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29 August 2016

A letter to my forthcoming AP Physics 1 class

School starts for me in a couple of days.  I've got a wonderful first-world problem to deal with: I have more students signed up for my AP Physics 1-equivalent course than I have desks in my very large classroom.  

We're going to eventually deal with this issue by moving in more desks.  But first, I want to be sure that these prospective students know what they're getting into.  I'm more than willing to teach an enormous class -- as long as everyone in the class is there for the right reasons.  

Below is a letter I've sent to everyone who's currently enrolled.  Note that I've attempted to communicate my personal excitement and investment in the material -- those of you who read my blog know all about that, but students who don't know me well aren't familiar with my eccentricities.  See the part where I reassure both first-time and second-time physics students that this course is for them.  No calculus nor previous physics required, though previous physics doesn't mean you'll be bored.

And finally, note the direct approach to issues of mindset, pedagogy, and reasons for enrolling.  I've heard from large numbers of good physics teachers who are similarly direct and transparent with their classes, especially because AP Physics 1 is so fundamentally different from most any class my students have ever taken before.The advice I got was, manage expectations, plea repeatedly for students to have patience with me and with themselves... and then I'll be likely to have a great and exciting year because success will come sooner than the students expect rather than later.

GCJ

Hey, all... I have you signed up for Honors Physics 1.   I wanted to give you some background information about what this class is all about.

The course itself is exciting, with lots of hands-on laboratory work.  You'll learn in tremendous depth the rules that govern how objects move, how circuits work, how waves propagate.  I've been studying physics for more than a quarter century, and I still discover new and exciting things each year.  Physics is the best.

Honors Physics 1 is a college-level introduction to physics.  We will prepare you to take the AP Physics 1 exam in early May -- based on past history, you're likely to do well, almost always well enough to earn college credit.  When you take an actual college physics course, your experience here will make you the natural leader of your class.  You'll be the one explaining physics to your friends, often with enthusiastic hand gestures and quick experiments that you make up on the spot.  

Now, that said, I'd like you to consider your reasons for taking this course.  Success in physics cannot be attained by merely "hard work".  You will need to enter into this year with a growth mindset, willing to dive headfirst into learning new skills.  Homework, test, and quiz problems will NOT be essentially identical to the ones we did in class; every physics problem represents a new situation, a new puzzle to be figured out.  We will do extensive experimental work, in which you will not be given a list of instructions, but rather a task to accomplish in a creative way.

Are you taking physics for the first time?  That's fantastic.  Though some members of the class will have taken conceptual physics previously, I assume that you have no prior knowledge of physics -- nor any mathematical skills beyond algebra 1.  Honors Physics 1 can be a perfect introduction to rigorous college physics.  By the end, you'll know exactly how to learn physics, such that you can advance to the next level of physics in college; or such that you acquire a serious background in the subject even if you know that you never want to take another physics class.  First-timers are in the right place.

Have you had conceptual or general physics before?  That's also fantastic.  We will cover some of the same topics you've already seen, but at a much deeper level conceptually, mathematically, and experimentally.  You'll get a chance to answer some of those burning "why" questions that your teacher told you were beyond the scope of your first course.  We'll talk about motion, force, energy, momentum, waves, and circuits, but also rotation and universal gravitation.  Honors Physics 1 can be a great follow-up that prepares you well for (or, on the contrary, can exempt you from) college physics.  Second-year physics students are also in the right place.

But please think carefully.  Are you taking this course mainly so that you can pad your college resume or your GPA?  Is a primary motive that honors physics will make your transcript more impressive?  That you're more likely to advance your GPA above some target if you're in an additional honors course?  If so, this is definitely not the course for you.  It's not that my students' grades are ever really bad -- most everyone tends to get As and Bs, with Cs rare.  It's that if you're not exited about and intrinsically interested in the course content, the effort necessary to earn those grades will not be worth it.  You'll find yourself angry and resentful at a subject that can't be conquered by sheer force of will.

