25 February 2015

Two new labs for AP Physics 1 waves

I was asked via email how I've dealt with waves in AP Physics 1.  Remember, my approach will change over the years, as I see the sorts of things asked on the exam, and as I get new ideas from shop talk.  For now, I've started by teaching AP Physics B waves, with a bit more detail about how standing waves are formed, and no credit for just mimicking the equations fn=nv/2L etc.  In order to develop a deeper understanding of standing waves, I tried two new labs this year:

(1) I used the pasco wave generator at the constant 60 Hz frequency attached to a long string.  The string was attached over a pulley, with a hanging mass providing a tension.  I had students change the tension (which changes the wave speed), and measure the wavelength of the resulting standing wave from node-to-node-to-node.  

So we didn't spend years pounding the calculator, I provided a lookup table mapping each hanging mass to the correct wave speed.  I used excel ahead of time with the linear density of the string that I measured and the equation v = root ((tension) / (linear density)).  This graph is linear; the slope was 60 Hz, which was the frequency of the generator.  Each group matched the 60 Hz frequency within their determined uncertainty.

The real pedagogical purpose of this experiment was to give students kinesthetic experience with standing waves.  I did not introduce harmonics to the class before this experiment!  We only discussed how standing waves are the result of interference between periodic waves traveling in opposite directions in a fixed space; and I showed them that the wavelength was twice the size of one "hump."  They found out for themselves that sometimes these standing waves didn't form -- they had to move the generator left and right to adjust the string length in order to get the standing waves to show up.  That was a nice transition into harmonics, and to the next experiment.

(2) I used adjustable-length pipes, open at both ends, with an iphone frequency generator to produce resonance in the tubes.  Each group plotted their pipe length at resonance vs. the frequency of the generator, changing the freqency in small increments so as to remain at the same harmonic.  Each group was then asked to make a linear plot from which the harmonic number that they used could be determined.  

Since we did this experiment after the one described above, it reinforced the condition under which standing waves occur.  When on subsequent homework a student was confused about standing waves questions, I explained in terms of these two experiments -- the pipe didn't resonate except at one or two special lengths, just like the string didn't show the humps unless you got the string length just right.  And just as you could lengthen the string by exactly one hump and get standing waves again without changing the frequency, you could lengthen the pipe for the same frequency and get another resonance.  How far would you need to lengthen the pipe?  One "hump" in the standing wave, i.e. 1/2 wavelength.

Now, there's more to be done, of course, but this is where I started.  In Physics B I might have done the first of these labs; I have more time in the new course, so I added the second.

As for homework or test questions to ask... check out the experimental question from the 2012 Physics B exam.  It proposes a similar experiment to number 2 above, but asks for a determination of the speed of sound.  That's a good follow-up a couple of weeks after the waves unit.

16 February 2015

White Paper from the AP Development Committees: "Paragraph Response" Expectations

The College Board has published several paragraphs detailing what the readers will be looking for in answers to "paragraph response" questions.  Take a look here.  I don't have much to add to their statements, which I think are clear and useful.  I will likely pass out their page-long discussion for my students to read during our exam review.  

The two points I'd highlight:

(1) "It should make sense on first reading."  Your students don't get to come to Kansas City in order to follow their exam from reader to reader saying "let me explain what I meant."  You only get one shot -- do not miss your chance to blow the reader away with your logical arguments.

And thus, in your class, don't allow a student to argue about his score on this kind of problem.  If it didn't make sense to you ON FIRST READING, it's wrong -- and you have backup on that point from the AP Physics Development Committee itself.

(2) "Full credit may not be earned if a paragraph-length response contains...: 
* Principles not presented in logical order
* lengthy digressions within an argument
* primarily equations or diagrams with little linking prose."

In other words, it's a paragraph -- use your words, younglings, and stay focused.  You can not earn credit by throwing everything that comes to mind at the wall and hoping something sticks.

