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13 March 2017

"Does that make sense?" Don't take 'yes' for an answer.

I am at heart the most straightforward, literal person in the universe.  I mean what I say, and I say what I mean.  And I hear the words that people say, too often without considering the body language and social cues behind the words.

Consider the friendly sophomore from Norte Dame Academy, at the, I dunno, 1988 or so Kentucky State Latin Competition.  We met there and had been talking throughout day.  Her team's bus was leaving before the award ceremony.  She gave me her number, and said, "please call me tomorrow to tell me the results." So, the next day I dutifully called.  I gave her the results.  I congratulated her.  I said goodbye.  I never saw her again.  Sorry, Lisa.

Or, the wonderful woman in grad school who, after we had hung out together several afternoons, said "Can you come over to my apartment tonight?  My roommate will be out.  I'll cook you dinner." I accepted.  I thanked her for the yummy meal, and left.  Sorry, Michelle.

Or, and more pertinent to this blog, the diligent junior in the weekly problem solving sessions that my college paid me six bucks an hour to run.  I showed her how to solve a problem involving the work-energy theorem.  I asked her if the approach I suggested made sense.  She said, "yes."  I took her at her word.  Sorry, Alex.

I suspect that most readers are shaking their heads at the first two stories, wondering how I could be so clueless.  Had I recognized Lisa's or Michelle's body language and tone of voice, events would have turned out less dull, or at least differently.  And decades after the fact, I now have the perspective to recognize what I missed.  Most people wouldn't have misunderstood these cues in the first place, of course; I had to work consciously on interpreting social subtext, even though such interpretation comes naturally to others.

Over twenty-plus years of teaching, I've similarly had to continually analyze and re-evaluate my students' body language and tone of voice.  In 1994 I believed Alex when she told me she understood my explanation.  Why would she have said "yes" if the real answer was "no"?  In retrospect, there could be any number of reasons.  Among others:

(a) I'm a proud, diligent student, and I cannot admit to myself or (especially) to a peer that I don't get something; 

(b) I don't quite understand this right now, but I have irrational confidence that if I stare at the problem for another 20 minutes I'll magically see the light; or 

(c) I really wish Greg would shut up and stop explaining, and the only way I can tell him that without seeming rude is to pretend I understand.

Nowadays, when I explain something one-on-one to a student, I still ask, "does that make sense?"  But I'm ignoring the verbal content of the response.  I'm watching for and listening to body language and tone of voice.  Students often use words they don't mean.  Their tone usually gives their true thoughts away; it's practically impossible for a high school student to send false messages with body language.  

What am I looking for in response to "does that make sense?"

When I explain how to approach a physics problem, I always make the student go back to his seat and write up the solution in his own words.  So I'm watching how he leaves the vicinity of my desk.

The student who truly understands my explanation can hardly wait to get back to his seat to put his newfound knowledge into practice.  He usually moves with confident purpose.  Sometimes he'll have a bit of sheepishness about him, because he realizes he should have figured this out earlier.  

The student who's still confused walks much slower, with his eyes turned upward or downward.  He's in no rush, because either he's still thinking about what I said, or perhaps he's frustrated that I won't just tell him the right answer and he's throwing a wee tantrum.  

So, when the confident student comes back a moment later, I can move him along without thinking about it -- he's got it.  

But even if the less confident student comes back with a correct answer, I still push a bit.  I ask a few more questions to test for understanding.  I make him write each step of reasoning explicitly, even though I might have let the confident student slide by with some things implied.  I don't harass or embarrass, of course... I simply recognize that this student has shown me through his body language that I have to do more to help him.

02 March 2017

Woodberry Forest Conceptual Physics Tournament -- want to be an "examiner"?

My school has for years given three sets of exams, one each trimester.  This year, though, we're limited to two written exams.  For the last trimester, we're encouraged to create a cumulative project of some sort in lieu of an exam.  Yay.

