Book Review and Philosophical Comments: Regents Physics Essentials by Dan Fullerton

Dan Fullerton emailed me a few weeks ago asking for me to review his new Regents prep book.  As he offered to send me a free copy, I readily said yes.  I might even have guaranteed a glowing review had he included a can of Skyline Chili.

I knew I was predisposed to like the book simply because Dan is a physics teacher.  Check the authorship of a prep book before you buy it.  If the book is not attributed specifically and predominantly to a high school physics teacher, be skeptical.  Graduate students and freelance physics writers do not necessarily have the same perspective about what students need to know, and how to present that information. 

Consider what students need from a test review book.  They have taken a physics course all year, with or without a strong teacher.  The review book is for catching up on material that might not have been covered in class; for providing reminders of topics from early in the year; and for providing practice problems and tests.  

From the student perspective, this is an excellent book.   Since the Regents Physics tests (with answers!) are easily available publicly, a prep book for students must go beyond just presenting practice problems.  And, since students have a textbook that already tried to explain the material, a prep book must give concise topic reviews, and then specific and clear explanations for each answer.  Dan's book does this, in spades. 

Each of the bazillions of practice questions is followed immediately by the answer, along with a brief but thorough justification.  I couldn't ask for more.

From the teacher's perspective:  I'd recommend this book as a solid resource for general-level physics teachers, whether or not the New York Regents exam is part of your curriculum.  Here's where I experienced some philosophical angst, so I'll explain thoroughly.

Regular blog readers will notice that while I share my assignments and teaching ideas freely, I don't tend to post solutions to the problems that I pose.  An enormous -- and too often ignored -- part of teaching physics is knowing the subject matter cold.  My high school students are regularly amazed at my ability to solve introductory-level physics problems on sight.  I try to explain that it's not that I'm smarter than they are, it's that I've been solving these kinds of physics problems ever since I started teaching in 1996.  I never rely on a solution manual for answers; I work through every problem myself.*  I recommend to all physics teachers that they do the same, even if that's tough at first, even if they occasionally have to rescore a multiple choice key.  I know I've had to rescore my share of tests.

*Using AP-style rubrics for grading open response items is not "relying on a solution manual" -- in order to understand the rubric, you have to work through the solution! 

My colleague Alex, who's in his second year of physics teaching noted how wonderful this book was because it provided access to solutions -- not just answers, but explanations.  And he made me pause for thought.

I remember how many times, especially in my first few years, that I could get an answer right without being able to form a coherent and straightforward explanation that a student would listen to.  It took years of experience to bring explanations down from the M.S. level to the high school level.  Alex works his rear end off preparing for classes and writing tests.  If he's going to use a question from this prep book on one of his tests, he's going to solve the problem.  But, he wants to have the book available in case he gets tongue-tied with an explanation.

The point that Alex DIDN'T make but he might have:  How many times is a newish physics teacher faced with a know-it-all student trying to make a tortured, lawerly argument that he should be given credit for an answer that the teacher knows is wrong?  This prep book has detailed enough answers that it can be used as an authority.  "Shut up, kid, and look at this detailed solution.  I'm right."  Obviously this approach is a last resort for a student who simply will not listen to reason.  However, that happened to me enough times that I know how useful the authoritativeness of this prep book's explanations can be.

Dan Fullerton's book is the size of a novel, and is paperback.  The size limits the layout possibilities, so that the text looks dense and it's difficult to thumb through to look for things.  (That's the only weakness we noticed.)  Diagrams are clear; the graphics are humorously drawn and appropriate. 

If my kid were taking Regents Physics, I'd buy this for him; if I were teaching Regents Physics for the first time, I would want this book available to me.

GCJ

It is just fine to give a quiz based on the homework that's due today

Last month, my colleagues who teach 9th grade conceptual physics started using nearly-daily quizzes in their classes.  Great move.  The students initially rebelled a bit, but they started preparing better for class each day when they saw they would be held accountable for the course material.  (Daily quizzes are best established at the beginning of the year so as to avoid the resistance to change.  But these work any time.)