The College Board has released one paragraph-response question each for AP Physics 1 and 2, in the free response section of the practice exam.  I have one more about static equilibrium that I wrote for my tests that I'd be happy for someone to post on PGP-secure -- please, someone email me, I'll send you the file, and you can post it for me.  Anyone else have good, vetted paragraph response problems?  


14 February 2015

First exercises in rotation: Newton's Second Law and Rotational Inertia

At this point in AP Physics 1 for upperclassmen, students are used to the idea that a new topic brings new facts and equations, which are then applied to make predictions to be verified experimentally.  Rotation provides an opportunity to introduce the topic directly with individual laboratory exercises, especially since the concepts of inertia, force, and acceleration are already familiar.  We are simply applying the concepts to a rotational setting.  

I spent way too long creating three versions of the pictured setup.  An object of mass between 10-200 g hangs from a string, which is passed over a pulley and wrapped around an axle.  The axle is attached to a wide and massive disk.  The hanging object is released from rest, causing the disk to accelerate rotationally.  I have the expensive PASCO version; a similar apparatus can be created for just a few dollars from PVC pipe placed over a ringstand, kind of as shown on problem 3 of the 2001 AP Physics C Mechanics exam.

A set of seven exercises is available for you to download and try out at this link.  I hand out the first to everyone, and help each student create an angular velocity vs. time graph for the rotating disk.  Then, each student individually, with his own unique graph, answers each of the questions, getting my approval before moving on to the next one.

Creating that ω vs. t graph requires some ingenuity.  The simplest way is to use the smart pulley and photogate; in fact, the PASCO apparatus provides a screw specifically aligned so that the photogate can easily be placed just right.  Problem is, I have Vernier photogates, which conveniently don't fit with the PASCO equipment.  D'oh.

So I set up a photogate vertically, a bit more than one disk-radius away from the rotational axis.  I cut a piece of paper such that its width was a known angle -- I calculated that with the 11.7 cm-radius disk, a 0.9 cm width paper subtends an angle of 0.08 radians.  Don't ask me why I chose that value -- I did, it works, and now I ain't gonna do any more cutting and taping.  (You can check my math, though.   Using x = rθ, 0.9 cm does in fact equal 11.7 cm times 0.08 radians.)  

Next, I set up my labquest to read the photogate in "gate" mode, with a "distance" of 0.08 m.  Thus, the labquest thinks it's making a linear velocity vs. time graph in units of m/s.  I fooled it, though -- it's really making an angular velocity vs. time graph, in units of radians per second.

Once I finished the setup, the data collection was a breeze.  Students on their own could create beautifully linear ω vs. t graphs, as shown to the right.  Then they figured out to take the slope to determine the angular acceleration; they calculated torque with force times lever arm; and they calculated the rotational inertia of the disk.  I deliberately had half the class using the gray disk by itself, and the other half using the gray disk with a heavy ring on top; sure enough, the half of the class with the extra heavy ring calculated a significantly larger rotational inertia.

The subsequent exercises each ask the student to redo the experiment, changing one of three things:

(1) Changing the net torque by changing the hanging object's weight
(2) Changing the net torque by changing the lever arm
(3) Changing the rotational inertia by adding or removing the heavy ring

In each case, students predict the new angular acceleration using semi-quantitative reasoning, and then measure to verify their prediction.  Results are generally accurate well within 10% of the predictions.

Postcript:  Throughout these exercises, I'm making the approximation that the tension in the rope that provides the torque is equal to the weight of the hanging object.  This is not precise -- since the hanging object is accelerating downward, the tension in the rope is a big less than the weight of the hanging object.  So what.  When I do the precise calculation, I find that the effective rotational inertia of the whole system is increased by mr2, where is the hanging object's mass and r is the lever arm of 1-2 cm.  Since that is SO much less than the rotational inertia of the disk itself (where the disk's mass is significantly larger than m and the disk's radius is ten times larger than r), I've made a good assumption.  Eventually, when someone asks about the string's tension not being truly equal to mg (as someone did on Thursday), I can have a nice conversation.

05 February 2015

Use a quiz question to set up a lab investigation

I give daily quizzes with a variety of purposes.  And my lab exercises in AP Physics often involve creating a curved graph with direct data collection, followed by linearizing that graph.

