Jacobs Physics

Common misconceptions -- parallel resistors

2012-01-27T09:19:00.000-05:00

Parallel resistors each take the same voltage, which is equal to the total.

Now ask a student: "Two 100 ohm resistors are connected in parallel to a 12 V battery. Determine the voltage across one of the two resistors." What does the student say?

Generally, that student reasons, "Parallel resistors take the same voltage. The battery provides 12 V to two resistors equally, so that's 6 V across each." D'oh.

How do I attempt to remedy this misconception? Give everyone the chance to predict and then MEASURE the voltage across several resistors, as in this laboratory exercise. When a student comes to my desk for me to sign off on his correct measurement, I throw the common misconception in his face. I say, "Hey, Will, that doesn't make sense. Seems to me, you've got two parallel resistors here, you should only get half the battery's voltage across each." Will generally has two points to his rebuttal: (1) "That's not the correct rule, Mr. Jacobs, the voltage across parallel resistors is equal to the total." And, most importantly, (2) "That's not what I measured. I get the same voltage across everything."

Just The Facts: circuits

2012-01-25T18:04:00.002-05:00

Been busy busy here, preparing for the USIYPT and writing 6000 words worth of 3rd marking period comments. Colleagues and readers have asked a few times, "what do I need to teach about foo?" where foo is some sort of physics topic in AP, honors, general, or conceptual physics. I've wanted to be able to QUICKLY point to a text or handout that gives a good, clear answer.

Problem is, textbooks tend to cover way too much -- the whole point of the textbook is to be comprehensive so the professor can choose what portions of each topic to teach. The College Board's or the Regents Exam's course descriptions either give too little detail by saying merely "teach circuits", or they go into impenetrable edujargon ("The student should be able to compute the equivalent resistance of a set of series resistors, parallel resistors, or combinations thereof including but not limited to up to 5 resistors connected or not connected to a DC power source, unless there are more than two men on base.")

My colleague Curtis has asked me to write some blog entries giving "just the facts" that I feel are appropriate for an honors or AP introductory physics course. Without knowing it, I had given him a useful blueprint for teaching conservation of momentum in collisions with this post. I gave more detail than he wanted in this fluids lesson plan I wrote for the College Board, but he still found the article a useful basis for answering the question "what do I need to cover in static fluids?"

So today, I will list briefly Just The Facts that I teach when covering circuits in my honors physics course. When I cover this or any unit, I usually start by writing key facts and equations on the board, then quizzing the students the next days to make them remember those facts and equations. Over the course of a week or two, the class develops their ability to reason with the equations and facts, and to solve problems in the topic area.

In circuits, we need to know the following:

Definitions:

* V represents voltage, measured in volts (V). Voltage is measured across a circuit component using a voltmeter.

* I represents current, measured in amperes (A). Current flows thru a circuit component, and is measured with an ammeter.

* R represents resistance, measured in ohms (Ω).

* The symbols for batteries, resistors, ammeters, and ohmmeters

Ohm's Law

Ohm's law relates voltage, current, and resistance by V = IR. Ohm's law may only be used if the current I and the voltage V are experienced by the resistance R. (That means we can't randomly pick a voltage and a resistance from the problem and divide to get current; we must be sure the voltage we plugged in is actually measured across the resistance we're considering.)

Power

Power is given by IV, subject to the same usage restrictions as ohm's law.

Series Resistors:

* The current through each is the same, and equal to the total current

* The voltage across each is different, and adds to the total voltage

* The equivalent resistance is given by straight addition of individual resistances.

Parallel Resistors:

* The current through each is different, and adds to the total

* The voltage across each is the same, and equal to the total

* The equivalent resistance is given by an inverse formula, 1/R = 1/R + 1/R

Solving DC circuits up to 4 or 5 resistors with a single battery

* Simplification of basic resistance networks

* Calculating current, voltage, resistance, and power

* qualitative questions: "when another resistance is added in series, what happens to the current from the battery?"

Light Bulbs and circuits in a laboratory setting

* A light bulb's brightness is determined by the power it dissipates.

* A bulb has a known resistance which doesn't change no matter what the bulb is hooked to.

* An ammeter is connected in series with a circuit element

* A voltmeter is connected in parallel with a circuit element

{The following are also required on the AP exam}

Kirchoff's rules

* Current entering a junction equals current leaving a junction, a statement of charge conservation

* Voltage changes around a closed loop equal zero, a statement of energy conservation
* Deal with multiple battery circuits, but NOT with three-equation three-variable problems

Resistance of a wire based on the wire's properties

* R = ρL/A

Please communicate with me

Is this sort of post useful? I mean, this is everything I teach in circuits. Sure, I haven't discussed the exact methods by which I teach how to solve for current through the 100 ohm resistor, or the lab activities that I do. I actually discuss many of those things elsewhere on the blog; please search. And you may agree or disagree with what I consider fundamental for a first-year physics course. Conceptual physics would probably eliminate the calculational aspects; AP Physics C needs to include RC, RL, and RLC circuits. My question is, is this list of facts and skills a useful starting point for you to figure out your own list of facts and skills for your students to understand? Please comment.

GCJ

A quantitative demonstration with springs... one that DOESN'T work!

2012-01-19T20:45:00.000-05:00

All year long, the majority of my in-class time is spent doing quantitative demonstrations, in which the solution to an example problem is verified live in class via measurement. Each demonstration seems to end the same way: I perform the measurement, we all see that the measurement matches the prediction within 10% or so... everyone exhales, and I say "Physics Works."

It's not a problem, per se, but by November or so the novelty of my approach has worn off. Instead of bright shiny faces anticipating whether or not the experiment will match the prediction, I start to see resignation: "Yeah, physics works, I know, we've done this a million times." I've got to throw a changeup.

Once we've introduced the force and potential energy of a spring, I set up what looks like a routine quantitative demonstration. I hang a mass from a spring, as shown in the diagram. I determine the spring constant via the 5-second method that I discuss in this post. This particular spring (the one on the left in the picture) has a spring constant of about 7 N/m.

Next, I hang 100 g of mass from the spring, and allow the spring to come to rest. Using F=kx, I derive that the mass should stretch the spring by 7 cm; sure enough, a ruler placed alongside the spring shows 7 cm of stretch. Physics works.

Now, I use the ruler to measure an additional 5 cm of stretch beyond the equilibrium position. The question: After I release the mass from rest, what will its speed be when it passes through the equilibrium position again?

[Note to readers before you flame me about these next couple of paragraphs: Keep reading. Trust me.]

I use the force on a spring equation, F=kx, to calculate the force on the mass to be (7 N/m)(0.05 m) = 0.35 N. Then, Fnet = ma, so the acceleration of the mass is (0.35 N)/(0.10 kg) = 3.5 m/s².

I take a brief interlude, if someone asks, to (correctly) explain that with a vertical spring, it's completely correct and most simple to treat it as if it were a horizontal spring, but with the x = 0 position at the place where the mass would hang at rest. In other words, it is acceptable to consider that the spring force kx is the net force, as long as we define x = 0 at the resting position.

Now we have enough information to make a kinematics chart. The mass starts from rest, its acceleration is 3.5 m/s² and it will move a distance of 5 cm. Using the kinematics equation v² = v_o² + 2ax, the speed at the equilibrium position is 0.59 m/s, or 59 cm/s.

"How do we verify this prediction?" I ask the class. They quickly and accurately tell me to place a motion detector below the mass, and to look at the velocity-time graph. I do so, I read the v-t graph, and I see that it says about 40 cm/s. Physics wor------ oops. Physics DOESN'T work.

All year, I've conditioned the class to expect measurements accurate to 10 or 15%. I'm not even getting within 30% this time... that's not a matter of "experimental error," especially when I try again and get the same result; or even more especially when I try it with the other spring, and I'm still off by more than 30%. So, why didn't physics work?

Despite the desperate grasping at straws from some students, someone usually comes up with the right answer: I used kinematics when acceleration was not constant. The force of the spring was only 0.35 N immediately after release. As the spring compressed, the spring force got smaller by F = kx. So the acceleration got smaller. So the mass didn't speed up as rapidly, and ended up going less than 59 cm/s.

How do we solve this problem correctly? Using conservation of energy, of course. Spring potential energy is converted to kinetic energy, 1/2 kx² = 1/2 mv². Solving, I get v = 41 cm/s. Now, physics works.

Side note: Sure, occasionally a student will try to stop me from using kinematics with changing acceleration. My response is a quick "shhh!!!," Dr. Evil Style, but with a smile.

GCJ

Collisions -- how much detail?

2012-01-14T09:42:00.000-05:00

In a typical college physics textbook, the end-of-chapter problems about collisions begin with the simple and move on to the unreasonably complex. I'm frequently asked by AP teachers: How far do I go before complexity becomes "unreasonable?"

In judging the depth necessary for this or any topic, first recognize the motivation of the textbook authors. They're not making a considered, pedagogically sound choice about what material is important, or even about the best way to present said material. No, they quite reasonably want the largest audience possible. The publisher is far more likely to hear "I didn't choose your book because I like to derive the formulas for inelastic collisions in two dimensions with a coefficient of restitution e, which isn't covered" than "I rejected your book because it had too much information." Thus, we get 10³ page* tomes that touch on every possible aspect of "introductory" physics.

* And 10²dollar

Don't ever use the textbook as a sole guide to what's important. Of course that begs the question: how do you figure out what's important when teaching an AP or college-prep high school course? The simple answer is to look at AP exams since about 1996* for guidance. Summarize to yourself the kinds of questions that are asked in each format (multiple choice or free response). Then, certainly if you're teaching AP, be sure to cover the types of questions that showed up; and ignore anything else, even if it's in the textbook.

*1996 approximately marks the transition on AP Physics B exams between the "Shut up and Calculate" era to the "Justify your answer" era. Sorta like when major league baseball lowered the pitcher's mound in 1969.

But what about those who DON'T teach AP, or who aren't particularly fond of the College Board's curriculum or their funny little ways? What if we were to start from first principles, and decide philosophically how much detail SHOULD be included in an advanced high school physics course? Fair question.

I want to cover the basics both conceptually and calculationally. But we don't want to perform any calculations that are so complicated that the mathematical methods outweigh the physics approach. In an algebra based course, I assume fluency in basic algebra, and in using sin, cos, tan. A multi-variable system that cannot reasonably be solved in a couple of minutes is out of bounds; similarly with any trig identity beyond sin/cos = tan. This limit on calculation is born of philosophy -- I never want to do math for math's sake, or I would have gone into teaching math -- and of practicality as well -- if I put a detailed calculation on a test, I can't ask more than one or two questions in a 45 minute period. (Plus I'd be testing math ability, not physics ability.) So here's what I teach about collisions:

1. The fundamental meaning of "conservation" of momentum. Everyone's got to understand the idea of an unchanging quantity; but also how an individual object's momentum can change without violating conservation. We would test this understanding with conceptual questions like "A ball bounces off a wall. Did its momentum change? How is that consistent with conservation of momentum?"

2. Basic computations with momentum conservation in one dimension. A no brainer. "A cart moving 30 cm/s collides with and sticks to an identical resting cart. What is the speed of the carts after collision?" Carts can bounce, stick, be moving in any direction.

3. Definition of "elastic" collision. Although some books and teachers split hairs over the precise definition of elastic, most define an "elastic collision" as one in which kinetic energy is conserved. While momentum is conserved in all collisions, kinetic energy is only conserved in elastic collisions. Colliding objects may not stick together in an elastic collision, though a collision is not necessarily proved to be elastic just because objects bounce off one another.

4. Calculation to determine whether a collision was or was not elastic. Note that this is NOT the two-equation, two-variable calculation to predict speeds of two objects after an elastic collision. No, all I'm suggesting here is that we teach students how to add up the total KE of all objects before a collision, add up total KE of all objects after a collision, and compare. The question generally takes the form "Was the collision elastic? Justify your answer."

5. The vector nature of momentum, the scalar nature of kinetic energy. "Two identical carts move toward each other at the same speed, stick together, and remain at rest. Does this violate conservation of momentum? Does this violate conservation of KE?" Everyone has to recognize that momentum in opposite directions can "cancel out," but that the phrase "kinetic energy in opposite directions" is silly.

6. Ability to consider horizontal and vertical momentum separately in a 2-d collision. Once again, I would not ask for anything that required multi-variable system analysis. But we can arrange problems such that the horizontal conservation of momentum is simple to solve; and where vertical momentum was zero before the collision, so must be zero (in sum) after collision. Usually, such questions will be limited in scope to very simple calculations, or to conceptual questions: "Calculate the initial vertical momentum of the system before collision. What is the system's vertical momentum after collision?" Or, "Is magnitude of the red ball's vertical momentum greater than, less than, or equal to the magnitude of the green ball's vertical momentum? Explain."

That's about it. No coefficients of restitution. No proof of why 2-d elastic collisions always produce final velocity vectors at a 90 degree angle to one another. All of the types of questions above can be phrased in a straightforward manner, allowing for answers in a couple of minutes. The list of six ideas allows for both conceptual and calculational questions. Good.

Equal length spring set

2012-01-10T23:25:00.000-05:00

I hate doing unpaid shilling for deep-pocketed companies. However, when PASCO provides exactly the right tool for teaching a physics concept, as they so often do, I can do nothing but spread the good word.

Take a look at the three springs you see in the picture to the right. All are clearly equal in length and diameter. They seem identical in every respect except color.

But when I hang a 500 g mass from each spring, the springs stretch different amounts. The spring constants can be ranked, calculated, used for prediction of extension under a new load, etc. What a great lab tool.

PASCO sells a five-spring set via the link here. The red, blue, and yellow springs have a book value spring constant of 25 N/m, 30 N/m, and 35 N/m, respectively. In my picture, the yellow spring is slightly less stretched than the blue one, but only slightly. Well, that's okay, because (a) the yellow spring is supposed to have a larger spring constant than the blue spring, and (b) PASCO only lists the accuracy of each spring constant as +/- 5%. It could well be that the blue spring is at the top edge of the 5% tolerance, or about 1.5 N/m too high; the yellow spring might be at the bottom edge of its tolerance, putting the stretch close to, but not quite, identical for each.

Now, for years I've used cheap-o springs that I bought in bulk from random sites online. But these springs get stretched past their elastic limit, intertwined with other springs, and generally destroyed very quickly. PASCO's set of five springs comes in a storage box, and these springs are tough to tangle. Plus the color codes allow you to determine very quickly how carefully a lab group has done an experiment. I'd suggest getting at least a demonstration set of these, if not a class set, unless your budget is lilliputian.

I always argue that physics equipment should be bought over many years, a few pieces at a time. That's not the reality of most schools' budgeting processes, which generally give more money than you know what to do with all at once, but then nearly nothing for years on end. That's simply not practical. You want to be able to buy new toys when you find out about them; don't buy too much at once, spread your purchases out over the years.

Well, my colleague Curtis bought a set of these, and now I'm jealous. Good thing we ordered another set for me for next year... Thanks, Curtis, and thanks, PASCO.

GCJ

Mail Time: Approaching energy concepts in junior-level general physics

2012-01-06T20:13:00.001-05:00

Erik Born, a colleague here at Woodberry, teaches our junior-level general physics course. We aim this course essentially at the New York Regents exam, with a few tweaks of topics (e.g. we teach an astronomy unit, and we don't teach electric or magnetic fields). Erik wrote to me the other night:

I was wondering if you can give me a short overview of how you approach energy concepts. I am used to starting with work, and moving from that into energy, but I'm following the order of your problem sets, which has started out with introducing KE and PE first. I was wondering if you could give me some advice about conversions between KE and PE without talking about work or total mechanical energy. Maybe you have a specific blog post on it?

