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31 December 2019

Classic whirling stopper experiment, with smart phone video

In the classic old-fashioned circular motion experiment, students whirl a rubber stopper in a horizontal circle above their heads.  The stopper is tied to a string.  The string is threaded through a hollow tube - that’s what the student holds to whirl the stopper - and attached at the other end to a mass hanger. The equipment for this experiment can be procured from your storeroom  -- don’t buy the “discover centripetal force” kits  that are now down to $20 from $39.

My class's version keeps the mass on the hanger constant.  Students vary the radius r of the circular motion in each trial, measuring that and the speed v of the stopper's circular motion.   They plot a graph of v2 on the vertical axis and r on the horizontal axis, and take the slope.

Experimental tips: I don't ever give handouts with procedural instructions.  For this experiment, I demonstrate the acquisition of one data point, ask for a graph of v2 vs. r, and shut my mouth.  In that demonstration, though, students see rather involved and somewhat difficult technique:

  • This is the one experiment all year where I insist on lab goggles.  It's easy to get poked in the eye.
  • The whirler should keep an eye on the hanger.  If it's moving up or down, the stopper's speed isn't constant.
  • The stopper's speed is measured by dividing the circle's circumference by the period.  A decade ago, we measured ten periods with a stopwatch - I was never happy with the precision here, because it's tough to keep constant speed for that long.  But now, we use "hudl technique" or "coach's eye" apps.  That is, we take a video of one cycle, and use frame-by-frame advancement to find the period to the nearest hundredth of a second.
  • The radius of the circular motion is measured with a meterstick immediately after the video is complete.  That's a trickier measurement than you might think - students have to pay attention so that the string doesn't slip along the plastic tube.
Analysis: Since the hanger is in equilibrium and the rope is assumed to be horizontal, the tension T in the rope is equal to the weight on the hanger.  And that tension is then equal to mv2 / where m is the mass of the stopper.*


*Not the mass of the hanging thing!  When setting a net force equal to ma, the mass in question is the mass of the thing that has the acceleration.  That's the stopper here.

The goal is to use the slope of the graph to determine the stopper's mass.  In my formulaic method of teaching graph linearization, students begin by writing the relevant equation and solving for the variable on the graph's vertical axis.  Then, they write the equation for a line y = mx + b.  They circle the variables that match the y and x axis... what's left is the physical meaning of the graph's slope (or y-intercept, but that's usually zero).

We do this analysis in class, where I talk students through each step of the process above.  I check their graph, check their slope calculation, make them communicate in writing every analysis step, and then verify that they have a reasonable mass for the stopper.  Not the right mass of the stopper - they're not allowed to measure that directly with a scale!  No, I'm making sure that answers like "15 kg" or "1.5 kg" or "0.15 g" are exposed as unphysical - without even entering the lab, a person who knows what a kilogram is could reject these as possible masses of a bottle stopper.  And I'm checking that everyone is using two digits throughout.* 

*Not because we have to memorize rules of significant figures for the AP exam! No!  Because (a) two digits is the best we're going to measure pretty much anything in a first year physics laboratory, (b) the precision of this particular experiment is limited by the two-digit radius and period measurements, and (c) most importantly, insisting on only two digits throughout the year on everything (rather than ignoring excess precision, or teaching those sig fig rules that no high school student understands) is one of the ways in which I help my students develop habits of mind relating numbers to physical reality.  

Once everyone finishes, I do use a scale to show the class the stopper's mass.  I give a prize to whichever student(s) got closest.  Since we started using frame-by-frame video on smartphones, our mass values have been not just reasonable, but often correct within 10% or so.  

I've fallen back in love with this experiment now that the long road to getting the analysis right pays off with good results.  I do mean long road.  The analysis by itself might take more than an hour; data collection is 30-45 minutes for well trained students.  

26 December 2019

Circular motion linearization: Grocery Cart

We were asked on the "Pretty Good Physics" message board to give ideas for linearization experiments with circular motion.  Here's an old-fashioned version that uses 1960s equipment.  If I remember, I'll post a second old-fashioned experiment, but with a modern twist.

Grocery cart: My colleague Wayne did this one in my first year teaching.  He cleared out the desks in the classroom, and marked with tape the biggest circle he could possibly fit.  Wayne had, somehow, acquired a standard wire grocery cart, the kind we all used to love riding in.*

* or on, much to our parents' dismay.  Hah, hah, Mom, I never fell off and** had to go to the hospital, did I.


** Ed. note: use of "and" not "or" is deliberate here.


One student rode in the cart.  Another student pushed the cart from behind.  And a third student stood in the circle's center, pulling on one of them giant spring scales that can be read across a classroom.  The scale was connected via rope to the student in the cart.

The pushing student - chosen as someone who had rhythm - walked at a steady pace around the circle.  While the center student read the spring scale (to get the net force F), others used stopwatches to measure the time it took to go around the circle.  The crew repeated for many different speeds.