Historically, I've struggled getting students to understand graph linearization.  Only a few students have truly understood how to figure out which variables go on which axes, and what the slope of the graph means.  Most of the class has needed multiple consultations with me and with their friends to get each experiment done; and more often than not they haven't been able to reproduce their analysis later on.  Graph linearization is abstract and difficult.

This year, I made graph linearization a common topic for daily quizzes.  I started simply:  

 I make a graph of the net force experienced by an object on the vertical axis, and the acceleration experienced by the object on the horizontal axis.  What is the physical meaning of the slope of the graph?
I teach that we solve the relevant equation for the vertical axis... then using the equation y=mx+b, identify the y and x variables.  What's left is represented by the slope of the line.  In this case, the relevant equation is F=ma.  The vertical axis is F, the horizontal axis is a, so the slope is the cart's mass.

The biggest misconception is to deal with units not with variables in an equation.  Someone will get the answer right by saying "the units are N/(N/kg), which is kilograms.  That's mass."  Well, that sometimes works.  It sometimes is too difficult to mess with (i.e. for those who don't recognize alternate forms of units for N or m/s/s).  And it is very often wrong.

In the lab, a student releases cars from rest on an incline, and measures the distance they travel on the incline.  The relevant equation is x = vot + ½at2, with vo = 0. The student keeps the time of travel constant while changing the cart’s acceleration.  He graphs the distance traveled on the vertical axis, and the acceleration on the horizontal.  What is the meaning of this graph’s slope?

Now the vertical axis is distance x, and the horizontal axis is a.  That leaves the slope as (1/2)t2.  The student doing a unit analysis might get the t2 part, but he certainly won't get the factor of 1/2.

Things get even more complicated when I ask students to figure out for themselves what to graph.  But I'm still using daily quizzes to get them to practice -- primarily because I can do one every day or two, and give them instant and brief feedback on their answers.  

Last week I did the standard period-vs.-mass-of-a-spring experiment.  I have students collect period vs. mass data, then they linearize such that the slope of their graph allows determination of the spring constant.  When they're all done, I use my five-second spring constant measurement method to check each group's result.  

Try this quiz.  It asks directly what a graph of period vs. mass for a spring looks like.  (Learning to sketch the shape of a graph is a different skill that I'm also working on through daily quizzes.)  Next, it asks for a possible linearization and the meaning of the slope.  

Not only do we go over and grade this quiz for immediate feedback, we go straight into the lab to do the experiment.  I've primed my students' brains to know what to expect from the experiment.  Then when it's time to linearize, there's much less fussing than in previous years.  We just discussed the linearization, and for a grade, even.  Everyone paid careful attention (because they care deeply what grade they get on a quiz).  That doesn't mean everyone interprets their graph perfectly... but we're five stepping stones ahead of where we were in previous years, even though I've done fewer experiments in this style.  Quizzes work!

02 February 2015

USIYPT 2015 -- results, and problems for USIYPT 2016!

This past weekend, Woodberry Forest School hosted the 2015 US Invitational Young Physicists Tournament.  Nine schools from around the country and the world participated in "Physics Fights," ritualized discussions about research projects.  The teams included:

The Harker School, CA - CHAMPIONS

Woodberry Forest School, VA - Second Place

Rye Country Day School, NY - Final Four

Renmin University HS, China - Final Four

Nanjing Foreign Language School, China - Swartz Poster Session Champion

Pioneer School of Ariana, Tunisia

Shenzhen Middle School, China

Princeton International School of Math and Science, NJ

Phoenixville Area High School, PA

At the closing ceremony, the trophies are awarded, and then the teams are given their "homework assignment:"  The four problems for USIYPT 2016 were revealed.  