Well, I do now, I suppose :-)

At the AP / Honors level, Erik knows that I introduce the definition of work, and then my own version of the work-energy theorem: W_NC = (KE_B – KE_A) + (PE_B – PE_A). You can see my reasoning for why and how I use this formulation at this post.

But at the general level, I approach energy concepts very differently. I ask the class to state and write out all energy conversions IN WORDS.

For example, a ball drops to the floor -- how fast is it going? They must start by writing, in longhand, (gravitational potential energy) converts to (kinetic energy).

Or, a waterskier takes off from water level at 14 m/s, and ends up going 13 m/s at his max height. They must write: (kinetic energy) converts to (gravitational potential energy) and (kinetic energy).

If a block is moving fast and stops on a rough surface, they must write (kinetic energy) converts to (thermal energy). If you want them to call this (kinetic energy) converts to (work done by friction) that's fine, too.

We haul up a block by a rope: (Work done by the rope) is converted to (potential energy).

In each case, once they write the words, then they translate the words into an equation: KE = 1/2 mv² , PE = mgh, spring PE = 1/2 kx², and work = Fd. Then they solve for whatever needs solving.

Erik continues: How do you deal with positive and negative work?

In regular physics, I *don't*. If we're writing the energy conversions in words, like I described, then we don't have to worry about positive and negative work. The sign of the work comes out in the wash of the equation written from the description. Examples:

Block is moving, comes to rest on a rough surface. (kinetic energy) converts to (work done by friction). * 1/2 mv² = (Ff)d. Yes, I know that kinetic friction does negative work, but that's not necessary in this formulation. The equation and statement in words provide both conceptual understanding AND a path to solution for any relevant value, with no negative signs involved.

* I let them know that a source of "thermal energy" is "work done by friction." The distinction isn't important at this level; however, recognizing that the relevant equation for thermal energy here is (force of friction) x distance *is* important.

Block is pulled up by a rope. (Work done by the rope) converts to (gravitational potential energy). (tension)d = mgh. Once again, it's not important that work done by the rope in this case is positive: The sign comes out in the wash.

As a comparison for a teacher (not for the students), many textbooks teach a similar approach to calorimetry: don't use positive and negative signs, write out the heat gained or lost in words. For example, write (heat lost by hot iron) = (heat to raise liquid water to 100 degrees) plus (heat necessary to convert water to steam). Then mcDT_iron = mcDT_water + ml_steam.

Hanging Mass on an Incline lab

2012-01-04T10:00:00.000-05:00

Mr. Johnson shows off his hanging mass setup

In my general physics labs, we follow a familiar formula each week.:

(1) Students collect data, constructing a linear graph as they go.

(2) They take the slope of a best-fit line using far-separated points on the line that are not data points, including units on the slope.

(3) They use a relevant equation to relate the physical meaning of this slope to a measurable physical quantity.

That's it. I keep things as simple as possible so as to work on just these three skills. The trick is, of course, finding straightforward yet interesting experiments which lend themselves to this approach. Oh, and these experiments must stick within the topic areas in general- (approximately Regents-) level physics.

The procedure is essentially the same each lab day. I demonstrate a method of data collection. I write on the board the graph that students are to make. Students collect and graph their own data in groups of two. Once I've approved a group's graph, then I hand them a two-page homework assignment for them to work on either the rest of the lab period, or that night if they need more time -- no one leaves early.

Ideally, I'm designing an experiment such that I know what the value of each group's slope should be, but the students do not. This is a bastardized version of the "recurrent lab" as described by Mikhail Agrest. Students earn credit either for predicting something using their slope, or for matching their slope to an independent measurement.

So, Greg, give us an example of such a laboratory activity. Sure -- see the picture. I have students set up an inclined track, on which they place a Pasco cart. The cart is connected over a pulley to a hanging mass. The hanging mass is adjusted until the system hangs in equilibrium. The angle of the incline is what they are eventually going to predict; I surreptitiously come around during the period to measure each incline with my iPad clinometer app.

We graph the mass of the hanging stuff on the vertical, with the mass of the Pasco cart on the horizontal. Some mass is added to the Pasco cart, the hanging mass is adjusted to equilibrium, and another data point goes on the graph. Rinse and repeat for an easily obtained straight-line graph in about 30-60 minutes (including setup and cleanup).

The homework assignment based on this lab activity is available here. In sum, students take the slope, and then are guided to identify the slope as the sine of the incline's angle. Most groups easily match my measurement.

This is one of my better lab exercises, because (a) it fits the formula we've been using all year with no deviation, (b) it allows for accurate prediction of a measurable but initially unknown quantity, and (c) it reinforces the content in the problem solving portion of the course. Try it... post comments or questions.

GCJ

The first first law assignment -- qualitative justifications of signs

2011-12-31T13:35:00.000-05:00

The drawing shows a PV diagram in which a gas expands at constant pressure from A to B, and then goes from B to C at constant volume. Determine the signs of ΔU, Q, and W for each of the two processes. Justify your answers.

This is the first PV diagram question which I assign in my honors or AP course. We have discussed the definitions of the variables in the first law, and how to determine the value of each variable from the PV diagram.*

*Including the fact that the value of Q cannot be determined directly from the diagram without using the first law.

The solution, in the language and logical order that I prefer:

A-B:

ΔU is positive, because the product of P and V is larger at point B than at point A.

W is negative, because the volume increased.

Q must be positive by the first law, Q = ΔU - W, (+) = (+) - (-)

B-C:

ΔU is positive, because the product of P and V is larger at point C than at point B.

W is zero, because the volume did not change (or because there is no area under the curve from B to C)

Q must be positive by the first law, Q = ΔU - W, (+) = (+) - (0)

Note that I'm not yet asking for any quantitative answers. That's too much for the first problem set. I try to get my class totally comfortable identifying facts, assigning signs, and using the correct vocabulary for each term before I ask for numerical answers.

Also, look how straightforward the answers. ΔU is (3/2)PV; W is the area under the curve; and Q is determined from the first law. It takes a lot of effort on my part to get students disciplined enough to used this approach. They invariably want to, somehow, somewhere, talk about "molecules moving around:" "Q is positive because when the pressure increases, the molecules have to move around a lot faster, leading to more heat." Such a statement is worse than nonsense. PV diagrams refer to macroscopic systems, and must be interpreted with reference to relevant equations and facts, only.

This year, anticipating the difficulty of convincing students to use a disciplined, macroscopic approach to the first law of thermodynamics, I promised that the penalty for any reference to "molecules moving around" in a first law justification would earn double points off. And sure enough, I had a student who lost double credit on this very problem. But only one this year...

Summer 2012 with Jacobs Physics

2011-12-28T14:30:00.000-05:00

Several folks have asked about my summer schedule. As usual, I'll be running several AP summer institutes.

Do note -- you don't have to be teaching AP to come to an AP summer institute! We discuss far, far more than simply "How do I teach my students to game the AP exam." In fact, we don't discuss gaming the test at all. Rather, we discuss physics teaching as professionals.

I share what has worked for me, and for other teachers who have taught me; participants share their own ideas. I do quantitative demonstrations on a variety of topics. I share my tests and problem sets, for all levels that I teach. You get to take home a CD containing not only some of my own handouts and ideas, but also the official College Board released exams -- with rubrics. All of these materials can be used at every level of physics teaching.

Want to sign up? Here's where I'll be:

June 25-29, Richmond, VA (through VASS, Virginia Advanced Study Strategies. I don't know whether this one is open to the public or not -- send an email to the link at the VASS website, and ask!)

July 10-13, Kennesaw State University, Georgia (This one's four long days rather than five short days.)

July 16-20, North Carolina State University, Raleigh

July 30-Aug. 3, Manhattan College, New York City (Manhattan College is in The Bronx.)

Just the basics, not the sources, of electric, magnetic fields

2011-12-26T21:22:00.000-05:00

Electric and magnetic fields frustrate me each year. They're abstract, leading to few simple quantitative demonstrations. They always seem to take their turn in the dark, cold, depressing months of January and February.* And students are perennially confused between the source of an electric or magnetic field, and the victim of said field.

* Except that these were the most wonderful months of the year when I taught in Florida.

Ah, but this year I'm going to do something about that last point.

The AP Physics B redesign is said to be emphasizing "big ideas," physics themes which resonate beyond a particular topic. For example, the idea of a conservation law permeates physics from mechanics, to rotation, to electronics, to nuclear physics... It takes a substantial level of real physics understanding to explain what quantities might be conserved in a specific situation, and why they are conserved, and just what exactly it means that a quantity is conserved. Once the concept can be clearly and thoroughly articulared, the algebra involved in applying conservation of foo is generally trivial. And so it goes with the concept of the field: Once students get comfortable with the idea that a field of any sort is used to calculate the force on an object, using that force in a Newton's second law calculation becomes trivial.

Students become unintentionally familiar with the gravitational field g as the "conversion" between kilograms and newtons -- one kilogram on Earth weighs 10 N, but on Mars weighs only 4 N. W = mg serves as what I call the "bible equation" for the gravitational field -- it relates the force on a massive particle to the gravitational field. Once that gravitational force is known, this force can be drawn on free body diagrams and used in a newton's second law calculation just like tension, friction, or any other force.

Now, those of us who are experienced physicists know that the source of this gravitational field is the enormous mass of the Earth applying on all other massive objects, via Newton's law of gravitation F = GMm / r². But I ask you... who in his or her right mind teaches first-year physics students F = GMm / r² BEFORE W = mg? No one. Don't be silly.

So why, why, why does every textbook in the universe teach F = kQq / r² before F = qE?!?

For many years, I've begun electrostatics with the definition of an electric field via F = qE, completely ignoring what might cause such a field. A field simply exists in space. If a charge is placed in the field, that charge experiences a force qE in the direction of or opposite to the field, depending on the sign of the charge. Only much later have I broached the confusing subject of fields produced by point charges or parallel plates.

Not only has this approach been effective in getting students to succeed on AP Physics B - style electrostatics problems... in their second year calculus-based AP Physics C course, my students have little trouble with electrostatics. We can calculate an electric field using superposition, Gauss's law, calculus, whatever -- everyone understands that, once we have an electric field from any source, F = qE.

Currently I'm teaching Honors Physics I, which is intended to anticipate the AP Physics I redesign, rather than AP Physics B. The "big idea" of a field permeates several different physics topics, and so is ripe for conceptual investigation. In Honors Physics I, I will ignore sources of electric fields completely. I want the class to be able to explain what a field does to a charged particle, not necessarily how the field came to be. And I'll do the same thing with magnetic fields: We'll discuss the bible equation F = qvB, and the right hand rule for the direction of the magnetic force on a charged particle. That's it. Magnetic fields due to current-carrying wires can wait for Physics C.

I encourage you to try ignoring the source of the electric or magnetic field. If you're teaching to an exam (i.e. AP or Regents) that requires discussion of a field's source, throw that in as part of review at the end of the unit, or even at the end of the year. Electricity and magnetism will never be easy for first-year students, but by simplifying the initial introduction to fields, you'll get better results long term.

How many soda bottles in Brian's raft?

2011-12-21T08:17:00.000-05:00

The question from Dec. 14:

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.

While the majority does not always rule in physics, in this case "they" were right on. My reasoning:

Call Brian 80 kg or so. His weight is then 800 N. That weight must be supported by the buoyant force, which is equal to the density of water times the displaced volume times g. If each bottle is fully submerged, it displaces 2 L, or 0.002 cubic meters. The buoyant force created by one bottle is then (1000 kg/m^3)(0.002 m^3)(10 N/kg) = 20 N. To get to 800 N at 20 N per bottle, you'd need about 40 bottles.

What if Brian's not 80 kg? Well, as I have to point out to people, 80 kg is a reasonable estimate for Brian, but college guys who drink soda are often heavier; and, in a recent development of Haverlore, I have discovered that Brian supported a second person on the raft as well. Furthermore, even if Brian were 75 kg, 40 bottles would have to be nearly fully submerged, leaving essentially no safety margin, and getting Brian's feet* wet. This is an order of magnitude estimate... why not double the estimate to 80 bottles or so? Then the bottles are in the neighborhood of halfway underwater. Brian can sit dry, he can bring a friend, he can eat at the COOP** all he wants; 80 bottles will support him.

* Or more likely, his tuckus

** The yummy snack bar... it used to be too expensive for me, but now I find out that students can make their parents pay for the COOP as part of these newfangled meal plans. Ach, and nowadays students can access email from their rooms, too.

What about the weight of the soda bottles themselves? Some students will tell me "the soda bottles are of negligible weight." Okay, but are they? What's the evidence?

Some students found that an empty bottle has mass about 40-50 g, for a weight of about half a newton or so. That means that each bottle will only support 19.5 N of Brian rather than the 20 N previously conjectured.

Does that mean, as some say, that the proper answer is "41 bottles?" No, certainly not. As discussed in the previous paragraph, the uncertainty in Brian's mass, and in just how much of the raft is submerged, far outweighs this 3% change due to the weight of the bottle. The answer is still somewhere around 80 bottles, or better yet, some dozens of bottles.

Group work and in-class problem solving

2011-12-18T18:09:00.000-05:00

How do you arrange for effective group work in class?

Last week, at the tail end of my class's study of static fluids, I had to miss a class for a debate tournament. I decided to borrow a page from my colleague Curtis Phillips, who has been patiently teaching freshmen how to collaborate effectively in physics. Occasionally, he puts his students in pre-assigned "pods" of three desks each, and assigns a problem for the class to work on. He collects the assignment from everyone; however, he randomly chooses a single paper from each pod to grade. All three members of the pod earn whatever score is earned by the random paper.

Now, I remember being furious at such arrangements in middle and high school. Too often, I'd get an idiot in my group who didn't give a rip, and so was unwilling even to make an attempt; or occasionally I'd have a "partner" who enjoyed doing a poor job just to make me angry at him -- he didn't care about a silly score on a class assignment, but he thoroughly enjoyed watching me blow my top, then impotently appeal to the teacher for help.

And there lay the problem with such an approach. The teachers who attempted this "group learning" method were not invested in the idea -- I found out that these teachers had been directed from above that they were to employ group learning methods, which of course would improve the performance of the lower-end students. In practice, the teacher would assign the assignment and then sit at her desk grading papers. My complaints about disinvested students fell on deaf ears... "I'm sorry, Greg," the teacher would say condescendingly. "In the working world you will be forced to deal with different types of people. You must learn to get along."*

* In the working world, of course, the analogous situation would result in either (a) the idiot being fired by a competent boss, or (b) me leaving for a different job where the employees and bosses do their respective jobs. Interestingly, now that I've been in the "working world" for a quarter-century, I've been involved with both situations (a) and (b).

Despite my own crapulent experiences with "group learning," the approach Curtis proposed can be sound. The teacher simply must, must, must be personally invested in the students' work.

I have seen Curtis perform his magic. His groups of three are usually either hunched over, hard at work; or they are engaged in animated discussion. And where's Curtis? In the middle of the room, his wide eyes manically scanning the class as if he were at Helm's Deep watching for the approaching Orc army. A student slumps in his desk; Curtis asks him a question about the problem. A student starts talking about the upcoming semiformal; Curtis's adroit verbal manipulation lets him know, in so many words, to shut up and get back to work.