The speed of the cart v was calculated to be the circle's circumference divided by the measured time.  A graph of F vs. v showed a parabola.  To linearize, we plotted F vs. v2.  The slope was the mass of the cart+rider divided by the radius of the circle.  The class compared that slope to a direct measurement of these masses via a bathroom scale.

Finally, in this K-12 school, Wayne kidnapped* a small child to ride in the cart.  The class repeated the experiment and graphed F vs. v2 on the same axes. Even without any calculation of slope, it was apparent that the smaller mass in the cart had created a shallower slope.

* "Want to take a break from your class to ride in a grocery cart for a science experiment with high school students?" The child joined Wayne willingly, though I could not easily interpret their teacher's expression.



24 December 2019

Notes from observing a poetry class - three things that DIDN'T happen.

As part of my school's faculty development program, we're asked to observe a teacher of our choice outside our department.  In 2015 I watched John Amos's 9th grade English class.  This year, I watched Ansel Sanders teach poetry to 11th graders.  I saw an enjoyable class.  But I also noted three things I didn't see: no soapboxing, no trolling, and no negging.

I'll begin with the same prologue I gave to my previous English class observation.

So many "Physics Educators," and "educators" in general, have the Soviet attitude that if only everyone did things my way, students would learn better.  I disagree.  I've always been open at my workshops and on this blog: my ideas, philosophies, and suggestions are mine alone, developed in the context of my personal strengths and weaknesses, and shaped by the ecosystems of the three schools at which I've taught.  What I do cannot work for everyone.  Yet, it's still worth sharing my thoughts, techniques, and ideas.  Not in the sense of "do these things and you will become a great physics teacher;" but rather, "here are a few ideas you may not have considered; try them, and then either throw them out or adjust them to make them your own."

So here's my extensive reaction to Ansel's class.  I will not be adopting wholesale any of his particular techniques; but I appreciate the exposure to some different ways of approaching my craft.  Many of Ansel's ideas are in the back of my brain now, ready to manifest -- consciously or subconsciously -- in my own classes.  In other words, I bought myself a few new tools.  Whether and how I use them is discourse for a future time.

What happened in Ansel’s class? Ahead of the class, Ansel sent me a packet of about five quatrains to read.  The students had been discussing the definition (or, as students and he pointed out in class, the not-definition) of poetry; they had been discussing how to read and understand poetry, and how that differed from reading and understanding prose.

In class the previous week, they had discussed Dudley Randall’s "Ballad of Birmingham" - discussed meaning, audience, how the audience’s own experiences affect the meaning, etc.  I would have loved to have seen that discussion with this particular group of students, most of whom I know and respect from other areas of school life.

In Monday’s 8:45 AM class, then, Ansel began by asking groups of students to write poetry word association on the board - basically anything they wanted to write to “get the brain juices flowing.”  This led to a review / follow-up discussion about the purpose and not-definition of poetry.

In the last 15 minutes of class, Ansel assigned groups to go deeper into poetry consumption.  We discussed three ways in which people can engage with poetry, and what each means - poetry reporter, poetry interpreter, poetry performer.  Each group was assigned to engage with a poem of their choice in each of these three roles.  By the end of class, my group had reported on the who-what-when-where of "Sadie and Maud" by Gwendolyn Brooks.  One student seemed amused to know that I had TWO great aunt Sadies, one on each side of the family.  That fact, and rareness of the names in later generations, helped us approximate the “when” of the poem.

I particularly enjoyed watching a member of my group read "Sadie and Maud" for the first time.  He did what Ansel said to do - he read it several times, even talking aloud a bit.  He reacted viscerally… “yeah, I’d rather be Sadie, you don’t have to do exactly what your parents say.”  That comment spoke to exactly what Ansel had been getting at… every person is a unique and biased audience for a poem.  This student's reaction was pure, and in the moment. He hadn’t been prejudiced by his classmates’ interpretation, or what the teacher might have said, or the compiler’s essay, or even the teacher’s expectation - Ansel wasn’t anywhere nearby, and the student was treating me like a classmate.  This was authentic.  I’d never seen that before, at least not when I knew what I was seeing.

That's a summary of what happened.  

It's just as important to ask, What didn’t happen in Ansel’s class?  Three things jumped out at me.

(1) No one got on a soapbox to overemphasize the moral rectitude of their interpretation.  At least, not that I saw.  That’s part of why I would have liked to have seen the previous discussion of the "Ballad of Birmingham" in this multiethnic class.  In my college English class, too many of my classmates would have insisted on an interpretation that advanced their political agenda.  Ansel (a white guy in his 30s) mentioned his own visceral reaction to the poem from the perspective of a parent of three daughters… but in my college English class, the response would likely have been, “well, I suppose, but you don’t understand the African-American experience, so let’s stick to what the author obviously intended.”  And that would have been coming from a rich white 18 year old from Princeton, New Jersey.  Ansel emphasized taking personal meaning from each poem, even though each person in the poem’s audience brings his or her own biases, perceptions, backgrounds.  

