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10 June 2017

Making students - not parents - self-select for an honors or AP course

An oft-repeated refrain: due to the ignorance of counselors and pressure from helicopter parents, too many students who aren't ready tend to be placed in advanced physics courses.

Understand that I believe in physics for all, not just for the best and brightest.  However, in order for a physics class to be successful, the participants have to be ready academically for the level of the course.  When students reach to take a level of physics that's beyond them, they generally have a miserable time... and they drag down the class such that everyone has a sub-optimal experience.  

Why reach?  When there's a general-level physics course available, the only people who should be placed in a higher course are those who would be bored by the simplicity of the general course.  Honors placement isn't a prize to be won, it's a match to be made.  Epidemic at the high school level is the student who is inappropriately pushed to take honors-level science and math courses, then successfully whines and argues for grades, just to be placed in an even higher-level course then next year... then crashes and burns in college, where the student-emperor is revealed to have no intellectual clothes.

I've talked to more than one high school teacher who adapted in ridiculous but practical fashion by cutting out unweighted, general-level courses altogether.  These folks label their basic course "honors physics," and their advanced course "AP physics."  They teach "honors physics" sort of the same way I teach my ninth grade conceptual physics.  Whatever works, I suppose.

I never want to shut a student out from ever taking an advanced physics course.  When physics teachers kvetch about unprepared students in their classes, the classic riposte is that "tracking" permenantly marginalizes those who don't have resources at home to push themselves academically.  This is a legitimate and important point.  Many not-so-great students could, in fact, handle advanced physics if they had been introduced to high-level quantitative skills early in their academic careers.  One of our goals as high school physics teachers should be to cast a wide net to catch everyone who can possibly learn our subject at some level.  

And right there is why I love teaching conceptual physics.  Any college-bound student - and probably a significant fraction of non-college bound students, too - can handle rigorous physics with no calculator use.  And a large fraction of conceptual students are then fully capable of success in AP Physics 1 as a second year course.

The trick, then, is to identify students ready for AP Physics 1 as a first-year course, while at the same time teaching an outstanding lower-level course to those who don't meet that bar.  How to do that in a political environment in which parents whose special children aren't selected for AP Physics feel personally slighted and storm your boss's office demanding retribution?

Your answer must depend on your particular school environment.  It likely begins with relationship building among the science faculty and administrative decision makers.  Make sure your counselors and principals and deans not only understand your placement procedures, but also the reasons behind your procedures.  Reassure them that you are serving all students, that those pitchfork-wielding parents' children will still be well-served by your program.

An elegant solution that has worked for us has removed placement decisions entirely from parents and administrators.  We place all 9th graders in a general-population conceptual physics course at year's beginning.  Three weeks in we resection, creating one AP Physics 1 section (labeled as "honors physics.")  Below is the procedure, as it's described to interested faculty and parents.

Students who are interested in honors placement have been asked to do two things.  We have been very clear with all sections, both orally and in writing, about the process.

(1) Honors practice problems.  We are posting one to two extra problems each week which are at the level expected of honors students.  Those who are considering honors are asked to solve these and turn them in.  We encourage the students to discuss their solutions with us before they are turned in if they have questions.  

(2) Honors quiz/test questions.  Each of our first three weekly assessments includes an honors-level question similar to the honors practice problems.  We ask the honors candidates to attempt these problems -- this gives us a gauge of how well they understood the practice questions.

After three weeks of class, the physics teachers will choose the honors section based on a holistic evaluation of all interested students.  We look at their performance and effort on the honors practice problems; at their performance on the honors assessment questions; at their effort and performance on the regularly assigned work, including laboratory work; and at whatever progress they do or do not make in the first three weeks.  We've found that the class is nearly self-selecting, in that those who attempt the honors problems figure out within a week or so whether they can -- or whether they want to --  handle that level of work. 

One important point about honors selection is that students must themselves want to take on this level of work.  We’ve had a number of students over the years who could possibly handle the material in honors, but they chose not to do the test questions, and thus to remain in regular conceptual.  That was a good choice universally for those students – they earned high grades, then had the opportunity to take the honors course in their senior year.  We are purposely trying to divorce the honors decision from the parents, advisors, and even physics faculty -- the students are the ones who are in large part deciding whether they can or want to do the work.

04 June 2017

Deriving expressions in AP Physics 1

Reporting from the AP reading here in Kansas City, where I've discovered that Jack Stack barbecue is excellent, but still no match for Gates.  And, where I've been immersed for days now training people on the rubric for the 2017 AP Physics 1 exam problem 3.  

Based on my experience here, I think it's worth a reminder to teachers about the expectations for "deriving" an equation on an exam.

Introductory physics is all about communication of ideas, and not as much about getting the One True Answer to a problem.  Physics is not a math class.  

Students in my class may whine (early on, at least) about not getting full credit for a poorly presented problem that nonetheless includes the correct answer.  Okay, so your English teacher requests an essay with textual evidence analyzing Shakespeare's characterization of the Romeo/Juliet relationship.  Your entire essay: "He loves her."  You earn a failing grade, of course.  How effective or intellectually honest do you think it would be to whine that your essay deserves an A because the answer is right?  I mean, the answer is in fact right...

A derivation, like any physics problem, is an exercise in communication -- but a derivation requires communication primarily in mathematics.  Just because the answer is right, just because a student knows in her head what mathematical steps she intends to take, that doesn't mean the derivation has served its purpose.

So what SHOULD we expect from students on derivations?

1. Start from first principles, and explain what first principles you're using. That means something from a "facts of physics" list: Newton's laws, Kirchoff's laws, conservation principles, the definition of acceleration or impulse or power... most anything on the AP equation sheet or on my fact sheet will work.