Think how you will react when a test asks you about kind of situation or experiment that you've never seen before in class.  If you'll say, "you didn't cover that, that's not fair, how did you expect us to know", this physics class is not for you.

But if you'll say, "cool, here's my best shot, I hope Mr. Jacobs lets us try this in lab next week to see whether I'm on the right track", then you are perfectly placed in honors physics.

I'm always ready to talk about physics.  Feel free to call or email.

Thanks!  Can't wait to do some physics on Wednesday.

GCJ

19 August 2016

The five-foot rule: one approach to encouraging effective collaboration

We all want our students to collaborate effectively on problems.  Problem is, there's a very fine line between working together to solve a difficult problem, on one hand; and simply copying another student's work, on the other.  And, no matter how obvious the difference may be to us, students don't necessarily get it.

It took me a while to learn about this disconnect between my own academic experience, my expectations, and those of my students.  At a previous school I became very frustrated and angry with students who seemed like they were copying each others' homework solutions.  And, they were copying, without question.  In their minds, though, they were merely reporting together the results of their effective collaboration -- that same collaboration that I had encouraged so strongly.  So they weren't happy with me for being unhappy with them for following my own instructions.  If you follow.  

The most important step I took toward resolving this difference of understanding was to re-cast the issue so it wasn't about academic integrity.  I couldn't say "don't copy and don't cheat" if the students and I had such good-faith but widely varying ideas of the definitions of "copy" and "cheat."  Rather, I had to find a way to give clear guidance to define the line between collaboration and copying, without invoking the emotionally charged language of academic integrity.

What I came up with, and what has served me well for decades now, was the Five Foot Rule.  My syllabus states*: 

The Five-Foot Rule
We encourage students to help each other.  You may even verbally guide a friend step-by-step through his solution to a problem.  However, do not under any circumstances just give someone your solution “to look at later”.  A friend may, in your presence, look briefly at your work to start himself in the right direction, but no one should ever be using another student’s written solution as a detailed reference.


Thus, when you are actually writing something to be turned in, you must be located at least five feet from any other physics student.  Do not do your homework while sitting next to someone; rather, sit well apart from one another in a dorm or conference room; or, have a discussion, then separate yourselves to write up your solution.

* Remember, I teach at a boys' school, so my use of gendered language is deliberate.  Please don't flame me.

Students who obey the five-foot rule are hardly likely to be copying, unless they have x-ray vision.  The point is for all students to explain the result of collaborative discussion in their own words.  

Then, when inevitably you find two identical problem sets, you can avoid making accusations of dishonesty or cheating.  You can simply discuss the obvious violation of the five-foot rule, and ask that this rule be adhered to.  If the violations continue, and you have to get parents or administrators involved, you are likely to get support.  

Accusations of cheating or copying carry harsh implications. Parents instinctively defend their children, logic be damned.  Administrators question whether it's worth their political capital to engage in a fight over small-scale homework copying -- especially when you expressly encouraged collaboration!

But you're not accusing anyone of cheating, no, not at all.  You're merely asking for cooperation in enforcing and adhering to a straightforward class rule.  Just as students are expected to treat laboratory equipment carefully, just as they're expected to show up on time with their homework finished, they're expected to sit five feet from anyone else when they write work to be turned in.  That's a reasonable enough procedure to follow that students look like idiots if they protest. 

So they don't protest.  And they follow the rule.  And so they do their own work... often with help, often by rephrasing what a friend told them.  But that's fine -- rewriting in one's own words is a significant step toward deep understanding.




10 August 2016

Secret to AP Physics 1: Build *gradually* from calculations to verbal-response

Last year, I swore a blood oath that I would never teach juniors and seniors again.  I loved so much my 9th graders' growth mindsets, their puppyish enthusiasm, their enduring trust in an expert teacher who cared about them.  I could not have been happier teaching the conceptual and the AP 9th grade course.