Thus, we are creating the Woodberry Forest Conceptual Physics Tournament.  This competition for our 9th graders, to be held at 1:00 on Sunday May 21 2017, replaces their final exam.*

*No, to be clear to all, we're not giving an A to the winner and an F to the person in last place.  That's silly.  We're just having a fun, competitive tournament, to determine a winner.  Judges aren't awarding grades.

How does this tournament work?

On May 2, I will reveal a slate of three problems to the 73 participants.  These problems will be old AP Physics 1 "paragraph response" questions.  Except, rather than just answer in a paragraph, the students will spend the month of May setting up experiments to provide evidence for their answers.  By tournament time, each student will be expected to be prepared to discuss the solution to two of the three problems, with both theoretical and experimental support.

At the tournament, each student will participate in two "physics fights."  Think of these physics fights like a miniature version of a graduate thesis defense.  Students will have a strict limit of three minutes to present their solution to the examiner.  An examiner then will engage each student in conversation about the problem for five minutes.  The students are judged by the examiner not only on the quality of their solution, but also on their ability to discuss the solution, to confidently hold a conversation with the examiner.

How do the students prepare?

Starting on May 2, all conceptual physics classes the rest of the year will be devoted to tournament preparation.  They'll set up experiments in class, they'll be assigned to write up their solution as homework, they'll practice presenting.  

Most importantly, my AP physics classes will spend their final weeks of the school year serving as mentors to the conceptual students.  I will assign each AP student to lead groups of three or four 9th graders.  The AP student will dive into the problems with the freshmen, helping to create and analyze experiments, helping the freshmen to understand the details of their presentations, and serving as mock-examiners in practice sessions.  This mentoring serves as the final project in lieu of the exam in the AP classes.

We need examiners.

The key, I think, to any class project is external assessment.  I and the other conceptual physics teachers will play the role of coach and advocate, always encouraging and helping the students to deepen their understanding of the problems and to improve their presentations.  Our relationship will be purely supportive, enthusiastic, positive.  

We can't then turn around and grill these same students as examiners!  That'd be like our football team's coaching staff refereeing the state finals.  Even -- especially -- if their officiating were fair, the coach-student relationship, both in practice and after the game, would be irrevocably compromised.

So we need examiners.  We can pay.

Would you like to come to Woodberry on May 21 to be an examiner?  My guess is we'd ask you to arrive at lunch time, like 12:00.  We would have a meeting of all examiners in our beautiful dining hall over lunch.  

Then we'd ask you to be the examiner for a couple of hours' worth of physics fights -- depending on how many examiners we get, you'd probably be asked to run 8-12 rounds.  Then, we will gather everyone into our auditorium for the top two participants to engage in a final physics fight for the championship.

In any case, my goal is to be done by 3:30, or possibly (it's our first time running this) 4:00 if there are logistical issues.  No later -- our students will be attending the final seated meal with their advisors that night followed by study hall, so we can't run late.

We will pay you $100 plus lunch (and even dinner, if you'd like to stick around) for your time.  (If you're coming from more than a few hours away, we can put you up on campus on Saturday or Sunday night.) I think you'd find that the camaraderie among the examiners and the engagement with the students will make the trip worthwhile.

Who's eligible as an examiner?

Certainly any physics teacher, or anyone with a physics / math / engineering background.  I'm inviting alumni whom I've taught in an AP or AP-equivalent course to come back to judge.  I'd also welcome any alumni of your advanced physics class, even if they're still seniors in high school.  As long as you can engage in conversation about physics at the AP level, as long as you can recognize good and bad physics, we'd love to have you.  When I run the USIYPT, I find the mixture of undergraduate / graduate / professor / high school teacher / industrial physicist / retired physicist on the juror panel allows some amazing relationships to develop.  I'd love to create a similar vibe here.

How can I sign up?

Send me an email, or contact me via Twitter, or call me -- my contact information is on the Woodberry Forest School faculty page.  I'll send you more information, including the three problems, and our current draft of the judging rubric.

22 February 2017

Rank the voltages: experimental evidence

 The question: 

The three circuits above are all connected to the same battery. Each resistor represents an identical light bulb.  Rank the circuits from greatest to least by the potential difference across bulb A. If more than one circuit has the same potential difference across bulb A, indicate so in your ranking.