2. Communicate the reasoning for each step.  I think words are best here -- an annotated derivation can hardly fail to earn credit where correct.  Try circling terms and explaining what they mean.  Try telling the reader why you've substituted various terms into the equation you began with.

3. Show enough detail that a strong physics student at another school can understand without asking for clarification.  The audience should NOT be the expert physicist.  I personally don't need to derive an expression for the acceleration of a three-body system connected over a pulley, because I've done so many of those problems that I can write the answer based on memory and instinct.  My students, though... they need to start with Newton's second law for the system, explaining what expression is used for each term and why that expression is relevant.  

4. Use algebra to communicate, not to solve.  I often see students take three steps merely to rearrange terms in an expression, using annotations like "commutative property" and "divide both sides by m."  Assume the audience knows how to do math.  Use the way the math is laid out to highlight reasoning.  For example, if you have energy terms before and after a collision, write all terms clearly in a single line, with before the collision left of the = sign.  Label each term with a circle and a couple of words.

I'm sure readers - both blog readers and AP Readers - may have some further thoughts.  Please post in the comments.  

20 May 2017

Conceptual Physics Tournament Sunday May 21 2017

[The following is a letter to my school's community describing our project-in-lieu-of-exam that will happen tomorrow.  If any blog reader is interested in creating something similar at her or his school, please let me know.  I'd love to help out!]

Folks, tomorrow is the first ever WFS Conceptual Physics Tournament.  

Instead of preparing for an exam, our students have been preparing to present and discuss the solutions to some rather deep problems, which are attached to this email.  Mentors from the AP Physics classes have helped the 3rd formers conduct experiments, to understand the underlying theory, and to deliver a two-minute talk.

Tomorrow, each student will be assigned to report in two "physics fights."  Think of the physics fight as a thesis defense.  The reporter presents his/her two-minute talk; and then the examiners engage in conversation with the reporter for five more minutes.  The examiners are probing how deeply the students truly understand the problem, and how clearly the students can articulate their understanding.

Physics fighting is a spectator sport.  We encourage all members of the community (including parents of 3rd formers!) to come out to watch a few physics fights.  These will take place in Manning and Kenan.  We will run approximately eight rounds, beginning at 1:00 and ending around 3:00.  The specific fight schedule will be posted in the dining hall and to the news folder around 12:30 Sunday.

Alex Tisch and Colin Manning have done tremendous work preparing their students, not just in the past couple of weeks, but all year.  The mentors have taken to their task with relish.  The 3rd formers have worked very hard, and are ready to demonstrate their knowledge.  Come see the fruits of their labor.  


11:30: Examiner arrival, lunch in Terry Dining Room
12:00: Examiner training in Terry Dining Room
12:30: Posting of fight card
12:50: Examiners and students move to fight rooms

1:00: Round 1
1:12: Round 2
1:24: Round 3
1:36: Round 4

1:48: Break; examiners switch partners

2:00: Round 5
2:12: Round 6
2:24: Round 7
2:36: Round 8

19 May 2017

AP Summer Institute: June 26-29, Mahopac, NY

Folks, a quick bit of advertising here... we're still looking for a few teachers to fill up my AP Summer Institute in Mahopac, NY from June 26-29.

At this and all of my summer institutes, I'll take you through all aspects of my AP Physics 1 classes.  We'll do some of the different kinds of experiments I've discussed on this blog.  We'll share ideas with each other - I leave every institute with new ideas to try out.  And I can discuss physics teaching beyond AP Physics 1, including conceptual physics as well as AP Physics 2 or C.

For those looking to meet various certification requirements, this particular institute allows you to earn graduate credit.

Please contact Mark Langella, the institute director and a pretty dang impressive AP chemistry teacher, for signup details.  You can contact him via the Putnam-Westchester Industry and Science Teacher Alliance.  

I hope to see you in New York...


04 May 2017

2017 AP Physics 1 solutions

I enjoyed writing my solutions to the 2017 AP Physics 1 free response questions.  You can find the questions linked via the official College Board exam site, here.

I very much like the direction the "quantitative-qualitative translation" question has gone.  Twice, students were given an equation, and asked why it does or does not make physical sense.  That's such a great skill to develop, and to test.  And I loved the experimental question... the experiment itself was quite straightforward.  But the "based on this data, how do you feel about this conclusion?" question was amazing.  It gets at the heart of evaluating quantitative evidence, at basic numeracy.  If every journalist and politician in America could answer this question accurately, the world would be a better place.

Okay, now I'm going to link the solutions.  But, please note that due to College Board copyright rules, only teachers can access them.  The PGP-secure website requires verification that you are a teacher in order to sign up.  

One of my favorite people, Gardner Friedlander, runs this teachers-only wiki.  He became quite frustrated last year because so many students asked for access -- many pretended to be teachers. Folks, Gardner isn't stupid.  He verifies that you're a teacher.  Please don't make him come after you for impersonating a teacher -- he will take away your birthday.

So, students, do you want access?  Ask your teacher to join PGP-secure.  Your teacher may share the solutions "for face-to-face teaching purposes."  

As always, I guarantee that I've earned a 5, but not that I get every detail right.  Please note my mistakes in the comment section.

My solutions can be found via this link, at PGP-secure.  This is a wiki for physics teachers only.  If you are a teacher but don't have access yet, follow the instructions at the linked page; you should be approved in a few days. 


01 May 2017

How long should my answers be on the AP Physics 1 exam?

Quick answer: probably shorter than you think.

Below are a variety of AP Physics 1 prompts, and how I would suggest structuring your answer.  Please note that, while I do grade the exams every year, I am writing here in the role of independent observer.  I am not a representative of the College Board.  These are my own simplified instructions to my own students, which may not be perfect in all situations.