More importantly, he has no tolerance for the student who just doesn't care. Now, you can propose what to do with such a student. Give him an automatic F; remove him from the classroom; call his advisor or his parents; give him 50 lashes with a wet noodle. I honestly don't know what Curtis would do with such a student, and neither does his class. Everyone knows that Curtis has nuclear tools at his willing disposal, and so they try to avoid making Curtis resort to them.

But effectively moderating a problem solving session requires more than just a state trooper-style presence. Especially since he teaches freshmen, Curtis is continually teaching the students how to collaborate effectively. He's showing them skills we take for granted in our own or our seniors' academic lives. For example, he'll say, "You look like you're stuck. You haven't written anything down for ten minutes. Why not ask your neighbor there for help?" Or, "Okay, Joe, you've told John how to do the problem. Now, John, you try it for a few minutes by yourself. Don't ask Joe for help again until you are well and truly stuck." Or even, "All three of you are working together. So you should either all have the same final answer, or you should be arguing vehemently. Which is it gonna be?"

What I did: In my own 11th and 12th grade college-level class, I gave them a fun problem (see the post about the soda bottle raft.) I insisted that everyone work silently for 5 minutes until everyone had written down a reasonable approach. After 5 minutes, collaboration was unlimited amongst the entire class. They were told that I would collect a problem from everyone, but that I would grade only one, chosen randomly. Everyone would earn the same score.

Afterward, I graded the randomly-chosen problem, cut off the student's name, and posted his work on the bulletin board with the grade. Two of my sections earned essentially full credit. One section earned just 1/10, though. And interestingly, that student's work has been simply fabulous over the past week -- I think he took a bit of ribbing from his friends.

Soda Raft Question

2011-12-14T11:37:00.000-05:00

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!

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

2011-12-12T11:49:00.000-05:00

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!"

Laboratory quiz question: pressure in a static column

2011-12-07T09:16:00.000-05:00

A primary laboratory skill, one that is frequently tested on the AP exams, is determination of the physical meaning of the slope and intercept of a linear graph. My own approach to such a question is to solve the relevant equation for the vertical axis of the graph, then to identify the variable representing the horizontal axis. Anything multiplying this variable is the slope of the best-fit line; anything added to this term is the y-intercept. We religiously go through this process of identifying the slope and intercept of a straight-line graph in every laboratory activity.

However, just doing laboratory work isn't enough to develop this skill. In a 90 minute lab period or a lab report, a large subset of students will parrot their friends' answers or my suggestions without sufficient understanding.

So then, how do I check for "sufficient" understanding? I give quiz and test questions that ask directly about the physical meaning of graphs that the class hasn't seen before. For example, a recent "justify your answer" question showed a graph of weight on the vertical axis, and mass on the horizontal; what is the physical meaning of the slope of that graph?

It was instructive to read the justifications. Most folks got that the slope is g, the gravitational field. The stronger students recognized the relevant equation weight = mg; since weight is on the vertical and mass on the horizontal, whatever is multiplying m must be the slope.

The weaker students, though, got the correct answer reasoning from the units of the axes. The vertical axis, they said, "was" newtons. The horizontal axis "was" kilograms. Since we've shown that g has units N/kg, the slope must be g.

I've got to force these weaker students to get away from the crutch of using units to determine a slope's meaning. While such an approach is better than nothing, often the units of the slope won't obviously match any known quantity; or, a factor of 1/2 or 2π will be missed. It's not like the method I'm proposing (of first writing the relevant equation) is too difficult for anyone.*

* The correct method does require remembering or looking up the correct equation, though, which is sometimes an obstacle; but that's a separate issue.

Below is a quiz that will help practice the skill of identifying the physical meaning of a slope. Note that, by this point in the year, if we just graphed GAUGE pressure vs. depth, most of my class would have little trouble seeing that the slope is ρg. The addition of the Po term in the equation for pressure in a static column causes difficulty.

1. In the laboratory, you are given a tall graduated cylinder full of fluid, along with a pressure probe which reads absolute pressure. You submerge the pressure probe in the fluid and record the reading in the probe P at various depths d below the surface. The pressure at the surface is 1.01 x 10⁵ Pa.

A graph is made of P on the vertical axis and d on the horizontal axis.

(a) Is the graph linear, or curved?

o Linear

o Curved

(b) If the graph is linear, explain how the density of the fluid r could be determined from the best-fit line. If the graph is curved, explain what quantities could be graphed in order to produce a linear graph from which the fluid density r could be determined.

Want to referee a physics fight?

2011-12-03T15:10:00.000-05:00

Okay, that title is overly dramatic. Sorry. But it's kinda technically accurate...

At the United States Invitational Young Physicist Tournament, teams present their solutions to four low-undergraduate research problems. Then, the presenting team is evaluated and questioned by another team! This process is called a "physics fight," a methodology developed by the International Young Physicist Tournament and adapted for the American version of the tournament.

The actual event resembles a combination of a thesis defense crossed with a scientific conference presentation crossed with a Lincoln-Douglas debate. Teams are judged not only on their physics knowledge, but also on their ability to engage in questioning and discussion in a search for the truth of the problem.

Want to be a juror? See, I'm the president of this tournament's sponsoring organization. We are in the process of recruiting jurors to referee these physics fights. If you're a high school physics teacher or college physics professor, then we want YOU. Everyone who has ever seen this USIYPT in action has fallen in love with the friendliness among participants, the outstanding physics, the poise of the contestants, and the professional camaraderie amongst teachers, students, and jurors. (Several invited jurors have liked it so much they've brought a team the next year.)

This year, the USIYPT will be at Oak Ridge Associated Universities in Oak Ridge, TN on February 3-4 2012. The kicker is, the organization is supported only by student fees, for now. We can't pay an honorarium, or even for a hotel room.* But if you can get to Oak Ridge, we'll get you on the field for our intellectual Super Bowl.

*Not yet, anyway. Anyone know a company or non profit that wants to grant us a budget for this thing? :-)

Go to usaypt.org for further details about the tournament; email me at greg.jacobs@woodberry.org if you'd like further information or a formal invitation as a juror. (And I'd be happy to talk about physics fights at length on the phone as well if you'd like.)

GCJ

Static Fluids with Quantitative Demonstrations -- Detailed Class Notes

2011-11-30T08:55:00.000-05:00

What's the buoyant force on a lionfish? I ain't doing this
demo, but you can see the demonstrations I do do at this link.

Regular readers are probably aware that my typical class period consists of one or more quantitative demonstrations -- I don't just solve an abstract example problem from a book, I physically set up the example problem as an in-class experiment. Any calculation we make in class is verified by measurement.

One of the questions I'm most asked is, "Do you have a list or writeup of all of your quantitative demonstrations?" Unfortunately, I don't. When a publisher (or the NSF) offers me a five figure advance, I'll consider writing a book.

Until that glorious day, you ask, where do I look to find quantitative demonstration ideas? Well, start by searching through this very blog, of course. Sign up for one of my AP Summer Institutes (I'm doing four, I think, in 2012). Every time you're choosing an example problem to use in your class lecture, think, "could I set this up in my classroom?" Use a homework problem as the basis for a laboratory activity, and make your students create the setup. Talk to other physics teachers, including those who are listed as followers of this very blog.

Now, if you'd like an extraordinarily detailed description of what a class with quantitative demonstrations might look like, check out this piece I wrote for the College Board a few years ago. They asked me to provide a "lesson plan" for AP-level static fluids. I described each experiment, each check-your-neighbor question, each measurement that I make during class. (If you've been to a summer institute, you'll recognize a few of these demonstrations.)

Do you have a quantitative demonstration that you use in class? Tell me about it. I'm open to guest posters on this blog...

Vernier Video Physics for the iPad 2: A Winner

2011-11-27T10:57:00.000-05:00

For Thanksgiving, my family headed to a very nice cottage in West Virginia. It had a number of wonderful amenities, not including internet, television, or cell phone service. That was okay by me, because I spent several days grading exams and writing comments. It’s amazing how much more focused I can be when I don’t have the option to check my email real quick, or to just see what the score of the game is. It’s also amazing how much more boring it is to grade papers without any sort of electronic distraction. Guh.

My eight year old occupied himself for hour after hour with a hand-held Pokemon video game. In the rare moments when he tired briefly of having Waylord fight Trogdor (or whatever), he explored this loaner iPad 2 that I got from my school’s library.

For those who have followed Jacobs Physics for a while, you might remember that a year and a half ago my school provided me with an iPad, for use in physics class, while broadcasting football and baseball, and at debate tournaments. My summaries of the iPad’s usefulness can be found here and here.

Now, before you say “oh, my school could never afford that” or “what an extravagant place you teach at, Greg!” think about the actual cost-benefit analysis. I don’t use a smartboard – I tried it for a year, and found out that I never used any features that couldn’t be done with a dumbboard.* I’ve found the iPad to be worth far more than the smartboard; yet, the iPad generally costs less than half a smartboard. If your school can afford computers and smartboards, it can afford an iPad for the physics department. The question becomes, is such a purchase worthwhile?

* A “dumbboard,” as I learned over the summer, refers to a computer projector shining directly onto a whiteboard. Annotations to the screen can be done with dry-erase marker.

Now that the iPad 2 includes a video and still camera, the answer is unequivocally “yes.” Our department has had a high-quality digital camera for years. When I want to take a picture of an experimental setup, I walk down the hall to get the camera. I take the camera out of the bag, remove the lens cap, take the picture**, remove the USB cord, replace the USB cord and remove the correct USB cord, insert card into the card reader, click a mouse a few times, and voila – there’s the picture. Finally.

**often the shutter won’t press without the magic incantation that goes, “Why the #$@@ won’t the dang picture take? Is it on autofocus or something?”

With the iPad 2, the picture isn’t nearly as high resolution. However, the picture taking process is reduced to (1) press button, (2) email picture. That capability by itself might be worth the price of the iPad 2. Think of all the measurements that can be made live, in class, with instant photography!*** And, portable skype is nothing to sneeze at. I can show an equation during a live video chat; I can even show a live experiment to a remote viewer. Not that I’ve done that yet, but if you would like to listen in to my honors or research class via skype, just let me know.

*** Of course, those of you who were smart enough to purchase smartphones have probably been doing this for years. I still have a landline, and an office phone. Sorry.

And with the Vernier video physics app, the revolution is complete. Vernier’s logger pro software has always allowed easy frame-by-frame video analysis on the computer. But the time to upload video and then to convert it to a usable format has always been an annoying barrier to using this feature except for research purposes. On the iPad 2, the process is simple and quick. The video collection can be done within the Vernier app itself – no saving and importing videos unless you want to. The interface is easy to use and understand. Within a few minutes, you can have position- and velocity- time graphs for any captured motion.

As a testament to this app’s ease of use, I produced a useful video and graph within minutes of first opening the app, without reading any sort of instruction manual. Then, I showed my 8 year old how it worked. He spent a couple hours taking and analyzing videos, proudly showing his grandmother that the dropped ball was going 600 cm/s, but the dog’s nose only went 150 cm/s. I approve.

For $2.99, I can't imagine a more useful physics app. Now, Vernier, your challenge is to make all your probes work wirelessly with an iPad version of logger pro. Go for it.

Two Masses and a Pulley, and a New Misconception

2011-11-17T19:09:00.000-05:00

The badly sketched picture to the right shows a classic mechanics problem. Two equal masses are connected by a string over a pulley. In this case, the table is frictionless.

Typically, a student is asked to determine the tension in the rope and the acceleration of the masses. Great -- that's (mg)/2 and g/2.* This problem is richer, though, than a mere calculation might suggest. Take a look at a quiz I gave the other day:

* The quick way to get this is to consider both objects as a single system. The net force on that system is the weight of the hanging mass, mg; the mass of the system is 2m. By Newton's second law, a = g/2.

1. A block of mass m is attached over a pulley to another hanging mass m, as shown above. The surface is frictionless. The system is released from rest.

(a) What is the direction of the hanging mass’s acceleration? Explain.

(b) Is the acceleration of the hanging mass greater than, less than, or equal to g? Explain.

2. A block of mass m is attached over a pulley to another hanging mass m, as shown above. The surface is frictionless. This time, the top block is given an initial velocity to the left and released.

(a) What is the direction of the hanging mass’s acceleration? Explain.

(b) Is the acceleration of the hanging mass greater than, less than, or equal to g? Explain.

Ideally, 1(a) is answered with a kinematic approach -- the hanging mass is speeding up and moving down, so acceleration is also down. For 1(b), I've defined "free fall" as the situation in which no forces besides weight are acting. Since a tension acts upward on the hanging mass, the mass is not in free fall and the acceleration is less than g.* And in 1(c), acceleration is downward, so net force must also be down. That means down forces greater than up forces, so the tension is less than the weight.

* Okay, sure, if the upward tension is twice the block's weight, the acceleration could be g, upward. That's highly unlikely in hanging-block-and-pulley problems.

Of course, question 2 is identical to question 1! The hanging mass is moving up but slowing down, so acceleration must still be downward. (Or, one could argue that the block on the table still experiences only one horizontal force, that of tension, so its acceleration must be to the right; the blocks must move as a unit, so the hanging block has downward acceleration.) Once it's established that acceleration is still down, questions 2(b) and 2(c) follow as in 1(b) and 1(c).

By far the most common misconception here is that the net force must be in the direction of movement. A student will commonly get question one reasonably correct, but then say "the block is moving upward, so up forces must be bigger than down forces." This question is just one more salvo in my arsenal aimed at that piece of nonsense.

Another typical misconception is that in question 1, since the hanging block is falling near earth, its acceleration must be g. That's taken care of with a request to state the definition of free fall and a sheepish look from the student.

And, a common mistake is to justify (a) and (c) with circular reasoning: The acceleration is downward because the weight is greater than the tension; the tension is less than the weight because the acceleration is downward. This student doesn't earn full credit, but I'm not worried so much about his comprehension.

I discovered a new misconception today, though. One of my brighter students said acceleration was equal to g, and he stated the definition of free fall accurately. He asked, "since the surface is frictionless, the block on the table doesn't require any force to move. So why won't the rope will be slack, the tension zero, and gravity the only force on the hanging block?"

At first I was flummoxed. I set up two carts on my track, and showed him that the string was in fact not slack. But why on earth would he think that no friction leads to a slack rope?

In further conversation, I discovered that he was referring back to our class's multiple conversations about how no net force is necessary for motion at constant speed in a straight line. A mass on a frictionless track, once moving, keeps moving, even without any tension to pull it. My student wasn't processing that this block on this surface was accelerating, not moving at constant speed. Once I pointed out how the blocks must move together, and therefore accelerate together, he got it.

How much is this post worth?

2011-11-15T08:43:00.000-05:00

Woodberry Forest 21, EHS 12 in 2011. But this picture
is from 2010.

Students, and too often parents and colleagues, usually approach a high school course as a point-earning game. While points and grades must exist -- they *do* motivate, and besides, you're not gettin' very far with your boss if you tell him "I'm not giving grades this marking period, okay?" -- you can send a consistent message that you are an impartial arbiter in the game, not a teammate or an opponent.

Consider the most commonly asked question in class at my school this time of year. These are the High Holy Days at Woodberry Forest -- last Friday night was the bonfire*, and Saturday was The Game, a football match against our chief rival school. This week marks review for exams, which start on Thursday.

* Think the PAGAN ritual scene from the Dragnet movie, probably without the virgin sacrifice but with far more goat leggings

So, on the day before The Game, I passed out an exam information sheet containing basic form and content data. In every section, without fail, someone asked, "How much will the exam be worth?" To me, that's taking the point earning contest too far. I'm not going to allow you to make a strategic decision about whether or not to study based on my answer.

