Framing appropriate questions for conceptual physics

I've been working a bit with my colleagues on our 9th grade conceptual physics course.  We teach a rigorous physics (not "physical science") class to all 9th graders.  It's a difficult proposition to aim the material at the correct level.  Many students have not taken algebra, and those who have are certainly not fluent in algebra skills.*  We want to minimize arithmetic, and concentrate on conceptual skills.

* Those top-15% students who are fluent in algebra are broken out into a section of Honors Physics I.

Nevertheless, we want to teach serious physics, not merely a set of facts to be learned or situations to be memorized.  We still teach physical reasoning from equations, for example... but in the sense of "mass doesn't change, speed doubles, so by ½mv² , kinetic energy quadruples."  This is some of the same fundamental understanding expected from AP-level students, but at a slower pace, with fewer equations, and without a calculator necessary.

Problem is, it's tough to find questions at this appropriate level.  Hewitt's conceptual physics text is a great source, of course, but I'm talking about finding a huge bank of questions that will allow you to write numerous quizzes, tests, and exams.  For college-level physics, the AP program provides more questions than you'll ever need.  At the general but quantitative level, the New York Regents exam is the way to go.  I have not yet found a good non-quantitative, published source of questions that are ready to copy-and-paste into your tests.

Now, the Regents exam includes occasional qualitative questions.  These can be used nearly verbatim in conceptual physics.  Most of the Regents questions include arithmetic or algebra, though, often emphasizing the mathematics through the phrase, "show all work, including the equation and substitution with units."  I have no complaints about this quantitative approach; in fact, I train my junior-level general class to handle Regents-style questions.  I just know from our department's experience that, for freshmen, "substitution with units" presents a considerable barrier to physics understanding.

Try turning a quantitative Regents question into a no-calculator conceptual physics question.  For example, from the January 2006 exam:

The speed of a wagon increases from 2.5 m/s to 9.0 m/s in 3.0 s as it accelerates uniformly down a hill.  What is the magnitude of the acceleration of the wagon during this 3.0-second interval?

(1) 0.83 m/s²     (2) 2.2 m/s²      (3) 3.0 m/s²       (4) 3.8 m/s²

Four different ideas occur:

Ask about the acceleration's direction instead of its magnitude.  Freshmen can learn the fundamental fact that speeding up means acceleration and velocity are in the same direction, while slowing down means acceleration and velocity are in opposite directions.  I'd write...

A wagon travels down a hill.  The wagon's speed increases from 2.5 m/s to 9.0 m/s in 3.0 s.  What is the direction of the wagon's acceleration?

(A) up the hill       (B) down the hill   

(C) straight down     (D) straight up

Ask for a straightforward calculation of the acceleration.  Even though I'm making the problems accessible without a calculator, I'm not ignoring quantitave reasoning entirely.  It *is* important that a student recognize that acceleration depends on the change in an object's velocity, not on the velocity itself.  So, I'd write...

The speed of a wagon increases from 9 m/s to 12 m/s in 3 s as it accelerates uniformly down a hill. What is the magnitude of the acceleration of the wagon during this 3.0-second interval?

(1) 1 m/s²     (2) 3 m/s²      (3) 3.5 m/s²       (4) 4 m/s²

Trying to just divide any old velocity by 3 s leads to an incorrect answer.  The the correct answer can be determined at a glance, even by a mathematically inept ninth grader.  (Math teachers will cheer now, because we're forcing students not to grab a calculator to manipulate (12-9)/3.)

Ask for a comparison to familiar values.  The only acceleration that our students probably have a feel for is g.  So, ask...

The speed of a wagon increases from 2.5 m/s to 9.0 m/s in 3.0 s as it accelerates uniformly down a hill.  Is the magnitude of this wagon's acceleration...

(A) greater than Earth's free-fall acceleration

(B) less than Earth's free-fall acceleration

(C) equal to Earth's free-fall acceleration

Such a question does NOT necessarily require a direct calculation of the wagon's acceleration.  If the student thinks in Hewitt-ese, then speeding up in free-fall means gaining 10 m/s of speed every second of fall.  This wagon accelerated for 3 s, and gained nowhere near 30 m/s of speed, giving (B) as the only possible answer.

Ask about the physical meaning of numbers.  Even without calculators, our students should develop a feel for the physical reality represented by numerical answers.  Speeds in m/s can be estimated in mph by multiplying by 2 and adding a bit.  But I'm not asking anything truly quantitative here:

The speed of an object increases from 2.5 m/s to 9.0 m/s in 3.0 s as it accelerates uniformly.  Which of the following objects could NOT reasonably perform this motion?