In 2016, the tournament will be held Jan. 29-30 at Randolph College in Lynchburg, VA.  Let me know if your school would like an invitation to participate, or if you would like an invitation to judge.  Problems include:

#1 --  Domino Toppling: On 6 August 2014, in Charlotte, North Carolina, a team from Prudential Financial broke the Guinness World Record for toppling the largest domino stone, measuring roughly 30 ft x 15 ft  x 3 ft.  Each domino in the chain had the same aspect ratio of 10:5:1.  Study this phenomenon, then design and construct a domino chain whose overall lateral length before toppling is 3 meters, that starts with a domino stone that you can hold in your hand, and will topple the tallest possible stone. You may change the aspect ratio of your domino stone chain, however all stones must have the same aspect ratio, and all stones must be constructed of the same materials and in the same manner. You must launch the initial, smallest stone with a gentle finger push that topples that stone.

#2 – Blender Lift: If you hold an immersion hand blender's blades under water in a beaker or pot or pail, under certain circumstances you can lift the beaker and the water by lifting only the hand blender as shown in the picture below.  Study this phenomenon for a wide range of the relevant parameters comparing your theory that explains the effect to the experimental results.  Predict the
maximum weight of water and container that your blender can lift and verify this prediction by experiment.

#3 -- Transformer Impedance Reflection: the recently posted YouTube video titled "Transformers – Experiments and Demos" (v=y0WrKT45ZZU) shows a demo at the 4 minute mark.  The demo purports to show that removing a light bulb in the secondary circuit of a transformer will cause a light bulb in series with the primary to turn off, i.e., "a impedance reflection." Analyze this demo and the published explanation of this effect (W. Layton  Transformer Impedance Reflection, The Physics Teacher 52 (7), Oct 2014, p. 426-427).  Provide theoretical and experimental evidence to explain or refute this effect.

#4 -- Bouncing Laser Beam: – a laser will curve and even bounce in a medium whose index of refraction decreases with height.  Although there are several ways to produce this medium, the photo below was created by pouring thick, transparent Karo syrup into a tank and then pouring water on top of the syrup.  Approximately 12 hours later, the bouncing laser beam can be observed.  Create this apparatus or a similar one, study the theory of this effect, and use your results to measure the index of refraction of the medium as a function of height from the bottom of the tank.

26 January 2015

Embrace Chaos: science teaching and New England's deflated footballs

Which football is Belichickian?
In the runup to Super Bowl XVXIVXIVXIVXIVIXVIX, the NFL is investigating the New England Patriots for, perhaps, systematically underinflating the footballs they use on offense.  The sports media has gone crazy wearing out the "deflated ball" meme with puns and giggles well below the maturity level of the 9th grade boys I teach.  

In the true spirit of American anti-intellectualism, those who live outside New England condemn the popular and successful Patriots for cheating without waiting for any evidence better than "Cheater, Cheater, Pumpkin Eater."  Meanwhile, those who live *in* New England reflexively condemn the haters who dare to impugn the saintly Pats, even though not even his staunchest supporters would deny that head coach Bill Belichick would trip his own aged grandmother in a race if doing so raised the probability of victory.  

[For those of you who do not follow American football, the above paragraph must sound made up.  Trust me -- the students, faculty, and staff of my school have talked about little else for days.]

Our department has been asked to articulate "best practices of science teaching," things that we do that might be foreign to teachers in other disciplines.  Paul the chemistry teacher's response: 

Embrace chaos. What I mean by that is that, while organization and having a plan for where a lesson is going are important, it's equally important to leave room for serendipity. The "what would happen if we do this?" question that I'm not expecting is one that, as often as possible, I try to answer with "let's try it and see." Those questions are little clues as to what about the topic is going to be the hook of interest that keeps the student going through the difficult parts. Those are also authentic science experiences, in the sense that it's the way science really works---someone has a question and tries to find out the answer, and that investigation doesn't always go in the expected direction.

Paul embraced the chaos of the sports media's obsession with inflation pressure of footballs.  He asked the football team equipment manager to provide him with two new footballs, one inflated to 12 psi, one to 10 psi -- this was roughly the originally reported difference between legal footballs and Patriots footballs.*

*subsequently, it was found that reporters or someone had exaggerated -- the Patriots footballs were only 1 psi short of legal, not 2 psi.  That's going to be important to the next calculation.

