Use unlined paper for problem sets in honors / AP physics

I do a lot of posting about what has worked for my class.  Today I post about an idea I had that didn't work like I expected.

About a year ago, I redesigned my problem sets for honors students.  For over a decade, I had simply assigned end-of-chapter-style problems via email, and required students to answer each on a fresh page of unlined paper.  I changed the assignments so that each problem was typed out on the front and back of a page, AP free response style, with space to answer under each part.  These new problem sets looked like worksheets, not end-of-chapter problems.

The theory was, I wanted to get better attention to the meaning of the answers, and specifically to each step in the problem solving process.  By asking the question in stages, each of which couldn't be ignored, I thought I'd set students up for success, minimizing the helpless feeling of "I don't know where to start."  Furthermore, I figured I'd be able to grade more quickly and accurately, because I could turn directly to the part of a question that I most wanted to see answered.  No more hunting through a poorly-presented page of work!

In general, my "theory" was proven correct.  Grading was quicker, I got fewer students trying to hide the fact that their work was incomplete, I got full sentence answers to direct questions like "justify the reasonability of your answer to (c) by comparing it to speeds with which you are familiar."

It was the unintended consequences that proved dastardly.  Primarily, the perception of the homework as a worksheet to be filled out damaged the collaborative culture of the course.  

Students would check their answers to part (d) with each other.  But if they found that their answers were different because of an issue earlier on in part (b), they would not take the time to deconstruct part (b).  Previously, when the problem had been presented on a blank canvas, everyone saw the problem as a whole (even if the original text on a different page used parts (a) (b) (c) ) -- and so they discussed their whole solutions. 

I asked a lot of "place a check by one of the following, and justify your answer."  Students would verify with each other that they had checked the correct box, but would not discuss their justifications (figuring, I guess, that they had "collaborated" by looking to see that the right box was marked).  Without the checkbox and the space for answers, I used to get too-long essays as justifications; but the students communicated with me in writing, and with each other both in writing and in face-to-face discussions.  That's what I wanted. 

Yes, grading was quicker and less intellectually taxing,  because I could quickly find the student's response to each part of the question.  The unintended consequence was that collaboration became less intellectually involved, too, because the students never had to read each other's work.  When using a blank page, I often saw students going line-by-line through each others' solutions, trying to find mistakes or common ground.  (And I saw their presentation get better as not only I but also their peers criticized sloppy and haphazard solutions.)  When I dictated presentation style through my worksheets, student-to-student discussions became nasty, brutish, and short.

Note that I've been very happy with worksheet-style assignments in regular physics, and I'm going to use that style in conceptual next year.  In those classes, though, most students aren't ready right away for substantial multi-step, creative problem solving.  

I had wanted to move to the AP worksheet-style homework assignments for years, and only recently found the time to write the worksheets.  Turns out, that effort was essentially wasted.  Next time I teach honors or AP, I will be back to requiring a full page of unlined paper for each problem.

Soda Raft Question

And if any soda company would give me money, I'd use their
brand name in the problem statement. :-)

The following is a true story.  I use it as a problem in static fluids every year.  This year I assigned it when I was absent -- an upcoming post explains how I assigned the problem in class.  

For now, though, look at the poll at the left of the blog -- vote for your estimate!

1. Mr. Jacobs’ friend Brian Jackson saved two-liter soda bottles throughout his senior year of college.  During “Haverfest," he duct taped the bottles together to form a raft.  He then successfully floated himself out onto the duck pond.

Estimate how many bottles Brian used.  Explain your reasoning thoroughly and show all calculations for full credit.

A Tale of Proctored Study Hall, and Serious Written Attempts

Today's post: making our horses drink.

Part of my job as a boarding school "master" is to spend about one night a week on dorm duty.  This year, I've been assigned to supervise the Proctored Study Hall.  See, most of the school spends a couple hours nightly in quiet study time in their dorm rooms, in the library, or unsupervised in classrooms.  But, students are assigned to Proctored if they get a D, or if their advisor thinks they need a more structured nightly study environment.  Once a week, I have to be that structure.  Guh.

The nice aspect of Proctored is that I'm in regular contact with some students who truly need and want my academic help.  They appreciate that I show genuine interest in their assignments, even those outside of science.  It was established very early on in the year that proctored is a time for serious, diligent, but relaxed study.  The group knows by now that they are to get on with their work without distraction.