Well, um... sometimes the Patriots need Troy Brown to switch from reciever to defensive back; sometimes the Yankees need Alex Rodriguez to play third base rather than his natural shortstop.  And, needs must in the physics department, too.  I've gotta pick up the junior-senior AP Physics 1 class this year.  Unless I'm mercifully struck by lightning for breaking my blood oath, anyway.

The good news is, I've made and learned from a bunch of mistakes in teaching this course a couple of years ago.  See the series of three posts (starting here) from April 2015.  

You've heard over and over that AP Physics 1 requires deep understanding and verbal reasoning.  I've told you, the College Board has told you.  The released free response require zero -- ZERO! -- numerical calculations over four exams.

Yet, my problem sets through the first several months require calculations.  My first test in September is constructed based on old AP Physics B items, which require numerical calculation.  Even my mid-February test includes two Physics B-style free response questions along with a paragraph response item.

Of course, these problem set and test items are hardly just "find the right equation and plug in numbers" questions.  They include "justify your answer" parts, qualitative-quantitative translation, "explain what would change", and all sorts of questions that probe understanding beyond just calculation.  But they start with calculation.  Why?

Because I learned the hard way how fixed-mindset juniors and seniors approach this new and intimidating subject.

My students are used to math class, where the method is subordinate to the answer.  Explaining how to solve a problem is less important than clever use of various routines to get to the answer.  The test of whether a problem is done sufficiently is simple -- compare the student's answer to the teacher's or textbook's answer.  Black and white, right or wrong.

Yet, in their writing classes, much is negotiable.  Style is personal, both to the student and the teacher.  Is this piece of literature referencing Homer's Oddyssey?  Very likely a clever student can make a resonable argument, however tortured, which will -- if phrased with good grammar and big words -- earn high marks.*  My wife the English teacher tells of pointing students to clear rules in grammar books, only for the students to tell her that the rule doesn't apply to their particular paper, or that the rule itself is wrong.

* The teacher may give these high marks as much to avoid the inevitable protracted lawyerly discussions about why the marks should have been higher as because the paper actually deserved high marks.

The skills required for AP Physics 1 are far closer to those used in English than in math.  A problem is similar to a page-long essay.  The explanation is as important as the conclusion itself, as is demonstrated by the released free-response rubrics which award little credit for answers in the absence of clear justification.

And therefore, veteran students revert to English class mode.  I can't tell you how many quasi-confrontations I had with upperclassmen:  

"What's wrong with this answer?"  

"Well, as we discussed in class, you've gotta connect the conclusion that the distance increases to the fact that the mass is in the denominator with all else constant, and thus is inversely related to distance." 

"I said that."  

"No, you just said 'distance increases because of the mass.'"  You have to explain the connection between mass and distance with reference to the relevant equation."

"Yeah, I know, that's what I did.  Now what's wrong with that?"

"Who's on first?"

Start the year with calculation in order to avoid these frustrating converstaions; and in order to build the skills that will allow for better and better explanations throughout the year.  When I assign calculational questions, no one ever asks "what's wrong with this answer?"  They know: the numerical result doesn't match my numerical result.  Instead, they ask, why didn't I get the right answer?  That discussion is usually extremely productive.  And, I can follow up those discussions with a targeted quiz question about how a common error led to a wrong answer.  

Point is, instead of blaming me for their own inadequacies, students who get numerical calculation questions wrong tend to be willing to hear about the source of their own misunderstanding.  The process of correcting their work, of identifiying common errors, teaches the very skills that AP 1 demands.

By March, I can give exclusively AP Physics 1 items, with no calculations whatsoever.  That's because I've weaned the class off of numbers as a crutch, or of numbers as a way to avoid an unproductive argument about points.  After months of exposure to physics problem solving and laboratory work, my students understand the point: not to earn points, not even to get the right answer... but to explain how the natural world works based on the facts and relationships we've studied.  


