Can I borrow a calculator?

More than a hundred students enter and leave my classroom daily, and each of them owns at least one calculator.  Thus it's not surprising that calculators are frequently left, recovered, misplaced, trodden upon, etc.    I'm convinced that my room contains an aether of vacuum fluctuations which produce calculator-anticalculator pairs according to the energy-time uncertainty principle.

While I am sympathetic to the likelihood of misplacing a calculator -- after all, I left my cell phone at a hotel last weekend -- I've become ever more frustrated at the sheer number of students who wait until moments before a test to ask to borrow a calculator.  I am not the calculator supplier, but nevertheless students expect that it's not a big deal to ask to borrow a calculator.  It's distracting to everyone, and obnoxious to me, to spend ten minutes tracking down calculators, and then ensuring their return.

I snapped a month or two ago, when more students in a section asked to borrow a calculator than brought a calculator.  How to solve this problem without being a total jerk who (essentailly) says "Yes I have a calculator but no you can't borrow it because you're an irresponsible arse ha ha"?

Firstly, it's important to remember that the $100+ TI92bs or whatever Texas Instruments is currently colluding to foist upon our students is NOT NECESSARY for physics at any level.  Yes, the graphing calculator was the tool that precipitated a revolution in calculus teaching.  The ability to visualize the graph of a function instantly allows a novice calculus student to focus on slopes and areas rather than just what the graph of x^-3 + 2x² might look like.  But for physics, the older, cheaper scientific calculators are easier to use.  I've tried to spread the gospel of the cheap calculator for decades now, but students are too wrapped up in their TIs to care.

What did I do?

I personally bought a bunch of Casio fx-260 solar calculators (pictured above).  They cost me $10 each online, including shipping -- I got them from Office Depot, but they're available pretty much anywhere online.

In this new regime, I won't lend anyone a calculator because I can't -- I've purged the classroom of any "department calculators" or "Jacobs calculators."  But, students may *buy* their own Casio for $10.  I sell them the calculator in the original packaging, along with a label to put their name on the calculator right then and there.  I never chide anyone for irresponsibly misplacing their own calculator -- instead, I say with a smile, "This will be the best purchase you've ever made for physics.  You've got the best calculator in the room now."  And this is true.  

Amazingly (or not), the result so far has been more students keeping track of their own calculators.  And those who have bought have been satisfied with the purchase, as I knew they would be.  After class, when I show them the button that allows them to add fractions, their eyes get wide.  That button alone is worth the $10 to me.

Describing a procedure concisely

From Homestarrunner.com.  Don't get the reference?  Check out
"English Paper" at the homestarrunner wiki.

Much of the physics teaching world, and I, have leapt away from multi-page, badly written "formal lab reports."  Instead, it's typical now for students to be asked several directed questions about an experiment.  Formal lab reports are only useful if the instructor takes the time and energy to truly teach the scientific writing process -- that means grading drafts, participating in writing conferences, paying as much attention to style and language as to results.  I decided long ago that the benefits of the formal lab were in no way worth the costs.

That said, I still do teach a few writing skills.  Particularly, my class learns how to describe an experimental procedure while defining relevant variables.  AP exams, as well as my Honors Physics exam and even the Regents exam, occasionally ask for a description of an experiment.  Your class needs some minimal tutelage so that these questions become easy rather than time- and stress- consuming.

Describe the procedure you used to measure T, q, and any other relevant parameters.

This is a question I ask after our first experiment, phrased identically to the style of an AP question.  I explain to the class that they should use no more than three sentences, telling me in prose what they measured and how they measured it.  I expect an answer such as:

We kept a cart in place on an inclined track using a string held parallel to the track.  The tension in the string, T, was measured with a spring scale tied to the string.  The angle of the incline from the horizontal, q, was measured with the "clinometer" iphone app.

Note how everything, including definitions of variables, is included as part of the prose.  Some folks want to just give a list of variables* ; they lose considerable points in my attempt to get them to write sentences.  