The (very much in-depth paragraph-style) answer: Since all bulbs are identical, they have the same resistance.  By Ohm's law with the same R for each, whichever bulb takes the largest current also has the largest voltage (i.e. potential difference) across it.  

The equivalent resistance of the parallel combinations gets smaller the more parallel resistors are added.  So circuit 1 has the largest equivalent resistance, with circuit 3 the smallest -- consider each resistor to be 100 ohms, and you get 200 ohms in circuit 1, 150 ohms in circuit 2, and 130 ohms in circuit 3.  

Bulb A takes the total current in each circuit, so consider Ohm's law for the circuits as a whole.  In that case, the voltage of the battery is the same for each; the circuit with the smallest equivalent resistance takes the largest total current.  So rank the circuits 3 > 2 > 1.

The common misconceptions: I gave this to my class as a quiz, and most got it wrong.  I saw four typical categories of wrong answers:

* Since the batteries are the same, each bulb in each circuit takes the same voltage.  (No, just each circuit as a whole takes the same voltage.)

** Since the batteries are the same, they each provide the same current.  (No, batteries provide voltage, not current.)

*** Since bulb A is closest to the battery, it must take the greatest voltage.  (No, "closeness" to the battery has no bearing on a circuit problem.)

So far, this is standard fare misconception-bustin' physics teaching.  Because I posed this problem as a quiz, the class waited expectantly for me to reveal The Answer.  Ho hum... those who got it right reflexively pumped their fists, those who got it wrong either made sad eyes, or used some sour-grapes reasoning to convince themselves why they could have gotten it right.  And then they forgot the whole thing.

Or did they?

"Okay, there are the light bulbs.  You know where the wires and power supplies are kept.  Go set up the three circuits and show me which bulb A has the largest current.  Take a picture of your circuits to show me."

Ah, sh*t just got real.  

The photos are by my student Clay Tydings.  He conveniently labeled bulb A in each picture.  Now we can all see that bulb A is brightest in circuit 3.  

To address the misconceptions above, you can have the students measure voltage across the battery, and across each bulb, with the voltmeter.  If you're brave, you can even have them measure current from the battery.  They'll see The Answer, that bulb A carries the largest current in circuit 3.

But they also see that (*) the bulbs take different voltages, (**) the battery takes the same voltage every time but different currents, and (***) the voltages across each bulb don't change even when we place bulb A "last" rather than "first" by switching the leads from the battery.  

I find myself asking the class to set up the experiment proposed by a quiz problem all the time in AP Physics 1.  We've established the class's lab skills; we have introduced and practiced all topics at a basic level; we have 90 minute class periods with which to work.  So why not make the students verify an answer experimentally?  The AP exam will certainly ask them how to design experiments!

16 February 2017

Mail Time: I can't find the other force acting on this block!

Reader Josh writes in:

The system shown is traveling at a constant speed.  There is friction between block B and the ground, and there is friction between block B and block A.  We've been arguing where the second force is in the horizontal direction on block A is, if it even exists.  The forward force on A would be the static friction but I'm lost on where the other one is.  This is driving me bonkers...

Have we written a bogus question? If not, can you tell us where we're going wrong?

Ooh, what a great question.  Constant speed, eh?  In a straight line, so equilibrium? 

I think we all agree on the BOTTOM block's free body:  normal force of ground on B upward, weight downward, contact force of A on B downward, force of rope on B forward, and friction force of surface on B backward.

There's no horizontal forces acting on block A.  If there were, it'd be speeding up or slowing down, which it's not.  

You say "the forward force on A is static friction."  Well, static friction takes on any value up to the maximum.  I agree that static friction must act WHILE THE BLOCKS SPEED UP.  Once they attain constant speed, though, the static friction force drops to zero.  If the block slows down again, then the static friction force on A will be backward. 