30 July 2016

Why four rather than five choices on AP Physics 1?

Blog- and AP- reader Barbara sends the question:

Any idea on the rationale for moving from five voices on the MC to four?

Barbara, mainly this was a reading density issue. 

Reading, writing, and understanding English* are inescabable and fundamental parts of learning physics.  Nevertheless, we want the language in questions to be straightforward and minimalist, such that the language doesn't become an obstacle to demonstrating physics knowledge.

* Or another language, of course... but the AP exam is in English. :-)

The College Board and ETS do psychometric** research investigating their exams, and their examination techniques.  For example, they've shown that deducting 1/4 of a point for an incorrect multiple choice answer doesn't differentiate between students any more than just scoring the number of correct answers directly.  At the AP reading, investigations have shown that grading a physics problem holistically*** produces scores indistinguishable from traditional grading.  

** I may have made that word up

*** Meaning something like "2 points for a complete answer, one for a partially complete answer, 0 for a lousy answer" as opposed to assigning each point to a specific element of the response

In terms of five vs. four multiple choice choices, data shows that either approach differentiates students of varying ability appropriately.  (I don't know, 'cause I never asked, whether five-choice questions differentiate better.  The statement I'm remembering is that four-choice produces statistically significant and reliable differentiation.)  

Once the case for the statistical validity of a four-choice exam was made, then it was a shoe-in as the superior option.  Statements from test developers suggested that question authors too often seemed stretched to create four incorrect choices that each made sense -- they got too many questions where some choices could be ruled out on the grounds of "this sounds totally silly and made up."  With only four choices, it's easier to create three incorrect yet plausible responses that directly test student misconceptions.

The bigger issue, though, was the reading burden on the student.  Even for a very well constructed five-choice item, the student still must take the time and intellectual effort to read an extra choice.  The psychometric studies suggested that most students were not, in fact, reading and understanding all five choices; and, that students who DID read all five choices often had to read them multiple times to make a reasonable decision as to the best answer.  

It was clear from the beginning of AP Physics 1 that this new exam would require considerably more verbal expression than AP Physics B did.  So the College Board and ETS made several changes to the format of the multiple choice, with the goal of minimizing the reading comprehension burden:

* Item authors are now required to justify the incorrect choices, explaining how each choice helps differentiate students who understand the physics targeted by the item from those who don't

* The multiple choice section has been reduced from 70 questions to 50 questions, giving students more time to digest the more involved language used in the new exam

* The "roman numeral" question type has been replaced by "multiple correct" items.  (You know, those questions that gave I, II, and III, and THEN gave lettered choice such as "I only" or "II and III, only".  The studies showed that the reading comprehension burden was especially high on these.  However, simply choosing the two out of four correct choices does not require significant additional reading over a standard question.)

* And, as we're discussing... the number of choices was reduced from 5 to 4.

Now that I've taught extensively under both four- and five-choice regimes, I do prefer the four-choice.  My observation is that on the occasional wordy conceptual problem, students can more often than before appropriately eliminate three incorrect choices in preference to identifying the correct answer directly.  I think -- based on no evidence but my own decades-honed instinct -- that with fewer choices the test does zoom in more sharply on my students' physics skills than if those students had to wade through and weigh one more option in every item.  If nothing else, I don't perceive the same level of mental fatigue after a practice test.  And that was kinda the whole goal.

GCJ


25 July 2016

Justify the ones you missed for homework -- adapting to an every-other-day schedule

It's time for me to adapt to a new ecosystem.  

For the last nineteen years, my classes have met five days a week.  Thus, my assignments and course structure have been adapted to that schedule.  At boarding school, an assignment has been due every day, because students have structured study time each night; at day school, longer assignments were due twice a week, knowing that the students liked to plan to gather about twice a week to do their problem sets together.  In class, I've saved the longer laboratory exercises for my single 90 minute period each week, using the other meetings for quantitative demonstrations and shorter experimental activities.