Thursday night, I was approached three separate times by three different 9th grade physics students for "help."  The first two came with a blank paper asking a specific question about a problem; the third had some work done, but not on the problem he was asking about.  

I gave the same response to all three: look, I'm happy to help, but (a) it's the middle of study hall, and a long discussion here would ruin the quiet atmosphere and distract your peers; and (b) I need to see your first, written effort before I help out.  So, please go back to your desk, make your best attempt, and then come back here at the break.  I'll talk you through the problem then.

Any guesses as to what happened next?  Go ahead, teachers who are reading this, write your guess in your notebook.  

(pause a beat while you guess)

When the bell rang for break, I individually reminded each of the three students that I'd be pleased to help them out now.  All three responded:  "No worries, I figured it out on my own, but thank you!"  

There's a lesson here.  Physics is a difficult subject, and physics teachers tend to work very hard to avoid gaining the reputation of  an unapproachable jerk.  Fair enough.  But in our zeal to be helpful, do we do our students a disservice?  I say, much of the time, yes.

A story from my first year of teaching:  I had been repeatedly berated by colleagues and parents for being mean and unapproachable.*  So when one of my honors seniors asked me for an individual appointment at the end of the next school day, I agreed -- even though that meant staying at the school three hours after the end of my last class, even though it meant going home in rush hour.  In came the student, right on time, with his book and problem set.  

* Interestingly, most of the folks calling me unapproachable were doing so without ever attempting to approach me.  But that's a different issue.

He said, "So, I'm having trouble with question number 1.  Can you help me?"  I dutifully pointed him toward the relevant equation, discussed with him how to approach the problem, and I waited patiently while he used his calculator to ensure that he was going to get the right answer.  Here I was, being approachable, helping a poor student learn physics!  People would stop complaining any day!  Right?

The boy filed question 1 away with a satisfied look.  He looked back at his problem set, and said, "Now, can you help me with question 2?"

This time, I was suspicious.  I asked, "Where did you start?"  He hemmed and hawed a minute, and then in response to my direct question, he admitted that he had not really done anything yet on any of the problems.

Well, that's simply unacceptable.  My job as a teacher is not to sit with my students, holding their individual hands until they get questions right.  My job in class is to give them the tools with which to approach problems.  Then, it's my job to set up an environment in which direction is available when people get stuck.  But they must first get legitimately stuck before they seek direction!  

A few years into my career I simply made the blanket statement that, while I love to help people with physics problems, I will not even entertain a question unless I first see a serious written attempt.  

Do you have a packed classroom during a morning or afternoon tutorial period?  Do you feel like you're overburdened because you have too many students who need your help, and not enough time or energy to help them?  Well, try implementing the serious written attempt rule.  I guarantee that the number of people who think they need your help will be cut in half; and, the time you need to spend to help each person will also be cut in half, because everyone asking for assistance is thoroughly familiar with the problem already.

Then the next step is to make anyone you help use their newfound knowledge to help the next student who asks:  "I'm glad you asked that, George.  Billy just asked me the same question... Billy, could you explain that issue to George while I help Mike on this other problem?  Thanks!"

Rewriting Problem Sets for Honors / AP Physics

Above is an example of the layout style I'm applying to
problem sets.  Every problem will require both verbal
AND mathematical response.  See this link for a
google docs example:
projectile problem on google docs

Traditionally in my algebra-based AP-level physics course, I've assigned about two homework problems per night.  When I began teaching AP, I selected these problems from the textbook.  All textbooks seem to label their end-of-chapter problems by difficulty:  level I or * means easy, level III or *** means hard.  In every major textbook, the problems at the middle level of difficulty tended to be approximately on target for AP.

Now, there's much more to learning college-level physics than solving end-of-chapter problems.  Although textbooks are trying to improve, still their problems are heavily calculational.  Conceptual questions requiring verbal responses are shunted off into another section, rather than integrated into every problem.  That's not how an AP exam is structured. 

An AP free response question will have 3-5 lettered parts.  Some of these parts will likely require calculation; some parts will require explanation.  It is rare nowadays that a single free response item does not include BOTH verbal and mathematical sections.  I want to mimic this style in my own nightly assignments -- partially as a tool to prepare for an AP-style exam, but primarily because I think it good pedagogy to integrate verbal and mathematical questions.