(2) No one was intellectually dishonest - no one knowingly chose a ridiculous interpretation, then died on a hill with a smirk defending their deliberate but attention-getting stupidity.

I’ve thought deeply over my career about culture building in the classes I teach.  I’ve always focused on building a positive and “safe” class culture, where students can make mistakes and share their thoughts without fear of being put down by their classmates. Nevertheless, especially in physics, we can’t engage in relativism, we can’t think that all ideas are equal.  They’re not.  Right and wrong do exist.  In an educational environment where students have been trained that being wrong is equivalent to being a BAD BOY, it’s very difficult to strike a balance between freely sharing thoughts, and learning right answers from wrong answers.  But that’s the heart and soul of culture building.

In physics, right and wrong isn’t determined by the teacher or by peers - right and wrong is always by reference to experiment.  When a student irrationally insists that his idiosyncratic interpretation of Newton’s Second Law must be correct, I can say, “bet you $100?” and do the experiment.  It’s not mean ol’ Mr. Jacobs telling the student he’s wrong, it’s not his classmates shouting him down, it’s the universe itself.  Hard to argue with the universe.

In English, in poetry, right and wrong so often are in the eyes of the beholder.  Yes, poems can and should mean different things to different people.  But the "Ballad of Birmingham" is NOT a reference to the Odyssey; "Sadie and Maud" (published in 1962) is NOT a deliberate prequel to The Handmaid’s Tale.  

(The more likely trollish interpretations in this time and place would be something like “It’s racist against white people to assume that 'Ballad of Birmingham' might have unique personal meaning for a Black person from the South,” or “'Sadie and Maud' tells us what happens when abortion is illegal.”  Guh.  Don't know how I would've reacted.  Thank goodness I didn't have to find out.)

I know - from hearing students and faculty talk - that Woodberry students do in fact play the troll in class on occasion(s).  And I know that faculty and some students are in fact frustrated with said trolls, but don’t know what to do about them.  Engage their arguments on their merits, and you legitimize them (both the arguments and the trolls); ignore them, and they scream ever-louder for attention.  

My own approach is prevention… no one is generally shouting all-out bold bullcrap to start the year.  They test the teacher with small-scale trolling at first.  So, at the very first sign of a bad-faith comment, I shut it down hard and move on before the proto-troll can argue.  

I wonder, what has Ansel done to eliminate trolls?  Is he just lucky that this class is devoid of troll wannabees?  Has he shut down proto-trolls?  Does he have a different approach, one that I could learn from?

(3) No one put down classmates for their thoughts - not verbally, not with body language.

Just as it bothers me when students take faux-intellectual positions in defiance of reality, it’s disturbing to me to hear about classes who gang up to otherize a teacher or a peer.  I felt this as a student in my own years-ago English classes - if I said anything that peers might disagree with, or anything that my peers had to work to understand, I got withering scorn.  I know some of this was gendered, as 16-20 year olds in a co-ed setting were often as interested in jockeying for social status and sexual partners as in authentically discussing literature.

Obviously discussions aren’t generally gendered at Woodberry Forest.  [It's a boys' school.]  But our boys yearn to belong to the "Woodberry brotherhood."  The social norm of the brotherhood as I see it in many classes is that we take intellectualism seriously but not literally.  That we go through the motions, we get good grades, we have personal interests, but as a group in non-honors classes we don’t engage authentically with authority figures.  (We bro it up with teachers - that’s different.)

But Ansel’s class did engage authentically, with him and with each other.  Sure, one student was falling asleep, but he just stayed out of discussion - and the one thing he said was on-point to advance a discussion.  Pretty much everyone made a good-faith contribution.  I’m aware that this level of engagement doesn’t happen in December without some serious work on Ansel’s part in September.  Does Ansel have any techniques that he consciously uses to build this positive and open class culture?  Are there things in his personality or class structure that naturally build culture?

I see one thing that jumps out at me… Ansel is loud and enthusiastic, his eyes roam the room, fixing on student after student.  And not just his eyes - Ansel roams the room, making it seem like he’s having a one-on-one dialog with a person who asked a question, while simultaneously engaging the rest of the class with his body language.  He has, in a word, stage presence.  In two words, anyway.

It’s clear who the alpha dog is in Ansel’s classroom.  I’ve always said, freshmen are like puppies - once they know that the teacher loves them and that the teacher is unquestionably the alpha dog, they’ll do anything the teacher asks.  Juniors are big dogs… yet, Ansel has convinced them that he’s the leader of the pack, that he’s worth following.  I'm impressed.