This year, though, my class meeting schedule has changed.  My classes will meet for 40 minutes on Mondays... but then two more times in the week for 90 minutes each.  That's less actual meeting time than previously; but I'm not losing much in terms of effective teaching time.  See, 90 minutes straight is much more effective than the two separate 40-minute periods that are being replaced, simply because we don't have to stop working, clean up, and rev up again the next day.

Thus, the way we spend in-class time will hardly change at all.  I already go to great lengths to keep students moving around, focused but relaxed, doing a variety of activities with clearly articulated goals.  Generally, my class already says "aww, crap, can I just finish this real quick?" when I tell them to clean up for departure.  So teaching for 90 minutes straight will be a godsend, not an obstacle.

How I assign homework will have to change, especially in conceptual physics.  The whole theory behind an every-other-day schedule is that without the grind of having to prepare for every class every day, students can pay better attention to engaging intellectually with each night's work.  So, um, that means our faculty have been specifically instructed NOT to simply double the homework we used to assign each night.  I fully support this initiative, as problem solving is a creative process with a law of diminishing returns.  (If you can't lift weights every day in preparation for football season, you can't simply double the number of pounds you're lifting every other day.)

The way I'm thinking now is to divide a night's assignment into two parts.

* The first part is a standard nightly problem set, like I've been assigning for decades.  Remember, a "problem set" is far more similar to an English essay than to a night's worth of math problems.  Written explanations and justifications, not numerical answers, are the dominant feature.

 * The second part begins with a set of multiple choice questions to be done individually.  (The requirement for individual work can be enforced by giving five minutes at the end of class to answer; or, you could use webassign or the equivalent to randomize the questions and the order of the answers, so collaboration would be ineffective.)  I'm going to use socrative to collect student responses electronically.  

Each student will see immediately whether his answer is right or wrong to each question.  The actual assignment, due the next class day, is simply justify the ones you missed.  

Think of the incentive for the students to take these multiple choice questions seriously.  No matter what kind of or how much work you assign, in class or out of class, it is beyond useless unless the students are thoroughly engaged in discovering and understanding the correct response.  Practice doesn't make perfect -- only perfect practice makes perfect.

In this case, the opportunity to avoid doing more homework is what motivates everyone to engage carefully with each multiple choice question.  

Get it right, and it's done and dusted.  

Get it wrong, that's okay.  There's no grade penalty, no disappointed sigh from the teacher, no whipping with a wet noodle.  Every question that's wrong does require some major work to discover, understand, and then write up the correct solution, but that's work that the student knows needs to be done.  After all, he just got the answer wrong, so it's obviously important to figure out how to do it right, right?


08 July 2016

So what does an ohmmeter read when it's directly connected to a non-ohmic bulb?


The previous post describes my students' results showing that a flashlight bulb's resistance varies.  Over the available voltage range of 2 V to 8 V, the resistance (determined by the slope of a voltage vs. current graph) varied from about 50 V to 80 V.


The question was, what does an ohmmeter read when placed directly on this bulb?

Consider how an ohmmeter generally works.  It puts an awfully wee voltage across the bulb, and measures the resulting wee current through the bulb.  Then the meter essentially uses ohm's law to calculate resistance.  (That's why you have to disconnect the bulb from the battery in order to use the ohmmeter.)

In the context of our experimental voltage-vs.-current graph above, the ohmmeter is measuring an out-of-range data point, way off down and to the left of the portion shown.  By extrapolating the curve shown, we could guess that we should get a shallower slope and thus a smaller measured resistance.

Sure enough, the meter measured about 8 ohms, a full order of magnitude less than the resistance in the bulb's operable range.  

Again I caution teachers: this is a cool and somewhat unexpected result.  Nevertheless, it's rather irrelevant to the typical practical analysis of a bulb.  The bulb only glows at all with a volt or two across it; the bulb is only rated to about 6 V, meaning it is likely to burn out over that voltage.  In the operable range, the resistance is reasonably steady.  The resistance only drops by an order of magnitude when the voltage is dinky.