Yet I think teaching is much better done by simple guidelines rather than legalisms.  If you want the legalisms, go to the College Board's course and exam description; and look at the AP Central page where they go in to great detail about the requirements for a paragraph response.  I don't think a student wants to see such detail.  I think, in fact, that we should actively discourage students from a rules-bound approach to any answers.  Encourage your students to simply answer each question, and move on.

On my last day of class before the exam, I will remind students of the types of prompts below, and my guidelines for the length of the response required.  And then I will let go, and wish them the best.

"Briefly Explain:" or "Briefly justify"  Answer in one sentence.

"Derive an expression:"  Use variables only, start with an equation from the equation sheet or a fundamental principle.  It will help to annotate your work with words, but complete sentences are not necessary.  Full credit can usually be earned without words at all as long as the mathematics is communicated clearly. 

"Describe a procedure:"  Two to three sentences, never more.  Say what you will measure, and what equipment you'll use to measure it.  And stop writing.

"Explain" or "Justify your answer:" About two sentences, or perhaps one sentence with reference to an equation.

"Answer in a clear, coherent, paragraph-length response:"  Five sentences, four is often enough.  Do not repeat the question in the answer. Get to the point.

For all responses except mathematical derivations:  Use sentences with subjects and verbs, but without fluff.  

What if I need more space than the question provides?  Then you are writing too much.  The amount of space provided is deliberate, and reflects the length of response expected.  Yes, I know you are allowed to use scratch paper and staple it into the book.  You're also allowed to publish your bank account information online.  Just don't.  

Don't fear for the lost point.  Students tend to write page-long essays because they fear that the grader will "take off" if they miss one small detail.  But those students miss the bigger picture.  Running out of time on question 5 could cost them seven points, while writing an extra page may in their imaginations earn one point.  And writing that extra page is far more likely to lose credit for an incorrect statement than to gain credit.  

Please don't be afraid.  Answer each question briefly and confidently.  If you have to guess, guess briefly.  Believe it or not, we readers know when you're just writing random crap because you have no idea how to approach a problem.  And rubrics are written such that they are unlikely to award credit for baloney.

Kick arse tomorrow.  Let me know how it goes.  I'll post my solutions when I can.


28 April 2017

Mail Time: Last-minute questions before the AP Physics exams

The AP Physics 1 exam is next Tuesday.  Remember, no studying after Monday's class!  Lots of last-minute questions coming in.  Here are a few quick ones, with responses that sometimes are merely links to other posts.

From Nikki:  I'm confused on the AP Physics 1 Practice Exam Question 2. I understand the explanation in scoring guidelines, but it seems like they have ignored the PE due to the gravitational pull of the Earth and I don't understand why. Any chance you have some insight into this?

Nikki, the PE is for the earth-spring-object system, and is 1/2(k)(x^2) measured from the equilibrium position of the spring/object. This post gives further details.

From Paul:  If a student uses the language of calculus to justify or explain an idea on the AP exam, will that be accepted by the AP reader?  This came up because it is an algebra-based course.

Paul, please take a look at the second answer in this post.

From Matthew, four questions:

1) If you give practice exams ... What percentage on the multiple choice do your classes typically average? I am just curious as a gauge for myself and my classes moving forward.

Probably 60-65% on average with authentic physics 1 questions.

2) On the first FRQ part b is says a student would receive a point "for recognizing that the force causes a change in momentum or a change in velocity." Would the student have to state that? The question asks to calculate the magnitude of the external force on the system.

State or imply, mathematically or verbally.  Just writing "F=ma" doesn't cut it, but writing that and then trying to calculate a change in speed for a would probably earn the point.

3) If a student answer a part of the FRQ correctly and then adds something that is incorrect would they receive credit for the correct response?

No.  When there are multiple responses, we pick the one that earns the fewest points.  They can't game the test.  :-)

4) Is there any type of final reminder you cover with them before the exam?

Try this post here, about "BOUX" day.

From Michele: On the MC questions that are multi-select (two correct answers), how are they scored? Do students need to get both choices correct in order to receive credit?

They need both choices right to get credit.  No half points.

From Michael: For AP grading, are points taken of for not simplifying expressions?

Michael, as long as the solution is as required -- "solve for a in terms of given variables and fundamental constants" -- then any form of the solution is acceptable.

Got others?  Go ahead and post a comment or email me.  I'll see what I can do.

21 April 2017

Reviewing for the AP Physics 1 exam: No big practice exam, but Big Butt Fundamentals Quiz

I take an approach to exam review that's consciously different from what other teachers do.  I am doing no tests at all this month, no practice AP exams.  We're solving one authentic AP Physics 1 free response in each assignment; we're practicing a couple of multiple choice questions each day.  We're doing corrections on anything we miss.  I'm getting students to grade other students' work to an AP rubric wherever possible.

Why am I not doing practice exams?  Because every test we've taken all year has been in (or close to) AP format and style.  My students know how to pace themselves so as not to run out of time.  They know how to communicate enough to get credit, but not so much that they waste time and ink.  They know the level of difficulty they will face on multiple choice and free response problems... because we are doing some each day.

Importantly, while I'm giving some questions for homework, I'm doing others as brief in-class quizzes.  It is critical that students have practice working on AP level problems without a safety net, without the ability to ask friends or teachers clarifying questions.  But we do that all year, on every test and quiz!  Since I never allow students to ask questions on tests or quizzes, I feel no pressure now to give any further authentic AP practice.