* "T:  measured with a scale"

But consider what I often see at the AP reading, or after my class's first experiment:

We came into lab today in order to find the tension in a string when we hold a cart at many different angles.  First we found are partners; I worked with Joe.  Then we gathered our materials:  A 250 g cart, some string, scissors, an aluminum track, and a spring scale.  Goggles should be worn, as always in the laboratory.  We tied the string to the cart, being careful that the string could be held parallel to the track.  Joe tied a sailor's knot so that we could attach the spring scale to the cart.  I downloaded an app from the itunes library that shows an angle.  Now, with all materials in place, we could begin the experiment.  Joe carefully read the scale to the nearest 0.2 N, and he wrote down both readings in his notebook.  Finally, I graphed the data on a graph with a pencil, which I forgot to include in my materials list above.

[Is it considered satire if it's true?]

My purpose here is not* to make fun of a student who would write the above passage.  The question is, how do we get this student to write a proper, brief, clear, 3-sentence procedure?

*primarily

I've had some success reminding the class of their audience.  They are not writing a "how to" manual, they're not writing for their English teacher who is ignorant of laboratory methods; the audience for a laboratory procedure is OTHER SCIENTISTS.  I make the audience even more concrete by identifying a recent alumnus: "Peter Chen, whom youall know took my class last year, should be able to figure out what you measured, and how you measured it."  They see with minimal prodding that Peter doesn't need to be told to gather materials.  Peter doesn't need a silly safety lecture.  Peter doesn't need to be told to record data carefully -- we take all these basic "skills" for granted, because we are scientists.  

The other useful reminder is about time.  A procedural lab question like this might be worth three points on an AP exam.  At the going rate of one point per minute, the test expects a few minutes of work -- no more. If you spend a lifetime writing multiple paragraphs, even if such paragraphs are pulitzer-prize worthy, you will earn... three points.  And you will NOT earn the other seven points available in this problem, because the bell has rung, the sun has set, and the exam is over.

It's important to model the correct writing style for the class at some point.  This is a different kind of writing than their English teacher has required -- after all, I used no drama, no interesting transitions, nothing about my feelings.  They have to see for themselves that it is okay to be short and "boring."  

And finally, perfect practice makes perfect.  Some folks will ignore all your advice until you take off points; then their next writeup will be perfect.  Others will need a figurative bashing over the head.  But with patient, persistent work, you can get your students comfortable with describing experimental procedures.

GCJ

The Four Minute Drill

My class is preparing for the second trimester exam.  Even though I provide an equation sheet on the exam itself, I still think it important for everyone to know the relevant equations cold. Without such knowledge, students approach tests as a game of "find the equation with a Q in it."  [See this post for some detailed analysis of how to use an equation sheet properly and improperly.]

My philosophy about memorizing equations relies heavily on, of all things, my seventh grade civics class.  Nowadays I couldn't tell you offhand who the governor of Virginia is, or who sits on my local county board of supervisors.*  But in 1985-86, I was the nearest thing to expert about Northern Kentucky and national politics.  I knew who Paul Simon was before he ran for president.  I knew that Kenton County's highest governmental position was called the "Judge-Executive."  And I still know these things... As we drove through Louisville over the summer on the "Gene Snyder freeway," I began singing Congressman Snyder's radio jingle while I explained to Burrito Girl why his district encompassed BOTH northern Louisville AND suburban Cincinnati.*

*Or if Madison County, Virginia even has a board of supervisors.

* Burrito Girl is my wife and sidekick.  As is so often true of my explanations, she didn't care.

Why did I, and do I still, know about civics?  Because Keen Babbage taught middle school civics at my school in 1985.  He didn't care that, even in pre-internet days, it was child's play to look up facts about local and national government.  In his opinion, all educated citizens knew off the top of their heads the length of term for a US senator.  And so, he made us learn these things.

Keen's crowning technique was the "4 minute drill," which I have adapted to physics.  He placed a list of civics facts on his podium.  He asked a question of each member of the class in turn; upon a correct response, the class earned a point, and he moved on to ask a new question of the next student.  If that student didn't know the answer, he could say "pass," and the question passed to the next student.  

Fast forward a quarter century.  My class takes "fundamentals quizzes" regularly.  But quizzes aren't always enough incentive to memorize facts; furthermore, even those who study diligently don't necessarily study effectively.  I use the "4 minute drill" to ensure that everyone at least learns their equations.

About twice a week, I run a 4 minute drill using the equation sheet.  I prompt something like "Force of friction;" the student has to say, "mu times normal force."  I only allow each individual to pass twice per drill; if someone has to pass a third time, we sit there awkwardly until he either gets it right, or until the 4 minutes are over.  We always run through the equations in the same order, so that we get farther and farther into the sheet over the course of a few weeks.  