The next question: How can we experimentally extend this graph?

My variable DC supply only goes down to 2 V.  I could get a 1.5 V battery to get one more data point, but that's all I can think of.  Does anyone have a suggestion of a way to explore the parameter space below 1.5 V?

GCJ




05 July 2016

More on the light bulb that doesn't obey Ohm's law

Data collected by my students showing a non-ohmic bulb
Before I get into a discovery about the non-ohmic nature of a flashlight bulb, an important caveat:

Until the very end of your circuit unit, treat bulbs as regular old resistors.

Like everything in introductory physics*, it's important to start simple and build complexities in gradually.  Teach your students to deal with ohmic bulbs.  The only difference between a bulb and a resistor should be that a bulb produces light; the brightness of the light depends on the power dissipated by the bulb.


* And in high-level physics research, as well

Then, ask them in the laboratory for experimental evidence that the bulbs actually do or do not obey ohm's law.  My students' evidence is shown above -- click to enlarge.  Over the available range of voltages of about 2 V to 8 V, the bulb's resistance (determined by the slope of the V-I graph) varies from about 50 ohms to 80 ohms.  

Importantly, that doesn't mean that the first approximation of a constant-resistance light bulb is a bad one, any more than the first approximation of no air resistance invalidates the study of kinematics.  In most laboratory situations in introductory physics, the ~30% difference in resistance -- less difference if the voltage range being used is narrow -- will still produce quantitative and qualitative predictions that can be verified experimentally.  For example, the typical "rank these bulbs by their brightness" will give correct results pretty much irrespective of the non-ohmic nature of the bulbs.

Asking a new question -- what will a resistance meter measure?

In my AP Summer Institute in Georgia last week, a couple of participants set up this experiment (it's based on the 2015 AP Physics 1 exam problem 2), getting results pretty much exactly as reported above.  Then the question came up, what would a resistance meter measure?

Here's where, in class, I'd give everyone a minute or two to write their thoughts down on a piece of paper.  You can do that too.  I'll wait.

In fact, I'm not giving the answer yet.  I've posted a twitter poll here where you can give your thoughts.  Answer coming in a few days.

(Yes, Jordan and Hannah who did this experiment... you may vote.  Just wait to comment here until the votes are tallied.  :-)  )

GCJ

01 July 2016

Cure, don't innoculate

Public health initiatives are perhaps the greatest ever victory for the marriage between civic policy and science.  We don't cure polio -- we get vaccinated against polio.  So, so many diseases have been wiped out.  Many chronic conditions have been mitigated by not just vaccinations, but also by initiatives we take for granted such as employee hand washing and "no shirt, no shoes, no service."

Into this atmosphere dives the physics teacher, someone who stands directly on the boundary between civic policy (in the form of the education establishment) and science.  It's not a surprise that we instinctively take our philosophy from that of public health, that an ounce of prevention is worth a pound of cure.  We forewarn our students about common mistakes.  We take pains in our presentations and instructions to minimize incorrect answers on the problems we assign.  We'd rather students listen to us and avoid mistakes rather than submit silly wrong answers on homework or tests.

Problem is, when it comes to understanding physics, that philosophy is dead wrong.  

Look, I know you don't want your students to mess up.  So you give them hints and warnings ahead of time. "Be sure not to use kinematics when the acceleration isn't constant.", you say.

How effective have those warnings been?  Evaluate objectively.  On one hand, I expect that you've thrown up your hands and screamed at the students* who used kinematics to solve for the maximum speed of an object on a spring, despite your advice.  "They didn't listen," you'd say.  Possibly, possibly... it's equally likely that they did listen but didn't make the connection between your advice and the actual problem solving process when the moment was right. 