When I began teaching AP, I scoured my textbook for good, level II, end-of-chapter problems.  The assignment would be stated as, "Do chapter 10 problems 29 and 64."  After I had taught the course for a few years, I began to add my own additional parts to the textbook problems, such as "... for problem 64, also describe as you would to a non-physicist the size of the boat."  And in the past few years, I've re-written most problems entirely to phrase them the way I want.

This summer, I've revised my assignments again for the express purpose of integrating verbal and mathematical responses into every problem.  I've typeset the assignments in MS Word, so that each night's assignment takes up a single page, front-and-back, with room for the answers.  You can check out this projectile problem on google docs as an example of the format and style of an assignment.

Why the room for answers after each part?  For a long time now I've observed that students will tend to use whatever space you provide for problem solving -- no more, no less.  If they use their own lined notebook paper, problems are crammed into as few lines as possible.  When I've provided full sheets of blank paper, they use most of the full sheet -- great, but sometimes I get an essay when I wanted a two-sentence response.  My hope is that I will get my class in the habit of giving just the right depth of response by subtly showing them the space that should be filled.

For those of you who are in their first few years of physics teaching, I would suggest you file this post away for future reference.  It takes enough time at first to figure out how to solve and explain the problems; don't worry about whether the problems are perfectly phrased, or well-typeset.  Just get the students in the habit of communicating their solutions.

But if you've been teaching a while, and if you're wondering how to make your assignments shorter yet more effective, I think this style is worth a try.  Make students write verbal responses on every problem, so they see that physics is about so much more than getting the right number. 

Assigning multiple choice exercises as homework

I'm in the process of writing nightly problem sets for my new Honors Physics I course.  These are essentially the same problems that I used for AP Physics B; however, I'm rewriting the problems to include more verbal explanations, and so that they're typeset on the front and back of a single page. 

Most of my homework assignments are simply rewrites of textbook end-of-chapter problems to make them AP style, and to explicitly demand verbal responses.  Occasionally, though, I want students to work through a set of multiple choice questions.  I *could* give these as a quiz in class; but to make the quiz worthwhile, I'd have to go over the quiz in detail.  I usually want to use class time for other purposes.  How can I usefully assign multiple choice problems for homework?

The issues are probably obvious... It's too easy for students merely to copy the (presumably) correct answer from friends without thinking through the answer thoroughly.  The simplest response is to require students to justify every answer with verbal reasoning.  I do this occasionally... but I don't want to assign more than three or four multiple choice per night in this manner.  How can I get folks to work through a longer set?

Once in a while, I'll pass out a 20-question-or-so multiple choice exercise and a scantron form.  I require each student to answer each question on the scantron by himself, without collaboration.  (You can enforce this either with an honor pledge, if you can trust it, or by using 20 minutes of class time.)

Next, I require each student to check his answers with classmates.  Everyone's final answers go on the reverse side of my two-sided scantrons.  I only grade the final answers.  The trick is, if a student changes his answer based on collaboration, he must write a verbal justification.

Grading is easy, since I can scan the scantrons, and spot-check the justifications.  The assignment is not excessively long, because students only have to write justifications for the ones they missed initially, and since the discussions with classmates when they are finding out which ones they missed will make justifications quick.

Sometimes I'll ratchet up the grade incentive for useful collaboration.  I'll take off one point for the first wrong answer, but two MORE points for the second wrong answer, and three more for the third... someone who gets 16 of 20 right would thus earn a 50%.  This grading system has led to wonderful physics arguments within the class, which of course is the whole point of any homework assignment. 

Rules for Turning In Daily Work: The secret to effective collaboration

Solitude... the counterintuitive secret to effective collaboration.

Ever have a student miss every part of a homework problem because his free body diagram was incorrect?

Ever have a student ask, "How were we supposed to do the problem when you didn't give us the mass?"

The relevant question for these students is, "With what other student(s) did you discuss the homework problem?"

So many folks knowledgable about learning physics will emphasize the benefits of collaboration.  I have my own story about how the only A I earned in an undergraduate physics course -- I worked on the weekly assignments myself on Sunday night, then I had four separate scheduled meetings with four different other students during the week.  By Thursday night, I was so familiar with the problems that I was providing cogent explanations to the procrastinators.  These folks thought me to be really talented at advanced quantum physics; Thomas and Jen, who worked with me on Monday and Tuesday, knew better. 

I'm sure you have your own story about how you or an acquaintance discovered the usefulness of regular collaboration in learning physics.  Our challenge, as physics teachers, is to push our students toward their own epiphany sooner rather than later.