More to the point, what will the class response be to a dispassionate direct answer of "20% of the trimester, as stated in the syllabus?"

(1) Half the class will instantly get out a calculator in order to determine the minimum exam score that will allow them to pass, or to maintain the grade that won't provoke parental ire. Students who can't solve 3x = 5 for x will perform this calculation quickly and flawlessly.

(2) The follow up question will be on the order of, "but, if we do well on the exam, will you weight that more heavily in our final grade?" or, "Can we do extra credit?"

Why even engage in such gaming the system? Considering the background of the big football game, I looked sadly at each student who asked that question. I said, "Mr. Clark, when the football team gathers after practice today for one last conversation together before The Game, would you even consider asking 'Coach, how much is tomorrow's Game worth?' And how would Coach react if he knew that the reason you were asking was so you could weigh just how much effort to give?"

Point made. No follow-up questions about grades. And we moved on to discussing physics.

Nacho, Nacho Day... and trimester exam review

2011-11-11T10:10:00.000-05:00

This is just a repost that answers several frequently asked questions:

(1) How do you help your students review for a major cumulative exam?
(2) Why does your email say "Nacho Man?"

The point is, extra credit and food provide significant incentive to bring students into the classroom during what otherwise would be wasted independent study time. Once students are in the classroom working diligently on physics questions, learning is happening even if music, conversation, and nachos are happening simultaneously.

Check out this post.

Peter Chen, a student who is well-versed in video production, intends to create a "cooking show" style clip about Nacho Day in our physics department. I'll post the link in a month or so.

GCJ

No credit for ridiculous answers -- an impulse problem

2011-11-08T17:16:00.000-05:00

I work very hard to differentiate my physics class from merely an applied mathematics class. We do quantitative demonstrations nearly daily, in which a mathematical prediction is checked via direct measurement. I frequently ask on homework problems, "Justify the physical reasonability of this answer." My class is incessantly discussing how to figure out whether or not answers make physical sense, regardless of whether arithmetic is done correctly or not.

I amended a problem the other night from (I think) the Serway & Vuille text. I gave them the graph to the right, and wrote:

1. A possible force vs. time curve for a ball struck by a bat is shown in the figure.
(a) Calculate the impulse delivered to the ball.
(b) This 0.25 kg ball was initially moving toward the bat at a speed of 20 m/s. Calculate the exit speed of the ball.

For part (a), most of the class figured out to take the area under the graph, which they better have -- that same day in class I had discussed how impulse can be found as the area under such a graph. Some students estimated an average force, which would be around 4000 or 5000, and multiplied by 1.5 ms. Fair enough.

Understandable mistake #1:A few made the error of multiplying the MAXIMUM force of about 8,000 N by the 1.5 ms time interval. I took off one point out of fifteen for that -- these students were at least approaching the problem with relevant physics. This mistake makes the impulse wrong by a factor of 2.

Understandable mistake #2: A few also failed to read the horizontal axis, and multiplied by a time interval of 1.5 s, not 1.5 ms. These students also were approaching the problem with correct physics, but made an arithmetic error. Granted, the answer for impulse was off by a factor of 1000, giving them 7500 Ns instead of 7.5 Ns. But I can't really expect anyone to have a serious physical understanding of orders of magnitude for impulse calculations, especially in the first two days of studying the topic. So I took off just one point.

On to part (b).

Understandable mistake #3: The most common error was to fail to account for the direction change of the momentum vector. The ball has a momentum of 5.0 Ns toward the bat before the collision. The ball's momentum changes by 7.5 Ns. But, that doesn't give the ball a final momentum of 12.5 Ns! Since the ball changed directions, the momentum must have first DECREASED by 5.0 Ns to zero, and then increased in the direction away from the bat by 2.5 Ns.

With the failure to account for the direction change of the ball, the exit speed works out to 50 m/s -- a lot, but still not unreasonable, as baseballs hit for home runs routinely exit the bat with speeds above 100 mph. The correct answer is 10 m/s, or about 22 mph -- not a very hard hit, but also not unreasonable. Anything related to a baseball in the tens of miles per hour is just dandy. I took off just two points for failure to account for direction in a momentum calculation.

(Aside -- I'm an American, and I watch baseball. However, if someone had assumed no direction change for the ball, given me the 50 m/s answer, and then discussed how the cricket batsman is allowed to propel the ball in the direction in which the ball was already moving, that student would have earned full credit and a piece of candy.)

What about the student who compounded error upon error?

Understandable mistake, combo platter: The student who used the max force rather than the average force to calculate impulse, AND who didn't account for the ball's changing direction, got something like 68 m/s. Well, that's about 150 mph, and still not horrid -- after all, that's only 40% above the typical 100-120 mph exit speeds in the majors. (I'm recalling my Physics of Baseball by Robert Adair; I hope I have that value right. Please correct me in the comments if I'm wrong.) That answer loses only the two points for the direction change issue.

Terrible, Horrible, No Good, Very Bad Mistake: Oy. I had several students who failed to see the units of ms, and found an impulse of 7500 Ns. Then they carried through the mathematics in part (b) to find an exit speed of 30,000 m/s. Oh, I say, whoa there. Really? 30 km/s? Mach 88? Okay, Bugs Bunny threw faster than that in the Christopher Columbus episode (when he threw a ball around the world in about 2 or 3 s)... but other than in a cartoon world, NO. These students lost an ADDITIONAL 5 points out of 15. One sheepishly said, "well, the math said 30,000 m/s, but you didn't ask us to justify the reasonability." I pointed out that in physics, physical reality always will trump mathematical manipulation. It doesn't matter whether I *ask*, one should *always* be conscious of physical reasonability.

Epilogue: One lone student made the Terrible Horrible No Good Very Bad Mistake, got 30,000 m/s... and pointed out "that is nonsense, a baseball can't ever go faster than 100 m/s or so, the answer is ridiculous but I don't know what I'm doing wrong." He lost the one point for failure to read the graph properly, and one point for an incorrect answer... and that was all. Reward those who demonstrate their commitment to physical reality.

"Group Quiz" on impulse-momentum

2011-11-05T13:53:00.000-04:00

Happy and Sad Balls -- which one produces
more force when dropped onto a force plate?

I can't count the number of articles I read that sanctimoniously preach how physics teachers need to "actively engage learners," involve students in "peer instruction,", provide "inquiry-based interactions", or any other set of edu-buzzwords you can create. These articles push a fundamentally correct point: that I'll have enormously less success if I merely talk at the white board than if I somehow get the class to involve themselves in the topic at hand.

But as with any other educational method, active engagement only works if it's done right. The trick is to get students to care about the answer to the question you posed, and about the justification of that answer. I don't want to read any other literature telling me that active engagement can be effective. I want to know specifically how other successful physics teachers get their students to actively engage.

I incessantly ask "check your neighbor" questions, in which I give students time to write an answer; I give time for class discussion; and then I survey the class, or call on a random student to summarize his thoughts. These are generally effective. However, after a few weeks, the shine has gone off of this novel (to the students) activity. I can see the beginnings of apathy cross my students' faces... "Oh, again with the neighbor arguing thing. Gee whiz."

I've got to vary my approach if I'm going to keep class activities fresh and interesting. I tend to ratchet up the reward for correctly justified answers to my check-your-neighbor questions. One thought that I've detailed previously is to call on a random student after discussion... if that student can clearly and correctly answer my question, I'll cancel the next day's quiz.

I generally give a daily quiz at the beginning of class.* My colleague Paul Vickers modified my daily quiz to an occasional "group quiz," in which he assigned groups of 2-8 students to answer a check-your-neighbor-style question for a quiz grade. The fact that it's called a "quiz," that the students perceive that their performance will directly affect their grade, keeps everyone focused and on-task. Yesterday, I tried a new hybrid approach to a check-your-neighbor question.

* Why? Because students *care* whether they get the answers right, so they pay attention when I go over the quiz better than they would pay attention to the same conversation without the context of a quiz.

The question: I have a happy ball (one that bounces nearly to the height from which it was dropped) and a sad ball (one that hardly bounces at all). I drop each ball from the same height onto a force plate. Both balls have the same mass; both balls are in contact with the scale for approximately the same time.

Question 1: Which ball experiences a bigger momentum change?

Question 2: Which ball causes a larger reading on the force plate?

The method: I began like a standard check-your-neighbor question. I wrote the questions on the board, and asked the students to write and justify an answer in their notebook. After about a minute or two, I asked everyone to argue with his neighbor. Nothing to see here, really; I did let the discussion go on a bit longer than usual, making sure that those who were still making physics points to each other had a chance to hash out any disagreements.

Finally, I gave everyone a blank card. I told them to write and justify the answer to each question as if it were a quiz. I promised that I would choose a student's card at random to read to the class. A correct answer with justification on the card would be worth an extra credit point for EVERYONE on that day's quiz.

Oh, boy, did I get careful justifications. One class's random delegate explained the answer perfectly, earning the credit with no doubt. The other class's delegate explained beautifully (but incorrectly) that since the balls have the same weight, the force plate must read the same value, and thus both balls will have the same momentum change. Knowing that many class members had convinced themselves of this mistaken fact, we talked about why the force plate would NOT read the weight of the ball.

Right or wrong, making the check-your-neighbor question into a quasi-quiz convinced all my students to write clear descriptions of their thoughts. Even though I only looked at one answer per class, everyone took the writing seriously, and everyone could evaluate for himself the quality of his arguments.

I may get away with this quasi-group-quiz once or twice more before it becomes just another day of class. Then I'll have to provide a different sort of incentive for careful, invested participation. I'm open to ideas -- email me, or post a comment.

GCJ

A cool thin lens script in honor of our 50th follower!

2011-10-31T13:08:00.000-04:00

Wow... 50 followers now! Thanks to Pal Fakete of Sydney for becoming the 50th.

Frequent contributor Michael Gray sent me a wolfram alpha script this morning on the thin lens equation. Wolfram alpha, if you're not familiar, is a wonderful site that will suck you in with all the crazy things it can do. You can use it as a calculator, equation solver, equation grapher, and more. My students have occasionally used it to check their algebra or calculus on homework problems. All I can say is, I wish this had existed in 1993 when I took my differential equations class. I learned to use integral tables, that's for sure.

(What's an integral table, you ask? Get off my lawn, whippersnapper.)

Anyway. This particular script will solve the thin lens equation for any variable given any input. Great -- so will your calculator. What I love is that the script will include a ray diagram! Your students can not only check their answers to lens questions, but they can see visually if their inputs make sense.

Why is the diagram so useful? Well, any man jack can plug numbers into the thin lens equation. What's tough is getting the signs of the input quantities right, and then interpreting the output. The resulting ray diagram allows a student to interpret physically, not just numerically, whether an answer is reasonable. A diverging lens gave me a real image? Oh, I must have missed a sign.

Let's find another 50 readers, and I'll keep posting. Send in your requests!

GCJ

"Gravity!" Fundamentals Quiz

2011-10-26T10:10:00.000-04:00

The word "gravity" is, by itself, utterly ambiguous. Nonetheless, our students will refer to a wide swatch of constants, principles, and equations by this single word. While that's not necessarily a problem in the context of a conversation with friends, the lack of specificity can get students confused and blown up when trying to solve test problems.

To the right is part of a recent fundamentals quiz about "gravity." (You can click on it to read it at full size.) I listed every possible equation or constant that has any tenuous connection to "gravity," and I asked students to identify these items in words. Here's a summary of correct and (real) incorrect answers:

(a) Correct: Net force on an object in uniform circular motion, or just centripetal force.

Incorrect: centrifugal force, net force, centripetal acceleration, gravitational force

(b) Correct: Gravitational force exerted by any massive object on another, or just gravitational force.

Incorrect: Newton's law, gravitational field, g

Incorrect: centrifugal acceleration, acceleration, centripetal force, net force, gravitational acceleration

(d) Correct: Weight, force of a planet on an object on the planet's surface.

Incorrect: free-fall acceleration, mass

(e) Correct: Gravitational field produced by a planet, free-fall acceleration

Incorrect: Force of gravity, force of g, Newton's law, force of a planet, centripetal force

(f) Correct: Gravitational field, or free-fall acceleration

Incorrect: Force of gravity, gravity, weight, free-fall force, gravitational constant

(g) Correct: Universal gravitation constant

Incorrect: Newton's law, force of gravity, free-fall acceleration, gravitational field, gravity

What if my force vs. length graph for a spring is weird for small displacements?

2011-10-22T09:30:00.000-04:00

Tim and Andy measuring the force applied by a spring

I think every physics class in the known universe does the F vs. x experiment for a spring: The force on a spring is measured with a spring scale or hanging masses, and is plotted on the vertical axis of a graph. The length of the spring (or the displacement from the resting position) is measured with a meterstick and plotted on the horizontal axis. Because F = kx, the slope of this linear graph is the spring constant k.

(As an aside, I've written up a detailed approach to this experiment for the College Board -- take a look here.)

This experiment is beautiful because the data are easy to take, and because even the worst experimenters get something resembling a line. However, occasionally you'll see something weird -- the graph will be a line most of the way, but very small displacements will give a significantly steeper slope. See the graph to the right (and click on it to enlarge if you can't quite see).

What's going on?

First of all, quash the inevitable misconception: "Oh, that makes sense because the more the spring stretched, the more force we had to use." Well, of course -- that's what F = kx means. We should need more force to stretch the spring for larger displacements.

The slope of this graph represents the spring constant k, which indicates the stiffness of the spring. What's happening here is that the spring is significantly stiffer under about 3 cm of stretch. Does that make any physical sense, though?

Well, in this case, yes. If you get this sort of data, take a careful look at the spring you're using:

See how many of the coils are touching each other? I asked the class to be very quiet... and then I began to stretch the spring a couple of centimeters. We could all hear the "poing!" sounds of the individual coils unsticking from each other. All the coils were fully separated when I had stretched the spring... about 3 cm.

Fact-based criticism: test corrections and fundamentals quizzes

2011-10-18T17:44:00.000-04:00

Don't get eaten when you have to give a C.

I haven't posted in a week 'cause grades and comments were due today. And when I say "comments," I don't mean checking a box that says "He's a nice, hard working boy." I mean a 3-30 sentence narrative discussing each of my 57 college-level physics students.

This year, more students than ever took my Honors Physics I course. Of my 49 students in that class, 30 earned A's for the first marking period... that's far more than I'm used to. The Honors Physics approach that emphasizes verbal explanations has been working well.

However, 10 students earned C's, and one earned a D. Usually I have only one or two C's in the first marking period, and none for the full year; I haven't given a D in this course, even for a marking period, in a decade. None of my students is misplaced in honors; all seem intellectually capable of handling the material. I'm thinking that the expanded numbers in the course gave me more students who are, for now, unwilling to adapt to the deep thinking that is required on every problem set and every test.

Now, the political atmosphere surrounding grades is different at every school. At Woodberry, no one is going to complain when I give a C or a D. However, if I want to avoid an awkward or hostile conversation with advisors, parents, and the department chair, I'd better provide unambiguous narrative support for the grade; and, I'd better be able to show that I've made attempts to help each student raise his* grade. Just "he's not working hard enough on his homework" doesn't cut it, even if that's the nuts-and-bolts truth of the matter.

* I teach at a boys' school -- this pronoun usage is deliberate and accurate.

My grade calculation weighs homework and test performance heavily, to the tune of 85% of the overall grade. But parents don't want to hear about poor homework performance. They believe their son when he says it's too tough and too time consuming, because they see him frustrated while doing the homework every night. Parents don't want to hear about poor test performance. They believe their son that "no one" did well, and that the teacher never went over the type of problems that were on the test, because that's likely consistent with their own physics experience two decades ago. Parents don't expect students to get C's just because the subject matter is difficult.