What a great AP Physics 1 question.  More complicated than you thought, I suspect.  :-)

06 February 2017

USIYPT results 2017 from University of the Sciences, Philadelphia

The 2017 United States Invitational Young Physicists Tournament was held last weekend, January 28-29, at the University of the Sciences in Philadelphia.  I can't thank the hosts enough -- Elia Eschenazi, Michele Albert, and the rest of the folks from USciences who helped out were most hospitable and supportive.

Congratulations to all, but in particular, to Rye Country Day School (pictured) and coach Mary Krasovec.  They won their second title behind a particularly strong presentation of their experimental measurement of Planck's constant.  

The final round scores and places, noting that by tradition the finalist teams share first through fourth place:

Rye Country Day School , NY         77 points, champions
RDFZ of Beijing*                             72, 2nd place
Phillips Exeter Academy, NH          71, 3rd place
The Harker School, CA                    70, 3rd place
Qingdao No. 2 High School**          68, 3rd place
Woodberry Forest School, VA          56, 4th place

* Officially The High School Affiliated with Renmin University, China; known also as RDFZ.
** First-time participants from northern China

The Clifford Swartz Trophy is awarded annually to the winner of the USIYPT poster session.  First-time participant Vanke Meisha Academy won this prize.

And this year, the US Association for Young Physicists Tournaments for the first time presented the Bibilashvili Medals for excellence in physics.  These are awarded not based on ranking among the schools, but on overall score regardless of place.  This year, in addition to the trophy winners and final round participants, Pioneer School of Ariana, Tunisia earned a Bibilashvili medal.

This was the largest tournament in the ten year history of the event, with thirteen schools participating, including:

Shenzhen Middle School, China
Phoenixville Area High School, PA
Cary Academy, NC
Princeton International School of Mathematics and Science, NJ
Nanjing Foreign Language School, China

What about 2018?

The 2018 USIYPT will be held on January 27-28 at Randolph College in Lynchburg, VA.  The four problems involve measurements of the moon's orbit, coupled mechanical oscillators, projectiles in air, and radiation from incandescent light bulbs.  Full problem descriptions are shown at the USAYPT problem master's blog. 

If you'd like to know more about the USIYPT -- a physics research/debate tournament for high schools all over America and the world -- please contact me via email.  We're particularly interested in recruiting physics teachers, professors, graduate students, and industry physicists as jurors.  


Physical versions of energy bar charts

Like many of us, I use energy bar charts extensively.  Though my students don't all understand every detail of them all the time, the charts are the best way I know of to get them to stop plugging numbers into equations and think for a moment about how energy is transferred.  Just as "why don't you draw a free body diagram" generally gets students un-stuck on a force problem, "why don't you draw an energy bar chart" usually sets everyone on a path to success when energy is involved.

My personal touch on the energy bar chart is to insist that each bar be annotated.  Even just a couple of words help, like "it's moving" under the KE bar, or "at its lowest position" when the PE bar is zero.
Still, I don't have the sense that my class internalizes the deeper meaning of the bar chart: that the total energy on the left side, plus the "work done by external forces" column, must equal the total energy on the right side.  They know only because I tell them repeatedly; it seems an afterthought for my students, rather than the entire raison d'ĂȘtre for the chart.

How can I help my students understand intuitively that bars in the chart must be transferred among columns rather than just drawn randomly?  How can I help them see that the "work done by external forces" column is the only place where it's okay to add or remove bars?

Kelly O'Shea and Chris Becke -- and I'm sure others, but these are the ones I've seen recently -- have made physical versions of the bar chart.  I'll show you both...

Physical energy bar charts from Kelly O'Shea, @kellyoshea
Kelly tweeted this picture.  Her setup seems so simple: just a bunch of wooden blocks, pegs, and post-it labels.  Simple, maybe, but elegant.  Each setup is just the right size to put on a lab table for each small group to use in their problem solving.  I can imagine asking each group to take two pictures of the blocks: one representing the initial energy configuration, and one representing the final energy configuration.  Then I could ask something like "why are there two more blocks in the second picture than the first?  Where did they come from?"  And I'd expect an answer referencing work done by external forces.