First he had his students thrown the footballs around a bit.  While they all suspected that at least one was illegally deflated due to their overexposure to the sports media's "deflategate" meme, to the students both felt like normal footballs.

Next, Paul revealed that sure enough, one football was legally inflated, and one was underinflated.  He asked the class to handle the footballs and guess which was which.  The results showed that, even upon close examination, noticing the difference was pretty much a random proposition.  Paul is not entirely sure of his notes, but either his students today identified the correct ball by a 19-13 margin; or, they were dead split, 16-16.  I made my own guess, which happened to be right, but I was in no way sure of myself.

Finally, Paul introduced the ideal gas law to his students by way of a football inflation calculation.  We checked that a football was properly inflated to 12 psi in our 20 degree Celsius office.  Imagine now that we take the football outside on a 50 degree Fahrenheit day, like the day of the most recent Patriots game.  That would drop the Kelvin temperature by about 4 percent.  By the ideal gas equation, that would likewise drop the absolute pressure in the football by 4 percent.  Absolute pressure in the football would be the 12 psi gauge pressure plus the 14.7 psi atmospheric pressure.  Reduce that by 4% and then subtract the atmospheric pressure again and you find that the gauge pressure would drop to... 11 psi.  Down by 1 psi from the legal standard as measured by the officials before the game.  And exactly what recent reports indicate was measured by the NFL.  And that's a controversy, apparently.  

We haven't had the time yet to do the experiment -- we should leave the ball outside overnight to see if the pressure reading does in fact change by 1 psi or more.  That's next on the list.

Now, if Paul wanted to make this lesson truly interdisciplinary, he might discuss how the NFL conveniently leaked word of their investigation, knowing that the two-week media vacuum leading up to the Super Bowl would thus be dominated by ball inflation questions rather than pointed queries about the NFL's coverup of multiple instances of domestic abuse by their players this season.  Or Paul would discuss Mike Tanier's investigative report that found the Patriots footballs to be primarily filled with nitrogen.*  But Paul says he'll stick to chemistry.

* as well as the wonderful responses from the humor- and science- impaired.

13 January 2015

Mail Time: How do you convince a student that motion is not always in the direction of the larger force?

Two identical blocks of mass m are connected by a string over a pulley.  Block A is on a horizontal, frictionless surface; Block B hangs from the string. Consider now that, having previously been given a brief initial shove, block A is sliding to the left across the smooth tabletop.

•Is the tension in the rope greater than, less than, or equal to mg?

One of a reader's students asked, "Why is the tension less than mg if the block is sliding left?"

She continued... "How can it slide left and the tension not be greater than mg if the block is pulled up even if it is slowing down?"

The reader explained that block A's acceleration and net force are to the right, since the system will slow down after the initial push. If tension is greater than mg then block B would have an upward acceleration, which would mean that the block would speed up while moving upward -- that doesn't happen.  And finally, the FBD  shows the block on top with only one force, that being to the right -- rightward net force on Block A requires a downward net force on Block B.

She wasn't satisfied with these explanations. Is there a better way of putting it?

I wouldn't say I have any better ways of explaining this issue; I use all of the above explanations.  This student is still conflating force and motion.  Any object -- not just these blocks -- can move opposite the direction of the net force acting on it.  That just means the object is slowing down.

Ask her and the class for examples of objects that move in one direction while experiencing a net force in the other direction.  A ball moving up in free-fall is the canonical example.  

I'd then set up this described system* in class, using a force probe or a spring scale to measure the tension in the string.  It's fun to watch the spring scale reading dip below the weight of the hanging mass as soon as you let go.  If your class is too large for all to watch the spring scale dial, use the Vernier force probe and project its reading on the screen.

* It's often called the "modified atwood" when two block are connected by a string over a pulley, but one of the blocks is on a horizontal surface.  See AP Physics B 2012 exam problem 1.