We as teachers know that the actual reason this guy got frustrated on his homework every night is that he never listened in class, never asked a friend for help, never kept working after an initial 15 minutes, no matter how many times we suggested these things might be a good idea. We know the reason he did poorly on the test is that he didn't get enough serious problem solving practice on the homework. But when our honest evaluation goes head-to-head with a student's plausible excuses, parents will invariably side against us. How can we convince parents and colleagues that (in my friend Pete's words) we are merely the publisher, not the author, of a bad grade?

Understand that performance on my first test was good. I initially graded it on an approximate AP-style scale: 27 students earned 5s, 11 earned 4s, 9 earned 3s, with a single 2. I'm pleased with that distribution... but even though a 3 on the AP exam is "passing," it also means only about 35%-50% of the answers were right. I make students correct their tests to get the right answer, and I give half credit back for the corrections.

This year, I had more students than ever who did a half-arsed job on the corrections. They repeated the same mistakes; tried to justify their answers with "common sense;" or just left several corrections blank. Well, they didn't get much credit back... and as a result, a test that should have produced virtually all As and Bs put ten students in the C and D range.

Interestingly, but not surprisingly, virtually all of those who did a poor job correcting their test also had very bad scores on our weekly fundamentals quizzes. These quizzes don't test problem solving skills, they test memorization of facts.

So in my comments, I didn't refer exclusively to poor homework and test performance. In fact, I was invariably upbeat about test performance: "Will earned a 3 on our first AP-style practice test, and I have confidence that he can improve to a 4 or higher eventually this year." But then I dropped the hammer, with specific reference to an undisputed fact: "Will had the opportunity to correct the test problems that he missed. With diligent corrections, he could have earned a B for the test. However, most of his corrections consisted of mere guesswork, and some were even blank. He earned only 2 of 15 possible corrections points, and his test score became a D+."

In a similar vein, I cited a student's scores on fundamentals quizzes, emphasizing that performance on these is a matter of recall rather than synthesis. I exhorted the student to prepare more diligently for fundamentals quizzes, and reminded him that memorization of facts is a precursor to success in any academic class, not merely physics.

The above is not to say that every parent, colleague, and student will be placated after seeing a C on the transcript. I also have to calmly explain that it's still early in the course, there's plenty of time to improve, and so on. I'm merely offering the observation that it's worth providing the opportunity to correct a difficult test, worth providing the opportunity for a student to improve his grade through a memorization quiz. These are useful exercises pedagogically, certainly; but these also help back the lazy or ill-prepared student into a corner when he tries to make excuses for poor performance.

What happens next? Very often, the student with a C makes a serious effort on fundamentals quizzes and does a much better job correcting the next test. Then he finds that the homework isn't quite as tough anymore, because he knows the basic facts. Then, because he's taken a step to engaging with the material, he finds his performance on the trimester exam to be pretty danged good. Amazing.

Multiple Choice quiz: two-body problem in an elevator

2011-10-12T08:46:00.000-04:00

Diagram for today's problem, modified from
something in (I think) Serway & Vuille

A couple of nights ago, I assigned a two-body problem in an elevator, from (I think) Serway & Vuille. Two blocks were hanging from an elevator as shown in the picture; the acceleration in the original problem was upward. On the homework, I asked (among other things):

Draw a free body diagram for each object.
Is the tension in the lower rope greater than, less than, or equal to 35 N?
Calculate the tension in each rope.
The ropes have a breaking tension of 85 N. Calculate the maximum acceleration that will cause a rope to break.
When a rope is observed to break, explain how the elevator was moving.

This problem is one of the best at separating those who are following an appropriate physics problem solving procedure from those who are just trying to plug numbers into some random equation. The students who used the free body diagrams to write (up forces) - (down forces) = ma got the right answers, and got them quickly.

On the other hand, the students who didn't carefully write the equations were confused for most of an hour, got the final answers correct because they asked friends for help, but usually earned little credit -- if after collaboration they just wrote "T = ma + 35 N, so T = 40 N" I marked the answer wrong. Why? Because I saw no evidence of how they got to that equation, other than listening to a friend without understanding. Would an English teacher give credit for a one-sentence essay, even if the one sentence is spot-on in its conclusion? Of course not. So why on homework should I reward the correct numerical answer when it was essentially derived through magic?

I invited in for extra help the students who didn't follow the correct method. They now feel much more confident about two-body problems, because they see that all they have to do is write the correct Newton's Second Law equations from the free body diagrams. But it's still worth a follow up quiz -- either I build significant confidence, or I discover further misconceptions.

Below is today's three-question quiz that I'll give at the opening of class. (It refers to the diagram above, in which the acceleration is DOWNWARD. Yeah, I switched the direction of acceleration for the quiz.) The "distractor" answers in the second question quote some students verbatim.

Two 3.5 kg blocks hang from ropes in an elevator, as shown above. The acceleration of the elevator is 1.6 m/s², downward. While the elevator has this acceleration, the tension in the bottom rope is 29 N.

Which of the following best describes how the elevator’s speed is changing?

(A) The elevator is speeding up.

(B) The elevator is slowing down.

(D) Whether the elevator is speeding up or slowing down cannot be determined.

Which of the following describes the meaning of an acceleration of 1.60 m/s²?

(A) The elevator gains or loses 1.6 meters per second of speed each second

(B) The elevator gains or loses 1.6 meters each second

(D) The elevator travels 1.6 m/s² more or less each second

(E) The elevator is either speeding up or slowing down by 1.6 meters for every second squared.

Now the magnitude of the elevator’s acceleration is doubled to 3.2 m/s², still directed downward. What is the tension in the bottom rope now?

(A) 41 N

(B) 35 N

(D) 24 N

(E) 0 N (i.e. the rope goes slack)

How tall is an Angry Bird?

2011-10-08T08:39:00.000-04:00

Screenshot from Angry Birds on Google Chrome

The question from yesterday's post was, how big is an Angry Bird, really? Using the screen shot to the right, and assuming we're on earth (so that g = 10 N/kg), we can figure this out.

The screenshot showed an elapsed time of 4.2 s, as I measured with a stopwatch. I count 98 dots from launch to the ground, for a dot rate of about 23.5 dots per second. (Be careful: I don't believe that dot rate to be a general truth of the Angry Birds game. In other firings I measured different frame rates. I suspect that the game is designed always to produce a similar *distance* between dots rather than a steady dot rate. But I digress.)

The bird hits its highest point at about the 47th dot. At 23.5 dots per second, that's 2.0 s from launch to the peak height. So, we can do vertical kinematics with a final velocity of zero, acceleration -10 m/s², and time 2.0 s. This gives an initial vertical velocity of 20 m/s, and a vertical displacement of 20 m.

The maximum vertical height of the bird's launch on the screenshot was 8.0 cm above the launch point, as measured with a ruler. Now we know the scale of the picture: 8 cm to 20 m, or 1 cm to 2.5 m. We're essentially done.

The piggy and the bird are both about half a centimeter high on the screenshot. Knowing the scale, that gives a "real-life" height of 1.3 m, or about four feet. The tower is 5 cm off the ground in the picture, or about 12.5 m.

So, is the video reasonable? NO! The bird in the video hit the car window. Car windows aren't anywhere near four feet tall top to bottom. And, a man had to stoop in order to cower under the bottom floor of the tower next to a piggy. In the screenshot, the bottom floor of the tower measures 2 cm, corresponding to 5 m. Not even Kareem Abdul-Jabbar would have to bend his knees to duck under a 15-foot ceiling.

I was considering buying Burrito Girl, my wife and sidekick, some of the plush Angry Birds toys for Columbus Day. But I don't think I have room in the house for a stuffed toy that's taller than my Siberian Husky.

Activity for the "fifth day" of class

2011-10-07T14:28:00.001-04:00

Screenshot from Angry Birds on Google Chrome

Because I've been teaching "Honors Physics" this year*, I have been trying to run on a four-day teaching schedule: Three days of what you'd call a standard class (quizzes, quantitative demonstrations, and discussion), and a day of experimental work in laboratory, each week. The fifth day -- Friday or Saturday* -- is held in reserve.

* Honors Physics is intended to foreshadow the future AP Physics I course. It is college level, algebra based, covering about 60% of the AP Physics B curriculum.

** Two of my honors sections meet on Friday for the last class of the week; another meets on Saturday instead of Friday. Yes, I do teach on Saturday.

I intend to give a fundamentals quiz each week on the fifth day. The rest of class I plan at the last minute. Perhaps the lab took longer than I expected -- we can finish up. Maybe we need to practice a two-body problem that I don't have time to assign for homework. Point is, I can do anything I want, because the pace of the course assumes that we don't truly NEED that fifth class.

I suppose this "fifth class" approach is my own politically correct response to the fact that we miss so many Friday and Saturday classes due to special events and athletic trips -- for example, when the football team has to leave for an away game, my class is cut nearly in half*** . Rather than complain, I make it so students WANT to be in class on Friday or Saturday, and they truly are a bit sad to miss; but also so that no one is truly at a major disadvantage because of a legitimately missed class. If they just make up the fundamentals quiz, they will be right back with me on Monday.

*** Yes, 22 of my 49 Honors Physics students are on the varsity football team.

In today's enrichment class, I divided the class into pairs randomly, and gave each pair the screenshot from Angry Birds that is shown at the top of the post. I showed the class this youtube video, which acts out a "live action" version of Angry Birds. I asked each pair to answer, and justify their answers to, this set of questions:

How tall is an Angry Bird?

How tall is a piggy?

How tall is the tower?

Is the video reasonable?

One of the AP Physics readers -- I forget who, since my iPad lost my notes from un-professional night last summer -- suggested the idea of determining g on the Angry Birds world using frame-by-frame video analysis and a size estimate of the birds. I thought it would be fun to go the other way... we'll assume g = 10 m/s^2, and figure out the size of the stuff on the screen. My answer in tomorrow's post.

Disjointed thoughts on test construction

2011-10-06T09:47:00.000-04:00

I'm giving the first test in my new "Honors Physics I" course, the course that's intended to foreshadow the future AP Physics I. I've also been helping to write and prepare tests in conceptual and general (Regents) level physics. Thus, I've been reflecting a bunch lately on methods of test construction.

Lyle Roelofs, who (perhaps tied with Walter Smith) was simply the best teaching physics professor ever, emphasized repeatedly to anyone who might teach physics: "The only time a teacher can be sure of a student's full attention is on a test. So use tests to your advantage." Thus the origin of my test corrections, the test-question-writing exercise, serious exam review, and more. But, if I expect my students to take the tests seriously as study tools, I have to take serious care in the construction of the test.

That care starts with a professional-looking test. There's nothing wrong with handing out a nightly problem set via a sloppy email or via a handwritten slip of paper. Practice multiple choice problems sometimes consist of faded xeroxes from 30-year-old master copies. No problem, 'cause no one is expecting every night's problems to be beautiful. However, a TEST should include clean, nicely-formatted proofread copies. Mistakes should me not just minimized, but eliminated -- how do you justify docking a student's test grade for a lack of units when you yourself misprinted the units of acceleration? Sure, stuff happens, but if more than one test in a year contains a major typo or a substantive error, you need to proofread better.

The format of each test, I think, should be generally consistent throughout the year. Students are taught not to read directions on the SAT. Why? Because the directions for each section are the same on every test, every year; and because these directions are available ahead of time for preparation purposes. A physics test is supposed to be a measure of a student's content knowledge. Sure, careful reading of individual problems is essential to a student's successful performance... but we shouldn't surprise anyone with a different kind of question than they're used to.

In an AP class, I give tests in a format identical to the AP exam: Multiple choice, followed by free response. In my general, honors, and conceptual classes, the format is always free response, short answer, multiple choice. I hand out the instruction sheet and any reference tables before the test, so that students know what to expect.

In Honors Physics I have control over test design, since we're not yet formally teaching to an AP test. So I combine free response, short answer, and multiple choice into a single time period: 2 hours for the end-of-year cumulative, national exam, and 80 minutes for the monthly in-class tests. The rule of thumb for timing: about a minute and a half per mulitple choice item, about three minutes per short answer item. For AP-style free response, give a bit longer than one minute per point -- for example, in an hour I expect students to be able to solve five 10-point problems, or two 15-pointers and two 10-pointers. (As a comparison, the AP Physics B exam allows 90 minutes for 80 points of free response; the AP Physics C exams allow 45 minutes for 45 points of free response.)

If you're not teaching AP, consider switching the traditional order of the test. I put the free response questions at the beginning of the test, and multiple choice at the end. Why? Because I've too often seen students get captivated by a one-point multiple choice question, leaving no time even to make a reasonable guess at the 15-point free response question. If, on the other hand, someone gets hung up on a free response question, there might be time to make reasonable guesses at the multiple choice questions at the end.

The content of each test should be transparent, even if that means "everything we've ever covered." I thoroughly approve of cumulative tests; why should I bother teaching in September if everyone's allowed to forget what we learned? But I also approve of a clear course outline, indicating the general topics that have been covered in class and that will show up on the test. A cumulative test is not a licence to play "gotcha!" If you're consistent all year in what you expect students to understand in each unit, and if every test includes something from each previous unit, the class will recognize and meet your expectation that they learn physics for the long term. The nice side effect is that final exam preparation becomes a piece of cake if all tests are cumulative.

Someone stopped me in the hall yesterday after the first test, and said, "Mr. Jacobs! That was like an EXAM, not just a test!" I smiled at him... imagine how seriously he'll take my actual trimester exam, now that he knows what my monthly tests are like. And imagine how comfortable he'll be in May on a cumulative, year-long, national exam like the AP or the SAT II.

GCJ

What does g mean?

2011-10-03T09:22:00.000-04:00

(From a note to my class folder after a lab writeup:)

From NASA: Recognize the guy in "zero g"? (Or *is* he
in "zero g"?)

The variable g represents the gravitational field, which near earth is 10 N/kg.

Or, the variable g represents the free-fall acceleration, which on earth is 10 m/s².

The variable g does NOT represent the "force of gravity" or the "gravitational pull." The force of gravity on an object is the object's weight, or mg.

The variable g does NOT represent the "free-fall velocity." Such a thing does not exist.

And finally, the variable g does not mean "gravity." That's ambiguous -- lost of quantities are associated with this nebulous thing called gravity. There's gravitational field and free-fall gravitational acceleration, but also gravitational force, gravitational potential energy, and the universal gravitation constant.

GCJ

Parents' Night: Teach a Class!

2011-09-28T14:19:00.000-04:00

Parents' night, but not at Woodberry Forest
(Actually a parental awareness class
in India, via Wikimedia Commons)

This weekend is "Parents' Weekend" at Woodberry Forest. Since we're a boarding school, the weekend is a Big Event, one of the two or three times when we encourage and expect as many parents as possible to be on campus. The weekend begins Friday with football and soccer playing simultaneously, followed by a nice dinner in the dining hall.* Then comes the key event: Academic Mini Classes.

* The axiom at all colleges, which persists despite its clear falsehood, is that food services saves the prime rib for Parents' weekend, and puts out dog food the week before. Thing is, we're having prime rib (and challah!) Wednesday night as part of a special Rosh Hashanah dinner. I wonder what we'll have on Friday night...

What we call "Academic Mini Classes" is generally referred to as "Open House" at day schools. Parents go class-to-class through their son's schedule sitting at desks among peers just like the students do. Each class lasts ten minutes. What we do with those ten minutes can set a tone for the entire year of parent-teacher relationships.