(A) A car on an interstate  

(B) An airplane during takeoff  

(C) A lab cart on a track in the classroom

(D) A bicyclist going down a hill

There you have it -- FOUR different conceptual physics multiple choice items inspired by a single Regents question.  And any one of these questions can be expanded into an open-response test item,  or assigned for homework, by adding the phrase, "justify your answer."  

Honors Physics I: Course Description

As detailed in the previous post, I don't feel like waiting for the AP Physics B redesign.  Woodberry Forest is going to begin teaching according to the principles of the proto-AP Physics 1 and 2 courses right away, beginning in 2011-12.

We're calling our first year college-level course "Honors Physics I."  We're modeling the course structure on the AP program.  That means we're going to commit ourselves ahead of time to a weighted topic coverage list.  That means we have a course exam written which will remain locked away until mid-May, and that will not be changed on a whim.  And, I'm going to arrange for *external* validation of the exam -- I've talked to a few AP readers about a possible "trade and grade," in which I grade a set of their tests or exams, and in return they grade my Honors Physics I exams to the rubric that I send them.

The course topic coverage outline for Honors Physics I can be found here via google docs -- so please forgive any formatting issues.  My goal, approximately consistent with the College Board's goal for AP Physics 1, was to cover about 60% of the current AP Physics B curriculum.  Please remember -- this outline is NOT necessarily related to what the College Board has in development for AP Physics 1.  Nothing about AP Physics 1 topics that has been officially released, because even the people in charge of the redesign have not settled on a final distribution of topics.  My outline represents what I would do if I were solely in charge of the redesign. 

The quick rundown of the six content areas I've included:

Mechanics (40%): Pretty much everything on AP B mechanics, except torque.

Fluids (10%): Static fluids only, i.e. static pressure and buoyant forces.

Thermal Physics (15%): PV diagrams, the ideal gas law, and the first law of thermodynamics.

E&M (15%): Forces due to fields, but NOT the source of E or B fields.  Basic DC circuits.

Waves (10%): Basic properties; sound & light; Snell's law; but not standing waves or optics.

Nuclear Physics (10%): Definitions of particles, conservation laws, mass-energy equivalence.

Also in the linked course description you'll see the exam format.  I've made the exam two hours, so as to fit better into my exam periods.  It's in three sections, but without formal separation; all sections can be worked on at will during the two hours.  Calculators, a constant sheet, and an abbreviated equation sheet will be accessible during all sections.  (Why?  That makes administration easier.  And the calculator won't really help much on the multiple choice, anyway.) 

My major divergence from the current AP exam format is the third "short answer" section.  I'll ask ten brief questions that will usually involve a verbal explanation.  You know how every recent AP free response question includes a lettered part that says "justify your answer?"  Well, these short answer items will each be similar, except in isolation, without the context of a larger problem.  While I have no idea whether such items will appear on the future AP Physics 1 exam, I do know that all formatting options are on the table.  It sounds likely that the current dichotomy of just multiple choice and 10 or 15 point free response items will be adjusted.

Want to use this course?  Go for it.  I'll be happy to send you more materials:  a pratice test that I'll give in November, and hard-copies of the final exam with a rubric next May.  I only ask a couple of things in return:  (1) Collect the exams when you're done, ensuring that they don't get posted online; (2) Report to me how your students did on the final exam, whether they did well or poorly -- I'll keep that info private except for saying globally how everyone did; and (3) Send me a can of Skyline Chili.* 

* or equivalent.  Condition (3) is not mandatory.

If you teach an honors course, this might be just the thing to prepare your students for the AP B exam in 2012-13.  Or, you could use this course and exam to demonstrate the rigor of your non-AP course to parents, administrators, and colleges.  Try it -- I think you'll like it. 

AP Physics 1 and 2 Redesign (as it stands now) and Honors Physics I

So, you may have heard that the College Board has been working on a revolutionary change to the algebra-based AP Physics course.  In its current form, AP Physics B requires an enormous breadth of material.   As it stands, teaching AP Physics B well is as much about organization, scheduling, and pace as it is about presenting the overly-numerous physics topics themselves. 

The College Board's plan, as they have discussed at their annual conference and with readers, is essentially to split AP Physics B into two courses, AP Physics 1 and AP Physics 2.  In principle, each of these separate courses would mimic a semester's worth of college physics, in the style of AP Physics C and its two independent exams.  The overall combined AP Physics 1 and 2 curriculum would allow even more broad coverage of physics; but since the material is intended to be spread over two years, a single course will cover *less* breadth and thus be manageble for a wider student population.