I ain't saying this experiment will solve all your student's misconceptions, but it should at least stop her from arguing.  That's what I love about physics: my students can argue, sure, until a smiley but facetious "Bet you $100 that the experiment works the way I say it will?" shuts them up a treat.  :-)

07 January 2015

Adapting an AP Physics 1 question: motion graphs of a student in an elevator

The picture to the right is from the first problem on the 1993 AP Physics B exam.  That problem
asked for calculations and numerically correct graphs of position-, velocity-, and acceleration-time graphs given the force vs. time graph shown.  

When I adapted this problem for my AP Physics 1 class, I took into account two major considerations:

(1) The AP Physics 1 exam is not likely to require twelve(!) sets of kinematics and Newton's Law calculations.  So I need to find and ask about the conceptual essence of the problem.

(2) Short answer questions on the AP Physics 1 exam are only 7 points.  The original AP Physics B problem was graded on a 30(!) point scale*, looking at the results and methodology of each calculation and graph segment separately.  The revised question must be doable in 15 minutes -- that generally means only three lettered parts to the problem -- and scored with "fatter" points.

* The 30-point score was divided in half to get a standard 15-point problem.  This is the only AP Physics B problem in recorded history with such a nonstandard rubric.

The point of this post is not to show you a finished product, ready for the College Board to pick up for a future exam.  Note that I also am not correlating this question to any standards or learning objectives.  No, I'm just trying to respond to the numerous questions I've received about how to write test questions for AP Physics 1, while we don't have much in the way of officially published resources.  This question ain't perfect, but I hope I'm revealing some of my own thought process in writing problems; and then I hope you'll take my thoughts and make them your own.

Here's the revised AP Physics 1 style problem.  The rubric is below, too.  

(a) Describe the motion of the elevator.  In each of the five-second segments, be clear about the direction of motion, and whether the elevator is speeding up or slowing down.  Justify your answer.  [Comment: This question takes a good bit of writing to answer.  But it really rewards students who understand the physical process represented by the original graph.  No one can skate by, or even get partial credit, with just memorized equations.]

(b) On the axes below, sketch a graph of position vs. time for the 20 s shown in in the graph above. 

(c) On the axes below, sketch a graph of velocity vs. time for the 20 s shown in in the graph above.  [Comment:  Parts (b) and (c) are subsets of what the original problem asked, just with no calculational element, nor a justification.  When we do test corrections, I ask for justification with respect to facts about position-time and velocity-time graphs.  But since I asked such a verbally intense part (a), I don't think students would have time to justify these parts as well.]

The rubric I used to grade this problem:

(a)        3 points

1 pt for using N2L to correctly justify that acceleration or net force is upward from 5-10 s, zero from 10-15 s, and downward from 15-20 s

1 pt for describing upward motion the entire time from 5-20 s

1 pt for describing speeding up from 5-10 s, constant speed from 10-15 s, and slowing down from 15-20 s

(b)        2 points
1 pt for curved graphs of any sort from 5-10 s and 15-20 s, coupled with a straight graph of any sort from 10-15 s
1 pt for completely correct graph

(c)        2 points
1 pt for straight segments throughout
1 pt for completely correct graph

Remember, this rubric hasn't been vetted by anyone else; it seemed to work okay when I graded my one class's work one time.  At the real AP Physics 1 exam, we'll be grading three orders of magnitude more student responses than I graded.  I've no doubt that this rubric would have to be amended somewhere, somehow.


26 December 2014

Teaching seniors after Christmas: hints and ideas

Our faculty is currently involved in a brainstorming exercise in which, without practical constraints, we suggest how the school could or should change programmatically to better address our students' needs.  Certainly I'm hearing some excellent ideas (though some of them are only excellent in the absence of friction and air resistance, so to speak).

A large number of these ideas suggest sweeping changes to the structure of the senior year.  I've many times heard our faculty -- and other faculties -- hold forth on the moral deficiencies of late-season seniors.  Amongst all the kvetching and suggestions for change, I wonder... are we trying to solve a problem that doesn't exist?  Or, at least, are we trying to solve a problem that could better be prevented than solved?

