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

How to justify an answer: Equations, Calculations, or Facts

One mole of an ideal gas expands from a volume of 5 L to a volume of 10 L at atmospheric pressure.  Does the gas's temperature increase, decrease, or remain the the same?  Justify your answer.

Justifications are tough for novice physics students, especially students with weak verbal skills.  Look at some common unacceptable responses to the question above:

* Increase, because the volume increased at constant pressure.  [This answer is a tautology -- it simply restates information given in the problem.]

* Increase, because the temperature had to go up to increase the volume.  [Still a tautology.  "Had to" doesn't add any physics understanding.]

If we're not vigilant about scanning justifications for tautologies, we will get them all the time.  Our students do not have the same ability to reason logically as we do.*  But rather than merely kvetch about these dang kids who couldn't justify their own existence, the onus is on us to teach the skill of justifying an answer in physics.

*One student's impeccable logic:  "One time I saw some unexplained lights at night.  I called the local airport control tower, who confirmed that they knew of no aircraft operating in my area.  Therefore, I was visited by a space alien."  And no, sorry, I am NOT kidding.

My students seem to respond well to my demand for one of three possible elements to make a justification legit.  They must include either equations, calculations, or facts of physics.  In some problems, only one of these will be of any use; in the question I posed above, any one of them might be useful.  For example, some reasonable justifications:

(1) Using equations:  "Solving the ideal gas law for temperature, T = PV / nR .  Here n is constant because it's a sealed container, and pressure is constant because the problem stated atmospheric pressure the whole way.  The only variable is volume, which is in the numerator.  So, when volume increases, temperature must increase as well."

(2) Using calculations:  "Use the ideal gas law, PV = nRT.  In the initial state, plug in values:

(10⁵ Pa)(0.005 m³) = (1 mol)(8 J/mol K)(T), so T = 62 K initially

Now in the final state:

(10⁵ Pa)(0.010 m³) = (1 mol)(8 J/mol K)(T), so T = 125 K finally

Thus, the temperature has increased.

(3) Using facts of physics:  "An isobaric process looks like a horizontal line on a PV diagram.  Isotherms are hyperbolas assymptotic to the axes on a PV diagram.  So, a horizontal line with increasing volume must jump to an isotherm that is farther from the origin, and thus representing a higher temperature.

Once I've demanded these elements of justification enough times, the class gets the idea.  And when someone is lazy, forgetful, or simply wrong, I don't have to argue about the legitimacy of his answer.  I just ask, "Did you use equations, calculations, or facts?"  If the answer is "no," the student usually hangs his head in shame without any further prompting.

Common misconceptions -- parallel resistors

Parallel resistors each take the same voltage, which is equal to the total.

Now ask a student: "Two 100 ohm resistors are connected in parallel to a 12 V battery.  Determine the voltage across one of the two resistors."  What does the student say?

Generally, that student reasons, "Parallel resistors take the same voltage.  The battery provides 12 V to two resistors equally, so that's 6 V across each."  D'oh.

How do I attempt to remedy this misconception?  Give everyone the chance to predict and then MEASURE the voltage across several resistors, as in this laboratory exercise.  When a student comes to my desk for me to sign off on his correct measurement, I throw the common misconception in his face.  I say, "Hey, Will, that doesn't make sense.  Seems to me, you've got two parallel resistors here, you should only get half the battery's voltage across each."  Will generally has two points to his rebuttal:  (1) "That's not the correct rule, Mr. Jacobs, the voltage across parallel resistors is equal to the total." And, most importantly, (2) "That's not what I measured.  I get the same voltage across everything."