One type of major assessment that I do use is the "Big Butt Fundamentals" quiz.  I give students 30 minutes to answer 30 questions that are, for the most part, straight off the fact sheet.  The first twenty questions are pure recall; the last ten require some processing, but are still testing misconceptions or ideas that are fundamental to students' knowledge of physics.  Feel free to use this quiz in your own class.  I create it by randomizing the fact sheet, and then just riffing off each fact.

The purpose of the Big Butt Fundamentals quiz isn't to play "gotcha".  It's to get students' noses into their fact sheet.  It's to show the students what they know well, building confidence; it's to show students what they might have forgotten, leading the students themselves to look up the correct answer or to discuss the question with friends.

I ask students to correct the Big Butt quiz by writing a complete sentence stating the reasoning or fact behind each answer.  Rather than just writing "kx", they'd write "the force of a spring is kx."  They are putting their answers in context.  

I don't ask for complete sentences as a punishment, or because my ed school training or my teacher's edition told me to... I'm making the students write so that they have a better chance of remembering a fact that they already got wrong once.  My students are generally cooperative with this rationale, because (a) I don't ask them to do much this time of year anyway, and (b) they see by now the connection between correcting what they get wrong the first time, and strong performance on future physics problems.   As we say, practice doesn't make perfect.  Perfect practice makes perfect.

20 April 2017

A large bug on the edge of a DVD

A large bug of mass 5.0 g lands on the outside edge of a DVD*.  The DVD has mass 9.0 g and radius 6.0 cm.

*DVDs are still a thing, right?  Or, at least I expect that most of my 15-18 year old students know what a DVD is without further explanation.  Or, I'm an old man.

I use this setup to introduce newton's second law for rotation, and the additive nature of rotational inertia... and then to discuss conservation of angular momentum.

(a) Does the bug's presence significantly affect the rotational inertia of the DVD?

By itself, the DVD is a disk, with rotational inertia (1/2)MR2.  That gives 160 g*cm2 as the disk's inertia.

The bug adds its rotational inertia algebraically.  The bug should be treated as a point object, whose rotational inertia is MR2.  That gives 180 g*cm2 as the bug's inertia.

The rotational inertia of the bug-DVD system is then 340 g*cm2. The addition of the bug nearly doubles the DVD's rotational inertia; thus the presence of the bug is significant.

(b) Initially the bug and DVD are rotating at a constant angular speed.  Then, the bug moves to a new position 3.0 cm from the DVD's center.  Explain why and how the DVD's rotational speed changes.

No external torques about the center are exerted on the bug-DVD system ('cause no net force at all acts).  Thus, angular momentum is conserved.

Angular momentum is When the bug approaches the center of the disk, the bug's (and thus the system's) rotational inertia decreases because the R term in the inertia formula decreases.  To keep angular momentum from changing, then, the ω term must increase.  The DVD will speed up its angular velocity.

(c) Does the bug exert a torque about the DVD's center as it moves toward the new position?

Tricky.  There's no EXTERNAL torque on the bug-DVD system.  But angular momentum can still be conserved when internal torques act.  The torque of the bug on the DVD would be internal to the bug-DVD system.

Consider the DVD by itself.  It changes its angular speed.  So by Newton's second law of rotation, it must experience a net torque.

What can possibly provide that net torque?  The weight of the DVD and the normal force of the spindle on the DVD both act through the center of the DVD; they provide no lever arm, and thus no torque.

The only other possible provider of torque is the bug.  But how, in terms of torque equaling force times lever arm, can the bug do that?

Since the bug rotates with the DVD, a static friction force must act between the DVD and the bug.  That friction force acts tangent to the rotation of the disk, and thus has a lever arm with respect to the disk's center.

17 April 2017

Mail Time: Why do released AP Physics 1 exams include only 40 multiple choice?

Reader Aaron Shoolroy asks, in the comment section of a separate post:

The Physics 1 exam description says 50 MC questions, but it seems like all of the secure exams available through the course audit page have 40 questions. Does anyone know how many MC questions will be on the actual exam this year? 

Aaron, I'm sure you're not the only person wondering.  The AP Physics 1 and 2 exams will, as stated in the course description, include 50 multiple choice questions.  The last five of these will be "multiple correct", requiring the student to select both of the correct answers for credit.

So then, why do the released exams only give us 40 multiple choice?  Long answer coming.

During the Physics B dynasty, multiple choice exams were only released every five or so years.  See, a subset of the questions on each test are re-used on future tests in order to provide concordance from one exam to another.  For example, if the student population taking the test does better on these re-used questions, then the overall exam scores should go up -- even if performance on the rest of the test doesn't likewise improve.  That repeated subset of questions serves as an experimental control.

In order to keep a statistically significant bank of these re-usable questions, the College Board carefully hoarded them.  By only releasing exams every five years, it was easily possible to keep a secure set of questions in circulation.

During the development of the AP Physics 1 and 2 courses, one of the major points of pointed feedback to the committees said, please stop with the learning objectives, and give us practice questions.  I know I delivered that message more than once, and I wasn't the only one.  

See, people listened.  The College Board pledged to release the international version of the test nearly in its entirety every year, for the purpose of providing materials for use in class.  That's an enormous wealth of material for teachers, to the extent that we're only three years into the course yet I haven't been able to assign all available questions this year.  

(By the way, most of those released exam items are only available to those with an active AP course audit account.  That's to ensure that these items remain secure enough that it's unlikely students can simply google the solutions to them.)

I know the development committee and the ETS physics people have had to work extra hard the past few years in order to meet the demand for all these test items.  I have told them in person, I'll continue to tell them in person, and I'll say it here -- THANK YOU.  By releasing so much authentic exam material, they've allowed teachers and students to get a real sense of the form, content, and degree of difficulty of the exams.  They've allowed me to assign authentic practice in the lead-up to the exam.  They've provided me with practically unlimited laboratory ideas - virtually every question can be investigated experimentally.