The general approach was to have an in-class discussion, demonstration, or presentation; assign some problems for homework; and take a brief multiple-choice quiz the next day about the previous day's class and the homework.

A major student complaint sounded something like "We did the homework, but then we had the quiz before you graded the homework and gave it back.  How were we supposed to know whether we were doing the homework right?  It's not fair that we have to take the quiz before we get the homework back."

Well, one of the teachers accepted that argument, and postponed his quizzes until at least a day after he had returned the homework.  I ask, will the quiz scores be substantially improved by this postponement?  I say, "no."

There is nothing wrong with giving a quiz based on homework problems that are due the same day. 

A principal battle that I fight about homework is to establish a "correctness" rather than "completion" mindset.  A decade of schooling has convenced my students that homework is a mindless chore that must be done for the sake of doing it.  I think of homework problems as practice, as ways to remember and reinforce problem solving methods learned in class.  Without active participation in the problem solving process, homework is useless.  Whether the answer to a homework problem is right or wrong is immaterial -- what matters is the student's engagement.

A quiz can check that engagement.  Did the student figure out the most important step in the problem?  Can the student solve the problem again with the numbers changed?  Can the student explain why the answer makes sense, or doesn't make sense?  If not, then the homework problem didn't have the desired effect.

This follow-up quiz must be given right away.  By waiting, you're telling the class that the homework isn't really that important... it's okay to give a half-arsed effort because I'll just tell you the answer if you wait a day.  And, if the student didn't check his answers with friends or ask the teacher about a difficult idea on the night he was supposed to do the problem, what is the likelihood that he will follow up after the problems are graded?  What are you doing every day in class in the meantime, while you wait one night to grade the problems, and another night for students (in principle) to look at their graded work and study?  You can move along to new or more complex material immediately if you insist that students pay attention to their problems the very first time they're assigned.  If there's substantial misunderstanding, the quiz can provoke a good class discussion about the problem in a way that "Anyone have any questions?" cannot.

Homework is not merely busywork.  Regular grading of the homework, along with quizzes and other creative accountability methods, promote the appropriate attention to detail on daily work.  Without such attention, you might as well not even assign problems for all the good they'll do.  :-)

Don't neglect "review" for lower-level physics exams

Young fool... only now, at the end, do you understand.

Those of us who teach AP physics have gotten used providing an extended review for a difficult year-end cumulative exam.  Conversation with AP teachers indicates that anywhere from two to six weeks is generally reserved for review.

I understand that "review" is often a pejorative term.  In fact, I was advised years ago to avoid that term entirely, lest ignorant colleagues question my usefulness -- "He stops teaching six weeks before the exam to review, so why should the students bother to go to his class?  They should skip physics lab and come to AP history class, where we're still learning new material all the way until mid-May.  And we should give him hallway supervision duty because he's not teaching, anyway."

I renamed this segment of the year the "putting it all together" unit.  For that's what we're doing:  not merely reminding our students of topics we haven't explicitly covered since October, but showing how all topics interconnect.  A good physics problem integrates two or three disparate topics, asking students to make connections.  Only in April, after we've finally covered everything in isolation, can we truly show our students these connections.  Furthermore, students rarely learn a physics topic well the first time they see it.  The second and third time, though, techniques and concepts become old hat.  So correct pedagogy requires that we introduce projectile motion in September, and move on; we occasionally do a projectile motion problem as we introduce bernoulli's principle or parallel-plate electrostatics; and, most importantly, do a homework problem in April on projectiles again.

I'm not telling AP teachers anything they don't know already.  I'm posting this with regard to lower-level physics classes.

I disagree with the typical approach to tests and exams in a general-level physics course.  Tests in the second part of the year often explicitly exclude force and motion topics from the beginning.  (I find "unit tests" to be common, and also nearly useless as a teaching tool.)  Frequently, the "final exam" becomes merely an expanded unit test on the last couple of topics.  These are not authentic evaluations of physics skills!  If we want our students to remember physics, we must continue to require them to recall basic concepts, even from the kinematics we covered last September!