23 December 2019

Amy Johnson's AP Physics 1 Workbook: Use it. I will.

By now most AP Physics 1 teachers are aware of the new “Workbook”, available as a free download from a teacher's College Board course audit page.  If you’re not, get aware right away! Amy Johnson of the College Board spearheaded the production of a 350 page set of scaffolded activities.* All of them, of course, are perfectly aligned with the content, depth, and skills demanded on the AP Physics 1 exam.  They’re classroom-ready - once students have some exposure to the underlying facts and general problem solving approaches, these activities can be handed out and used without edits, even by the most persnickety AP teachers.**

* Oops, buzzword alert!  The workbook is in typical class coverage order - kinematics, then forces, etc.  The “scaffolding” means that the early units give lots of guidance, assuming less facility with the various skills we expect AP students to develop throughout the year.  For example, an early worksheet might present a justification in paragraph form but ask students to fill in the blanks; a late worksheet would just say “answer in a clear, coherent, paragraph-length response” as the exam does.

** i.e., me.

The workbook is for new or out-of-subject teachers.  We all know it’s common for people to be asked to teach AP Physics when they’re not confident in their own physics skills, let alone in their ability to choose, solve, assist students with, and evaluate practice problems. Or more bluntly: too many AP Physics teachers don’t know much about physics, and know nothing about physics teaching… yet they’re assigned to teach physics anyway.  What can these poor folks do, other than follow the poorly-written, six-decade-old* textbook?

*Yet in the 30th revised edition because the numerical values in end-of-chapter problems have been changed regularly, like diapers.

Now, they can use Amy’s workbook. A student who goes diligently through each page over the course of a year will be guided to develop a solid background in the necessary content AND skills required on the AP exam.

The workbook is also for experienced teachers.  I’ve taught physics for a quarter-century.  I’ve developed my class activities and practice problems piecemeal over that time, creating or revising one thing at a time.  

And, so has Workbook author Amy Johnson.  She’s a real physics teacher - plucked out of the trenches of the classroom, not out of the gilded halls of academia.  She’s also an experienced AP reader.  Thus, Amy has a tremendous sense of her audience.

The workbook certainly is inspired by the same best practices of physics pedagogy that underlie the AP Physics 1 exam itself.  Worksheets guide students to become fluent in multiple representations, to use verbal reasoning, to approach semi-quantitative and experimental problems.  None of the worksheets could possibly have been plucked out of the 1988 edition of Giancoli or Serway.  

Of course, there’s no shortage (anymore) of problems and activities that use best practices of physics pedagogy.  Released AP questions (on Collegeboard.com or via AP Classroom), TIPERS, The Physics Classroom, Vernier’s Pivot Interactives, and even the “Elite Student Edition” of the 5 Steps to a 5: AP Physics 1 book.  Why use the Workbook, then?

(1) It’s free.  The Physics Classroom website is free; the other items above all cost varying amounts.

(2) It’s aligned to the AP exam.  (TIPERS, The Physics Classroom, and Pivot are not explicitly aligned to AP.)

(3) It’s scaffolded.  (Even though the 5 Steps Elite Student questions are aligned to AP, they are not scaffolded.  5 Steps is intended as a review book.  The Workbook is intended to be used more like a textbook.)

How am I using the Workbook?  See, I already have a set of assignments and activities for each topic that are well-vetted.  That doesn’t mean I’m happy with all of them!  In particular, while my students end up doing fine with waves and sound, I know my assignments can be improved.  So, I’ll replace my in- and out-of-class waves/sound assignments with a bunch of the Workbook activities.  

Similarly, my colleague teaches an “honors physics” class that is close to AP, but doesn’t manage the entire breadth of the AP Physics 1 content.  Every year he has a few students who want to take the AP exam, but who need to learn about waves and rotation on their own.  Enter the Workbook - since my colleague has developed strong skills in these students, they will have little difficulty working through the Workbook to get themselves an appropriate background on these topics.

How are YOU using the Workbook?  I’d love to know.  Post a comment below...

05 December 2019

Can conceptual students learn calculational methods? Yes. Look at this voltage problem.

On the conceptual physics trimester exam, I showed the circuit above, then asked, "estimate the voltage across the 10 ohm resistor."

In conceptual physics, we teach, well, conceptual approaches to all problems.  That doesn't mean we never use equations or calculations, of course; it's just that even when a problem does require mathematics, students are generally required to explain an aspect of the mathematics in words.

For example, we teach students to approach this particular circuit problem with an equation:

* The current in each resistor is the same - that's a fact that "series resistors take the same current"
* Mathematically by V = IR, then, with the same I the bigger takes more voltage V.
* The voltage across series resistor adds to the total.  So the 10 ohm resistor takes less than 18 V, but more voltage than the 5 ohm resistor.

With this reasoning, we accept *any* answer more than 9 V and less than 18 V.

