object oscillating on a spring.  What happens to the object's maximum speed?" 

On one hand, you could make up values and solve the energy conservation problem for speed.  Do this twice, once with the amplitude doubled, and see how the result changed.  This is a straightforward method to teach.  The downsides are, it takes a long time for students to execute; it's all to easy for a student to make a calculational error; and most importantly, it's difficult for the student to extract what feature of the mathematics leads to the result, as the AP exam's "qualitative-quantitative translation" questions require.

So, solve in variables, you might say.  Good.  Yet students flounder with simple algebra, working themselves into a circular-reasoning state. "Converting potential to kinetic energy gives the equation 1/2kA^2 = 1/2mv^2.  Since amplitude is inversely proportional to spring constant, the spring constant goes down when amplitude increases.  Then mass is directly proportional to spring constant, so also decreases.  Now mass is inversely..."  Aargh! 

The more astute students solve for speed, getting A times root (k/m).  Great!  But then they start from the original equation again, plugging in (2A) instead of A.  The math that I've seen a thousand times:

Or,

Grrr.  This is what causes the good folks at my workshops to complain a la Gus the Theatre Cat.  ("And I say now these kittens, they do not get trained / in the algebra skills that we once all attained / They never do listen, they're dreaming of sex / And they think they are challenged by solving for x. Hah!)

I've avoided must frustration on my and my students' part by teaching the factor of change method.  This was taught to me about half a decade ago by someone in one of my summer institutes - I forget who, or I would credit her or him here.  (If it was you, please let me know and I'll update the post!)

In the factor of change method, you start by solving for the requested quantity just once, and in variables only:

Now, plug in a (1) for every quantity that doesn't change; and plug in a (2) for a quantity which doubles.  Or a (3) for a quantity which triples, or a (1/2) for a quantity that's halved, etc:

Look how the algebra difficulties have been cut through like a knife through hot tofu. The max speed is multiplied by 2.  Done.  

I do need to show students that a numerical value in an equation - like a 2 or a pi - cannot change, and so we plug in (1) in the factor of change method.  They get that very quickly.

What feature of the mathematics leads to this physical result?  Easy enough - the speed is related to the amplitude.  With k and m constant, doubling amplitude leads to a twofold increase in speed.  The factor of change method strips the mathematics down to the simplest, most comprehensible skeleton I can imagine.

Note: I updated this post when Brian Frank pointed out a math error in the original.  Grrr.  Thanks, Brian.  :-)

First year physics teachers - please don't despair. Plan for next year.

I have horrible memories of February 1997 - or rather, I have suppressed most of this era to the deep recesses of my inaccessible long-term memory, right alongside the times Chris Jobert secretly stole my math homework in third grade.*

* I got a C- in math that year, and was shamed for irresponsibility.  One day I even discovered the homework ripped up in the bottom of the garbage can by Jobert's desk - and I remember thinking, "When did I rip up my homework?  Why did I do that?  I'm in so much trouble..."  Things turned out okay: I ended up with a degree in physics, and Chris ended up with an arrest record.  Suppression time again.  Toot toot, here comes the happy train!

What was so awful about February 1997?  It was the depths of winter in Chicago during my first year teaching.  I had been (figuratively) beaten down for six months, with end of the school year not yet close enough to fathom, and in an inextricable downward spiral in relationships with my students and my colleagues.  Parents had complained about me so much that the school brought in a special mentor just for me - never mind that my middle-aged, "experienced" co-teacher needed mentoring or a good kick out the door far more than I did.  Students had been as successful in their smear campaign against me as Russian trolls were with Hillary Clinton - colleagues and administrators believed whatever negative things students said about me, no matter how outrageous, no matter how untrue.  My principal (who somehow, unfathomably, still has a job) once even sat by silently and allowed a parent to berate me for 45 minutes about claims that were exaggerated, spun negatively, or simply false.

I've said before - I really don't know why I stayed in this profession.  

I'll bet this sounds familiar to you.  Everyone was a first year teacher; some of you are right now.  I hear versions of this story so, so often in my workshops, in conversations in the physics lounge.  You feel like you stink at this.  Teachers and administrators offer condescending, unsolicited, and out-of-touch advice; the colleagues you observe seem to be holding classes and lab exercises every day that you might be capable of running once a month if you prep for hours.  You wonder why you're wasting your time and your life in a Sisyphean job in a hostile work environment where you're not appreciated.

Take a long-term view.   It is a sad, systemic indictment of our schools that we allow and almost expect first year teachers to be beaten down.  Yet things do get better. 

It's practically impossible to change a classroom culture in February.* That's as true in your 24th year as in your first year.  So don't try to work miracles!  If your students seem hostile in class at this point of the school year, all you can do right this instant is keep calm and carry on.  