I move very slowly in general physics, certainly in comparison to AP.  That's all the more reason to make every test cumulative, like I do in AP.  Early in the year, this is not a problem.  As the year progresses, and force/motion topics were covered longer ago, I find it more critical to do substantial review before each test and before the final exam. 

Through the month of April, my regular class covered optics -- waves, light, snell's law, lenses, and mirrors.  On the test in late April, I explained that the multiple choice would be exclusively these topics, but the "justify your answer" and "open response" sections would be on topics distributed throughout the year.  As preparation, for two days before the test we worked on a 60-question multiple choice practice sheet.  I set the sheet up as a game: we worked in randomized pairs, where each pair was awarded points not just for getting questions right, but for getting the DIFFICULT questions right.*

*The exact scoring was one point for each correct answer, and one additional point for each other group that got that answer wrong. This provides a disincentive from the class all relying on a single student to distribute the answers.

In the event, students performed better on this test than they had all year.  Only one student out of 22 earned less than a B.

I just tried the same approach again for yesterday's test:  multiple choice focusing on astronomy and optics, with the rest of the test cumulative.  We did a similar review exercise.  This time, though, about a third of the groups didn't take the review as seriously; we performed well on the test, but not as well as before.  There was a reasonable correlation between scores on the review multiple choice exercise and on the test.

The final exam is coming up in two weeks.  I'm not covering any new material.  Instead, we will build an AM radio, and continue AP-style review of the year's work.  I want to encourage preparedness for the general physics cumulative final exam the same way I do for the AP exam.

Do you teach a general-level physics course?  Do you have any general physics review ideas?  Post them in the comments.  I just might try out your idea next week.

GCJ



Single and Double slits -- the difference for first-year physics students

from wikipedia's diffraction article

The double slit is covered in detail on the AP Physics B exam.  Students should be able to explain why an interference pattern is formed, cite an equation for the positions of the maxima, tell a bit about where that equation comes from, and describe qualitatively how the brightness of the pattern varies along a screen.

The single slit is not covered in quite so much detail.  Good thing, too.  I spent some time last week learning the details about single slit diffraction.  You see, one of the problems for the USIYPT next year is about a pinhole camera.  To understand the image formed by a circular slit, one first has to understand how a one-dimensional single slit works.

At the Physics B level, we have to know that the positions of single slit minima are identical to the positions of double-slit maxima. That is, the relevant equation x=mλL/d for double slits gives bright-spot positions for whole number m's; for single slits, the same equation gives dark-spot positions for whole number m's.  The central maximum for single slit diffraction is much wider than for double slits.

Why?  I don't go into that in AP Physics B.  I tell the convenient mistruth that diffraction occurs simply because light diffracts around the edges of the slit, and interferes similarly to the double slit situation. The true reasoning is very, very complicated. 

At a deeper-than-introductory level, the single slit can be considered as an infinite set of point sources.  Constructive interference occurs at the central maximum.  Diffraction minima can be found by trigonometric analysis of when each of the infinite point sources can be paired with another whose path difference to the location on the screen is λ/2.  The diffraction maxima are not halfway between the minima; rather, their positions are determined by the solution to a complicated differential equation whose solutions are Bessel functions. 

(Confused?  Me too.  I spent a couple of class periods and finally understood the derivation of the minima, but the maxima derivation is still flummoxing.)

This year's operational (i.e. regular form, not "form B") AP Physics B exam asked about a single slit.  Students were to design an experiment to measure the width of the slit.  The fact that it was a single, not double, slit was nearly irrelevant in this case.  Using x=mλL/d still works, as long as x and m are described appropriately.  Measuring the distance between dark spots with m = 1 works just fine whether this is a single or double slit.