Water-based energy bar charts from Chris Becke, @beckephysics
Chris uses water in labeled beakers to represent energy.  By setting up in the front of the classroom by the sink, he can explicitly show how work done by external forces affects a system's energy status.  Look at his labels; the faucet is "+work" and the drain is "–work."  My students when they draw bar charts can just magically sketch a few more lines in the "Wext" column to add energy to a system.  Kelly's students have to at least physically grab or throw away extra blocks.  But Chris's setup requires turning on the faucet, or dumping water down the drain, in order to include work done by external forces.  The meaning of "external" just got real.

I don't mean to suggest that either Kelly's or Chris's physical bar chart approach is the superior one.  I'd personally use Kelly's blocks in my bog-standard style of class in which students and small groups work on predictions and experiments; I'd use Chris's faucet-based chart on occasions when I want to present demonstrations from the front of the room.  

I *do* mean to suggest that if you're going to use energy bar charts as a teaching tool, I think it's worth setting up some form of physical bar chart rather than just drawing on paper.  I'm gonna have to try these.

30 January 2017

The Physics Community - remarks from the USAYPT President.

We just finished the 2017 US Invitational Young Physicists Tournament at the University of the Sciences, Philadelphia.  Please congratulate Rye Country Day School of Rye, New York for their victory.  I'll post full tournament results in a few days.

Below is my brief, slightly edited, address to the assembled throngs tournament's closing ceremonies.  The audience consisted primarily of high school student participants.  

I need to make sure you all know where I stand, though it's not like you probably don't know already. 

I believe in physics fights.  I believe in this tournament.  I believe in having us all together every year, where we compete with each other; but where we are also colleagues. Where we award a trophy, but where we also talk to one another as physicists.  Where we have people from seven different American states, and two different other countries. (Five of our schools are from the same country - China - but they are from all over China, just like the American schools are from all over the USA.)  Folks, we have people from all over the world, of diverse backgrounds, all speaking the common language of physics.  That, above all, is what the USIYPT is about.

I cannot countermand executive orders.  I can not make laws in the United States.  I have no influence there.  And it's just as well that I have no influence there.  I am not a politician.

Where I do have influence, though: I can help all these folks get together to speak the common language of physics to each other in person, to build relationships... such that in ten or twenty years, when YOUR generation is in charge of this country or your respective countries, you will know good people in America.  You will know good people in China.  You will know good people in Tunisia.  You will have the relationships and the background -- both a scientific background and a cultural background -- such that you can make different decisions. 

And I hope that by then the world will be a better place, due in very small part to our efforts.  


16 January 2017

Mail Time: Rigorous definitions of circuit properties in AP Physics 1

Buckeye native Matthew writes in with a question about circuits in AP Physics 1.  He’s referring to my summary post of the topics on the exam

Greg - Happy New Year!. As I am outlining the second semester of the year I am having difficulty finding information about

Non-rigorous definitions of voltage, current, resistance
Rigorous definitions of voltage, current, resistance

Any information you could provide me about finding the differences between non-rigorous or rigorous would be appreciated. 

I am thinking (hoping) that I already address this and just have not been exposed to the terms non-rigorous and rigorous when it comes to the definitions?!?!

Matthew, great timing -- I just worked on this difference with my AP class last week.  

"Rigorous" and "non-rigorous" definitions are my own personal terms, not anything to do with materials published by the College Board.

I start circuits on the very first day with the non-rigorous definitions:

Non-rigorous definitions of voltage, current, resistance
Voltage is provided by a battery.  Voltage is measured in units of volts.
Resistance is provided by a resistor, a lamp, or any electronic device.  The units of resistance are ohms (W).
Current relates to the amount of charge flowing through a resistor.  The units of current are amps.
Ohm’s law states that voltage is equal to current multiplied by resistance:  V = IR.

With just these facts, I can have students graph current and voltage to verify or discover the relationships in ohm's law; I can have students measure brightness of a bulb as a function of voltage and resistance to discover the power equation. And then we can do basic semi-quantitative questions with single resistor circuits, like "I replace a 10 ohm resistor with a 20 ohm resistor, by what factor has the current in the circuit changed?"  