In recent years I've taken the bull by the horns, and simply required nightly collaboration.  Students must write down the name of the student(s) with whom they discussed the problems, or at least checked their answers.  No collaboration = not full credit.  Such a requirement is easily workable in a boarding school, where a classmate is guaranteed to live no more than 15 yards away.  It's workable in a day school, too, in the age of email and social media.  Discussion via facebook or twitter is okay by me.

Many readers, at this point, are staring at their computer screens skepticipickly.  "Sure, Greg, let's *encourage* our students to copy each others' answers.  Who cares about academic integrity, anyway!"  Ah, but read on... the secret to encouraging effective collaboration is...

...stringently requiring a brief, written, *individual* effort before beginning collaboration. 

Without guidance, students interpret "collaboration" as, "sit down in a group and let the smart guy tell us how to do the problems."  Just a few minutes of serious, solitary work -- reading and processing the questions, writing down the relevant equation, attempting to answer the first part -- provide significant context for later discussions.  Now the smart guy is going to face questions from his or her peers:  "Okay, I didn't think to try using energy conservation.  How did you figure that out?"  Or, possibly opposition:  "Didn't Mr. Lipshutz tell us that kinematics isn't valid here, 'cause acceleration is not constant?"  Since everyone has had a chance to process the questions, even those students who don't see physics instantly will develop confidence in their abilities. 

It's hard for someone to cheat on homework if he or she has put forth individual effort before collaborating.  The context for the solution was established by the individual work; other students are merely helping to fill in the details.  It is critical that the teacher avoid the appearance of being the cheating police.  Always assume good faith... I screwed up royally one year when I got overly frustrated with the couple of students who worked too closely together.  Sure, they cheated -- but by publicly expressing my anger and disappointment, I deterred all the honest and earnest students from legitamate collaboration for fear of punishment.  When a pair of students are working too closely together, talk to both of them quietly, and patiently help them understand your expectations -- even if you believe that they're willfully cheating.  Only go into punitive mode when the same students have three or four times openly defied you.  The goodwill you buy with the rest of the class is worth the occasional dumbarse who thinks he's getting away with something.

Fair enough, Greg, you say, but how in the *heck* can I enforce a serious individual effort?  Most of my students will not put forth that individual effort at home, and we're back to the smart guy carrying everyone through the course.

An effective day-school approach, described by several summer institute participants over the years, is to give studnets the last five or ten minutes of class to begin that night's problems, with no discussion or questions allowed.  When class is over, each student's "ticket out the door" is to show you his or her written progress.  You're not looking for correctness, and you're not offering suggestions or criticism.  No, you're just looking for some sort of physics-related writing on a page.  Early in the year, you might see simply the diagram redrawn and the problem rewritten -- fine.  As the course progresses, your expectations might also progress to seeing a relevant equation or principle written down.

I draw a red vertical line down the page on which I pose the nightly problem sets.  Individual work is required on the left; collaborative work goes on the right of the line.  I only grade the final answer, so incorrect individual work is not penalized.  Other methods can be developed as well -- let me know if you have a useful way to promote individual and collaborative work on nightly problems.

I've been most pleased over the years at the bonding that goes on among my students.  Since they have to work with each other, odd pairings sometimes emerge, leading to friendships.  Most importantly, though, discussions about problems with me can focus on settling arguments between collaborators, not on re-teaching yesterday's lesson.

GCJ

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. 

Rules for Turning In Daily Work: EXTENSIONS

Keeping track of extensions on the white board.  The check
mark means an extension was used.  The "Thr" means this
extension is due on Thursday.  The blue boxes
represent exemptions.

One of the primary principles of the "Less is More" philosophy of physics teaching is to assign very little homework, but to expect all homework problems to be done thoroughly and correctly. 

The first challenge to executing the "Less is More" vision is to select the homework assignments carefully.  You only get to ask your class to respond to a few questions -- which ones?  But problem selection is an issue for a different post, or a Summer Institute where I can give you a CD with all my assignments on it to use as a starting point for your class.

The bigger challenge to making "Less is More" work is to get students to pay careful attention to each night's assignment.  Your students might require an attitude adjustment, since previous academic experience has probably not prepared them for nightly homework beyond the level of rote drill.  How do you convince/force your students to take their problem sets seriously?