*Impossible to recover from a negative culture, yes, but the good news is it's also impossible to bring down a positive culture once it's well established.

Build what relationships you can.  Aim your teaching at the subset of students who are NOT hostile, who wish the loudmouth haughty disrespectful arses would shut up.  Consider that these students feel as helpless as you - and they've likely had to deal with the arses for many years, in many classes.  Develop your relationships with them.  Hold your head high for them.  Keep on working hard for them.  Think about them when you arrive home each day.  They do and will appreciate your efforts and attention.

Make plans for next year.  Though it's tough to change a classroom culture right now, you can consider how to pre-empt negativity from the beginning next year.  Some of that advice that seemed so disconnected from your current reality might work well if implemented next August.  Your initial idealism about this job has been blunted by hard-edged practical reality.  The positive spin on this is that you know what you need to do for next year.  Make plans.  Write plans.  Edit the activities that didn't work, and do so right now before you forget.  Keep everything you've done in soft copy; plan some time this summer to organize those computer files so that you have something to fall back on when you need a last-minute class idea.  Make notes about things you wish you had done or said that might have established a better tone.  Consider how you could have dealt better with the first kid's complaint, such that the second complaint was less likely to happen at all.

Epilogue.  I wasn't hired back at that first school.  

The students found this out right after spring break.  And a couple of days later, the headmaster found a petition on his desk signed by the vast majority of my 60 students requesting that he reconsider his decision.  The headmaster never said anything to me about this - the bastard - but the students did.  Many students.  Some students who I thought hated me.  Some who had been angrily silent at the stupidity of their peers.  Some who had been friends to me from the beginning, though I had been so depressed I almost had forgotten.  Some who suddenly became vocally upset that there wasn't a place at their school for a teacher like me.  

Point is, even in what were my darkest professional times, the students whom I had tried to care for cared back.  They noticed.  

Their petition was hopeless - since when can students get an administrative decision overturned, plus I had to politely explain that even if the headmaster changed his mind, my relationship with him and the school was irrevocably damaged.  Yet those students gave me strength and hope that perhaps I could succeed in this business.  Sure enough, I went on five interviews and had my pick of two good teaching jobs.  The next year, even at a new school, was far smoother because I didn't make the same mistakes twice.  (I made new mistakes, but I learned from those, too, in the long term.)

I still have occasional sleepless nights in which I seethe in anger at something school related.  That never totally goes away, unfortunately.  I wish that I weren't a permanent outsider to not just my current school's culture, but to that of every school in America; I wish bullies - both adult and teenaged, both deliberate and accidental - didn't exist; I wish that successful teachers garnered the same public respect as successful football coaches or singers.  I wish frogs had wings so they didn't bump their arses on the ground when they hop.

If you still believe you can help your students learn physics, I hope you'll stay the course.  Teaching can be overwhelmingly rewarding.

What do my students have to do to get credit on the AP exam? (They have to *communicate*.)

We're in the time of year in which AP classes have discussed enough material that they're trying out more and more authentic AP questions.  And teachers are grading to authentic rubrics, trying to give students advice about earning credit.  

There is only one piece of advice your students need:  communicate clearly.

Should I teach my students to box their answers?  If you insist... but who cares?  If your student clearly communicates the steps toward the answer, the reader will follow.  

But if they don't communicate clearly, won't the boxed answer help the reader find the answer?  Maybe, but credit isn't always awarded for just the correct answer.  (In AP Physics 1, there's hardly ever a numerical answer, anyway.)  I strongly encourage teachers not to teach games or tricks.  Rather, insist on clear communication from the get-go, such that "always box your answer" becomes as redundant as reminding an opera star to project her voice.

What if a student uses notation different than our textbook?  Is the student clear about what they mean?  Then it's okay.  For example, some texts teach to call rightward forces "positive" and leftward forces "negative", then add the forces using signs.  Others suggest subtracting the right forces from the left forces.  Who cares?  If the student clearly articulates their approach, if the student is consistent and correct in applying Newton's Laws, that's all good.  The exam is graded by physicists, not lawyers - readers rarely stand on ceremony about a notational issue unless it makes the physics wrong.

But what if they lose a point because...

Relax!  All these sorts of hyper-specific questions from teachers usually boil down to a student complaining about losing points on an assignment.  We have to elevate the conversation so that we're not arguing about points, we're teaching how to communicate physics principles.

When your student has an authentic question about how you applied the rubric, or about the physics concepts underlying the rubric, certainly answer as best you can.  But read your student's body language.  When they roll their eyes and throw up their hands, showing everyone that teacher is pond scum who obviously is too stupid to hold a job; or when they use the wheedling tone of a car salesman suggesting they might throw in free floor mats if you'll award the point; stop.  Don't engage.  You're not going to win the argument.