The Form B exam, though, really hit at the qualitative difference between the single and double slit.  It asked to graph the intensity as a function of location on a screen for a double slit; then for a single slit under the same conditions.  Answer:  the central maximum remains, double-slit-maxima become single-slit-minima. 

And  this is as deep as a Physics B question will get about single slits.   

GCJ

Brightness of a bulb -- quantitative demonstration

Pop quiz, hotshot:  The brightness of a light bulb depends on the bulb's

(A) voltage

(B) current

(C) resistance

(D) power

Answer:  POWER. 

Sure, for *identical* bulbs, voltage and/or current will kind of relate to brightness.  For a fixed resistance, the equations I²R and V²/R show that with the same resistance, power, and therefore brightness, will increase as current or voltage increases.  However, you'll eventually get into trouble assuming that a bulb carrying more current is necessarily brighter than one carrying less current.

It's pretty straightforward to show experimentally that voltage does not necessarily correlate with a bulb's brightness.  Just get a bunch of miniature flashlight bulbs and holders from Radio Shack or Harbor Freight or somewhere.  Be sure to get bulbs with different voltage and current ratings, so that their resistances are different.  Connect them in parallel to a battery -- they will take the same voltage, but will NOT be just as bright as one another.

Michael Gray, a veteran of my 2010 AP Summer Institute and a frequent contributor to this column, came up with a much cleverer and more subtle demonstration.  He showed with a single light bulb that the bulb's brightness depends on the power, not the voltage or current.  How?  He measured the bulb's brightness directly with a Vernier light sensor.  Of course!  Brilliant.

He connected a bulb to a battery.  He showed that, by the equation V²/R, doubling the bulb's voltage should not just double the bulb's brightness, but quadruple the brightness.  He darkened the room, and placed a light sensor a fixed distance from the bulb.  He zeroed the sensor for the ambient light, and turned the bulb on.  When he doubled the bulb's voltage, the sensor reading quadrupled.  Physics works.

I will certainly use this demonstration next year.  Thanks, Michael!

"Tapering" for the AP exam, and BOUX day link

Today was Boux Day in my AP classes.  Click on the link to see the classic Jacobs Physics post from a couple of years ago describing the final in-class activity before the AP exam.

I take a different approach to last-minute AP prep than most... I require that there be no studying after 5:00 Sunday evening for the Monday exam.  On Monday morning, students are exempt from class due to their afternoon exam; so we have a pool party. 

Could I instead have students study their arses off all weekend?  Sure.  At this point, though, academic burnout becomes a major concern.  My guys have been involved in numerous other AP exams all week.  Teachers for the other upcoming AP exams have been pounding the review both in- and out- of class.  The students' brains are hurting.

I've found considerable success by pushing my review time earlier in the school year.  Even though I do not do a complete and wonderful job of covering the last topics, I make sure to start true AP review in early April.  We did our last practice AP test around April 22.  Since then, we've been correcting that practice test, and doing a couple of review problems per day in class. 

Think of the last couple of weeks before the exam as a swimmer or marathoner "tapering" before an important race.  My students have built their endurance, they know their fundamentals.  The last-minute review time is NOT for learning new stuff that wasn't covered earlier in the year, or that was forgotten.  No, this time is for reminders of things that students already know.  Look at the "Boux Day" post for examples. 

Most importantly, my students head to the AP physics exam confident and relaxed.  Sure, I have a few students who could actually use a more intense practice session right before the test.  But the positive mood of the class, the feeling that everyone is as prepared as they're gonna be, and the knowledge that there's nothing more to do but perform is, to me, better than any number of finished review packets. 

Gauge your students' moods on Tuesday after the AP exam is over.  Ideally, they are either confident or fatalistic.  Either "Oh, yeah, most of those were straightforward," or, "Well, I knew how to do 1 and 5, but I confused myself on 2 and 6.  Can you use W=Fx to find the work done by an electric field?"  What you don't want to see is indignation ("I only got part (a), because the rest of that problem was so unfair!"), sour grapes ("I didn't know anything, but no one should be expected to do problems this hard"), or panic ("It was so tough that I froze up.  I only answered two of the free response questions!").

