Preparing for AP Physics 1: I will likely use "short answer" questions, even though they are not part of the AP exam

When AP Physics 1 was in its infancy, the AP readers were told that all formatting options for the new exam were on the table.  Among other things, options under discussion specifically included four-choice rather than five-choice multiple choice questions; "multiple correct" items; short and long free response items similar to those on the AP B exam; and "short answer" items.

Now, no one ever explained what a "short answer" item was, nor any details of how it could or couldn't be included.  And it wasn't included.  As it turned out, the new exam has only a few types of items: four-choice multiple choice, multiple correct, short- and long- free response.

But I liked the idea of the shorter item that required written justification for the answer.  For my own course, I wrote a short answer section into every test.

To write these items, I generally took a good multiple choice question and simply added, "justify your answer."  Or I eliminated the choices entirely and required an answer with work shown.  Or, I took a single part of a good free response question and asked it in isolation.  

One nice part about short answer items is the lack of restriction in format.  I've asked all kinds of things:

* Open ended calculation questions:  Here's two masses connected by strings, and I'm pulling on the front string.  Explain how you would calculate the ratio of the tensions in the strings.

* Multiple choice with as many (or as few) choices and answers as I please:  Rainwater fills a cart that's moving on frictionless rails.  Which of the following is conserved for the cart-water system: mechanical energy, linear momentum, velocity.  Choose all that apply.

* Graph questions with justification: A block attached to a spring oscillates on a level, frictionless surface between positions x1 and x2.  On the axes below, sketch a graph of the block's kinetic energy vs. position.  Then justify several features of your graph.

* Open ended explanations: Two satellites of different masses are launched into orbit around earth.  It is found when both orbit the same distance above the earth's surface, they both have the same speed.  Explain why the satellites' different masses don't require different orbital speeds.

For next year's inaugural AP Physics 1 course, I am considering including a section of short answer questions on my tests.  

But Greg, you're the biggest advocate in the universe for authentic testing, for testing exactly in the style and format of the AP exam.

Yes, yes I am.  For this new exam, I'm well acquainted with the format of the new exam, which has a very large time-to-item ratio.  We're talking two minutes per free response, and about two minutes per point for free response questions that could be each worth 7 or 12 points.  One issue is, even with an 80 minute window to give a class test during lab period, I can only give, say, 20 multiple choice and two free response questions.  In a standard 40-minute testing window my options are even more limited.  

In my AP Physics B classes, students have tended to do better on longer tests.  That's because long exams have a wider variety of questions to answer; students are more likely on a longer test to find a few questions in their wheelhouse that they can knock off quickly and correctly.  Then they have time to work through the tougher items.

In order to continue giving a variety of questions on my in-class AP Physics 1 tests, I will likely continue using a short answer section.  Let me know your own ideas, as my own class is still forming in my mind.

GCJ

Preparing for AP Physics 1: establishing the habit of writing

I'm in the infant stages of planning my AP Physics 1 course.  The big trick is going to be establishing my students' ability and willingness to write their reasoning, to get them to focus on communication rather than on getting a correct numerical answer.  Once it's clear that they are not taking a math course -- once they see that the solution to a problem looks much more like what they've done in biology or economics than in calculus -- I think the students will be able to move along quickly and enthusiastically through the material.

Students must get comfortable with calculation.  However -- as was correctly pointed out to me at the AP consultant meeting in April -- if we start the course with lots of pure calculation, students will think that getting the answer is the holy grail of physics problems.  If instead we begin the course demanding description, explanation, and all sorts of prose, students may become accepting of the idea that a numerical answer is merely the result of careful reasoning.

Consider the very first problem set I assign.  While I begin the year with static equilibrium, the first night's problem is not directly related to anything on the AP Physics 1 curriculum.  Rather, I'm establishing tone.  I'm showing the style of problem we will be solving, the interesting results that can be obtained via quantitative reasoning.  

Here's how I presented the problem to my AP Physics B students:

An average family of four uses roughly 1200 liters – about 300 gallons – of water per day. How much depth would a lake lose per year if it uniformly covered an area of 50 square kilometers and supplied a local town with a population of 40,000 people? Compare your answer to the size and/or depth of bodies of water you may be familiar with.