Oh, but you asked me a question, and I rambled.  Why are there only 40 questions on the released exams?  Because the College Board removed the 10 questions that will be re-used in future years for statistical purposes.  Losing those ten questions is more than a fair trade for 40 multiple choice and five free response items, which are more valuable than gold to an AP teacher this time of year.

08 April 2017

For April AP Physics 1 classes: Here's a list of experiments, go do them.

At this point in my senior-level AP Physics 1 class, we have learned all necessary fundamental skills.  We have practiced solving problems with forces, motion, energy, momentum, rotation, circuits, and waves.  We have learned the critical laboratory skills, including how various equipment works, how to present data graphically, and how to use the slope of a graph to analyze data.

In the last month of the course, I'm using class time to put all these skills together in practice.

I have two 90 minute classes each week.  In these, I've been starting with 20 minutes or so of preliminaries: a TIPERS-style quiz, discussing the quiz, taking questions on homework.  Then I release the class to play.

What do they play with?

I've given the class a list of seven experiments; I can come up with more as necessary.  The list is below.

A student picks one and begins work.  I am happy to help with equipment questions, but not with "how am I supposed to do this?" questions.  (For those, I ask them to collaborate with a classmate.  That works at this stage of the year.)

How do they report their results?

Very informally.

I ask for a few sentences describing what they measured, and what equipment they used to make the measurements.  I ask for a few sentences describing how the data was analyzed, and how the data answers the question posed.  That's it.  No "formal lab report", no "purpose / procedure / results / conclusion."

Sure, occasionally I get a student who tries to give me a page with a bunch of messy numbers on it.  I simply send him back to his desk to do it right.  But this removal of formality in lab work has worked wonders for years.  It mimics what students will be asked to do on the AP exam -- in just a few minutes, writing by hand, describe an experiment including procedure and analysis.

What if I don't have enough equipment for everyone for these setups?

Part of the beauty of this approach is that I never have more than a couple of folks at a time working on each experiment.  Students are directed to work in any order they desire.  Often they will choose based on which experiment's equipment is available.

If several labquests are on the fritz - as they often are - it doesn't matter.  Because (a) students will have incentive to choose an experiment that doesn't involve the labquest, and (b) students will have incentive to figure out new and interesting methods for measuring what the labquest can measure.  For example, rather than plug in motion detectors to the labquest, they might learn to use video analysis on their phones.

Here's my list.  Each one can take anywhere from 20 minutes to an hour.  You'll recognize some 'cause they're inspired by old AP problems.  One (number 7) was created by a veteran of my class when he needed a project in another class.  I'll probably post some other time with specific notes about each... but for now, these have been a good start to independent lab work in the spring.

1. A transverse wave is traveling on a string.  If the frequency on the wave machine is doubled, what is the new average speed of the point?  Use a high speed camera on slow motion to directly measure the average speed.

2. Use a pipe, a meter stick, and a frequency generator to determine the speed of sound at room temperature.  Find somewhere with a temperature below 50 degrees F, redo your measurement, and see if the speed of sound has changed.

3. A 1 kg object traveling on a frictionless horizontal surface collides head-on with and bounces off of a 0.5 kg object initially at rest.  Give experimental evidence for (a) the percent of total linear momentum that was conserved, and (b) the percent of total mechanical energy that was conserved.

4.  In the circuit shown above, the sum of the resistances of resistors R1 and R2 is 80 kΩ.  Resistor R1 and the 80 kΩ. resistor are now swapped.  A student claims that the current must always increase in the right-hand branch of the circuit, because the total resistance of that branch must decrease.  Test this claim experimentally.

5. Create two pendulums: one with 50 g of hanging mass, one with 100 g.  Release both from the same angle.  Predict and give experimental evidence to show how each of the following differ for the two pendulums:
Maximum kinetic energy
Maximum acceleration

6. We’ve learned that the period of a pendulum is independent of the amplitude.  Provide experimental evidence for this claim; present your results graphically.

7. You are given two objects to be placed on either side of a pivot, as shown above.  The total mass of the two objects is known.  You may vary the distances from the pivot at which you place the objects.  Use the slope or intercept of a linear graph to determine the mass of each object experimentally.

27 March 2017

That "hole through the center of the Earth" question

I'm always asked these sorts of things.  Go figure.  I suppose it comes with the job, like the Air Force general based in New Mexico who continually deals with Area 51 speculation.

If you dug a hole through the center of the Earth, and jumped in, would you stay at the center because of gravity?

This experimentalist's answer:

No, because (a) the engineering barriers to digging said hole are insurmountable, and (b) if you weren't crushed, you'd be asphyxiated or, more likely, burnt.  Look up the temperature of Earth's core.

The theorist's answer:

Assume the hole is wide enough that there are no forces other than the gravitational interaction between you and the Earth.  The gravitational field INSIDE the Earth is zero at earth's center, always points toward Earth's center, and gets bigger as a linear function of distance from the center.  (The mathematics here are the same as when using Gauss's Law to determine the electric field inside a sphere of uniform charge density.  The 1/r2 dependence only occurs outside the sphere.)

By definition, when an object experiences a linear restoring force, its motion is simple harmonic. Thus, you'd oscillate about the center of the Earth like an object attached to a spring.  If you jump in from Earth's surface, then, you'd speed up until you passed earth's center, after which you'd slow down, reaching the surface on the other side of the earth before you repeated the process ad infinitim.

13 March 2017

"Does that make sense?" Don't take 'yes' for an answer.