I've heard numerous theories and advice about how to approach Open House. Much depends on your personality, your pre-existing relationship with the parents, the size of your class, the number of expected attendees. I'll merely tell you what I do, not what you should do.

(I will tell you what you should NOT do: Don't read the syllabus and discuss grading and attendance policies. Doing so encourages the parents to help their kids game the system when the going gets tough; you want the parents supporting you, not giving their kids legal advice. More importantly, just reading the syllabus is BORING. If you need to communicate boring information, give everyone a handout to read later.)

During my ten precious minutes with the parents, I teach a class on a topic that we have recently covered. In the honors section, we've just covered projectiles. So, I bring out the moving cart that launches a ball straight up. Just as I do in class, I ask, "Does the ball land in the cart, behind the cart, or in front of the cart?" I make the parents write down their answer, then argue with a neighbor. We do the experiment, and discuss the reason the ball lands in the cart in language that they all can understand.

In general physics, I bust out the motion detector and use the fan cart (with the fan turned off) to create a position-time graph. I ask, what will the graph look like if I turn the fan on? I make the parents write down their answer, then argue with a neighbor. We do the experiment, and discuss the reason why the position-time graph is curved.

These parents think of physics class as old, balding man writing equations that no one can understand on the board. That's not what good physics teaching looks like. I need to open their minds to new possibilities in ten short minutes. By doing live, qualitative demonstrations, I convince this audience that physics is worth knowing; by using everyday language to explain the phenomena we observe, I convince the audience that physics is know-able. After that, the skeptical frowny faces of parents who are angry that Johnny got a 5/10 on a problem set turn to wide-eyed enthusiasm.

Now, you might have a different approach. Perhaps you show that momentum is conserved in Angry Birds. Perhaps you use live video from an ipad 2 in order to find the speed of a parent pitching a tennis ball. Whatever you do, I'm suggesting that you bring forth your best performance, using any necessary tools. Make the parents wish they could sit in on your class; make them sad to have to leave to go to boring ol' English class. The political capital you buy with a well-planned, enthusiastic performance will be worth a hundred thousand printed pages of class rules.

The OJ Simpson Question: Magnitude and Direction of Accleration

2011-09-23T09:19:00.000-04:00

Knowing what an acceleration vector means about motion is perhaps the biggest conceptual challenge in first semester physics. No matter how many times I say "the direction of motion has nothing to do with the direction of acceleration," this misconception (among many others) remains.

I ask students to memorize:

* Speeding up means acceleration is in the direction of motion.

* Slowing down means acceleration in the opposite direction of motion.

However, put these facts in the context of a velocity-time graph, or in the context of specific motion north and south, and heads explode. And that's really all we can do -- ask about the meaning of acceleration in as many different contexts as possible until the class is sick of such questions.

In the first several kinematics assignments, I've displayed a position-time or velocity-time graph and asked for a description, in everyday language, of the represented motion. In order to tease out the physical meaning of an acceleration vector, I switch up: I present a description of motion, and ask students to make a velocity-time graph.

1. In an alternate universe that still obeys our laws of physics, O.J. Simpson leaves a tollbooth in his white Bronco the morning after killing his wife. Soon after, he sees a police officer flash his lights. Hoping to get away, he slams the gas pedal to the floor, but then O.J. hits a concrete barrier and crashes. (a) On the axes below, sketch a velocity-time graph of OJ’s motion.[1]

[1] Sketch, according to the College Board’s course description, means to “draw a graph that illustrates key trends in a particular relationship, such as slope, curvature, intercept(s), or asymptote(s). Numerical scaling or specific data points are not required in a sketch.”

Most of the class gets this essentially right on the first attempt; the rest get it after a quick conversation with a friend. The real point of the problem comes next:

2. Describe in words the magnitude[1] and direction of O.J.’s acceleration as O.J. is leaving the tollbooth.

3. Describe in words the magnitude and direction of O.J.’s acceleration as O.J. is traveling along the road unmolested.

4. Describe in words the magnitude and direction of O.J.’s acceleration just after O.J. sees the officer.

5. Describe in words the magnitude and direction of O.J.’s acceleration while the Bronco slams into the wall.

[1] “Magnitude” in this context means, how much acceleration does OJ have? Answer relative to his acceleration at other parts of his motion. No numbers are required, though you are welcome to make calculations if you so desire.

I can tell almost immediately upon reading these responses who understands acceleration, and who does not. The ones who truly don't get it come in for a consultation, where we work on these concepts. How can I tell?

Well, the response I'm expecting to parts (c) and (d) refers explicitly to the v-t graph and/or to definitions that we've learned: "(c) When OJ sees the officer, the slope of the v-t graph is positive (a frontslash), so the acceleration is forward. The slope of the v-t graph is steeper than when OJ calmly sped up from the tollbooth, so the acceleration has a larger magnitude here. (d) When OJ crashes, the slope of the v-t graph is much steeper than anywhere else; so the magnitude of the acceleration is highest of all parts of the motion. OJ's acceleration is backwards, because the car is still moving forward, but is slowing down."

The most common mistake is to state the direction of MOTION rather than of acceleration: "(c) When OJ sees the officer, he speeds up rapidly. So his acceleration is moving forward. (d) When OJ crashes, he bounces back off the wall, so his acceleration is moving backward." Anytime a student says that the acceleration is "moving," I know that he is conflating acceleration and velocity, so the answer is marked wrong -- yes, verbal skills are part of physics.

A less common mistake is to think that the acceleration must change if velocity changes. "(c) After OJ sees the officer, his acceleration must change rapidly, because the accelerator pedal is on the floor. (d) When he crashes, OJ's acceleration changes from a high value to zero." No, constant acceleration means speeding up or slowing down; this student thinks acceleration must change in order for speed to change.

I do get about half the class writing clear, concise, and specific explanations that refer to the v-t graph or to the definition of acceleration. I will show a fellow student's good explanation to someone who's struggling, to show the difference in the style of prose. I'm teaching writing as much as I'm teaching physics, sure. But the time I spend now demanding clear writing pays off tremendously later in the year, when an AP-style free response test requires one-minute justifications.

GCJ

P.S. Only about half of my class had ever heard of OJ Simpson. That says something about pop culture in the post-internet era. What it says, I have no idea.

Where do I get constant-speed bulldozers for lab?

2011-09-20T18:02:00.000-04:00

Georgian Mark DiBois asks:

One weird thing... I still can't find a small toy bulldozer to pull a mass across the table... Where do you get those?

Simple answer: In the science supply houses you're looking for what's called a "constant speed vehicle." Fool around on google and you can see the device pictured above, available from Frey, Fisher, and others for $25-30 each. I *think* these can move forward or backward at the flip of a switch.

Better answer: PASCO offers two levels of constant speed items. In a rare event, PASCO undercuts the competition with their "constant speed buggy", pictured here. These are $8 each. They only move one direction, but they work just as well as the more expensive bulldozers.

Coolest answer: If you have a few bucks lying around for luxury purchases, try out the PASCO "variable speed motorized cart" pictured here. It lists at $159. But it has a knob for adjusting speed, and has traction enough to climb reasonably steep ramps.

My personal solution: I have two of the $25 bulldozers and ten of the $8 buggies. (I like to have some of each because they move at different speeds.) I use these for laboratory investigations. I also have one of the fancy-pants variable speed carts, which I use exclusively for demonstrations, or even research problems where necessary.

GCJ

Two Bad Questions

2011-09-19T09:10:00.000-04:00

Two Bad Mice ponder Two Bad Questions

As regular blog readers are aware, I'm adjusting my AP physics B course to cover only about 60% of the material in the AP curriculum, keeping a similar depth of sophistication in the coverage of each topic, but demanding even more verbal explanations and justifications. Part of this process is to redesign my problem sets so that some kind of verbal justification is required every night. (Details at this post and this one, too.)

Most of this month's problem sets I wrote while sitting at the Starbucks on the Pearl Street Mall in Boulder, Colorado. I do highly recommend such a retreat for summer planning. All I did was to copy the problems that I've used successfully for many years, adding explicit prompts such as "Explain why the tension is greater than the weight of the stoplight," or, "Describe, as to a non-physicist, how much force the string exerts by comparison to a force with which you are familiar. Justify your comparison." This approach has worked well.

However, I discovered -- too late -- a couple of minor mistakes that turned into ill-posed problems. As a mea culpa to my students, and pour l'encouragement d'les autres, I present to you these questions that you should not ask.

1. This one is based on an old Giancoli problem, but I copied it wrong:

In the design of a supermarket, there are to be several ramps connecting different parts of the store. Customers will have to push grocery carts along the ramps, as shown above. A grocery cart has mass 30 kg; the coefficient of kinetic friction is m = 0.10. Determine the maximum angle of the ramp such that the customer will not have to exert a force in excess of 50 N.

Sounds like a great question... but, as my students pointed out to me, it requires either numerical analysis on a graphing calculator or maximizing a function using calculus in order to solve. I promise the class that they will never have to use any math beyond algebra I and the definitions of the trig functions, so they were pretty confused.

The original question that I should have transcribed correctly asks whether a 5 degree angle would be too steep, knowing that customers should not be asked to exert more than 50 N. That's a straightforward problem mathematically, which allows the rest of the question to focus on a description of just how much force is 50 N, anyway. And the whole point was to provide an easy, confidence boosting problem for the class, who is finally getting the hang of equilibrium. Grr.

2. I just didn't think this one through at Starbucks:

A 150 N block sits on an inclined plane, as shown. The coefficient of static friction between the block and incline is 0.30. Calculate the angle of the incline and the force of friction on the block.

Simple enough so far... it's straightforward if you recognize that sin/cos = tan. Since that's the one trig identity that shows up in introductory algebra-based physics, I use this problem sort of as a reminder to know that identity. But then I screwed up:

Now imagine that the same 150 N block slides down the same plane at constant speed. Is the force of friction greater than, less than, or equal to the value you calculated previously?

Well, this question requires understand extremely subtle issues about friction, far more subtle than the AP exam or I cares about. The coefficient of static friction can take on any value up to a MAXIMUM of Ff/Fn. The question as stated is confusing to students who have had ten days of physics. On one hand, they see that equilibrium requires Ff and Fn to be mgsinθ and mgcosθ, respectively; so Ff should be unchanged with the same block on the same angled incline. But they also understand that the coefficient of kinetic friction is less than the [maximum] coefficient of static friction. So the friction force should be smaller. Which is right?

The correct answer is, don't ask this question to begin with. I don't care how cool the underlying physics is -- and really, static friction is pretty awesome when considered from an expert, dispassionate, and deeply intellectual perspective -- a justification question this early in the course without a definitively correct answer can spawn not just confusion but hopelessness.

Now, you might suggest that a college physics course can and should include problems at this level of difficulty. The course you took back in college sure did, and everyone got it wrong, and we were better for it, right? Well, no. We're not teaching physics majors here, we're teaching high school students at the college level. Their confidence is a fragile thing, and must be preciously guarded. In the first week, I have already "torn down" a number of students who struggled for a week just to draw a free body diagram and understand what a normal force means. I need to build back these students' confidence, show them that if they follow the problem solving procedure I've described in class, they can and will do well. But they don't see physics as "cool," they see it as "hard." Let's first convince the class that physics is "doable," so that at the end of the year they will be ready for "cool."

And, oh yeah, since I'm assigning rewritten problems, I'm going to write a solution to every problem set this year, starting now. I can't make this kind of mistake again. Mea culpa.

GCJ

AP-level Kinematics... In Just Two Weeks!

2011-09-14T08:42:00.000-04:00

I got a nice note last night from New Yorker Scott Marzloff, who attended my AP Summer Institute at Manhattan College. Scott noted that he started the year with equilibrium and torque using quantitative demonstrations, and that his approach was successful. Awesome. However, he asks:

I am getting ready to start kinematics and I am wondering how you get through all of 1-D kinimatics in what looks to be about 6 days? I know I can get through 2-d projectiles in a week, but 1-D with graphs, equations, and freefall I have never come close to covering in less than three weeks. Do you tie the equations in right away with motion diagrams and graphs?

Well, to be fair, it takes more like 8-9 class days to get through kinematics, including both one- and two- dimensions. And, I'm not saying that every one of my guys is ready to take AP exam problems on day 9. Nevertheless, I get through kinematics just that quickly, and we perform well above the national average on kinematics problems come May.

I begin with position-time graphs, demonstrating with a fan cart and Vernier motion detector. We predict qualitatively what a couple of graphs should look like, show that the slope of an x-t graph is velocity, explain how to find displacement from the graph's axes. On the second day I introduce velocity-time graphs. Acceleration is defined as the slope of a v-t graph. I take considerable time to get students arguing about how to use the fan cart to reproduce various straight v-t graphs.

Three hints about teaching motion graphs:

(1) Homework related to motion graphs is not purely quantitative. With every graph, I require students to describe the motion represented in everyday language, without terms like "acceleration" or "negative." For nearly a week, homework and quizzes hammer kinematics concepts rather than calculations. One night's homework is a 21-question set of multiple choice questions about motion graphs, on which I require detailed explanations for any question they initially get wrong. Make the class explain their thoughts in words.

(2) I don't (yet) stress over the difference between vector and scalar quantities. Kinematics is confusing enough without the subtlety of distance vs. displacement, velocity vs. speed. I use velocity and speed as synonyms on these first few days. Heresy, you shout? Perhaps, but it works. Try it.

(3) In the same vein as (2), don't even discuss sidebars, no matter how interesting. For example, curved v-t graphs simply don't exist during the two weeks of kinematics. If a student asks about them, I explain that a huge set of moving objects produce straight v-t graphs, and that the things that don't have constant acceleration simply aren't relevant right now. Other irrelevancies include a-t graphs, "jerk", anything involving calculus...

Graphs take at least half of my time teaching kinematics. Why? Because once we understand motion graphs conceptually, algebraic kinematics is straightforward.

I explain that all moving objects we consider will involve straight velocity-time graphs. But we want to be able to make predictions without having an actual motion graph in front of us. How can we do that? By using a straight v-t graph to derive some algebraic formulas. I show that taking the slope of a straight v-t graph produces the first of the constant-acceleration kinematics equations. I show that taking the area under the v-t graph, along with some algebraic substitution, produces the second of the constant-acceleration kinematics equations. (I simply state the third equation, without derivation -- they get the point.)

I do a set of quantitative demonstrations with the PASCO projectile launcher. In each problem, we define a positive direction, and fill out a chart in which we identify the five basic kinematics variables (vo, vf, Δx, a, t). We learn that the problem is solvable as long as we know three of the five variables. I don't spend any time on algebraic methods -- they figure out the most efficient algebraic techniques on their own by doing homework problems. (Exception: I do one example in which I demonstrate that we do not ever need the quadratic formula. There's always a simpler approach.)

At this point, one-dimensional algebraic kinematics problems become simple for the majority of students. Free-fall doesn't need a separate unit, like most books give it; free fall is just accelerated motion where a = 10 m/s², down. We very, very quickly move on to projectiles. Projectiles become simple, as well, once we learn to make two kinematics charts, one vertical, one horizontal. Horizontal acceleration is always zero; time is always the link between the charts. Since I taught equilibrium and free body diagrams first, no one is flummoxed when I show how to deal with an angled initial velocity using sines and cosines. Projectile motion becomes more a reinforcement and solidification of kinematics concepts rather than a truly new unit.

That's it.