But note how I've changed it for AP Physics 1, in order to evoke verbal reasoning and to de-emphasize the pure algebraic aspects:

 1. An average family of four uses roughly 1200 liters of water per day.  In the town of Bonk – population 40,000 – drinking water is provided from a lake that covers an area of 50 square kilometers.  

(a) In a clear, coherent, paragraph-length explanation, describe how you would figure out how much depth the lake loses each year due to the town’s usage.  

(b) Using the method described in #1, calculate the depth the lake loses each year due to the town’s usage.

(c) Describe as you would to a non-physicist the physical meaning of the answer to #2 by comparison to length of an object with which you are familiar; that is, something like “Each year the lake loses a depth equal to the height of a [foo].”

(d) Describe as you would to a non-physicist how much land area this lake covers compared to land references with which you are familiar.  Justify your answer.

I'm still asking for calculation; I'm still specifically asking about the physical meaning of the result.  What's different is part (a).  I'm demanding, ahead of the calculation, a "clear, coherent, paragraph-length explanation."  That's verbiage directly from the released AP Physics 1 exams.  I think -- I hope -- that my students will see immediately that a bunch of algebra by itself will earn no credit.

Now, I will definitely recommend to those having trouble with the verbal explanation that they might just try doing the calculation first, and then come back to explaining what they did and why.  A good number of students are substantially more fluent in the language of mathematics than in written English when it comes to quantitative problem solving.  That's fine.  It's my job throughout the year to bring my students to fluency in both mathematical and verbal communication.

Thing is, my students come to my class expecting the mathematical reasoning to dominate the course.  I must establish from day 1 that verbal reasoning cannot be ignored.

What is the added value of a good physics teacher?

Our incoming headmaster addressed the faculty last week.  I was pleased and impressed with the discussion he raised about our fundamental reason for employment.  Regular readers can probably infer that I'm generally UNimpressed by eduspeak, mission statements, anything suggesting that we should go forward into the future, twirling towards freedom.  Nevertheless, the headmaster raised an excellent meta-question, one worth pondering.

So much teaching is done the way the teachers themselves were (or wish they had been) taught.  The headmaster noted that in our day* information was scarce, so we were necessarily taught to spongily absorb facts and knowledge.  Today, information is over-abundant.  Thus, our teaching should change focus, toward "constructing stories to make sense of plentiful information."  He asks, as I paraphrase: What do our students most need from us given their time and place?  

* "Our" day... that's a scary thought: the new headmaster's kids are younger than mine.  Crap, I'm old.

This is not intended as a physics-specific question.  I know the physics answer: I teach all my students the "big three" physics skills, working through enough topics with those skills that they can perform on externally-validated AP or Regents-style exams.  That's not the issue.  The headmaster is asking a more general question.  

With the easy availability of textbooks, Khan Academy, and Webassign, a physics teacher could nearly automate his class.  In my own mind, a teacher running such a class would be criminally defrauding his school of his salary.  That's not teaching.  But, the headmaster asks, if that's not teaching, what is?  What added value can I personally provide, over and above the myriad of available resources, such that it's worth it for parents to pay me for my services?

I've got two answers.

One: I can teach my students about experimentation, and how experimentation relates to pencil-and-paper problem solving.  There's no video, simulation, or textbook description in the universe that provides the same hands-on experience with equipment that the laboratory portion of a physics course can.  By the end of the course, my students are well used to thinking "how could I check this answer with an experiment."  They understand that taking three data points and debating the pattern they form is crap science; they know how to plot data on a graph, and how to use that graph as evidence for the validity (or lack thereof) of theory.  

Two: I can teach my students to communicate their understanding of a quantitative subject.  My students are good, smart boys who are used to getting answers right in school.  They enter my class with the idea that their job is to understand the subject.  I ask them to do more -- I ask them to communicate their understanding via words, diagrams, equations, and numbers.  They learn that getting an answer is insufficient; even knowing how to get the answer is insufficient.  They must be able to explain in thorough detail the reasoning behind their answer, such that another person at the same level of physics can easily follow and understand their approach.  The English department doesn't accept a one-sentence essay along with a plea that "Come on, you know what I mean;" neither do I accept two lines of algebra as justification for an answer, even if the student claims to know in his mind how to do the problem.