* Or at least at their homework papers, which can no more hear your wails than can the Cincinnati Bengals coaching staff when I wail at the television.

Either way, the class time you took attempting to prevent these canonical mistakes has been wasted.  So has the political capital you used in insisting that your students sit and pay attention to your warnings.  (Don't underestimate the concept of "political capital."  You can only demand so much attention from your students; use it wisely.)  

What if, instead of trying to prevent the mistake, you allow your students to make a mistake?  What if you practically set them up to make a canonical mistake?  Then, when they screw up, they have the context for preventing future occurrences of the same mistake.  They used kinematics for non-constant acceleration; they got a wrong answer and lost points.  NOW, you can explain why kinematics doesn't work, that the work-energy theorem is the way to go.  NOW your students will listen, because they have a personal and immediate interest in figuring out how to rectify the mistake they just made.  Next time they're likely to remember both the incorrect and correct approach.  That's a natural learning process.

"Oh, that's cruel, Greg," say some readers.  "We shouldn't punish our students by setting them up to lose points.  Possibly a couple of students would have avoided the mistake if you had gone over this sort of question before assigning it.  

Huh?  I'll leave the emotionally loaded and incorrect language of "punish" for another rant.

My approach makes perfect sense if you're taking a long term view of physics class.  Saving a student a couple of points on this problem set is insignificant compared to building a lasting understanding of physics concepts such that he can perform well on the AP exam, the course final, on his college physics tests, in his job.  Setting a student up to make mistakes, which in turn create contextual learning opportunities, will save the class numerous lost points in far higher-stakes situations.

And finally, consider those couple of students who got the answer right initially due to your warning.  Ask them, "how did you know that you should use energy methods rather than kinematics?"  The answer is very likely to be, "because you warned us about this issue in class yesterday."  How does that build understanding?  You want them to build good problem solving habits and skills.  In introductory mechanics, those habits include, "check whether acceleration is constant when deciding on an approach."  Those habits do NOT include, "get my teacher to tell me how to solve this problem."

In physics teaching, an ounce of cure is worth a pound of prevention.

13 June 2016

Write two equations, but DON'T SOLVE

Our students come into physics expecting a frustrating math course.  Then many get even more frustrated -- not only do they have to solve math problems, but they have to create their own problems to solve, to boot!  Guh.

In an honors or AP level course, it's important early in the year to make a big show of separating the physics from the math in problem solving.  Firstly, here are some facts, concepts, and a routine that will set you on the path to a solution; then, here's how you know that the problem is set up appropriately, that doing ninth-grade algebra will in fact lead to a solution.  I go so far as to write, in big capital letters, PHYSICS IS DONE.  Students do the same, initially to poke some fun at me, but then as a way of communicating their problem solving.

The canonical technique for recognizing mathematical solvability is to write a relevant equation, then to identify known and unknown variables.  Once we have a single equation with a single unknown, the problem is solvable; similarly, two equations and two unknowns is solvable.  But don't underestimate how intimidating the actual mathematical solution process to a two-equation system is to a high school student.  They may have passed algebra 1, but I trust my students to get accurate solutions even less than I trust the evil bastards of the TSA to get me to my gate in a timely, convenient, and comfortable manner.

Very early in the school year, I assign the hanging stoplight problem.  You know, an object is suspended by two strings, each at a different angle; determine the tension in each rope.  The solution requires algebraic manipulation of a full-scale two-variable-two-equation-system.  Those of you who have assigned this problem and observed your students can probably verify my report that many of those students spend 30-60 minutes doing math, often getting lost along the way.  A significant fraction get so frustrated that they simply give up, or follow a friend's solution blindly.*

* I know this because quite often that friend's solution is itself incorrect.  

Here's a great chance to make my point about the separation of physics and math.  By this point, in class we've emphasized over and over and over the three-step approach to equilibrium problems:

1. Draw a free body diagram
2. Break angled forces into components, if necessary
3. Write (up forces = down forces) and (left forces = right forces)

The majority of the students who spent the better part of an hour on this problem didn't follow these three physics steps carefully; they got too worried about the forthcoming mathematics.  