I am at heart the most straightforward, literal person in the universe.  I mean what I say, and I say what I mean.  And I hear the words that people say, too often without considering the body language and social cues behind the words.

Consider the friendly sophomore from Norte Dame Academy, at the, I dunno, 1988 or so Kentucky State Latin Competition.  We met there and had been talking throughout day.  Her team's bus was leaving before the award ceremony.  She gave me her number, and said, "please call me tomorrow to tell me the results." So, the next day I dutifully called.  I gave her the results.  I congratulated her.  I said goodbye.  I never saw her again.  Sorry, Lisa.

Or, the wonderful woman in grad school who, after we had hung out together several afternoons, said "Can you come over to my apartment tonight?  My roommate will be out.  I'll cook you dinner." I accepted.  I thanked her for the yummy meal, and left.  Sorry, Michelle.

Or, and more pertinent to this blog, the diligent junior in the weekly problem solving sessions that my college paid me six bucks an hour to run.  I showed her how to solve a problem involving the work-energy theorem.  I asked her if the approach I suggested made sense.  She said, "yes."  I took her at her word.  Sorry, Alex.

I suspect that most readers are shaking their heads at the first two stories, wondering how I could be so clueless.  Had I recognized Lisa's or Michelle's body language and tone of voice, events would have turned out less dull, or at least differently.  And decades after the fact, I now have the perspective to recognize what I missed.  Most people wouldn't have misunderstood these cues in the first place, of course; I had to work consciously on interpreting social subtext, even though such interpretation comes naturally to others.

Over twenty-plus years of teaching, I've similarly had to continually analyze and re-evaluate my students' body language and tone of voice.  In 1994 I believed Alex when she told me she understood my explanation.  Why would she have said "yes" if the real answer was "no"?  In retrospect, there could be any number of reasons.  Among others:

(a) I'm a proud, diligent student, and I cannot admit to myself or (especially) to a peer that I don't get something; 

(b) I don't quite understand this right now, but I have irrational confidence that if I stare at the problem for another 20 minutes I'll magically see the light; or 

(c) I really wish Greg would shut up and stop explaining, and the only way I can tell him that without seeming rude is to pretend I understand.

Nowadays, when I explain something one-on-one to a student, I still ask, "does that make sense?"  But I'm ignoring the verbal content of the response.  I'm watching for and listening to body language and tone of voice.  Students often use words they don't mean.  Their tone usually gives their true thoughts away; it's practically impossible for a high school student to send false messages with body language.  

What am I looking for in response to "does that make sense?"

When I explain how to approach a physics problem, I always make the student go back to his seat and write up the solution in his own words.  So I'm watching how he leaves the vicinity of my desk.

The student who truly understands my explanation can hardly wait to get back to his seat to put his newfound knowledge into practice.  He usually moves with confident purpose.  Sometimes he'll have a bit of sheepishness about him, because he realizes he should have figured this out earlier.  

The student who's still confused walks much slower, with his eyes turned upward or downward.  He's in no rush, because either he's still thinking about what I said, or perhaps he's frustrated that I won't just tell him the right answer and he's throwing a wee tantrum.  

So, when the confident student comes back a moment later, I can move him along without thinking about it -- he's got it.  

But even if the less confident student comes back with a correct answer, I still push a bit.  I ask a few more questions to test for understanding.  I make him write each step of reasoning explicitly, even though I might have let the confident student slide by with some things implied.  I don't harass or embarrass, of course... I simply recognize that this student has shown me through his body language that I have to do more to help him.

02 March 2017

Woodberry Forest Conceptual Physics Tournament -- want to be an "examiner"?

My school has for years given three sets of exams, one each trimester.  This year, though, we're limited to two written exams.  For the last trimester, we're encouraged to create a cumulative project of some sort in lieu of an exam.  Yay.

Thus, we are creating the Woodberry Forest Conceptual Physics Tournament.  This competition for our 9th graders, to be held at 1:00 on Sunday May 21 2017, replaces their final exam.*

*No, to be clear to all, we're not giving an A to the winner and an F to the person in last place.  That's silly.  We're just having a fun, competitive tournament, to determine a winner.  Judges aren't awarding grades.

How does this tournament work?

On May 2, I will reveal a slate of three problems to the 73 participants.  These problems will be old AP Physics 1 "paragraph response" questions.  Except, rather than just answer in a paragraph, the students will spend the month of May setting up experiments to provide evidence for their answers.  By tournament time, each student will be expected to be prepared to discuss the solution to two of the three problems, with both theoretical and experimental support.

At the tournament, each student will participate in two "physics fights."  Think of these physics fights like a miniature version of a graduate thesis defense.  Students will have a strict limit of three minutes to present their solution to the examiner.  An examiner then will engage each student in conversation about the problem for five minutes.  The students are judged by the examiner not only on the quality of their solution, but also on their ability to discuss the solution, to confidently hold a conversation with the examiner.

How do the students prepare?

Starting on May 2, all conceptual physics classes the rest of the year will be devoted to tournament preparation.  They'll set up experiments in class, they'll be assigned to write up their solution as homework, they'll practice presenting.  

Most importantly, my AP physics classes will spend their final weeks of the school year serving as mentors to the conceptual students.  I will assign each AP student to lead groups of three or four 9th graders.  The AP student will dive into the problems with the freshmen, helping to create and analyze experiments, helping the freshmen to understand the details of their presentations, and serving as mock-examiners in practice sessions.  This mentoring serves as the final project in lieu of the exam in the AP classes.

We need examiners.

The key, I think, to any class project is external assessment.  I and the other conceptual physics teachers will play the role of coach and advocate, always encouraging and helping the students to deepen their understanding of the problems and to improve their presentations.  Our relationship will be purely supportive, enthusiastic, positive.  