Of course, I don't have all the answers, and certainly I don't have the only answers.  You do what works for you; in fact, I'd appreciate emails or comments giving different strategies that you have proved to be effective.  I can tell you three tricks I've used that have helped establish the correct tone for nightly work.  Today I'll talk about extensions; the next couple of posts will discuss consultation and collaboration.

"Extensions":  I can not stand excuses, either as a coach or as a teacher.  In baseball, you either made the play or you didn't; sure, analyze to yourself how you can do it right next time, but don't claim that your failure was the umpire's fault or otherwise out of your control.  Similarly in physics, your homework is either ready at the beginning of class, or it's not.  I'm not interested in why.

That doesn't mean students never have a legitimate reason why they didn't do homework.  Of course their lives don't revolve around physics every night.  I'm just suggesting that it is a fool's errand to wade into the judicial role of deciding what's a reasonable excuse and what's not.  It certainly seems obvious that "I went to the hospital with Grandma last night" is legit, while "The Cubs game went into extra innings and by the time I turned off the TV my mom made me go to bed" doesn't cut it.  However, the student with the latter excuse will still be angry and obnoxious when you tell him you don't accept his excuse.  And you're paid to teach physics, not to spend 10 minutes of class every day dealing with excuses, complaints, and appeals.

I assign problems every night, but I allow two, two-day extensions per 5-week marking period.  These extensions can be taken at any time, for any reason -- no questions asked.  The missed problems are due two days later, with absolutely no penalty.  Folks are shocked early on when they come to me with convoluted excuses, because I cut them off and say, "Don't tell me about it, take an extension."  The extensions also solve for "I did it, but I left it in the library so I don't have it right now."  No problem -- take an extension.  It only takes one student having to "waste" his extension this way before people start paying more attention to whether their homework is in their physics binder.

Extensions become somewhat like currency within the class.  Later in the year, after the routine is established, I might set up the opportunity to earn an additional extension, perhaps through a clean-the-lab rota, or by returning a few stacks of graded work to student boxes.  In the last trimester, I offer the chance to convert an extension into an "exemption," meaning the problems never have to be turned in at all.  (An exemption is generally earned only for perfect fundamentals quizzes, or for a week's worth of A-level homework.  See this post.)

What do I do when a studen runs out of extensions, but doesn't have his work?  I bring the hammer.  That's the topic of the next post. 

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.  :-)

Get your students to do your grading for you

In my honors/AP level junior/senior class, our routine is well established.  Everyone does their homework on a nightly basis, knowing that most assingments will be graded.  The class has separated, too, into some top students who get new material and difficult problems quickly, and some lower-level students who struggle with every problem.

At this point in the year, everyone still needs to be doing physics problems on a regular basis.  It's like athletics -- once a football or basketball player works himself into shape, his workout routine can relax a bit, but he still must maintain his fitness.  Even my top students must maintain their physics fitness.  The lower-end students, though, need to continue to review and develop their understanding.

In the third trimester I offer "exemptions" from nightly work to those who earn them by doing well on fundamentals quizzes, or through consistent strong homework.  (I first described the exemption process in this post.)

I've never enjoyed keeping up with the necessary grading in an advanced physics course.  Now that everyone knows how the class works, I can pawn off that drudgerous task -- to students.  Those top students (defined for me as those who earned an A or an A- for the previous trimester) don't need to do the problems every night.  So I've offered each student, in turn, the opportunity to grade problems instead of doing problems.

A student who accepts the offer to grade receives a detailed rubric, a class roster, and a set of papers.  He grades strictly according to the rubric, returning the papers before school the next day.  I glance through his work, and then return the problems.  Easy!

The student grader loves this idea -- even though grading the homework usually takes more effort than doing the nightly problems, it's different effort.  Grading to a rubric is a new and challenging skill for an otherwised unchallenged top academic dog.  These top folks don't necessarily learning anything new by doing more problems; however, they develop an entirely different perspective on physics and physics teaching by having to grade.  (And oh, the heady power... they get to take off POINTS!)

Furthermore, student graders cause the class to be more focused on their problems.  They're so used to me grading their problems that they almost don't notice where they went wrong.  But if their peer graded the assignment, they often pay more attention to common mistakes.  Discussion about common issues goes on outside of class -- and the fastest way to improving physics understanding is to engage in frequent conversation about physics.