So, why not give a quiz in which students are given explicit instructions not to solve the two-variable system?

See the quiz below.  I find that it relieves much anxiety from those who got lost in the mathematics.  It sends an important message to those who didn't follow the process, because they see just how quickly they could have gotten to the answer by, well, listening to the teacher and following his advice.

Finally, note that the AP Physics 1 exam will not ask students to solve a true two-variable system of equations, ever; but "write two equations which could, together, be used to solve" is a legitimate form of AP question.  

GCJ


Two ropes support a 33 kg stoplight, as shown above.  The goal of this problem is to find the tension in each rope, as on last night's homework problem.

I am NOT asking you to solve the problem completely in this quiz; rather, I want to see that you can quickly and accurately follow our four step procedure for solving equilibrium problems.

  1. Draw a complete free body diagram of the traffic light, including descriptions of each force. 
  1. Redraw the diagram, breaking force vectors into components where necessary.  Express components in terms of the given angles; i.e. do not simply write “Tx”, include the angle in your expression.
  1. Write two equations.  Circle the unknowns.  DON’T SOLVE.





07 June 2016

Report from the AP reading: Teach your class to write concise laboratory procedures. Please.

Howdy!  I've spent the last week grading, and training people to grade, the lab problem on the 2016 AP Physics 1 exam.  I'm a bit punchy, as you may expect.  Nevertheless, I encourage you to apply to be a reader -- I really, really love the people I meet here, even if I'm not always entirely enamored of grading papers for eight hours a day.

Part (a) of our question asks for a description of a laboratory procedure.  It could be answered in 20 words: "Use a meterstick to measure the height of a dropped ball before and after it bounces.  Repeat for multiple heights."

But oh, no... when America's physics students are asked to describe a procedure, they go all Better Homes and Gardens Cookery Manual on us.  Folks, it's not necessary to tell me to gather the materials, nor to remind me to first obtain a ball and a wall to throw it against.  Nor do you have to tell me that I'm going to record all data in a lab notebook, nor that I'm going to do anything carefully or exactly.  Just get to the point -- what should I measure, and how should I measure it.

Please don't underestimate the emotional impact on the exam reader of being confronted with a wall of text.  We have to grade over a hundred thousand exams.  When we turn the page and see dense writing through which we have to wade to find the important bits that earn points, we figuratively -- sometimes literally, especially near 5:00 PM -- hit ourselves in the forehead.  Now, we're professionals, and I know that we all take pride in grading each exam appropriately to the rubric.  Nevertheless, don't you think it's worth making things easy for us, when we be nearing brain fatigue?  Just as good businesspeople make it easy for customers to give them money, a good physics student makes it easy for the grader to award points.
 
Don't think I'm making fun of or whining about students here.  Writing a wall of text where a couple of sentences would suffice is a learned behaviour.   The students taking the AP exam are merely writing the same kinds of procedures that they've been writing in their own physics classes.  It is thus our collective responsibility as physics teachers to teach conciseness.  

"Okay, Greg, how do we do that?"  I hear you asking.  I have a two step plan.

(1) Give the students a word or sentence limit, and hold them to it.  For virtually any AP Physics 1 procedure, three sentences will do.  When your students list a twelvefold process, award no credit, and don't give in to the subsequent whining.

(2) Don't ever award credit for baloney.  When students have one nugget of valid description buried in a mountainside's worth of muck, just stop reading and award no credit.  The burden of proof is on the students to convince you they understand the methods they describe.  It's tempting to yield to after-the-fact whining and lawyering: "Well, if you really think about it, the meterstick could measure force if..." No and no.  

Fight the clarity and conciseness battles in October; then in May when your students take the AP exam, communicating experimental methods will be (a) easy and (b) quick.