Most of the class is reasonably skilled, at this point, but they still need considerable practice. But I don't give that practice in isolation. Rather, the practice is integrated into our next few topics. For example, next is Newton's second law. Most problems require both a free body analysis AND a kinematics approach. Well, when they have to use an acceleration they calculated from Fnet = ma to find how far an airplane goes on takeoff, they're practicing their kinematics skills. Later, when two blocks collide at the edge of a cliff, conservation of momentum yields a projectile problem. Practice in context is always more effective than rote practice. (So, when did you really, truly learn to evaluate integrals quickly and accurately: in your first three calculus courses where you were given explicit practice, or in your differential equations course, which took integration skills for granted in order to do more involved problem solving?)

Try moving along quickly in your simpler topics, so that either (a) you can cover more topics in the year, or (b) you can spend more time on the truly difficult topics later in the year.

GCJ

iPad Apps and Physics Teaching -- 2011 Followup

2011-09-10T07:59:00.000-04:00

I’ve been using a school iPad since July of 2010. I spent a good deal of time in the summer of 2010 searching through the app store for things I could use in physics. Generally, I found that the apps specifically branded for “education” were not of significant use. Most were silly, or available for free online (rather than for $1.99 from the app store). However, some apps that were NOT specifically designed for education were enormously useful, and I have used or will use them in class:

· The magnetic field sensor with 3-d compass and output reading in microTesla

· The “clinometer” angle indicator

· “Star Walk” astronomy program, which is a portable and dynamic version of what “Starry Night” does.

I wrote a blog post last year about the potential of the iPad in physics. This is the second-most-viewed post on my blog. I have had three personal emails asking for an update – what have I found out since last summer?

The answer is, I haven’t had the time to find new apps on the iPad since last August. I know that the pace of the mobile app technology has been furious. For example, the iPad 2 can take videos, and instantly import those videos into the logger pro software that we use to make position-time graphs. That app would cut a 1-hour lab to 15 minutes. My students found an app that uses the speaker to create a known frequency, essentially replacing my frequency generator. I have heard of other good physics apps, but I have not begun using anything else myself.

Aside from the apps in class, I’ve found two other unforeseen but critically important uses of the iPad.

When I am broadcasting football and baseball, I have instant access to the internet and to my email. Thus, I can report in real time on scores of other games (both professional games and Woodberry games). I have received in-game messages from listeners in order to better tailor the broadcast to their needs. At this point I have a hard time imagining a broadcast without the iPad at my side. And I haven’t even thought about electronic scoring and statistical software, which (as of last summer) is not yet at the point where I’m ready to use it, but should develop to a useful point in the near future.

As the debate team coach, I used the iPad incessantly. Students did research on the bus on the way to tournaments, looking up facts to back up last-minute arguments. After a round, students would report on new arguments they had heard; I would give them the iPad and advice about what to look up to counter the unforeseen argument. As a judge, I used the iPad to time the speeches – the advantage of the iPad over a stopwatch was that I could keep the timer running but flip the screen to google to look up disputed facts when necessary. [In one round, both sides disputed interpretations of the constitution. In no more than a minute, I had found the text of the 2^nd and 26^th amendments, to find out that BOTH sides had made devious misquotations.] And, it became nearly traditional that after the awards ceremonies, I would use the maps function on the iPad to find locations for meals that were on the way home but which provided exciting and different options. It was most useful to be able to show definitively that there was NOT a Chuck-E-Cheese within 30 minutes of Broad Run High School. And thank goodness. J

Is there a point to providing iPads for student use? Not right now. The arguments for or against iPad use for students remind me of the discussions 10 years ago about laptops. Some schools provided each student a laptop, provided network hookups at each student desk, and pressured teachers to use the laptops as an integral and indispensible part of their classes. Sounds great in principle. But:

(a) The laptops themselves were obsolete within a couple of years.

(b) Even the network infrastructure was obsolete quickly.

(c) Only a very few teachers had authentic use for the laptops. The vast majority of academic laptop “use” in class was done at the pointed request of administrators, and consisted of activities of questionable value. While I would never support the old-timey Luddites who would ban the internet from our students’ lives, I would nevertheless suggest that a teacher who does not WANT to embrace new technologies can not be effectively forced to do so. True progress in academic technology comes from having technology available for those who truly desire to use it.

(d) The easy access to the entertainment aspects of the laptops in class caused a problem that generally outweighed the benefits of the educational aspects.

Replace the word “laptop” with “iPad,” and I’ll bet one could write the same four statements in a decade. (Furthermore, I read an article noting that the “revolution” of educational television in the 1970s and of classroom computers in the 1980s had precise parallels to the laptop explosion in the 2000s. The four points above pretty much could be said about educational television and video (remember laser disks?) when those technologies first came out.)

Now, I have found good use for a class set of mobile app technology. When I had a free app that did something useful – like the angle measurer or the magnetic field probe – I encouraged students with ipones or ipod touches or ipads to bring them to class. The students were most comfortable downloading and using the apps on their own, and enjoyed the “coolness” of the device far more than they enjoy my standard equipment. The fact that the app was on a device with which they were already familiar broke down the barrier of “I don’t know how this works, I’m frustrated!” in the laboratory. That sentiment is not to be underestimated. But there’s not enough of this sort of thing to justify $600 per student for an iPad. I found that enough of our students already had a compatible device so that I could run the laboratory activity.

The iPad specifically is the only device I’ve seen on which a digital textbook would truly replace a paper text. Its screen is big enough, its processing quick enough, its display is full color, fully zoomable, and annotations could be done with a finger. The textbooks are not available yet, I don’t believe. But when they are, it would be extremely convenient for a student to carry the iPad rather than a stack of books. I already have been using the iPad as my library as I travel. I have a personal “nook” which I have synched with the iPad. When I travel, I can access all of my electronic books instantly through the nook app; in fact, Shari and I can BOTH access our electronic library, since I can use the iPad and she can use the nook. (Plus, I can buy a book instantly without going to a bookstore. Plus, I can subscribe to and read a newspaper while traveling. How awesome would THAT be for boarding school students?)

For now, though, the pace of the technology is changing so rapidly that I don’t think it useful to make any long term decisions about mobile devices. Let’s see the future of android devices. Let’s see whether the price of electronic books goes up or down. Let’s see whether textbooks become more widely available in digital format.

Greg Jacobs

Supplement Review: The AP Prep Book for Walker Fourth Edition

2011-09-07T09:26:00.001-04:00

Every summer at my AP Summer Institutes I'm asked, "Which is the best textbook?" And I answer, "None of them is good, none of them is terrible, and they're all essentially the same."

Publishers know this. One way they try to differentiate themselves in the marketplace is through supplementary materials. The online resources are usually a boondoggle -- you don't need to pay for physics materials online.

But I'm seeing increasingly strong AP-specific supplements. Publishers seem to be getting the message that you can't just hire a hack freelance writer with a physics degree to write good test questions for a college-level physics course. Nor can you hire a random physics professor, nor a graduate student. AP readers and exam authors are the experts who should be tapped.

Cutnell and Johnson jumped the gun years ago by getting Hugh Henderson, an AP reader and former member of the test development committee, to write their AP supplement. (Note that this is a 2003 edition... the newer edition does not have Hugh's name on it, and I have not read it.) Hugh included three AP physics B tests; I still use questions from these on my in-class tests.

This year, Serway got into the good-AP-supplement business. They hired a long list of very strong AP readers, including exam leader Shelly Strand and former exam leader Bill Pappas. (I won't review Serway's material because I contributed numerous free response items.)

The book that has caught my eye is the supplement to the James S. Walker text from Pearson, pictured at the top of the post. It's written by Connie Wells, a former member of the AP development committee, my table leader at the AP reading in 2001, and an all-around expert physics teacher.

My first, raw test of an AP prep book is to leaf through and look at topics. A depressing majority can be immediately defenestrated because they include improper topics, like calorimetry, rotational dynamics, or relativity. Others can be burned at the stake for including multiple choice questions that obviously require calculators. Connie's book passes this first test. She includes review of rotational kinematics and dynamics, because she seems to be tasked to parallel the chapters in the Walker text; however, she is crystal clear that these topics are NOT COVERED on the AP physics B syllabus.

Every problem that I looked at was right on-level for AP. She included some simple calculations in the multiple choice, sure, but the majority of her questions require serious conceptual application -- just like on the real AP exam. Solutions (not just answers) are included.

I was most pleased that I found laboratory-based free response questions. Connie was on the development committee while AP was still transitioning from the days of "shut up and calculate" to the current emphasis on verbal expression of conceptual understanding. She was the primary author of perhaps my all-time favorite AP physics B question, the one about the platinum resistor. (I can't post it here because I can't find a legit copy online; but look up 2001 problem 5.) Sure enough, Connie's book includes questions testing lab skills and concepts, including graphical analysis of experimental data.

I could not recommend this supplement more highly for teachers of AP or honors-level physics. In my new Honors Physics I course, which is intended to anticipate the College Board's future AP Physics I course, I need to create a whole host of tests and quizzes with new multiple choice items. Connie's book will be one of my go-to sources.

Should you assign seats?

2011-09-04T09:56:00.000-04:00

Should you assign seats in a high school physics class? The theoretical arguments could go either way, with fundamental principles of teaching contradicting themselves.

Rule 1 of teaching high school: Never condescend, or give the appearance of condescending, to your students. If anything you do in class might possibly be phrased in a singsong voice that begins "Now boys and girls," you're screwed. Fair or not, students are almost looking for an excuse to act disrespected -- they are quick to feel like they're being treated like babies. A seating chart seems like it should fall under this proscription.

Rule 2 of teaching high school: Trust, but verify. We all know that it is in our students' best interest to do homework, and we want to trust them to be self motivated to do their homework; but we nevertheless collect the homework, at least if we want it done right. Suggesting that students read their text has a very different effect from "Tomorrow there will be a reading quiz on chapter 2.3, on which you may use your reading notes." The method of verification can vary, and certainly does not have to be grade-based. But, veterans know that any rule, suggestion, or good idea that's not backed up by some sort of verification is ignored.

Along those lines, a junior or senior in high school has been told many times that it is a good idea to sit at the front, not the back, of the room. It's a good idea to sit away from those who might distract them. It's a good idea to sit next to people who aren't necessarily best friends, to promote focus during lecture and to possibly create new friendships through the shared experience in physics class.

So, if you don't assign seats, what happens? The back rows fill up first, and friends (or couples or wannabe couples) huddle together. And no one changes seats after day one.

When it comes to assigned seating, I think rule 2 trumps rule 1. I've assigned seats only twice in my sixteen year career... but now I wonder why I went so long without assigning seats. I use "check your neighbor" questions often in class. Now that everyone's "neighbor" may or may not be a good friend, the discussions are more physics-focused, and less likely to devolve into a discussion of weekend plans. I insist on regular collaboration amongst the class. Once everyone has been forced to discuss physics in class with a random classmate, they become more comfortable collaborating with that classmate outside of class, too. And though I've rarely had major problems with classroom management, I find behavior to be even less problematic when seats are assigned.

In order to avoid the appearance of using elementary school methods on the first day of class, I present assigned seats as a fait accompli. I certainly do NOT allow folks to sit down anywhere, only to move them to an official seat a few minutes later. No, I've prepared folded index cards with each student's name on them. When a student arrives on the first day, he finds the seat with his name on it. End of story -- no discussion, no argument, partly because no one realizes that an argument might exist.

I've found it especially effective to switch up seating a couple times a year. I re-distribute seats quasi-randomly in the second trimester, and again in the third. So, when a student complains (whether disingenuously or not) that his assigned seat is not conducive to learning, I point out that the seats were assigned randomly, and that they will change in a couple of months. If someone does have a particularly annoying seat, like in the back corner of the room or next to an obnoxious person, then I'll be very sure he gets a prime ticket next trimester.

Equilibrium: quantitative demonstrations (or, how I teach vector math without teaching vector math)

2011-08-29T10:14:00.000-04:00

That's a 2 N weight hanging by two strings. The left-hand
rope passes over a pully to a 1 N weight; the diagonal rope
is attached to a digital scale at the top of the picture.

In Honors or AP Physics, I begin the year with equilibrium, not with motion. In a few days, the class gets comfortable with free body diagrams, forces, and two-dimensional vector analysis.

Next comes motion in one dimension (graphs first, then algebra), followed by projectile motion. Finally, we cover Newton's second law. Since we did equlilibrium already, students are comfortable with free body diagrams and writing a vector sum of forces; since we did motion already, they already have some idea of what acceleration is. Rather than a tough *new* topic, the second law becomes a way to review and solidify the first two topics.

The picture shows my third or fourth demonstration of the school year. We begin by equating horizontal tensions in ropes pulling on a stationary block. Next, I hang a 200 g mass vertically to find the tension in the supporting rope. Easy stuff, so far.

And then, I attach a horizontal rope over a pulley attached to a 1 N weight. (In the picture, the hanging weight on the left is below the table, and out of the frame.) When we make the free body diagram, everyone's comfortable with the weight of the 2 N weight acting down, and the horizontal rope pulling leftwards. We draw the arrow representing the diagornal rope's force at an angle, of course. Then what?

The class has already been taught that in equilibrium, up forces = down forces and left forces = right forces. I ask, which is this diagonal rope, an up force or a left force? Someone always comes up with a reasonable answer: "both." I redraw the free body diagram, with the tension in the diagonal rope replaced by two arrows, one up, and one to the side.

The class is totally comfortable with the upward component being equal to the mass's weight of 2 N; and with the leftward component being equal to the weight hanging over the pully of 1 N. (They're also totally comfortable with me using the term "component" without preamble.) It only takes a suggestive diagram to get someone to suggest that the resultant tension in the rope itself will be not 2 N + 1 N, but the pythagorean sum of 2.2 N.

The clincher comes when I call a student to the front to read the digital scale attached to the rope. It reads... 2.2 N. Physics works. I can even predict (and then measure) the angle made by the diagonal rope.

The key to this whole process is that I'm *not* just telling the class how to solve abstract vector addition problems. I'm not telling them anything at all, really; I'm drawing diagrams and asking questions, getting someone in the class to suggest the next step wherever possible. I model the correct problem solving method for equilibrium problems on the board, of course, but everything I do flows naturally from the fundamental principles of equilibrium: up = down, left = right. I don't use any words like "vector" or "reference frame" or "coordinate system." The only technical term I'm introducing is "component," which was introduced organically.

The final demonstration with this setup involves adding a "mystery weight" to the stuff hanging over the pulley. I measure the new angle that the diagonal rope makes, so I have a chance to suggest how to use sines and cosines to "break an angled force into components." We predict the reading in the spring scale, and the amount of mystery weight that I added. Once again, physics works.

Forget spring scales, look what I found!

2011-08-26T16:39:00.000-04:00

At this year's AP reading, I was pointed toward dealextreme.com, a Big Lots style online retailer. You can't rely on them to have exactly what you want, but if they do have what you want, it will be cheap.

When I browsed the site last month I found some "portable electronic scales," pictured to the right. Huh... I use crappy spring scales that are easy to break. My set is in need of replacement.

This electronic hook scale doesn't measure in newtons, but does in kilograms (or ounces or pounds or "Jin," whatever those are). The range is up to 20 kg -- way more than I ever need -- and has a 10 g resolution.

Dealextreme sells these for 6.90 apiece, with free shipping. That's much less than I paid for crappy spring scales from a major science supplier last year.

The reader who recommended dealextreme.com warned me to order one of anything before I buy a class set. He said that sometimes the products are defective or just lousy. But because they're so cheap, it's worth the occasional lemon. I bought two of these portable spring scales, and both work fine. I'll set up my opening demonstration next week using these rather than spring scales; I ordered eight more so I'll have a class set for our first laboratory exercise.