Before you dismiss this idea out of hand, many perceived obstacles to student grading can easily be overcome.  After all, an enormous number of teachers have "student aides" who help with filing and grading.  If you're concerned about privacy, have students write numbers rather than names.  If you're worried about perceived fairness, just pledge to glance over the grading and correct any mistakes.  (My students are generally more careful graders than I am, so fairness is not an issue.)  If you're worried about cheating, I don't know what to tell you... the student who grades is himself being evaluated on how well he follows the rubric.  It is in his interest to grade honestly.  Just don't let someone who has had any honor issues be the grader.

Does anyone else have students grade nightly homework to a rubric?  Post a comment and tell us how it works for you.

Poll result: direction of electric field due to point charges

This problem originated with an exercise in Serway, but I've made an important change.  I'll explain that change at the end of this post.  First, answer the question:

The blue charge at the top left produces an electric field that points to the left (toward the negative charge producing the field).  The blue charge at the bottom right produces an electric field that points down the page. 

So the vector sum of the electric fields produced by the BLUE charges is 45 degrees down and to the left. 

The red charge produces an electric field that points up and to the right (away from the positive charge). 

The total electric field now is the vector sum of the fields due to the blue charge, and that due to the red charge.  That total electric field must point in either direction (a) or direction (d) as indicated in the diagram.  Sure enough, the vast majority of poll respondents were split between these two directions.  Which is correct?

The answer hinges on which electric field is bigger:  the one due to the red charge, or the one due to the blue charges?

Each blue charge has the same size charge, and each is the same distance from the position where we're measuring the field.  So each blue charge produces a field with the same magnitude; by vector addition, the total field due to the blue charges will be (root 2) times the field produced by one of the blue charges.

The red charge has the same size charge as the blue charges, but is a larger distance from the relevant position.  So the red charge must produce a field that is SMALLER than that produced by either blue charge.

The field due to the blue charges is larger than the field due to the red charges, and pointing in the opposite direction.  So the vector sum of all these electric fields is pointing in the direction of the larger field, the one from the blue charges, the one in the direction of choice (d). 

Now for the teaching point.  Why did I change Serway's diagram?  The original problem had the red charge as +2Q.  Well, in that case you'd need to think carefully about the red electric field.  The charge producing the field is farther away than the blue charges, but the charge itself is bigger.  To get the answer right, you need to plug carefully into E=kQ/d².  This problem is designed just to check my students' conceptual understanding of electric fields due to point charges -- I want to start simple.  Once everyone can merely find the correct direction of the electric field, once everyone can understand conceptually that a charge farther away from a field point produces a smaller electric field at that point, then we can start doing more complicated gemoetry and algebra.

GCJ

The pejoritive connotation of the word "homework"



Bad dog from discoveryeducation.com



What does the typical American think of upon hearing the word "homework?"  While I have no psychomological evidence of this, I suspect that the word is generally considered to be synonymous with "rote drill," and has a profoundly negative connotation.  On one hand, this is silly -- homework in any subject does not have to consist merely of rote drill. 



(What's wrong with rote drill, anyway?  I don't see the National Association of Music Educators campaigning to stop making violinists learn their scales; I don't see the National Association of Football Coaches minimizing the importance of conditioning, blocking, and tackling drills.  Done properly, and with the correctly limited scope, rote drill at any level of any subject is an important part of learning.  Anyway.  Ahem.)

Physics homework in particular does not, or at least should not, generally consist of rote drill.  Homework problems are used for practice, sure, but students are practicing the skills of creative problem solving, they're practicing to eliminate their crazy misconceptions, they're practicing their ability to explain concepts with reference to a relevant equation... Doing the homework, and moreover doing homework problems seriously and carefully and correctly, is an integral part of learning physics.

Nevertheless, students do not always take homework seriously.  In some upper level physics classes in particular, these very smart students say, I don't need to practice, I can just perform on the test.  (Then they perform poorly on the test because they didn't practice, and they say physics is just too hard.)  How do we get students to pay attention to homework?



Well, it starts (but does not end) with the homework grade.  I put a score on homework problems every night or two.  This score explicitly counts for 30% of students' course grade.  Of course, even with that explicit carrot, my lower level students do not pay appropriate attention to the homework.  They turn in hastily done crap, then just sigh when they see that their answer was wrong.  It never occurs to them to check BEFORE class whether their answers were correct; it never occurs to them that it would be a good idea to understand WHY their answers were wrong.  So the grade itself is a necessary but not sufficient motivator.