Although the curriculum is still in considerable flux, a few general principles have been released. 

Topics / "Big Ideas": The specific topics to be taught in each year, and the depth to which those topics should be taught, are currently unclear.  Partially this is because the redesign committee has chosen to prioritize "big ideas" of physics that cross topic areas.  For example, Newton's three laws and the relationship between forces, fields, and motion can be applied to more than just blocks on inclines; so, this "big idea" will be revisited in covering static fluids, electrostatic forces, magnetic forces, and so on.  Similarly, conservation laws can be applied across topics, at the introductory level including even (or especially) nuclear physics.  Topics will be chosen to fit the "big ideas" model of learning introductory physics.

Writing:  If you look back at Physics B exams from the 1970s and 80s, you'll see a lot of problems testing algebraic manipulative ability as much as conceptual understanding.  That focus changed substantially in the mid 1990s.  Laboratory-based questions, along with the proliferation of "justify your answer" items became regular features of the free response exam.  Everything I've heard about the new Physics 1 and 2 courses indicates that this emphasis on justifications and explanations will not merely continue, but will dominate the exams.  That doesn't mean that derivations and calculations will disappear, since those are part of physics, too.  However, you can expect that those who consider physics merely as the process of plugging numbers into an equation will be at an even more significant disadvantage than they already are.  Students will need to develop the skill of communicating understanding verbally, and concisely.

The redesign into two separate algebra-based courses provokes ideological struggle amongst physics teachers that sometimes approach Burr-Hamilton levels.  I will not get into the pro and con arguments here, at least not yet.  It's too early to panic or rejoice.  Physics 1 and Physics 2 will not begin for at least three years, and likely more.  The College Board is still in the process of getting buy-in from colleges, designing and norming the curriculum and the exam; then they understand that they need to provide significant lead time so schools can figure out how these new courses fit into widely varying science programs.

My message to teachers is not to worry about the redesign yet.  AP Physics B, in its current incarnation, will continue for a while. 

One great advantage of the upcoming Physics 1 course is the potential to truly serve a broad portion of your college bound population with a first-year AP course.  Those who teach "honors physics" or "college prep physics" will likely find that AP Physics 1 meets their needs beautifully. 

I and my department, we didn't want to wait.  We are teaching "Honors Physics 1" next year.  (Not "AP Physics 1," because that AP course doesn't exist yet, and we can't use the College Board's trademark on an unofficial course.)  In my next post I'll describe my school's course, which is intended to be my own version of what I hope AP Physics 1 might become.  I'll even provide some course materials if you're interested... read on.

Mail Time: Avoiding extensive homework review in class

Posted homework solutions
are like nuclear weapons...

Lisa Zavieh, an "acorn"* at the 2011 AP Physics reading, writes in:


* An "acorn" is a first-year AP reader, so called because her nametag includes a sketch of an acorn in the corner.  A "grasshopper" is a first-year AP table leader, so called because someone thought it sounded cool.

"One thing I have been mulling over for awhile is how to handle homework. I completely agree with grading homework, and with assigning minimal amounts daily with the expectation that students will present thoughtful thorough solutions.  I also do not accept late work, and like your extensions and exemptions policies.

I would like to avoid copious HW review during class, so my response has been to post homework solutions (in the past - on paper. Now I am considering video clips.)  What do you do in your class?"

It's great to hear from Lisa. The AP reading is an amazing source of teaching ideas. I'd say that 2/3 or more of what I do in my class is inspired by a conversation from the reading. Lisa's "video clips" thought is likely based on a brief presentation by Misissippian Marsha Hobbs, who showed us some wonderful videos of her doing physics problems. If I were taking a class online without daily personal contact with classmates, I would want access to a set of Marsha's videos.

But Lisa, to address your specific question, I think I recognize the in-class conversation you’re trying to avoid: “How do you do problem 2 in detail?” say the class. If you don’t go through every last little step of problem 2, it becomes “Mr. Jacobs is so mean and unfair. He won’t even show us how to do the homework. How are we supposed to learn physics if he won’t help us find our mistakes?”

For about the first seven years I taught, I posted homework solutions. I was able to tell the class, “If you have any specific questions about the problems, the solutions are posted. Take a look after class. But for now, let’s figure out how to do *tonight’s* problems…” That didn’t completely prevent the whining at first, but it allowed me to checkmate such a complaint. “My daughter says you didn’t go over the homework. How is she supposed to learn?” “Oh, she never came to talk to me, so I figured that she had compared her work with the posted solutions, and didn’t have any further questions. Did she study with the posted solutions?”