A number of teachers have quite positive in-class experiences with late-season seniors, without internships, final projects, field trips, or any other major gimmickry.*  If a class is truly important and useful, it should sustain students' interest regardless of whether those students need a good grade to ensure college admission.  To a very large extent it's the teacher's job to structure the class so as to keep students -- seniors included -- invested.

* MINOR gimmickry is abundant among the best senior teachers.

So how do successful teachers of seniors sustain interest, even though all seniors (to one extent or the other) have one foot out the door in the spring?  Here are some tips.  Some are from my own experience; many are from observation of and discussions with the best teachers of seniors that I know.  Please submit your thoughts in the comments.

* Deal with seniors are they are, not as we wish they were.  Seniors always prioritize things other than your class; as the spring advances, my class drops down the list.  I may not agree with their priorities, but it would be silly not to acknowledge them.  I set in my mind from the beginning that I am not going to take personal offense at seniors' attitudes, nor am I ever going to lecture them about their senior slide.  I vow to treat students with respect, even when their decisions don't command respect.

Front-load your course.  We know the senior slide is going to happen; conversely, we know that seniors are heavily invested early in the year, when their grades "matter."  So push, push, push the pace.  I cover at least half of my material in the first trimester.

Don't let one or two obnoxious seniors poison your mindset.  Even the best teachers of seniors don't have a 100% success rate.  When a student is being irrationally obstinate, do your best to patiently ignore him.  Don't let him rile you up.  If he's bringing the whole class down, dispassionately remove him from the situation (i.e. boot his arse out of class without drama); but whatever you do, don't engage or argue.  It's not going to help.  Think about how the rest of the class feels -- they're probably embarrassed about their obnoxious peer, but he's still a peer.  They don't want him disrupting class, but neither do they want the teacher to become angry or aggressive.  Be the welcome bringer of peace, not the fearsome champion of war.

* Develop positive relationships with the class early on.  While you are not expected to be best buddies with your students, they need to know that you care about them.  Expect the highest level of effort and performance, yes.  But in everything you do, from your words to your body language to your actions, show your students that you're doing it for them.  When someone screws up BEFORE the senior slide, treat him firmly, fairly, and compassionately.  Know that everyone is watching you, all the time.  If you react hostilely to one student, even if he deserves your hostile reaction, the rest of your class feels like you've reacted hostilely to them, too.  Don't underestimate the teenager's desire for vengeance against those who, in their view, take their authority too seriously.  

Conversely, don't underestimate teenagers' positive ethical underpinning.  If you are seen to be fair, patient, and on their side, the silent majority of your class will support you.  When that one bastard starts being a jerk to you in March, you want someone to take him aside and tell him "not cool, man, back off."  That does, in fact, happen... if you do the front-end work to earn such quiet support.

* Make even more effort to do something different every few days.  There's no cure-all for times when students would rather be cavorting in beautiful spring weather than sitting in your class.  Certainly the physics teaching literature, this blog, and shop talk will yield numerous suggestions of productive but different styles of class: whiteboarding, socrative, the physics walk, lab challenges, test corrections, and more are excellent ways to add variety.  Whatever the specific activities, it's that variety that's critical for seniors.  Freshman need routine; spring seniors need to break out of their routine.  

* Taper.  You might reasonably expect 45 minutes of work per night early in the year; by April, that expectation should be down to about 15 minutes.  It's a bad idea to stop giving homework altogether, or even to reduce the frequency with which assignments are due; however, each assignment can become smaller in scope.  Swimming and track coaches are familiar with this idea of "tapering" toward a championship meet.  The physics brain muscles are already strong from the hard work students have done early in the year.  In the spring, daily work is more about maintaining muscle memory, about remembering and cementing things students already know, rather than about learning new things and developing new ideas.  

* Be creative in holding students accountable.  Any assignment is useless if it's not taken seriously; any assignment, no matter how small, is useful if done with care.  Along with tapering comes the responsibility to ensure that students do the required work, and do it well.  Second semester seniors generally don't give a rip about their grades, especially if grades are used as negative incentive.  Use as many different positive incentives as possible.  I give exemptions from future work for particularly strong efforts.  I might announce an exciting activity like a physics walk, with the reminder that a complete assignment is required to go along.  Even small things like in-class music when everyone turns in the homework can help.

