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25 June 2012

Online Homework: I don't suggest unless you're desperate

Time to tackle one of the more frequently asked questions... Noah Segal, of Trinity School in New York, writes in to ask:

Have you tried an online homework system (e.g. WebAssign, WileyPlus, MasterPhysics, etc.)? If you’ve had experience with more than one of them I’d like to know how they compare. If you have tried one and went back to paper-based hw, that’d be valuable to know as well.

While I'm not thoroughly versed in the history of online homework systems, my understanding is that they developed in introductory university courses populated by hundreds of students each term.  There, the principle is sound: a professor can't possibly grade 350 homework assignments, and hiring student graders presents issues of cost, logistics, fairness, and competence.  Requiring online submission not only eliminates the headache of grading, it allows the professor to assign work more regularly, and to tell at a glance who is keeping up. Online homework is much, much better for such a professor than the alternative, which is, essentially, unevaluated homework. 

Once colleges started raving about online homework, the software providers decided to penetrate the high school market.  But for high schools, the cost-benefit analysis shifts.  I believe that in virtually all cases, online homework is an expensive, useless toy -- at best, technology for technology's sake; at worst, a lazy teacher's destructive, wrongheaded message about what physics problem solving is all about.

Drive to the heart of the matter:  what's the fundamental point of physics homework, anyway?  I don't assign homework just because it's a school expectation, or because I need to enter a grade into a grade book... homework problems are like football practice, designed to prepare students for the rigors of a game / test.  I'm making the class engage in the difficult, novel process of physics problem solving.  Homework provides a low-pressure chance to try out the types of problems they'll face on tests, but in a setting where collaboration is encouraged and help is available when they get stuck, and where losing credit for misconceptions is not really a big deal.

By grading through a stack of paper homework, I can tell who's keeping up, I can bring in students to extra help who need it, I can enter a grade in the gradebook.  But I can also use my grading to help communicate expectations and good ideas about problem solving.  Johnny didn't include a free body diagram on this equilibrium problem: he lost credit, which sent the message that "free body diagrams are an awesomely good idea" far better than nagging.  Jimbo did everything right, but got the answer wrong due to a calculator error:  he got almost full credit, more credit than Johnny did, sending the message that "the precise answer is subordinate to the process in introductory physics."  Joe got everything right, but his paper was identical to Frank's in every way: both Joe and Frank had to redo the assignment in extra help, and were politely reminded that pure copying is inappropriate and could result in trouble.

Thing is, on webassign, Johnny got full credit 'cause his answer was right.  He wasn't so happy a week later when he couldn't figure out a test problem that couldn't really be done without the free body.  Jimbo was marked wrong, and got frustrated, thinking he didn't understand the physics, even though he had done outstanding work.  Joe couldn't copy off of Frank, 'cause webassign randomized the input values to the problem; so Frank just showed Joe how to plug the different numbers into his final equation, and Joe got full credit for using a calculator blindly with Frank's work.  How that's different from copying, I'll never know.

I've been told that webassign and/or clones will, in fact, support conceptual questions requiring verbal justifications -- students type in their justifications, and the teacher can evaluate them online.  Well, um, that's pretty darned close to grading paper assignments.  If you think that's faster than collecting paper, okay... but I still have concerns about presentations.  Computer input doesn't allow for easy drawing of diagrams or writing of equations.  That's what unlined paper is for.

Now, there can be some benefits to webassign, even in high school.  If you can get past the sign-in issues,* you can check instantly for completion of some routine tasks.  Perhaps assign a quick question in which students need to plug-and-chug into the equation for the period of a pendulum.  Well, there's no escape for your class -- they have no choice but to look up the equation and use it to solve the problem.  You haven't taught any material, you haven't helped gain an understanding of pendulums, but you've made sure that the students have taken the first step toward at least recognizing and memorizing the correct equation, and that's a positive.  Perhaps you can use webassign to pose a couple of quick multiple questions that you would otherwise spend 5 minutes on at the beginning of class.  Great!  That's using technology to effectively replace something that would have required class time. 

I once visited a physics class early in the year, and most of the 40 minute period was spent answering student questions such as "I couldn't log in to my online homework account" and "once we log in, how do we input our answers, again?"

The question is, are these benefits worth the expense?  "Expense" includes not just money, but time and resources as well.  (Physics homework is less daunting to start if it requires only a blank page, not a webassign-enabled, networked electronic device.)  