We can't then turn around and grill these same students as examiners!  That'd be like our football team's coaching staff refereeing the state finals.  Even -- especially -- if their officiating were fair, the coach-student relationship, both in practice and after the game, would be irrevocably compromised.

So we need examiners.  We can pay.

Would you like to come to Woodberry on May 21 to be an examiner?  My guess is we'd ask you to arrive at lunch time, like 12:00.  We would have a meeting of all examiners in our beautiful dining hall over lunch.  

Then we'd ask you to be the examiner for a couple of hours' worth of physics fights -- depending on how many examiners we get, you'd probably be asked to run 8-12 rounds.  Then, we will gather everyone into our auditorium for the top two participants to engage in a final physics fight for the championship.

In any case, my goal is to be done by 3:30, or possibly (it's our first time running this) 4:00 if there are logistical issues.  No later -- our students will be attending the final seated meal with their advisors that night followed by study hall, so we can't run late.

We will pay you $100 plus lunch (and even dinner, if you'd like to stick around) for your time.  (If you're coming from more than a few hours away, we can put you up on campus on Saturday or Sunday night.) I think you'd find that the camaraderie among the examiners and the engagement with the students will make the trip worthwhile.

Who's eligible as an examiner?

Certainly any physics teacher, or anyone with a physics / math / engineering background.  I'm inviting alumni whom I've taught in an AP or AP-equivalent course to come back to judge.  I'd also welcome any alumni of your advanced physics class, even if they're still seniors in high school.  As long as you can engage in conversation about physics at the AP level, as long as you can recognize good and bad physics, we'd love to have you.  When I run the USIYPT, I find the mixture of undergraduate / graduate / professor / high school teacher / industrial physicist / retired physicist on the juror panel allows some amazing relationships to develop.  I'd love to create a similar vibe here.

How can I sign up?

Send me an email, or contact me via Twitter, or call me -- my contact information is on the Woodberry Forest School faculty page.  I'll send you more information, including the three problems, and our current draft of the judging rubric.

22 February 2017

Rank the voltages: experimental evidence

 The question: 

The three circuits above are all connected to the same battery. Each resistor represents an identical light bulb.  Rank the circuits from greatest to least by the potential difference across bulb A. If more than one circuit has the same potential difference across bulb A, indicate so in your ranking.

The (very much in-depth paragraph-style) answer: Since all bulbs are identical, they have the same resistance.  By Ohm's law with the same R for each, whichever bulb takes the largest current also has the largest voltage (i.e. potential difference) across it.  

The equivalent resistance of the parallel combinations gets smaller the more parallel resistors are added.  So circuit 1 has the largest equivalent resistance, with circuit 3 the smallest -- consider each resistor to be 100 ohms, and you get 200 ohms in circuit 1, 150 ohms in circuit 2, and 130 ohms in circuit 3.  

Bulb A takes the total current in each circuit, so consider Ohm's law for the circuits as a whole.  In that case, the voltage of the battery is the same for each; the circuit with the smallest equivalent resistance takes the largest total current.  So rank the circuits 3 > 2 > 1.

The common misconceptions: I gave this to my class as a quiz, and most got it wrong.  I saw four typical categories of wrong answers:

* Since the batteries are the same, each bulb in each circuit takes the same voltage.  (No, just each circuit as a whole takes the same voltage.)

** Since the batteries are the same, they each provide the same current.  (No, batteries provide voltage, not current.)

*** Since bulb A is closest to the battery, it must take the greatest voltage.  (No, "closeness" to the battery has no bearing on a circuit problem.)

So far, this is standard fare misconception-bustin' physics teaching.  Because I posed this problem as a quiz, the class waited expectantly for me to reveal The Answer.  Ho hum... those who got it right reflexively pumped their fists, those who got it wrong either made sad eyes, or used some sour-grapes reasoning to convince themselves why they could have gotten it right.  And then they forgot the whole thing.

Or did they?

"Okay, there are the light bulbs.  You know where the wires and power supplies are kept.  Go set up the three circuits and show me which bulb A has the largest current.  Take a picture of your circuits to show me."

Ah, sh*t just got real.  

The photos are by my student Clay Tydings.  He conveniently labeled bulb A in each picture.  Now we can all see that bulb A is brightest in circuit 3.  

To address the misconceptions above, you can have the students measure voltage across the battery, and across each bulb, with the voltmeter.  If you're brave, you can even have them measure current from the battery.  They'll see The Answer, that bulb A carries the largest current in circuit 3.

But they also see that (*) the bulbs take different voltages, (**) the battery takes the same voltage every time but different currents, and (***) the voltages across each bulb don't change even when we place bulb A "last" rather than "first" by switching the leads from the battery.  

I find myself asking the class to set up the experiment proposed by a quiz problem all the time in AP Physics 1.  We've established the class's lab skills; we have introduced and practiced all topics at a basic level; we have 90 minute class periods with which to work.  So why not make the students verify an answer experimentally?  The AP exam will certainly ask them how to design experiments!

16 February 2017

Mail Time: I can't find the other force acting on this block!

Reader Josh writes in:

The system shown is traveling at a constant speed.  There is friction between block B and the ground, and there is friction between block B and block A.  We've been arguing where the second force is in the horizontal direction on block A is, if it even exists.  The forward force on A would be the static friction but I'm lost on where the other one is.  This is driving me bonkers...

Have we written a bogus question? If not, can you tell us where we're going wrong?

Ooh, what a great question.  Constant speed, eh?  In a straight line, so equilibrium? 