In class, the students each conduct this kind of estimation, then set up the circuit on a breadboard.  They find out experimentally that the voltages are in fact 12 V and 6 V.  After a bunch of similar predictions and experiments, my 9th graders develop for themselves an instinct - in series resistors, the bigger resistor takes more voltage, and the bigger the difference in resistances the bigger the difference in voltages.  That's not written down anywhere, 'cause it's not exactly rigorous.  But these conceptual students can estimate voltages for series resistors better than most seniors can calculate them.

Greg, when your students get to college, they'll be asked to calculate precise voltages.  I know you love conceptual physics, but the vast majority of college physics courses are calculational in nature. Aren't you doing a disservice to your students by teaching physics in a manner so different from how they’ll be asked to learn in their future?

Before I address this (legitimate!) concern on its merits, I’ll point out that it is emphatically NOT my job as a high school teacher to “prepare students for college.”  I provide for my students what they need right now… not what they should’ve had in the past, not what they may possibly need at some ill-defined point in the future. (But in Zen-like fashion, even though I adhere zealously to this philosophy, I've nevertheless received overwhelming feedback that, four years out, my students feel extraordinarily well prepared for college and college physics.  Go figure.)

I have plenty of anecdotal evidence that those who start their study of physics primarily with concepts (rather than primarily with calculation) retain more and deeper knowledge, and perform better if they continue to another physics class.  If you want them, I know you can find academic-style research studies that say the same thing.  But let's talk about just last month's trimester exam. and just this question.

Remember, I did not ever teach, model, demand, suggest, hint, or advise students about a caclulational method to finding the voltage across each resistor.  Not once.  We did sometimes ask students to calculate equivalent resistance of series resistors by adding the resistor values.  We did sometimes ask students to calculate the current through each resistor, using the fact that says "In ohm's law, use the voltage of the battery with the equivalent resistance of the circuit."  But voltages across series resistors?  Conceptual students were only taught how to make an estimate.

Nevertheless.  On this exam problem... a large majority of the class made a correct numerical calculation!


Without prompting, so many students calculated the current by using the 18 V battery with the 15 ohm equivalent resistance to get either 1.2 A (or "6/5 A" because they had no calculator).  Then, they recognized - usually wrote out in words! - that the current in the 10 ohm resistor is also 1.2 A because it's a fact that series resistors take the same current that's equal to the total current.  And finally, they used ohm's law across the 10 ohm resistor to get (10 ohms)*(1.2 A) = 12 V.


In other words... when the class had only, exclusively been instructed on a conceptual approach, they nevertheless figured out for themselves a useful calculational approach.  And they did so in a few moments, under the pressure of an exam.  I'd say 3/4 of my class did this, and 9/10 of those who tried it did it right.

So am I doing a disservice to students by teaching them conceptual approaches?  Nope... they can learn how to calculate without difficulty.  They don't even have to be carefully taught.

01 December 2019

Don't present work = force * distance right away. Start with energy bar charts.

I've been using annotated energy bar charts to good effect for many years now.  They force students to define a system and to identify what forms of energy are present in that system before they consider the end goal of a problem.  In this manner they serve the same purpose as free body diagrams for Newton's Second Law problems - I don't care what you're supposed to solve for, draw the free body or the energy bar chart first, and then you'll be able to solve or explain any aspect of the problem.  These devices make problem solving about physics understanding, steering the process away from a game of "let's plug some numbers in to some equations and do some algebra to get the desired answer."

But I'd always been hung up on the definition of "work."  See, students can come to an operational definition of potential energies (both spring and gravitational) and kinetic energies just through their equations.  It's simple for a first-year student to see that gravitational energy must be included in the bar chart when an object has a height above the lowest point.  "Because PE = mgh and h is not zero" is a good enough reasoning for now.  Similarly for kinetic energy: "The cart has KE because it's moving, so it has a v in KE = (1/2)mv2."  Work isn't so simple.

Work can't be understood simply from the equation "W = Fd."  Students must understand the idea of a force being parallel or antiparallel to a displacement.  The scalar nature of work.  The meaning of negative work.  That this equation only applies when a force is steady.  The difference between net work and work done by an individual force.

Until this year, I'd always spent part of a class defining work, and giving examples of when work done by various forces is positive, negative, or zero.  I showed how the net work on an object is the (scalar) sum of the work done by all forces; or, how net work done on an object is just force times distance, where "force" is the net force.   Then we did a couple of problems for practice.

And every year, I came up against the corollary to Rule Two of teaching.

  • Rule Two: Your students don't listen to you.  That's okay, they don't listen to me, either.  
  • Corollary: Nevertheless, students have sharp and selective recall of what you say when it provides maximum inconvenience.
I always hoped and expected that, as we moved to energy bar charts, students would adapt to using "W = Fd" as the same sort of operational definition as "PE = mgh," only with complications that we'd discussed at the outset about the meaning of work.  