Whatever the incentives, though, be sure they are backed up with the inviolable requirement that all assigned work must be completed eventually and correctly.  Use every trick in your book to enforce this requirement, such that students recognize that it's easier and more fun to get the work done right and on time than to slack off.

* At some point, acknowledge the year is over.  Where that point begins is your judgement call.  But it's important, I think, to end the year on a high note.  I've had the class solder AM radio or robot kits; had them inventory and organize the lab; done the bridge building or egg drop contests... anything that requires no out-of-class effort.  

In late May, you're not teaching anything further to this year's seniors.  Instead, you're laying groundwork for the future.  Think about what you want this year's class to say to next year's.  Students talk to each other, and it's usually straight talk.  You want a reputation right in between "pushover" and "arsehole."  After a couple of years, that reputation will by itself minimize hostile relationships with seniors, as they will come to your course from the start with the expectation that the spring will be serious yet fun.  

13 December 2014

AP in-class laboratory exercise: Energy (And more on different approaches in 9th and 12th grade)

Above is an example of an in-class lab exercise for AP-level seniors
When I introduce a new topic in 9th grade conceptual physics, I hand out a sheet with a few facts and equations, then I dive directly into guided laboratory exercises.  You can see one set of such exercises, about collisions, here

I don't do any discussion, or example problems, or anything at all with me talking to the class. There's no point -- the freshmen don't have the attention span to listen, and they don't have the abstraction skills to apply what I show them to future problems.  Therefore, the 9th grade in-class laboratory exercises walk the students step-by-step through the solution to a problem, then guide them through the experimental verification of their solution.  No one can tune me out, because I'm not talking. Instead, each student himself has to wrestle with the problem, showing me his answer to each step. When someone does a step incorrectly, I help him, and send him back to his seat to try again.

When I tried the same approach with AP-level seniors this year, it didn't work.  

A freshman who's told his answer is wrong generally looks sheepish, goes back to his desk, does the problem right, and finally looks happy as a mollusk to move on.  

A senior takes the wrongness of his answer personally.  While the freshman just accepts my word that his answer was wrong, the senior tends to make ever-more-ridiculous arguments at me to justify his incorrect reasoning.  Seniors aren't sheepish about wrong answers; no, they're defiant, as if it were my fault that the universe doesn't work the way they want it to.  

On the other hand, I've had good success over the years holding seniors' attention with quantitative demonstration lectures.  So after Thanksgiving break, I went back to my previous approach in teaching the work-energy theorem.  It went well... I raced through a bunch of energy problems at the board over just a few days.

Then, after those few days of me solving problems and showing demonstrations, after a few days of problem solving on each night's homework, I handed out this in-class lab exercise.  

Each student got a different sheet.  The picture above shows problem 1 -- but the link includes seven different sheets, with seven different energy problems.  Three involve carts on a track, three involve objects on vertical springs, and one involves a sliding block.  Each problem requires students to solve in variables, then use semi-quantitative reasoning to produce a prediction.  The experimental verification can be done with motion detectors and/or photogates -- no other equipment required.

The seniors did much, much better this time.  They were no longer hostile -- they felt like I had shown them how to solve the problems, so that if they got something wrong, it was their own dang fault.  

And that was interesting... the freshmen never worried about blaming themselves or me for a wrong answer -- it was just wrong.  The seniors got very snarky if they felt that I hadn't showed them the correct approach at the board, or if I hadn't mentioned all relevant background information out loud in class.  They pouted at their seat if they were turned back more than once to try again.  

But once I had done my duty lecturing at the front of the room, the seniors enthusiastically took to the same kind of open-ended independent lab exercises at which they had thumbed their noses earlier in the year.

I will likely come to some broader conclusions about seniors in the new AP course after I experiment a bit more with my class this year.  I'd love to hear other teachers' experience with these or similar in-class exercises.