At the end of each drill, I write the class's score on the board.  The sections of the same course compete with each other.  Sure, I offer a wee bit of extra credit to the class with the highest score in the marking period, but they compete for pride.

If you'd like to try the 4-minute drill, get a copy of my 5 Steps to a 5 prep book.  In an appendix, I list the verbal prompt I use for each equation on the AP physics equation sheets.  You can easily run the drill by just reading each prompt in turn.  And if you're not teaching AP, that's okay -- just pick the equations you've covered and skip the rest.

Review / Prep Books for Physics C?

Good texts are available
for physics C...

Back in September I reviewed the AP B supplement to the Walker 4th edition text.  The one sentence summary:  author Connie Wells, formerly on the AP test development committee, did a great job.

That post has now spawned two official comments and some informal inquiry as to what good Physics C supplements are out there.  I should have tackled this question before, but I'll go at it now.

Problem is, the whole idea of a "good physics C supplement" doesn't make complete sense to me.  

In Physics B or Honors Physics or Regents Physics, novice students are covering only the basics of a variety of introductory physics topics.  Textbooks are not wholly satisfying in such courses, because they cover way more material and depth than is level- or exam-appropriate.  Especially for the Regents level, the available textbooks are such compromises of committee writing that straightforward, targeted physics explanations are lost in the eduspeak.  So the purpose of a prep book at that level is for focus:  Here's what you need to know for this exam, here's a one paragraph (rather than four page) explanation of a concept in plain language, here are practice questions in the style of the exam you'll be facing at year's end.

In physics C, though, the textbooks are generally solid.  The mechanics chapters in Halliday and Resnick, or Tipler, or Serway, are all reasonably well correlated to the AP curriculum.*  The end-of-chapter questions vary from way easier to way harder than the actual AP exam, but it's not hard to pick out questions that are on-level, and even in a similar style to what is seen on the exam.

* Or, perhaps, the AP curriculum is reasonably well correlated to these common textbooks.  Chicken or egg?

Consider the typical student in physics C, and what he or she needs from a "review" for the exam.  This student has been in a class doing problems and reading a textbook all year.  A prep book is useless if it just mirrors the explanations and problems found in a text.

The strength of a good prep book is concise, focused, readable, non-mathematical explanations of basic physics concepts.  Books at the sub-physics C level already do this.  My own 5 Steps to a 5 book, the out-of-print AP prep book written for Kaplan by Hugh Henderson and Connie Wells*, Connie's supplement to the Walker book that I link above... all provide explanations of the basic physics at a readable level, along with straightforward questions and problems.  And when students are doing last-minute review before a major examination, straightforward and readable is the key.  Most texts do NOT do a great job with the basics.


*NOT the current edition of the Kaplan book


However, if two days before the exam someone's looking for a detailed discussion of solving something deep, like a Biot-Savart problem with a non-uniform magnetic field, a prep book isn't going to help!  The more mathematically intense problem solving methods can only be learned through careful and repeated practice.  You want to get good at Biot-Savart two days before the exam?  Do 7 practice problems from a couple of textbooks.  No prep book necessary.

The available textbooks generally do an excellent job explaining the more difficult aspects of calculus based mechanics and E&M.  The problems available from Halliday & Resnick et al are generally better and more numerous than what prep book authors can come up with.  And released AP Physics C exams are so plentiful * that even the most diligent students can find enough practice to occupy them.

* The Physics B exam has changed significantly over the years, such that only the last two (2004 and 2009) released exams are truly representative of what students will see in May.  Physics C has not changed so much, such that the 1998 and even 1993, 1988, and 1984 multiple choice exams are still mostly solid.  Careful, 'cause calculators were allowed on some of those earlier exams, but usually the calculator wasn't necessary.


Thus, my recommendation for physics C exam prep is twofold: (1) Use a physics B-level prep book to confirm an understanding of the basics; and (2) Use the published textbooks and released exams for practice.

Don't neglect (1)... with limited study time leading up to the exam, students are generally making far better use of their time by reminding themselves of fundamentals rather than solving unusual and difficult problems, even though the difficult problems might seem sexier.  In exam review time, it's all about getting the most benefit for the time spent.  And that's why a B-level prep book is often just dandy for physics C students.