In practice, very few students ever looked at my solutions. And if they did look, they checked the answer and moved on. No matter how beautifully I modeled the problem presentation process, no matter the clear verbal explanations I included, a student didn’t care. Right answer? Great, move on. Wrong answer? Dang, move on.

Posted solutions were like nuclear weapons – they were for having, not for using. After a few years at the same school, parents and colleagues no longer questioned my competence, so I didn’t need the CYA aspect of posted solutions; and I had become good enough at problem solving that I didn’t need to write out every step of every assigned problem for my own sake. I saved a lot of time by not writing out solutions anymore. (I now have available a set of Giancoli 5th edition solutions in a couple of three-ring binders – bidding starts at one case of canned Skyline Chili.)

So how do I now preclude the calls to go over homework in detail? I *want* to discuss important physics issues about the problems, but I don’t want to do a problem step-by-step. Thing is, I know what the major sticking points will be on most problems. One of my daily quiz questions might refer to an issue on a homework problem: “Which of the following is a correct free body diagram for problem #2 last night?” By going over the quiz, I’m also going over the homework. I rarely ask, “any homework questions?” Rather, I ask the questions myself: “You weren’t given the mass of the roller coaster, so how did you solve the problem without that information?”

I make sure discussion is on *my* terms. This means questions about physics concepts are fine, but questions about how much credit they might get for their answer are unacceptable. If a student presses his questions beyond the scope I want to deal with during class, I politely offer to continue the conversation during the daily consultation period. Somehow, though I’m sincere in my offer, that student rarely ever shows up on his own time to talk physics with me. Go figure.  :-)

GCJ

Rules for Turning In Daily Work: CONSULTATION

Today's topic discusses consultation, or extra help, or tutorial, or whatever your school calls unstructured time when students can drop in to talk to you about physics.  The post in one sentence:  When a student's work is late, schedule a required appointment with him outside of class.

In the previous episode about extensions, I described my rather liberal policy of no-questions-asked homework extensions.  The question is, what happens when a student who is out of extensions doesn't have homework?  That's when I have to bring the hammer. 

It's important to note that I treat half-arsed homework similarly to absent homework.  The whole goal is to get every student to do every problem carefully and thoroughly.  I don't want to encourage last minute BS as a way of avoiding consequences. 

The trick that has been effective for me is *not* to emphasize a grade penalty for late or crappy work.  Sure, such work earns minimum credit, even if it's eventually done right.  But the mere threat of a bad grade is not effective amongst a certain subset of students.  The guiding principle that has worked for me:  I make it more difficult to do an assignment wrong than to do it right the first time.

A student without homework has already used up his numerous extensions.  That means it is the third or fourth time in the last five weeks that he hasn't done a short assignment.  He is aware of my policies, and has chosen to take the grade penalty.  Fair enough, say some.  Analagous is the guy who's been caught driving recklessly five times, and who pays his fines and raised insurance premium without complaint.  No, that's *not* "fair enough."  The goal is not to assess a fair penalty for reckless driving; the goal is to get this guy to stop driving recklessly.

We have another currency at our disposal other than grades: time.  Not only do I require students without homework to do the assignment correctly, I dictate the time at which they do so, and they do the work under direct supervision.

My school provides two time periods when I can require a student to show up to do supervised academic work.  The first is an afternoon study hall, which is reserved for those who need extra time to catch up with missing work.  "You're out of extensions and missing today's assignment.  So, you must attend today's afternoon study hall, because that will give you the structured time you need to catch up with your work."  Whether he's having to miss out on an hour of sports practice, or whether he just loses an hour of quality video game time, this student will have an hour of physics work forced upon him in replacement.
The other option is a mid-morning consultation period, during which classes are not in sesson.  Students usually use this time as they see fit, to finish homework, ask a teacher for help, or go to the snack bar for a break.  A student with poorly done or missing homework in my class, though, will be required to come see me during this time:  "This assignment was nowhere near correct.  I think you need some help understanding this material; please come see me during 9:30 consultation for a required academic appointment." 

Now, I'm lucky that my school's schedule provides these times for my use.  My students are well aware that teachers are encouraged to require them to attend these study times where necessary.  So, I don't get serious complatints, but I do have to be firm in not accepting excuses:  "I'm sorry that today's football practice is really important, but you have physics work missing."  "Yes, I understand that you were planning to finish your English paper during morning consultation period, but you need my help in physics, so you will attend the consultation period."  The only acceptable excuse is a prior commitment to meet with a different teacher, in which case I reschedule for the next day.
Your school probably does have a similar time of which you can make use, though you might have to be creative.  After school, before school, lunch time... whenever students and you are simultaneously uncommitted, require them to come see you.  If a student fights the requirement, engage -- this is a battle worth fighting.  Do whatever it takes to establish the procedure that missing or crappy homework automatically leads to a required meeting with you, because after mid-October, you'll hardly ever have to require these meetings.  Students will resign themselves to just doing the homework right the first time.