Well.  My class certainly did remember W = Fd.  As an equation to be applied with brute force in any and all situations, to the exclusion of the energy bar chart.  Which stinks, 'cause the vast majority of problems which ask "how much work is done..." should be solved by finding the difference in total energy at two positions - that is, using an energy bar chart, not the equation W = Fd.

I turned the tide this year - by ELIMINATING the discussion of the definition of work.

Yeah, that's counterintuitive, isn't it... but that's how so much of teaching works.  More often than not, the less you present formally, the more and better comprehension you get.

This year, we started with energy bar charts in the simplest of situations - just with gravitational energy, kinetic energy, and work done by an external force.  Importantly, I didn't say what exactly work is.  We showed how work could be positive or negative, depending on what the bar chart requires - for example, if kinetic energy decreases with no change in gravitational energy, then negative work was done on the system in order to keep the right number of bars in the energy bar chart.  The students had access to a fact sheet which explained the direction of force and displacement for positive and negative work, but I didn't discuss or even mention this in class.

And so, every problem became an energy bar chart problem.  

Evidence, Greg?

Our trimester exam included several energy questions.  No one tried to use "W = Fd" inappropriately.

In particular, I assigned the classic problem to test this misconception.  Consider a baton: two massive objects connected by a very thin, light rod of length L.  The object of mass m is vertically above the object of mass 2m.  How much work is required to flip the baton 180 degrees so that the heavier object is on top?

Most years, the vast majority of the class uses W = Fd, getting all sorts of incorrect answers.  They make the d term equal to a part-circumference of a circle, they use all combinations of mg and 2mg and 3mg for the ill-defined "force"... ugh.

This year, no problems at all.  They made an energy bar chart.  They saw that gravitational energy went from mgL to 2mgL.  They saw that there must have been mgL of work in order to make the bar chart work.  QED.

I've never seen such success on this problem.  And all because I *didn't* teach something from the front of the room.


03 November 2019

Make appointments for students to attend extra help

I know it happened to me regularly in my first years of teaching... how many times has it happened to you?

"My daughter says you are mean and unapproachable."

And I would respond, with naivete but full intellectual honesty, "That's ridiculous - she's never once approached me outside of class.  How does she know?"

Winning an argument with a parent certainly isn't the point here... but nevertheless, I never won this argument.  Parents went away angry, complaining to my bosses.  The students who hid behind "he's mean and unapproachable" knew they had won a political victory, and became ever more hostile - even as I tried to encourage them to let me help them.

I only managed to turn the tide when I began making appointments with struggling students... and making those appointments the moment they turned in poor work.

Most of us have some time available during which we can help students outside of class.  In some schools that time is easily accessible.  For example, I'm spoiled - my school provides a 30 minute "consultation" time three days a week, time when no classes meet, but when teachers are required to be in their classrooms, available to students.  AND, my students have at least one "study hall" period, during which they are allowed and encouraged to meet with teachers.  Your school might not have such generously allotted downtime to work with students, but most teachers have some sort of time they can use - lunchtime, before or after school, etc.

I don't recommend that you wait passively for students to come to you during these extra-help times.  I also don't recommend that you make a general suggestion to a student like, "Johnny, you really should come see me during extra help time this week."  That sounds like nagging; chances are, if he shows up at all, he'll show up the last five minutes of the last extra help time this week just so he can tell his parents he listened to your suggestion.

I'd recommend you make specific appointments with students.  In the first few weeks of school, I spend way, way more time arranging these appointments than I do grading my students' work.

In large part, that's cause my "grading" of daily in- or out-of-class work is essentially a holistic slapping of a number on a page.  I only have two purposes in grading an assignment:
  1. Make sure students know I'm paying some attention to the quality of their work, and
  2. Find out who needs an appointment to come work with me. 
Appointments are not for people who make math errors, or who make a common error that I will address in class via a quiz or activity.  No, appointments are for those who don't follow proper methods,* or those who all made the same fundamental error because they followed a friend's advice blindly, or those who keep making the same fundamental error repeatedly on multiple assignments.

Proper methods early in any class include starting with a fact written directly off the fact sheet I handed out.  Proper methods early in AP Physics also include free body diagrams followed by N2L equations, or kinematics charts.  

I go to great lengths to ensure that I have common time to meet with the students who performed poorly on an assignment; and to ensure that I've communicated with these students, so that they know not only that I've asked them to come work with me, but exactly when they're supposed to show up.

What does it mean, "great lengths"? I email* students appointment times.  I write names and times on the board so students are continually reminded of their appointments.  I negotiate politely and enthusiastically to reschedule the student who has a conflict with my appointment, and I go out of my way to be understanding of and care for a student who is overwhelmed with concerns beyond physics class.  But if a student passive-aggressively tries to avoid an appointment, or fails to show up without discussing with me, I escalate to a discussion with the student's advisor or parents.