I think we all agree on the BOTTOM block's free body:  normal force of ground on B upward, weight downward, contact force of A on B downward, force of rope on B forward, and friction force of surface on B backward.

There's no horizontal forces acting on block A.  If there were, it'd be speeding up or slowing down, which it's not.  

You say "the forward force on A is static friction."  Well, static friction takes on any value up to the maximum.  I agree that static friction must act WHILE THE BLOCKS SPEED UP.  Once they attain constant speed, though, the static friction force drops to zero.  If the block slows down again, then the static friction force on A will be backward. 

What a great AP Physics 1 question.  More complicated than you thought, I suspect.  :-)

06 February 2017

USIYPT results 2017 from University of the Sciences, Philadelphia

The 2017 United States Invitational Young Physicists Tournament was held last weekend, January 28-29, at the University of the Sciences in Philadelphia.  I can't thank the hosts enough -- Elia Eschenazi, Michele Albert, and the rest of the folks from USciences who helped out were most hospitable and supportive.

Congratulations to all, but in particular, to Rye Country Day School (pictured) and coach Mary Krasovec.  They won their second title behind a particularly strong presentation of their experimental measurement of Planck's constant.  

The final round scores and places, noting that by tradition the finalist teams share first through fourth place:

Rye Country Day School , NY         77 points, champions
RDFZ of Beijing*                             72, 2nd place
Phillips Exeter Academy, NH          71, 3rd place
The Harker School, CA                    70, 3rd place
Qingdao No. 2 High School**          68, 3rd place
Woodberry Forest School, VA          56, 4th place

* Officially The High School Affiliated with Renmin University, China; known also as RDFZ.
** First-time participants from northern China

The Clifford Swartz Trophy is awarded annually to the winner of the USIYPT poster session.  First-time participant Vanke Meisha Academy won this prize.

And this year, the US Association for Young Physicists Tournaments for the first time presented the Bibilashvili Medals for excellence in physics.  These are awarded not based on ranking among the schools, but on overall score regardless of place.  This year, in addition to the trophy winners and final round participants, Pioneer School of Ariana, Tunisia earned a Bibilashvili medal.

This was the largest tournament in the ten year history of the event, with thirteen schools participating, including:

Shenzhen Middle School, China
Phoenixville Area High School, PA
Cary Academy, NC
Princeton International School of Mathematics and Science, NJ
Nanjing Foreign Language School, China

What about 2018?

The 2018 USIYPT will be held on January 27-28 at Randolph College in Lynchburg, VA.  The four problems involve measurements of the moon's orbit, coupled mechanical oscillators, projectiles in air, and radiation from incandescent light bulbs.  Full problem descriptions are shown at the USAYPT problem master's blog. 

If you'd like to know more about the USIYPT -- a physics research/debate tournament for high schools all over America and the world -- please contact me via email.  We're particularly interested in recruiting physics teachers, professors, graduate students, and industry physicists as jurors.  


Physical versions of energy bar charts

Like many of us, I use energy bar charts extensively.  Though my students don't all understand every detail of them all the time, the charts are the best way I know of to get them to stop plugging numbers into equations and think for a moment about how energy is transferred.  Just as "why don't you draw a free body diagram" generally gets students un-stuck on a force problem, "why don't you draw an energy bar chart" usually sets everyone on a path to success when energy is involved.

My personal touch on the energy bar chart is to insist that each bar be annotated.  Even just a couple of words help, like "it's moving" under the KE bar, or "at its lowest position" when the PE bar is zero.
Still, I don't have the sense that my class internalizes the deeper meaning of the bar chart: that the total energy on the left side, plus the "work done by external forces" column, must equal the total energy on the right side.  They know only because I tell them repeatedly; it seems an afterthought for my students, rather than the entire raison d'être for the chart.

How can I help my students understand intuitively that bars in the chart must be transferred among columns rather than just drawn randomly?  How can I help them see that the "work done by external forces" column is the only place where it's okay to add or remove bars?

Kelly O'Shea and Chris Becke -- and I'm sure others, but these are the ones I've seen recently -- have made physical versions of the bar chart.  I'll show you both...

Physical energy bar charts from Kelly O'Shea, @kellyoshea
Kelly tweeted this picture.  Her setup seems so simple: just a bunch of wooden blocks, pegs, and post-it labels.  Simple, maybe, but elegant.  Each setup is just the right size to put on a lab table for each small group to use in their problem solving.  I can imagine asking each group to take two pictures of the blocks: one representing the initial energy configuration, and one representing the final energy configuration.  Then I could ask something like "why are there two more blocks in the second picture than the first?  Where did they come from?"  And I'd expect an answer referencing work done by external forces.

Water-based energy bar charts from Chris Becke, @beckephysics
Chris uses water in labeled beakers to represent energy.  By setting up in the front of the classroom by the sink, he can explicitly show how work done by external forces affects a system's energy status.  Look at his labels; the faucet is "+work" and the drain is "–work."  My students when they draw bar charts can just magically sketch a few more lines in the "Wext" column to add energy to a system.  Kelly's students have to at least physically grab or throw away extra blocks.  But Chris's setup requires turning on the faucet, or dumping water down the drain, in order to include work done by external forces.  The meaning of "external" just got real.

I don't mean to suggest that either Kelly's or Chris's physical bar chart approach is the superior one.  I'd personally use Kelly's blocks in my bog-standard style of class in which students and small groups work on predictions and experiments; I'd use Chris's faucet-based chart on occasions when I want to present demonstrations from the front of the room.  

I *do* mean to suggest that if you're going to use energy bar charts as a teaching tool, I think it's worth setting up some form of physical bar chart rather than just drawing on paper.  I'm gonna have to try these.