Winning the argument isn't the purpose of the exercise.

I understand the difficulty of a teacher's position here... if you're not an AP reader, you are trying your dangdest to interpret official rubrics, and to apply them to responses that you're not sure about.  Where can you go for guidance?  You're looking for hard and fast rules, clear boundaries between right and wrong.  You must recognize that such boundaries simply don't exist.  Even at the reading we see edge cases, responses that are quantum superposition states of earning a point and not earning the point.  

The best advice I can give is to ask, "did this student clearly communicate a physically sound approach to the problem?"  If not, don't award points.  The burden of proof is on the student.  When in doubt, it's wrong.  

Now, don't be nit-picky... consider that the audience for the clear communication is an intelligent person with the same level of physics knowledge as the student.  

But at the same time, don't read in to what the student has written; don't let the student argue about what they meant to say.  It doesn't matter what they meant to say; we grade what they did say.  I've never yet, in 20 years of reading AP exams, had a student follow their exam around the reading rooms lobbying for points, telling the readers what they meant.  And so I don't allow such a thing in my classroom.

In the end, grading AP problems is like calling balls and strikes.  Do your best to establish a zone.  When it's close, call a strike without hesitation or second thought.  When someone looks at you funny, smile and move the game along.  As long as your zone isn't ridiculous, as long as you seem kind but firm, everyone will just shut up and play.  And that's what we came to the field to do, after all.

US Invitational Young Physicists Tournament - results 2019

Last weekend (January 26-27, 2019) Rye Country Day School hosted the 12th annual USIYPT.  There, teams compete in "physics fights" over four problems, this year involving:  

     * Faraday's homopolar generator

     * Rainbow formation on this and other planets

     * Pneumatic tubes, and scaling them up for transportation

     * How a hammer twists in the air when tossed

This is not a science fair!  Teams report unique solutions, yes... but before the jurors say anything, the other team engages the reporter in conversation and questioning.  The jurors' job is to evaluate the strength of the physics in each team's discussion.  The USIYPT is more similar to a scientific conference than to a typical high school contest.

This year's winners, for the second year in a row: Phillips Exeter Academy of New Hampshire, led by physics teacher Scott Saltman.

In second place was Phillips Andover Academy of Massachusetts, led by Mika Latva-Kokko.

The winner of the Swartz Poster Session was the Pioneer School of Ariana, Tunisia, led by Safouen Rezgui.  

The overall order of finish is below.  Our rules state that a number of places are shared by similar teams - this is to emphasize that just participating, merely being able to engage in high level physics fights, marks a team as among the best high school physicists in the world.  

The ** means that this team won the prestigious Bibilashvili Award for Excellence in Physics.  It is awarded to teams with superior physics understanding, irrespective of their placement, at the tournament director's discretion.

Champion:

     Phillips Exeter Academy, NH**

Second place:

     Phillips Andover Academy, MA**

Third place:

     Woodberry Forest School, VA**

     Shenzhen Middle School, China**

     The Nueva School, CA**

Fourth Place:

     Cary Academy, NC**

Fifth Place:

     The Harker School, CA**

     Pioneer School of Ariana, Tunisia**

Sixth Place with Bibilashvili Medal:

     Rye Country Day School**

     

Sixth Place, in alphabetical order:

     Pioneer School of Menzah VIII, Tunisia

     Qingdao No. 2 High School, China

     Spartanburg Day School, SC

     Vanke Meisha Academy, China

How do you participate in the USIYPT experience?  

Our 2020 tournament will be hosted at Phillips Exeter Academy in New Hampshire, on Feb. 8-9.  I'd suggest starting out by serving as a juror.  We try to get jurors from all sorts of backgrounds... retired folks, industry professionals, university professors of all sorts, high school teachers, graduate students, undergraduates, etc.  Juries develop a deep and special camaraderie after a day or two discussing physics with each other and with students.  If you have a background in the physical sciences, we'd love to get you involved.  The sponsoring organization (USAYPT) can put you up in a hotel for the weekend, and we'll invite you to the much-anticipated annual Juror Dinner.

To bring a team, start by taking a look at the problems for 2020.  Your team must have a ten minute report prepared on three of these problems.  Then the physics teacher at the prospective school should email me to request an invitation.  Later in the summer, we will post information about fees; we'll issue invitations in September or so.

I'm always happy to discuss the USIYPT experience.  The tournament is, every year, the highlight of my professional life.  Those who participate contribute to a special, unique culture in which the "Search for the Truth" of physics leads to discussions, debates... and long-lasting friendships.

Greg Jacobs

President, US Association for Young Physicists Tournaments