* You probably want to text, or use an app like groupme.  Apparently people under age 30 don't read email anymore.  Since I'm at an isolated boarding school with a central email system which is the primary source of community information, we manage to get students to read email.  At least the subject lines, anyway.

Now, if you're going to die on the hill of get your arse in for extra help, you've gotta make the extra help worth the student's time.  The extra help can't feel like punishment, it can't be the teacher re-teaching from the front of the room, it can't be the teacher basically doing the problems for the student.  

But that's a (very important!) topic for a future post.  For now, solve your political battle by getting the students in your room.  Just that personal contact builds relationships.  Just that effort preempts a whiny argument that you would otherwise have to deal with.  

This is a LOT of work, Greg.  I know.  It nearly kills me, every fall.  One important suggestion is to stop grading anything other than monthly major tests carefully to a rubric.  Just find out who needs appointments, and make them.  Replace grading time with making-appointment time.  It's not easy.

But see, very likely, the number of students whom you need to bring in will drop as a power-law over the first months of school.  It's November - I'm seeing just a few students each consultation period now, and only one student hasn't adapted to using the methods I require (and so only one student is truly performing badly).  In early September, I had a room full of nearly 20 students every consultation period.  In December, after our first exam cycle, I'll rarely have to make an appointment with a student at all - and no one will be complaining that physics is "just too hard," nor that the teacher is unapproachable.  Because I've done the approaching for them.

This happens every year.  The brobdignagian front-end effort to make appointments is so worth it.

31 October 2019

It's not about the answer!

I grade assignments regularly... but really, I just look and slap a number on.  What matters to students and me isn't the grade, but whether the student used the correct method.  And if they didn't use the correct method, they need to redo the problem the right way.

Last week I assigned the classic elevator problem: A 50 kg person stands on a scale in an elevator, moving up and slowing down with an acceleration of 2 m/s/s.  What's the reading in a scale?

How I ask students to solve: 
1. Draw the free body, which includes the force of the scale Fs up, the force of the earth mg down.
2. Acceleration is downward (slowing down, acceleration opposite of motion), so write mg - Fs = ma
3. Solve algebraically for Fs to get 400 N.

How a bunch of my students solved:
1. Draw the free body, which includes the force of the scale Fs up, the force of the earth mg down.
2. N2L says a = Fnet/m.  So (2) = Fnet / (50), making Fnet = 100 N.*
3. Now 500 N - 100 N = 400 N.

* Well, as you'd expect, half the class just said "Fnet = 100."  Sigh.

That's the right answer!  And the method couldn't have been much wronger.

No, Greg, it's totally correct to subtract the net force from the weight here to find the force of the scale!  And I got the right answer!  How dare you count that "wrong!"  Show me the mistake!  Don't take off points because I used an alternate approach!

Um, back off there, student who's been in physics class all of a month, or parent or colleague who is suddenly an expert in physics pedagogy.  We are NOT going to talk about points, we are going to be sure that each student has communicated an understanding of the problem.

Yes, you must use the methods taught in class.  In English class, if you're given instructions about how to write a new style of essay, and you decide you will write something completely different from the assignment... that's okay now?  So why is it okay here in physics class?  Physics is not about getting the answer, it's about communicating an understanding of how the natural world works. 

I brought in the students who had solved using the "wrong" method.  I made them do the problem again using the correct approach.

Think I'm being too harsh?  Here's what I discovered.  I mean, I already knew these things, but they were exposed to the students in the process of redoing this problem the right way:

* Most of the students thought they were solving for mg, not the force of the scale.  When they wrote "500 N - 100 N = 400 N," they meant that the scale reading minus the net force was equal to the "new weight".

* Most had no clue why they were subtracting 500 N - 100 N.  Once I made them redo this problem the right way, I had them do the next problem as well... where the elevator was moving downward and speeding up with 2 m/s/s of acceleration.  For this problem, these folks had added 500 N + 100 N!  Now they found out for themselves that their incorrect method had actually obtained an incorrect answer - the acceleration is still downward here, so the solution should be exactly the same as in the previous problem! 

* Turns out, as I suspected: One of the students who had taken physics at a different school, and sounds smart and assertive, had told the group how to solve.  Most of the class had blindly followed.  No worries, collaboration like this is an important part of physics learning.  And, learning that the smart kid isn't always right, that it's important to argue with the smart kid, is an even more important part of physics learning.*

* For the smart kid, the most important part is finding out that even they have to communicate carefully using the methods taught in class.

Today's moral: When you're "grading" assignments, don't just look for the answer - look for one component of the correct method.  In this case, I looked for a correct free body and "mg - Fs = ma".  I didn't write any comments one way or another, because no one would have read them.  I just made anyone who didn't write this statement redo the problem. 