So Noah, I strongly recommend against online homework system.  Just like learning physics is hard work, teaching physics is even harder.  Grading homework papers is, I think, an unavoidable and essential part of helping our students learn.  While there are tricks and techniques to reduce time spent grading, I don't think it's possible to eliminate or even minimize paper assignments.


18 June 2012

You never know who might read your assignments...

I figure that this blog's readership doesn't overlap much with that of Deadspin, a sarcastic sports website.  So you may not have seen this post regarding a Chicago girl's math assignment. 

Story in brief:  Charles Tillman, an outstanding player for the Bears,* was making a public appearance.  A high school student showed Mr. Tillman her math assignment, which I present [sic]:

The Packers play the Bears 4 times in two seasons.  The Packers, being a much better team have an 80% chance of winning each game.  What is the probability that the Bears win all four games?
What is the probability that the Bears win at least one game?

My comments:  When you're asking a two-part question, phrase it like a two-part question.  Stem, separate line, part (a), separate line, part (b).  Your Englilsh teacher taught you to avoid run-on sentences... well, don't write run-on physics questions, either.  **

Charles Tillman's comments:  I quote partially from what Mr. Tillman wrote on the assignment, as documented by Deadspin:  This is Charles "Peanut" Tillman of the Chicago Bears... The probability that the Bears would win in my opinion is 100%.

* If you're one of those people who ignores American football: The "Bears," known within the city as Da Bears, are a Chicago-based football team who play their games in a spaceship.  The "Packers" are a rival team whose fans wear hats shaped like cheese wedges.  Ya know, maybe you ought to stick with the ignoring football.

**And watch your comma usage.

15 June 2012

Use language that you can expect your class to understand; and E should not equal h nu.

I've been thinking recently about written solutions to problems.  Between the revision of the 5 Steps to a 5 book that's coming out in 12 months, an editing assignment, the recent AP exam, and my own exams, I've been looking at a whole lot of text that tries to explain the answers to problems.

I've done a good bit of problem writing*, and I've discussed problem writing on this blog before.  But I haven't discussed much about writing solutions.  Now, I don't necessarily recommend you have a written solution available to every problem you assign.  But you will, at some point, need to write out the solution to a problem you posed.  Here are three important pieces of advice:

* When you write problems for your class, can you PLEASE get rid of the subjunctive wherever possible?  Say, "Determine the weight of a 3 kg wooden mass," not "If a block of wood has mass 3 kg, what is its weight?"  I thank you in advance.

(1) Use everyday language, words and sentences that you might reasonably expect an intelligent novice to understand.  When explaining the meaning of variables in applying Torricelli's theorem, why say "...where v is the horizontal velocity of efflux from the fluid containment system, d is the depth of interest, and g is the local gravitational field in SI units"?  Use a diagram, and say "v is the speed of the water, d is the water's depth."  If you need to define g at this point in the course, you've got trouble.

Similarly, try to avoid jargon.  I know that the θ term in magnetic flux = BA cos θ is difficult to define.  But it's worse than useless to start the explanation with "Let n-hat represent the outward unit normal vector to a given face of the box..."  Rather, say something like "the flux is biggest when the magnetic field lines penetrate directly into the box face, and zero when the field lines point along the face."

Certainly don't sacrifice the accuracy of a solution.  I ain't sayin' that.  Remember your audience -- you're not writing for your Ph.D. advisor, you're writing for a novice.  Make it short, sweet, and readable.

(2) Don't add extraneous information, however interesting that information is to you or to your favorite professor.  Consider writing the solution to, "Explain what it means to take the component of a vector."  After giving a basic definition, why tell the student that "it is customary to resolve vectors into components on mutually orthogonal axes"?  You just totally lost your audience, 'cause (a) any student who needs to be answering this kind of basic question would not consider an option other than mutually orthogonal axes, much like cows generally don't consider the benefits of stick over automatic shift; and (b) Your readers don't know what "mutually orthogonal" means.  Trust me.  And if they do, they probably belong in a different class.

Other examples:  If your class only studies inviscid fluids, don't add asides about what would happen if viscosity weren't negligible; if you're only considering spherical, not elliptical, orbits, then don't make a throwaway comment in a solution about how an elliptical orbit would behave.

I know some readers will make the (completely reasonable) point that your top students might be very interested in these asides, and that you don't ever want to quelch their curiosity.  Yes, I agree.  Answer those students' questions, turn them on to exciting resources in their textbook and online... but don't confuse the whole class in a written solution in anticipation of a possible question from your smartest student.