Oh, and if these do die in a year, they are no worse than what I ordered from Fischer or Flynn or Sargent-Welch.

Mail Time: What if everyone had physics last year, too?

2011-08-18T22:35:00.000-04:00

Joe Konieczny, who teaches in Georgia, writes in with a problem some folks would love to have, but a problem nonetheless:

This is my third year teaching AP Physics B and I'm at a new school with students who have already taken a year of Honors Physics (just switched from public to private school). The past two years my students have all taken the AP class as a first year physics course and so this year, three weeks in, I've yet to actually teach them something they don't know. I'm struggling to keep them challenged. How do you approach your AP students who have already seen a year of physics and keep them challenged?

Joe says he's "three weeks in" because in Georgia, summer vacation seems shorter than the lifetime of a muon.

Well, Joe, to be honest, I've never taught an AP B course in which ALL of the incoming students had taken physics before. And even then, the vast majority of those who have taken physics did so as freshmen. I just went at it as if it were a first year course, and everyone seemed happy.

The first step for you would probably be to evaluate to your satisfaction the scope and rigor of their previous physics course. Did all students take the same first-year course? Was it with the same teacher the whole way? Was the instructor competent? What topics did they cover, and how well do your students understand those topics? The first place to start, if possible, is to have a conversation with the students' previous teacher.

Next, right now in your current class, try getting into a topic they *haven't* seen before. Then you can get a sense of the students' true ability. Furthermore, depending on the topic, you might be able to see whether the students really understand what they learned last year. For example, maybe they didn't cover fluids last year. Dive in. (Hah!) See how they approach an Archimedes problem that includes equilibrium or Newton's third law. See how they handle a lab.

If your class truly has mastered the fundamentals of solving problems with Newton's Laws, energy conservation, and momentum conservation, then you can think of AP Physics B as applying those fundamentals in a variety of different topic areas, spending more time on the areas left uncovered last year. If, on the other hand, most of them keep saying things like "Wait, what do you mean, work done by friction?" then maybe the start-at-the-beginning approach would be better.

Regardless, by insisting on outstanding problem presentation with thorough explanations, it's likely that you can keep your strong students engaged, even if they think they have seen the material before. Setting sky-high expectations for problem sets is likely critical... if the students are acting unchallenged, then there's no reason they shouldn't be doing picture-perfect, suitable for framing in a museum, jobs on their homework. Perhaps you might think of last year's course as a wonderful head start, which could allow you to actually finish teaching all topics thoroughly in AP Physics B. This would make you practically unique amongst your peers.

Good luck. Let me know how things go, or if you have specific topics areas in which you want some feedback. It is *tough* to teach second-year physics when you weren't the first-year teacher.

Classic Posts: First Day of School

2011-08-17T10:13:00.000-04:00

Now might be a good time to refer readers to the classic post exhorting the masses to DO PHYSICS on the first day of school. In AP/honors, I start with forces, free body diagrams, and equilibrium; in general physics, I begin with motion graphs. In all cases I have live, quantitative demonstrations, which start within 15 minutes of the opening bell.

The "First Day of School: Do Physics" post is linked here for your reference. Enjoy!

GCJ

Rewriting Problem Sets for Honors / AP Physics

2011-08-14T08:59:00.000-04:00

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

2011-08-09T13:37:00.000-04:00

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

2011-08-07T20:00:00.001-04:00

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

Website -- how to use a breadboard for electronics labs

2011-08-03T16:05:00.000-04:00

pic from techdose.com

I'm at Manhattan College (in the Bronx) for an AP Summer Institute. We are doing my electronics lab, in which students hook up simple DC circuits.

Students struggle using the breadboard, at least until they get used to it. I used breadboards for many years in college, so I have no difficulty teaching their use, and understanding how they work. However, if you haven't used these thingummies before, you will have enough trouble learning their use, let alone explaining their use to a novice student.

Michael Morgante, from New York, asked me whether I have an instruction manual of how to use a breadboard. I didn't; but I googled, and found this wonderful guide through techdose.com. Read through the five or so pages, and you'll have a better clue.

Should you xerox this for your students? I don't think so. They ain't gonna read through five pages of dense text and diagrams during lab! But you will find this guide useful for yourself. Learn how to use the breadboard well enough that you can demonstrate its use to a class of novices, so you can answer simple questions. Hopefully this site will help.

GCJ

Framing appropriate questions for conceptual physics

2011-07-30T11:08:00.000-04:00

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

Three 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

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

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 might reasonably perform this motion?

(A) A car on an interstate

(B) An airplane during takeoff

(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

2011-07-25T18:13:00.001-04:00

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

2011-07-25T11:50:00.000-04:00

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

2011-07-14T08:29:00.000-04:00

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

2011-07-09T07:31:00.000-04:00

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

2011-07-04T12:24:00.000-04:00

"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

2011-06-30T08:40:00.000-04:00

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.

Classic Posts: In Opposition to the Summer Assignment

2011-06-27T10:08:00.000-04:00

While I'm working on some new post ideas (and on my classes for next year), why not check out a Jacobs Physics Classic inspired by my rising 3rd grader's summer calendar of reading and math? Check out the post in which I explain why it is generally NOT useful to assign summer work in physics.

In Opposition to the Summer Assignment

GOOD GRAPHS: a sequel to BAD GRAPHS

2011-06-23T08:50:00.000-04:00

I do have a couple more BAD GRAPHS. These are utterly obvious, so I won't post pictures:

(BAD GRAPH #9) Failure to draw a best-fit at all means the slope cannot be taken properly
(BAD GRAPH #10) Failure to label the axes of the graph and to include units means the graph is worthless.

Now that we've washed our hands of those, it's time for some GOOD GRAPHS.

GOOD GRAPH #1: y-intercept is clear

The y-intercept may have physical significance. Often it's useful to be sure that the y-intercept can be recognized by inspection. However, this is not the only GOOD GRAPH.

GOOD GRAPH #2: You don't HAVE to start scaling from the origin

This graph is just dandy. In fact, there has been at least one AP question (2005 problem 6) on which the scale could not have begun at the origin in order to scale the data to at least half a page. Students will attempt to demand a hard-and-fast rule about scaling graphs from the origin, but such a rule does not exist. The scaling of a graph depends on the circumstances of the data.

One warning, though, while we wrap up today's feel-good episode of GOOD GRAPHS:

GOOD GRAPH #3: If you don't scale from the origin, be careful about the y-intercept.

This graph is quite fine. Proper labels, scale, points, and best-fit. However, gotta be careful... the circled point looks to be the y-intercept. But no! The horizontal scaling starts from .01 kg. The actual y-intercept has to be extrapolated.

BAD GRAPHS: Summation
I've created this series of posts on request from several teachers. Our students come to us with essentially zero experience making useful graphs of experimental data. We have to bust all sorts of misconceptions.

Ideally, we bring our class to an understanding of the purpose of an experimental graph. A graph communicates not just the result of the experiment, but also the data acquired, the calculational methodology behind that result, the precision of the result. A scientist who says merely "From my data, I conclude that the density of this oil is 0.9 g/ml" must be taken at his word. It is so much more transparent to say, "The density of this oil is 0.9 g/ml, as determined by the reciprocal of the slope of this graph here." Of course, a BAD GRAPH undermines this point.

It's great if you can get your class to see why they should not make BAD GRAPHS. But the other usefulness of this series of posts is more functional. When your student tries to argue that his graph is okay, and when he's not listening to or believing your rationale, you can point him here: "Johnny, look at BAD GRAPH #5. That's why you're going to redo the graph you submitted."

Bad Graphs part II: don't force the best-fit through the origin

2011-06-21T08:47:00.000-04:00

In today's episode of Bad Graphs, we begin with another poor scale.

BAD GRAPH #4: Scaled to less than one-quarter page

As you can see -- or maybe you can't, it's so small -- these data points are plotted correctly, but in a teeny weeny portion of the page provided. A proper graph takes up well over half the available room on the page. The standard for credit on this particular AP problem (2010 B2) was for the graph to take up more than 1/4 page. Scaling across a whole page is a skill that must be taught -- it does not come naturally out of math classes.

BAD GRAPH #5: Can't see the data points without a magnifying glass

If you want to get extra-technical, the size of the data points on the graph should reflect the experimental uncertainty in each quantity measured. That is, if you could measure to the nearest milliliter, than the data points should be as big as half of a box in the vertical direction. (And if large uncertainty would make the points ridiculously big, then you're supposed to use error bars.)

For the purposes of AP exam questions or labs within my course, all I ask is that the data points be clearly visible, as in all of the other BAD GRAPHS shown in this post. The graph above, though, shows itty bitty dots and a nice best-fit. Sure, the best-fit will yield a reasonable slope, but without easily seen evidence of where that slope came from.

BAD GRAPH #6: best-fit line forced through the origin

A best-fit line should reasonably indicate the trend of the data. There is no one "best" best-fit, but rather a range of allowable best-fits. I've occasionally had my class draw the steepest possible best-fit, then the shallowest, and note that the value of the slope is somewhere between these two extremes.

The problem with the graph above is much more subtle than with some of the other BAD GRAPHs. This student has drawn the best-fit line by starting at the origin of coordinates, and only then trying to approximate the trend of the graph. Problem is, for one thing, the origin is not a special spot on the graph. The point (0 kg, 0 m³) is no more important than the point (.04 kg, .000054 m³). Even in the case where (0,0) is a data point, it's a data point like any other. Would you insist that the best-fit line always go through the third data point?

In this particular experiment from the 2010 AP exam, the y-intercept of the graph was explicitly non-zero. (In fact, the last part of the question demanded students to figure out that the y-intercept represented the volume of fluid displaced by the floating cup alone, without any additional mass.) Forcing the best-fit through the origin not only artifically steepens the graph's slope, but it obscures the physically meaningful y-intercept.

Of course, forcing best-fits through the origin isn't always as subtle. Trust me. When we graded this problem, we saw the not-totally-unreasonable version above, but also we saw plenty of these:

BAD GRAPH #7: Curved to get to the origin

Yuk. But this one takes the cake...

BAD GRAPH #8: Forced through the origin that isn't even the origin

It's perfectly acceptable, and sometimes desirable, not to begin an axis at zero. However, you gotta recognize that what looks like the origin isn't necessarily the actual origin, in that case. This grapher would have been fine, except for forcing that line through the origin that, after all, isn't the origin. Boux.

One more set of BAD GRAPHs tomorrow. But I promise, I'll include a couple of GOOD GRAPHs as well.

Bad Graphs -- Common mistakes on data-graphing test questions part I: horrid best-fits

2011-06-20T09:48:00.000-04:00

In the previous post, I discussed the rubric for an AP Physics question that required graphing data. A number of folks requested that I show and discuss the most common mistakes on this type of question. I should emphasize that while I am speaking in the context of grading the AP Physics exam, the graphing issues here are germane to experimental physics at any level. Even in the most basic conceptual physics course, even in our professional level Research Physics course, appropriate graphing skills should be developed.

Don't let your students' graphs look like these. You may laugh at some -- just the mere fact that you're reading this blog implies that your students would be less likely to make most of these mistakes. But understand that every one of these mistakes is made FREQUENTLY on the AP exam.

BAD GRAPH #1: Non-linear axes

Aarrgh! This is the most horrid of bad graphs, suggesting that this student has never graphed data in his life. The only time I've seen it in my own class was the first year I taught, in the first lab I assigned to my regular 9th grade class. That was an eye opener -- we stepped back and had a new lesson the next day. On one hand, I used to think that AP students generally wouldn't make this mistake; however, having graded graphs on the actual exam, I'd now bet that one exam in twenty does this.

BAD GRAPH #2: Dot-to-dot

At least this student has graphed data before. Connecting data like this implies that we have theoretical or experimental support that the slope of the graph is or should be different in each region. Since the slope of this particular graph is related to the fluid density, the implication is that the fluid density changes depending on what mass we float on the water. Really?

BAD GRAPH #3: Curve fudged to go through each data point

This is for the folks who have been told never to connect dot-to-dot, but who are still uncomfortable with the idea that data points indicate a trend -- they are not delivered unto us on stone tablets by the Almighty. Some students do even more obvious fudging, making sure their curves go through the center of every point. They are implying theoretical justification for a 6th order function modeling the data. I remember the eye-opening I experienced when someone pointed out that if you make excel use a high enough order polynomial, you can produce a curve that will seem to fit ANY data set perfectly. I counter this misconception not only by fiat (minus one million points for drawing a baloney curve), but also by insisting on an enormous amount of data in every experiment. It's hard even for first-year students to justify fudging a fit through 20 data points.

It's not hard, folks -- when there is theoretical support for a linear graph, and/or the data look linear, just place the danged ruler down on the paper, align it approximately with the trend of the points, and draw. When done right, a proper best-fit line takes much less time than any of the baloney above.

So that this post doesn't go on for pages, I'll stop here. Tune in tomorrow for the "scaling issues" edition of BAD GRAPHS.

Graphs in laboratory -- a rubric

2011-06-17T09:53:00.000-04:00

The 2010 AP Physics B exam, question 2, provides a typical lab-based question involving graphical analysis of data. Students were asked to graph a small set of volume-vs.-mass data on the axes provided; the density of the oil used in the experiment was then determined by the inverse of the graph's slope.

It's instructive to look at the portion of the rubric (look at pages 5 and 6) relating just to the graph. Graphical analysis is an important skill, one evaluated in our classes and tested on the AP exam. But an equally necessary skill is that of creating and presenting a graph in the first place. You might think that merely making a graph is child's play compared to understanding the graph's meaning, but even strong students don't usually do a good job presenting graphs until they've practiced many times.

Part of the students' issue is that they perceive the graph creation process as drudgerous busy work. "I've got the data my teacher told me to take right here in a table. Why do I need to bother making this graph? I'll do it because my teacher is making me, but it's stupid." And they make the graph as quickly and sloppily as they can.

Well, the creation and presentation of a graph was worth 4 of 15 points on AP Physics B 2010 #2. Maybe significant credit -- or loss of credit -- can convince students to make graphs properly. It's instructive to look at how those points were awarded. We can see and communicate to our classes the elements of a graph that college professors, the AP exam, and we as high school physics teachers are looking for.

Point #1: axes. Were the axes of the graph labeled properly, with units? On this particular problem, the axes were pre-labeled, but the units had to be included. On a lab in class, I ask the students to use the axes to communicate in words the quantity measured, along with its units.

Point #2: scale. The scale must be linear (i.e. the space between gridlines must always represent the same value); the scale should allow the plotted points to take up most of the grid. On 2010 B2, the standard for credit was that the scale must allow the data to take up more than 1/4 of the grid area. I'm more stringent in my class, requiring the use of more than 1/2 the grid area.

Point #3: plot. The points must be plotted correctly and visibly, such that the measurements could be correctly extracted from the graph. Earning this point is usually a matter of attention to detail, but part of experimental physics is attention to detail.

Point #4: best-fit. A best-fit line must be straight, meaning drawn with a straight-edge. It must never deliberately connect point-to-point. It must not be forced through the origin. (That's the most common mistake here.) It should reasonably represent the trend in the data.

However you grade your students' graphs, in lab and on tests, the elements in this rubric can provide a guideline for what's important. Train your students to check each of these elements before turning in a graph. Perhaps even make them redo a graph that is substantially missing one of these elements.

Point is, a scientist would never dream of presenting for publication a graph that doesn't meet each of these four standards. Your students shouldn't, either.

GCJ