The teaching of experimentation and scientific communication are both time consuming, intellectually intensive processes.  My students don't usually recognize the necessity of developing experimental and communication skills; they think that they already know about experiments from middle school, and they think that their communicative ability is already perfectly good because they can often get answers right.  So my job begins with convincing the class that they need to develop these skills in the first place.  Then I must ride herd all year, never allowing a substandard experimental graph or half-arsed justification to slip through unchecked.  When a student is honestly stumped as to how to improve his experiment or his justification, I have to find a way to patiently explain, to help him improve without merely doing the heavy thinking for him.

These skills of experimentation and quantitative communication transfer to most disciplines beyond physics.  Every science, every social "science", journalism, politics, business, sports, virtually everything my students might eventually do will be helped by their ability to collect data, evaluate data, and communicate an understanding of the meaning of that data.  And that's why physics teachers who help their students develop these skills should be in high demand.

Exam review idea -- do corrections, and use the white board to keep track of them

Okay, I know I'm posting this too late for AP exam review this year... but we still have a couple of

weeks until our other classes take exams.  We're in full-on review mode.

While a review must take on multiple modes in order that the students don't get bored, I'm always partial to making corrections a major component of any cumulative review.  Keep assigning worksheets and practice problems, yes...  but in order for the review to be effective, students must get these practice items right.  As Boscoe Brown used to tell our marching band on a daily basis, practice doesn't make perfect -- perfect practice makes perfect.

I'm assigning practice problems both at night and in class now.  I'm grading every problem carefully.*  Then every three days or so we are taking time in class to correct everything anyone got wrong the first time.  

* Or, often I'm having a top student grade a problem set to a rubric rather than do the next set of problems.  That's more effective learning for the student grader than doing another set on which he'll get nearly a perfect score.

It can be daunting to keep track of so much assigned work.  And even the most honorable students will tend to "forget" that they haven't finished correcting everything they missed, especially if I look harried as I flip through a bunch of papers to figure out my records.

So, using a suggestion offered to me at a summer institute a few years ago, I created a list on the board.*  I write the name of the assignment, and then every student's number who needs to do a correction on that assignment.  In class, students use the board to figure out what they have to do -- no asking me necessary.  When I check off their correction, I erase their number from the board, often

to an audible sigh of relief.

*The person who suggested this to me actually called it a "Wall of Shame."  I'm certainly not using that term, 'cause I have no intent to shame anyone for getting a problem wrong.  But it is quite amazing to me how much harder students work at corrections when their mistakes are laid bare for all to see.  They want so desperately to erase their number from the board, because they do feel a bit of shame if their number appears way more than anyone else's.

AP Atomic Energy Levels question: 2011 B6

Joseph Rao writes in to ask about AP Physics B question 6 on the 2011 exam.  (Can't post it, but follow the link.)  He notes:

The question said that an electron with KE of 4.8 eV can excite an electron in an atom upon collision even if the energy does not match the transitional energy from n=1 to n-=2. The energy difference between states was for 3 eV. 

Huh... this confuzzled me momentarily, too.  I would've gotten it wrong on first attempt.

What makes this problem unusual is that it's an electron -- a massive particle -- causing the transition. 

It's a PHOTON that can either be absorbed entirely or not.  There's no such thing as absorbing just some of a photon's energy.

However, an electron is a massive, classical particle, with speed that can vary.  It had 4.8 eV to begin with due to its 1.3 x 10⁶ m/s speed.  Nothing wrong with the electron slowing down, giving some of its kinetic energy to the bound electron in the atom.  The bound electron jumps states by gaining 3.0 eV.  (The bound electron must absorb only the amount of energy necessary to jump states.)  The free electron goes on its merry way, now with (4.8 eV - 3.0 eV) = 1.8 eV of kinetic energy.  You can work out its speed to be smaller now.

GCJ