(3) Use consistent, clear, common-sense notation.  I don't personally care whether you use d, x, or s for distance.  Just be consistent -- don't mix these variables from one problem to the next.  It won't confuse you, because you're a strong, experienced physicist who recognizes that the notational label is subordinate to the meaning of the physical quantity represented.  No, it will confuse most of your students, who sit there saying, "what is s?  I thought we were looking for the distance the particle traveled."

You'll have to make some judgement calls -- do you use T for the period of an orbit or a pendulum, like your textbook does?  Or is that too easy to confuse with T for tension?  Maybe use P for period?  Either way, just be clear and consistent.

However, please please PLEASE don't use ν for frequency.*  Yes, I know that many textbooks write E = hν and v = λν.  Apparently, according to my colleague, the AP chemistry exam still uses this notation.  The AP physics exam used "nu" until about 10 years ago.

* Every one of you just read that as "vee" until you got further in the sentence.  Right?  Right.  It's a Greek nu, I swear.  And "nu" is a wonderful word to know in scrabble.

Just replace the "nu" with an f for frequency.  You'll not have any notational contradictions, and your students will not be confused.  If your textbook uses the nu, tell them to ignore it and use f.  Everyone will be happier.

10 June 2012

Demonstration: Normal Force

Awesome normal force demonstration
Construction by Frank Anderson
The "normal" force is the force applied by a surface in a direction perpendicular to the surface.  It's called "normal" because, in mathematics, "normal" means "perpendicular."  The word is not being used in the sense of "typical" or "natural"; a normal force only exists when a surface is in contact with an object.

I essentially recite the above paragraph when I first introduce normal forces.  I repeat elements of the definition numerous times, as do you, I'm sure.  Yet I don't think any of us is powerful enough to prevent students calling it the "natural force," nor to stop someone from telling me that a mass hanging in the air from a string must experience a normal force so it doesn't fall to the earth.

How do I bust these misconceptions?  Repetition, and relentless hammering any time a problem set says something blatantly incorrect about a normal force.

An excellent homework problem that I made up one day, but found later in about three textbooks, says:

Describe thoroughly an example of an equilibrium situation in which:

(a) the normal force is equal to the weight of a wooden block
(b) the normal force is greater than the weight of a wooden block
(c) the normal force is less than the weight of a wooden block
(d) the normal force on a wooden block is zero

As with all physics concepts, the final key to cementing understanding is later review in context.  After a few days of equilibrium problems, I introduce equilibrium on inclined planes.  The only real difference between inclines and x-y plane problems is that the weight rather than some other force is broken up into components.  But inclines provide yet another opportunity to remind everyone of the true meaning of "normal" -- the normal force from an incline acts perpendicular to the incline, and NOT directly opposite the object's weight.

For the final inclined plane demonstration, I use the apparatus pictured above, which was constructed by my predecessor at Woodberry, Frank Anderson.  Initially, the bus of weight 2.2 N sits on a hinged wooden plank.  I set the plank at an angle of about 26 degrees.  The bus is connected to a rope that parallels the plank, over which a mass is hung.

We calculate that the string parallel to the incline must have a tension of (2.2 N)(sin 26) = 1.0 N.  Sure enough, I invite a class member to the front of the room to vouchsafe that the hanging mass over the right-hand pulley in the picture is 100 g.

Then we calculate that the normal force on the bus is (2.2 N)(cos 26) = 2.0 N.  This means the plank is pushing on the bus with 2.0 N of force.  

But what if I added a string pulling the bus perpendicular to the plank?  And what if this string had a tension of 2.0 N?  [I carefully and slowly add the 2.0 N weight over the left-hand pulley.  Unseen by the students, the bus's wheels now are barely touching the plank.]  What would happen to the normal force on the bus?  Well, the class reasons, the normal force would be zero; the string's 2.0 N would be sufficient to provide equilibrium.  And what does a normal force of zero mean?  It means no support by a surface.  

So, I ask, what's the point of the plank?  I allow the hinged plank to fall away from the bus... and the bus doesn't move.  You can see the bus's final position in the diagram above.  This never fails to induce a few "wow"s from the audience, even applause every few years.

I leave the apparatus out for a day or two after the performance.  I invariably observe some curious students fooling around with the strings and masses, trying different angles, different tensions, or just trying to reenact the demonstration I did.  

06 June 2012

Teach to the lower-middle of the class, even in AP

A couple years back I asked for advice about teaching Newton's Third Law.  John Burke, Jason Sterlace, and Chad Hodgkins chimed in with what boiled down to, "set N3L up from the beginning by describing every force in terms of interactions."