Experimental evidence that brightness depends on power

A year or so ago, Michael Gray emailed me a wonderful quantitative demonstration idea to show that brightness of a bulb depends on power, not voltage.  Basically, he used a light probe to measure brightness directly.  When he doubled a bulb's voltage, the brightness didn't double -- the brightness reading quadrupled.  And that makes sense, since power is  V²/R .

I took the light probe approach a bit further the other day.  I asked the class to sketch a plot for the brightness reading in the probe as a function of the bulb's voltage.  After some discussion, the randomly chosen student sketched a parabola*on the board.  Yes -- since a bulb doesn't change its resistance, and since power is V²/R, a power vs. V graph should be quadratic.  And since brightness is correlated with power, the power graph should also be quadratic.

* Though he called it, of course, an exponential.  What is it with teenagers that any concave up, increasing function is labeled as "exponential?"  Have *you* ever seen an e^x in any physics B equation, at least since half-lives were taken off the exam a decade ago, and besides that was e^-x?  Should I stop ranting now?

And so I turned out all lights, held the probe about 10 cm above the bulb, and increased the bulb's voltage at a constant rate (by turning the dial approximately uniformly).  As you can see, I was a bit jerky in turning the voltage knob.  But the principle was well-verified -- the brightness vs. time graph was clearly curved.

Circuit misconceptions, and an advance copy of a quiz

On a problem set last week, I gave students the simple circuit shown to the right.  I asked what would happen to various parts of the circuit when I decreased R₂.  One of the questions in particular said, "What will happen to the current flowing from the battery when the value of R₂  is decreased?"

The most common answer:  

"The current will not change, because it's the same battery, so it will always provide the same current." 

Silly students, a battery provides a constant VOLTAGE, not a constant current -- but that's a common misconception in the first week of circuits.

The second most common answer:

"The current will not change, because R₂ is the farthest resistor from the battery, and so the current hasn't reached R₂ yet.

Silly student with a common misconception again.  The "distance from the battery" should never be used to justify anything associated with circuitry, because "distance" from a battery is irrelevant.

I decided to use a quiz to bust these misconceptions.  I've often announced the topic of a quiz the night before, in the hopes that students will target some studying.  This time, I actually sent out the quiz below via email, along with a quick note that discussing the questions in advance was encouraged.  

Did it work?  Yes, in that I've pretty much eliminated the misconceptions I've listed (for now -- I'll have to try again in a couple of months during our review time).  Sure, a few students did poorly, because either they (a) didn't prepare at all, or (b) convinced themselves or their friends that the current of a battery is always constant.  Either way, this exercise was useful!  For the students in category (b), they will never make this mistake again.  Someone in category (a) hangs his head in shame when his classmates tells him, "Jeez, Will, Mr. Jacobs gave us this exact copy ahead of time, it was easy points!"

Coming Soon: I handed out tomorrow's quiz tonight (and USIYPT 2012 results)

Folks, I've been at the US Invitational Young Physicists Tournament in Oak Ridge, Tennessee.  It was a well-attended event with the highest level of physics in the tournament's 5-year history.  Attending were:

Rye Country Day School, NY

Woodberry Forest School, VA

The Harker School, CA

Vistamar School, CA

Oak Ridge High School, TN

Shenzhen Middle School, China

Calverton School, MD

The standings after the preliminary rounds put (in order) Woodberry, Harker, Rye, and Vistamar in the semifinals.  Woodberry and Rye advanced; Rye's Andrew Mollerus and Michael Thomas defeated Woodberry's Peter Chen and Damien Chang in a taut, tense final physics fight.  Congratulations to Rye on their first USIYPT championship.

So, um, I lived and breathed physics fights for days, and I'm still adjusting back to the school routine.  My pile of work is testing the compressive strength of paper.  So, you'll get the next real post soon.  Teaser:  I graded a homework that included many common conceptual mistakes, including the "fact" that a battery must always provide constant current.  I wrote a quiz to help bust the misconception, and I actually emailed that quiz to the class folder tonight in advance of the actual quiz tomorrow.  I'll explain why I did that, I'll show you the quiz, and I'll explain whether the gambit did or did not work.

GCJ