If you see reactions that you don't like on Tuesday, consider your overall approach to next school year.  I *do* get those untoward reactions from my students... but on our first test in October.  By May, it's quiet confidence that we want to see -- even if that confidence is a student knowing his limitations and pledging to get right the problems he knows how to do.

Good luck on Monday.  Feel free to email success stories.

GCJ

Basic astronomy unit in general physics -- can you help me?

For most of a decade I've been teaching a three-week "astronomy" unit to my general physics class.  The students are generally excited by the idea of learning astronomy, which is a boon to the teacher of a class of seniors in May.

My inspiration for the unit was a one-week summer course I took at the University of Montana called "The Celestial Navigation of Lewis and Clark."  Burrito Girl (my wife and sidekick) and I spent a week learning how to use a sextant, and how to determine latititue and longitude from the sextant reading.  We also visited some sites where L&C actually made camp, there finding National Park Service employees giving demonstrations of period instruments. 

*It was a bit disappointing to learn that the celestial observations that L&C diligently recorded throughout their trip proved to be essentially worthless.  By far the more accurate map of their journey was reconstructed from Clark's "dead reckoning" intuitive estimates of travel distances as recorded in his log.

The first day of class consisted of a crash course on local astronomy -- nightly and yearly motions of the sun, moon, and stars.  Though the terminology ("celestial equator," "ecliptic") was new to me, the general concepts were not new -- for example, stars, including the sun, apparently rotate counterclockwise around the north star.    To the majority of the class, though, who were not physicists, these ideas of motions of the stars and planets WERE new and difficult.  Even in their final presentation, a group of classmates indicated that the sun would be directly overhead in Montana at noon on June 21.  Oops.  I thought it might be useful for me to teach my classes some of these basics. 

Between the material from the U Montana course and some exercises I picked up from a CAPER* workshop, I took three weeks to cover:

*CAPER stands for Conceptual Astronomy and Physics Education Research. "Teams" of astro professors at several university work under this umbrella. At an AAPT meeting I picked up some of their "lecture tutorials," which have been most useful in this unit. Much of this sort of work is online -- search under "CAPER."


* motion of the earth, moon, and sun
* apparent motion of the stars
* measuring stellar distances with parallax
* use of a sextant to determine longitude and latitude

My fundamental goal is to bust the standard misconceptions.  If nothing else, I want students to know that seasons don't depend on the earth's distance from the sun, and that moon phases are NOT a result of earth's shadow.  Just getting this much retention is more difficult than you might imagine.

We culminate the unit with a nighttime observing session.  That's easy to arrange at a boarding school -- we just gather behind the dorms after lights out.  We use Starry Night software on a laptop, or Star Walk on an iPad, to help deterime what we're looking at. 

What about homework assignments?  Well, I do assign homework.  Many of the problems are based on end-of-chapter questions in the two astro textbooks I have.  These are based on what we did in class, but sometimes thought provoking -- "How high will the sun be at noon on June 21 at our latitude?"  "Star A is measured to move at most 2 arcseconds in relation to the fixed stars over the course of a year.  How many light years away is this star?"  "Using a map but not online search tools, choose an American city in which the sun sets as late as possible."

Your help?  I want to find multiple choice quesitons for quizzing and testing purposes.  For standard physics topics, I have AP and Regents and SATII and Physics Bowl test banks.  These provide a virtually limitless source of multiple choice ideas.  But for astronomy, I've only found a few online sources -- and these have been pretty danged lousy.

Can anyone point me to a well written bank of multiple choice questions based on basic astronomy concepts?  I can and have written some of my own questions, but I always like to have some external validation for what I'm doing.  Post a comment, or email.  And a future post will discuss the observing session -- assuming it's not clouded out for the third year in a row.

GCJ