They were so right, but the method took enormous patience, especially with the brightest students.

I start the year in honors / AP physics with equilibrium problems.*  Following John Burke's explicit recommendation, I expanded my free body diagram rules to include a description of every force in words:  not just w or mg or weight, but "w = the force of the earth on the hanging mass" and "T = the force of the string on the hanging mass."  

* I'll be demonstrating these demonstrations tonight, 6 June 2012, at 9:30 online at the Global Physics Department.

Consider first the pedagogical purpose and effect of this requirement.  Without careful instruction, students do not easily or correctly differentiate between the object experiencing a force and the object applying a force.  Then when they're asked about the third law, they're up a creek.  By requiring these written phrases on every diagram, I'm forcing** everyone to think about interactions on every single problem.  When it came time to formally teach Newton's third law, it took only a day:  just switch the applicant and the applicantee.  For the first time this year, my students truly understood the third law, and hardly ever missed a question about it.

** Hah!

But now put yourself in a (smart) student's shoes and consider his reaction to my requirement.  "Gawd, this is stupid.  I know that tension is the force of a rope.  I just didn't write it 'cause that's dumb busywork.  Then he took off points... Mr. Jacobs is an arse."

And consider your own personal reaction to requirements of this type when you were a seventeen year old high school student.  If you're reading this blog, you were probably a very good student, one who enjoyed difficult classes.  You yourself probably rebelled against this sort of requirement.  Perhaps you might have said,*** "Well, Mr. Jacobs is making us do that because the dumb kids need the endless repetition.  I certainly don't need it, though, so I'll just do things my way and not waste time writing all those words."  Then when your teacher took off points, you got snitty, you argued, you were sullen or sarcastic for a few days.  (You also missed a few more Newton's third law questions than you needed to, but you forgot about that.)  

*** In so many words, anyway, 'cause by 17 years old you were, unlike me, probably bright enough not to say this out loud.  

Fast-forward to today.  Teachers have a tendency to aim their teaching at students who were like them.  

Imagine that you ask the class, "Now, what do I write for the normal force?"  The bright guy says, "force of the ground on the block."  You say, "good," and move on.  

Ten minutes later, you're on another problem with a normal force.  When you were in physics class, you dreaded this moment.  You just knew that the teacher would pick the stupidest guy in class and ask him, "What do I write this time for the normal force?"  And you just knew that he would say something ridiculous like "um............................... um........................ the force of the normal block on the string?"  

So now that you're the teacher, you've pledged not to torture your good students like this.  Perhaps you write "Fn = force of ground on block" and ask, "Any questions?  Everyone understand?  Good."  Or perhaps you even just stop writing the interactions in words, assuming that you've shown the class how to do this already.  And sure enough, your bright students never get that exasperated-with-their-classmates look.  

Nevertheless, if you DID ask a random student to describe the normal force, what are the chances he would get it right?  It's your job to teach him, too, not just the students who are predisposed to becoming physics majors.  Teaching the lower-middle class successfully, while not entirely boring the top students, can be very difficult, but is essential to keeping the class positive and motivated all year.

My own technique is to review in context.  I do ask the question again.  "Billy, what do I write for the normal force?"  However, I'm always asking this kind of question in the context of new problems.  The most-talented students may have to wait a moment for someone else to answer a silly question.  But then we're right back to a new and interesting problem.  The lower-level students realize they can't just tune out, because I'm relentless about expecting them to demonstrate some basic skills.  Thus, while they'll always be a bit behind the leaders, they aren't nearly as far behind as they might have been.  They might need to review difficult topics three or four times over the course of the year, but they'll catch up in the end... because they've been continually drilled on fundamentals.

So when the bright kid says, "Mr. Lipshutz, I know this, why are you making me waste my time writing silly extra words on my homework," how do I react?  I start by wondering why it's such a big deal -- if he knows what to write, why is it so horrible to take a moment to prove that to me?  I might appeal to the idea that I want all of our problems to look similar, so that the class can help each other more easily.  I might be transparent about my pedagogy, giving an impromptu Newton's third law lecture to show the benefit.

In the end, if the student pushes my patience, the answer is, "Because you'll lose points if you don't.  You may drop the class if you think this requirement is overly onerous."  

I'm sorry, 17-year-old self.  I know I hated that answer.  I also hated it when mom said, "Eat your veggies because I said so."  But haven't you told your own kid that on occasion?