At a Virginia AP physics workshop, a teacher reported that he was forbidden by his administration from counting homework more than a token amount toward the course grade.  While I stared open-mouthed in a state of flabbergastation, others chimed in that they were under the same restriction.  But one clever physics teacher in my workshop had a solution...

I don't call my assignments "homework" precisely to avoid the negative connotation.  I use the phrase "problem sets" or "nightly problems," and I regularly make the comparison to the English essay -- I'm asking for the equivalent of a couple of well-written paragraphs every night in an English class.  The woman in my workshop took my phrasing and analogy a step further.

"Just call the homework an 'assessment'," she said.  "English teachers are allowed to count a series of take-home writing assignments as equivalent to a test.  So, we do the same thing.  These problem sets are the precise equivalent to a writing assignment, so they will be counted just as the English department counts them." 

And perhaps that trick might help the students as well as satisfy the clueless administrator.  If a student hears "this counts as a test," his effort seems to double.  I've noticed that students will repeatedly make the same kinds of mistakes on homework problems, but if they get the same exact question wrong on a "quiz" in class, suddenly they start remembering.

Why does the psychology of "homework" seem to work against the legitimate goals of nightly assignments?  I don't pretend to know.  All I can do is make the observation, and then use the observation to the benefit of my class and my students.

GCJ

Buoyant Force problem and demonstration with a crazy answer

A fluid mechanics problem I often assign is based on a problem from, I think, one of the older Serway editions.  It shows a beaker full of oil sitting on a platform scale.  A bar of iron is suspended in the oil from a rope which is attached to a spring scale.  The problem asks:

A 1.0 kg beaker containing 2.0 kg of oil (density = 916 kg/m3) rests on a platform scale. A 2.0 kg block of iron is suspended from a spring scale and is completely submerged in the oil.

(a) Which scale reading should be larger (or should they be the same)? Explain conceptually.

(b) When the iron is in equilibrium, what is the reading in the spring scale?

(c) When the iron is in equilibrium, what is the reading on the platform scale?

Most everyone gets the idea that the platform scale reads a bigger force -- after all, even without considering anything tricky (like fluid mechanics), the spring scale seems to read just the 20 N weight of the iron, while the platform scale seems to read the 30 N weight of the beaker/oil.  A bit more logic with buoyant forces convinces the students that the spring scale must read LESS THAN 20 N, because of the upward buoyant force on the iron.  No problem.

 

Part (b) is similar to a demonstration from class, and numerous example and practice problems in texts.  They know to draw a free body, calculate the buoyant force using Archimides' principle, and use the free body to calculate the tension in the string connected to the scale.  The only halfway tricky part is finding the volume of the iron, which is easily done once the density of iron is looked up.  The buoyant force is about 2 N in this case.

 

Part (c) is the part that causes trouble.  Most of the class, at least initially, says that the reading on the platform scale is just 30 N -- the weight of the oil plus the weight of the beaker.  Others get the right answer of 32 N, but for crazy reasons.  Some come to the conclusion that since the oil "lost" the 2 N buoyant force, that we must return these 2 N to the oil through the reading on the platform scale by conservation of force.  Others simply draw the buoyant force acting down directly on the beaker.  Many make no argument whatsoever, but just add in 2 N, presumably because their friends told them to and they couldn't quite explain it. 

 

I'm glad that so many students have the physics instincts to recognize that 30 N can't be right.  A few will say they made a lucky guess, but I consider such a guess good physics intuition.  However, only a very few students get the justification for why the platform scale reads 32 N.  Do you know?

 

It's Newton's Third Law.

 

The buoyant force is the upward force of the oil on the iron.  Therefore, there must be a downward force of the iron on the oil.  When we consider the oil-beaker system, the downward forces sum to 32 N, including the weights of the oil and beaker, and the third law companion force to the buoyant force.

 

Do you believe me?

 

My students don't, at least not if they didn't get the answer right in the first place. So I set up a similar situation.  The picture at the top (credit to Frederic Lamontagne, WFS class of '11, for the photography) shows a beaker containing a submerged aluminum weight, just like in the problem.  When I remove the weight from the water, the reading in the spring scale increases, but the balance scale goes out of balance!  I have to rebalance the scale to make up for the removal of that downward force of the aluminum on the water.  Since the spring scale reading increased by 0.2 N, I had to add about 20 g to the balance scale reading.  Physics works.