27 October 2019

How do I "grade labs"? In class.

I had students write lab reports for the first six or so years that I taught.  I worked hard on getting students out of their write-as-much-random-bullcrap-as-they-can-shovel report voice, and into writing clear, concise, and precise prose.  But it took enormous amounts of time and political capital to turn students from writing procedures like this

We came into lab today in order to accomplish the goal of discovering the effects of a pendulum.  First we found our partners, mine was Willie.  He and I cut a sting precisely to multiple lengths, measured precisely.  We tied a lab mass which is called Bob to our precisely cut string and let the mass go from rest at a carefully and precisely measured angle that was not too big for Mr. Jacobs to holler at us.  We recorded all our data carefully in our lab notebook.  I forgot to say we measured the period of the pendulum, too.
into writing this
A pendulum of various lengths l, measured with a meterstick, was released from rest at a small angle from the vertical.  The period T was measured with a stopwatch by timing ten back-and-forth cycles and dividing by ten. 
I mean, it seems so simple... but it's not.  Convincing just one student to adopt the simple but appropriate style in the latter paragraph took multiple re-writes, several writing conferences, and too often several arguments with students, advisors, and parents.  ("What do you mean, I failed, I wrote lots of words about a pendulum, didn't I?  That's not worth even a C?  My English teacher gives me a C for that!  This is entirely unfair.")

Multiply the time and mental effort investment by the 50 students in my classes, and, well... it just wasn't worth it.

So what do I do if not lab reports?

Nowadays, we do most lab analysis in class. The students collect data collectively, but they graph or re-graph that data individually - especially if they are linearizing a graph.  Next, they draw best-fit lines and take slopes using far-separated points on the best-fit lines that aren't data points.  This is all on a worksheet that looks like an AP Physics 1 free response problem - a grid for graphing is provided, and several questions are asked with space included for responses.

Students are asked to describe their procedure in "no more than three sentences", including what they measured and how they measured it.  They're asked to explain the physical meaning of the slope of the best-fit using direct reference to the y = mx + b equation of a line.  And then they are asked to determine that physical meaning, with an uncertainty.

Because we're doing this in class, students come to my desk after each part for me to check.  If it's right, they get a stamp and move on.  If it's wrong, they get immediate feedback and do it again right there - with 15 peers working on the same thing, so that they can ask questions and get help without trouble.

This is so, so much better than having students write lab reports or even answer lab questions at home.  See, they tend to do the work at home for the sake of getting done, right or wrong be danged.  (If you think the grade is what motivates the student, you're sorta wrong.  B or C students do the work as quickly as possible, right or wrong.  A students spend way too much time stressing about perfection, still getting the answers generally wrong, they just get angry and uptight about it.  And D or F students don't do the work at all.)

By working in class, everyone focuses not just on finishing, but on doing it right - in fact, they can't finish unless it's right.  And then if someone is slow, they can finish at home... but they've listened to me give feedback to all of their classmates, and they've had feedback themselves on the first part of the lab sheet, so they're more likely to get it right than if I had just sent everyone home to write a lab report.

30 September 2019

Right before the first test...

We are a month into my senior AP Physics 1 class.  Therefore, our first test is coming up.  It involves everything we've discussed so far - equilibrium, kinematics (including projectiles), and Newton's second law in one dimension.

Students have been solving AP level problems this whole time, both in class and on homework.  They've been taking (timed) daily quizzes, involving both basic fundamentals questions and more involved problem solving.  They've done lab activities, including data collection and analysis.  

But with the test coming up, &#*@ just got real.  I need simultaneously to build confidence, but also to create realistic expectations.  These folks will be working under some time pressure, and without a safety net - no collaboration, no questions, no notes, no coming back later to finish a tough problem.

So I gave the quiz below in the first five minutes of class today, the class before the test.  I had students trade and grade it (though I didn't collect it).  

My top students got 7 out of 11 on this quiz.  My not-top students, um, didn't get 7 out of 11.  Everyone had deer-in-headlights faces.  The subsequent discussion was about...

Building realistic expectations:  "Folks, these aren't just memorize-and-spit back questions, eh?  You've got to know your facts, but also how to apply them to completely new situations.  This is what an AP exam is like!  Better get used to it... the level of the exam comes from the College Board and their development committee, not from me.  It is what it is, and is not changing.  No whining.  Deal."

...but also building confidence: "Once I explained each answer, it made perfect sense, right?  I saw you nodding your heads, or smacking yourselves on the forehead 'cause you understood just fine in retrospect.  You get this stuff.  And, remember the grading scale: 65-70 percent is a 5; 50% or so is a 4.  Most of you got the equivalent of 3s and 4s.  You're expected to be brave, not perfect.  Relax, show me what you know, and expect to figure the rest out when we do test corrections."