Importantly, when I require a student to attend either of these study periods, I try to avoid any suggestion of punishment.  A slacker will very often try to play the victim amongst his classmates (and parents), seeking sympathy and confirmation that I am a power-hungry jerk.  If I were to thump my chest, deliver a lecture on responsibility, act personally offended that a student was too lazy or immoral to complete my assignments, then that slacker would find the sympathy he seeks.  Moreover, the slacker would invariably come to these study periods with a vicious, bitter attitude, as if it were my fault that he didn't do his homework.  That's not helpful to anyone.  As often as I can, I want the slacker to actually use the extra time I've given him to do a good job on the problems. 

Nevertheless, no matter how much I explain that consultation and the afternoon study hall are merely tools to help the students keep up with a difficult course, the students tend to see these tools as punishments to be avoided.  That's okay by me... because, how do they avoid the "punishment"?  They get the homework done on time and with reasonable effort.  Which is all I want.

GCJ

Why I make work due every day

"Moo"

I'm in the midst of a series of posts about course structure and rules for daily assignments.  Before you go all nuts and say "No, what you say would never work," it's important to recognize that everyone's class structure must be context specific. 

I teach 11th and 12th grade in a boys' boarding school; it's unlikely that you are in the same situation.  A commenter mentioned, quite reasonably, that he thought it *un*reasonable to assign work every night -- after all, high schoolers have lives outside of academics, which we should respect.  Assignments due every few days allow the student to execute a guiltless social life, and preempt the excuse that a given night's required events provided no possible time for homework.  Fair enough, in the right situation.

I've heard it claimed (and I even used to claim myself) that widely spaced, longer assignments help teach students to manage their time wisely, because the burden is on THEM to work ahead, and they themselves pay the price of catching up if they have procrastinated.  When I taught at a day school, I assigned sets of 5-6 problems each due about twice a week.  Virtually every problem set was, in practice, worked on only the night before it was due.  Groups of students deliberately planned social get-togethers twice weekly in conjunction with the assignment schedule.  That worked fine with those students' schedules.  However, don't think my students did much forward thinking:  I frequently heard complaints that I scheduled a problem set due the day after a ballgame, dance, or event.  The idea that they could or should work ahead since they had the assignments available a week in advance did not compute. 

The actual advantage of fewer-but-longer assignments at that particular day school involved collaboration.  These folks could and did arrange minor physics parties twice a week; I don't think they would have collaborated with each other so well on a nightly basis. 

When I arrived at the boarding school, I initially attempted the same course structure.  Thing is, my students here live on dorm, and have a nightly two-hour study period.  The facutly generally make daily assignments, with few long-term deadlines.  The students are used to looking no further than the work due the very next day.

So, I faced serious opposition to bi-weekly deadlines.  It worked like this:

    

* Monday night:  Nothing due Tuesday, so do no physics homework.

* Tuesday night: Nothing due Wednesday, so do no physics homework.

* Wednesday night:  Six problems due Thursday.  Spend 45 minutes working, see that there are still three problems to go.  Get work for other classes done.  Complain to department chairman that Mr. Jacobs is assigning more than the official 45-minute-per-night limit.

Aarrgh!  On one hand, it was easy to complain about those danged kids these days, don't know how to manage their time and plan ahead as of course everyone did in my day.  But it was *my* responsibility to adjust my course structure to fit my students' preconceptions.  And so I did. 

I quickly changed to nightly assignments.  Since everyone lives on dorm, collaboration is easy on a nightly basis.  Since study periods are considered sacred and are hardly ever canceled for other events, I am confident that everyone has the available time to invest in physics if that time is used wisely.  Of course I still tend to post assignments several days ahead of time, so that interested students can work ahead.  The nightly structure has served me well in terms of getting the homework done at all, and then in terms of fostering collaboration.

As you determine your daily assignment structure, try not to think in idealistic terms.  Think practically -- not what your students *should* do, but what structure will most likely actually result in carefully presented, vetted solutions to the assigned problems.  Author Terry Pratchett mentions that structuring a society's taxes is like dairy farming:  the goal is to extract the maximum amount of milk with the minimum amount of moo.  I'd say, treat homework the same way.

Some further ideas about fostering collaboration in the next post.