 

Mailbag: Forces on a Table

From Michael Herrin, from Chestatee High School in Gainesville, GA:

I’m having trouble working a problem. It’s from the Cutnell and Johnson’s book chapter 4, and I am curious if you could help point me in the right direction.

Mr. Herrin actually pointed me to a problem in the 5th edition, but I found a slightly different version in the newer edition. In the diagram shown, all pulleys are massless and the surfaces are frictionless. Find the tension in the rope and the acceleration of the masses.

The problem solving process that I teach for Newton’s second law problems is:

1. Draw a free body diagram.
2. Break angled forces into components, if necessary.
3. Write (up-down=ma) and (left-right=ma).[1]

This is a two-body problem; therefore, we start with not one but TWO free body diagrams: Look here -->

Note the tricksiness of the diagram for the 3 kg mass. The rope is pulling up TWICE on this mass: once from the left side of the pulley, once from the right side. So we put two tensions on the diagram.

Jacobs’ law of tensions says “One Rope Equals One Tension.” That’s why I didn’t label the tensions T₁ and T₂, but just T. The tension will be the same throughout.

Now, write Newton’s second law twice, once for each block. The direction of acceleration will be to the right for the 10 kg block, and down for the 3 kg block. (We can see that by imagining releasing the masses from rest, and seeing which way the blocks speed up.)

T = (10 kg)a and (3 kg)g - (T+T) = (3 kg)a

Now, the PHYSICS IS DONE: I have two equations and two unknowns, a and T. Everything else is a known value. All that’s remaining is mathematics.

I think it’s easiest to solve by addition – multiply the first equation by 2, and add the equations together. This cancels out the tension terms; solve to get a = 1.3 m/s²? . Plugging back into either equation, I get T = 13 N. That’s reasonable: the tension is less than the weight of either mass, but is on the same order of magnitude.

Now, ask your students: what would happen to the acceleration if we were to give the 10 kg mass an initial shove to the left. Would the acceleration be greater than, less than, or equal to 1.3 m/s²? Post YOUR answer in the comment section.

GCJ



[1] Well, okay, sometimes we write (right-left=ma), not (left-right=ma). How to know which is which? Determine the direction of acceleration, and start with that direction.

The Milk Problem

Finally, yesterday, I got to teach. On the first day, as discussed previously, I get into real physics: equilibrium situations in AP, position-time graphs in general.

I found a new problem appropriate for the first night’s assignment. I want to give students a sense of how physics will be different from math class, but I’m not yet ready to assign conceptual questions about the current topics – we haven’t gotten far enough. I use problems that require serious reasoning, especially those which lend themselves to order-of-magnitude estimates. The following is based on a problem from the Young and Freedman text:

Milk is often sold by the gallon in plastic containers. You are to solve by calculation and reasoning, not through research.

(a) Estimate the number of gallons of milk that are purchased in the United States each year. (Obviously, your answer should include both verbal and mathematical reasoning.)
(b) What approximate weight of plastic does this represent? Compare this weight to something with which you are familiar.

What an excellent question! Even if students WANTED to try to answer through library or google research, that’s a daunting task… as I found out.

My own reasoning: with 300 million people in the USA, figure about a gallon per week for a family of four. That’s around 70 million gallons per week, times 52 weeks, or somewhere near 4 billion gallons of milk per year sold in the US.

A bunch of googling produced

this article from the US General Accounting Office, suggesting that about 7 billion gallons of milk per year were sold in 2001. Hey! I’m well within a factor of 10, which is the goal of such a problem, anyway.

As for the weight of plastic… I originally guessed about 20 g from an empty milk jug, based on my experience with my hanging weights. This gives 108 kg of plastic for the billion gallons sold each year, or about 100,000 tons.

My chemistry colleague, the Atlanta Cracker, Mr. Paul Vickers weighed an empty half-gallon milk carton, getting 47 g. Woodberry Forest Librarian Phoebe Warmack turned up a claim that nowadays gallon milk jugs are less than 60 g. So my estimate was definitely good enough, because it gives the same ~100,000 tons of plastic as does a weight of 50 g or so.

And this is the whole point of the exercise. Not only do I want my students to gain their first exposure to “Fermi problems” and order-of-magnitude estimation, I also want to make a preemptive strike against the arguments I inevitably hear in class: “You said the answer was 5.9 N, but I got 5.8 N. What did I do wrong?” Or, as always, “isn’t g 9.8, not 10?” Hopefully they will see that a 2% difference is meaningless when making everyday measurements.