Then we move on to circuits with series and parallel resistors, then to combinations of resistors, then to light bulbs, then to circuits with switches, using ammeters and voltmeters. I like to give circuit TIPERs, but make the students set up the situations experimentally to verify their prediction.

During these first couple of weeks, I never mention Kirchoff's laws -- rather, we have rules about current and voltage for parallel and series resistors which are a poor person's statement of Kirchoff.  (“Voltage across series resistors is different for each, but adds to the total.”)

Finally, once we've done all of this... everyone has a personal, intuitive understanding of what current and voltage are.  That understanding has been built on experience through problem solving, lab work, right and wrong answers.*  In eduspeak, this personal, intuitive understanding is referred to as an "operational definition."

*Never through analogy, though.  If students create their own analogies, great.  But direct experience without analogy has proven far more effective at building knowledge and avoiding misconceptions than any analogy I've ever tried.  Voltage and current aren't truly LIKE anything else.  

So, with that personal understanding built, it's time to introduce the rigorous definitions:

Rigorous definitions of voltage, current, resistance
Voltage is energy per charge.
Current is charge per time.
Power is energy per time.
Potential difference is a synonym for voltage.

Remember, your students aren't likely to come into the course with an operational definition of charge; and gaining the experience necessary to develop what charge truly means requires, I think, a full-on AP Physics 2/C treatment.  And "energy" is still a bit fuzzy in students' minds.  (These rigorous definitions can actually help students develop their operational definition of energy and charge, since they're so solid on voltage and current.)

I therefore tell the students to translate from rigorous language into our non-rigorous definitions.  When they see a problem like "rank these bulbs based on how much energy is gained by an electron passing through" they recognize that as asking about energy per charge; that just means "rank by voltage," which my class is well trained to do.

The last bit about circuits we do is to use Kirchoff's laws, and to make voltage vs. position-in-circuit graphs.  Here I use the terms "electric potential" and "electric potential difference" with impunity.  But by this time voltage is such an ingrained concept that the class has little difficulty anymore.

08 January 2017

What advice can I give a student with a C right now?

This showed up in the comment section from my August 2016 post in which I write a letter to my upcoming AP class.  It deserves a response in a full post, because I suspect that many physics teachers are confronting just this kind of problem this time of year.

A very concerned mother here. My very strong student pulled her first C in her life in the first semester of physics. We have tutors, spoken multiple times to the teacher and everyone says that she understands the materials, and almost always does badly on the test. When asked, she says that the test is so different she does not know what to do. As an engineer who had taken high levels of physics, I am really at a lost to help her. As an experienced teacher what advice can you give her. We need to make the next upcoming semester rock! Appreciate your kind assistance.

Now, remember that I have no direct contact with this specific student, so I can't give anything more than general advice. That said, I've seen this pattern many times -- historically outstanding student who gets As in history and biology, diligent, willing to work hard with support at home from subject matter experts... yet does not perform on physics tests.

The general advice starts with recognizing that there is no magic bullet. Neither this student's parents, her tutors, her teacher, or I can instantly create success. Physics skills are learned gradually, over time. They come quicker for some than for others.

That said: It's very, very hard for me to train even good physics teachers to back off and make students struggle without giving away answers. Students (and parents!) with good intentions often treat homework as a "just get the answer" exercise without engaging in the process.  Thus, in so many cases as you describe, the student's extensive support network is HURTING rather than helping. When tutors and expert parents get involved, students tend to ignore the part about "here's how to approach the problem" and think instead "thank goodness, I got the answer" -- no matter how good the tutoring might be.

So my fundamental advice is to let your daughter struggle. Give her loving emotional support, just as you would if she were on a softball team and kept striking out. When she asks questions, don't solve problems with her, don't help her figure out mistakes.  It's her homework, let her do it. Instead, advise her to think all the time about the process of getting answers, the general approach to different kinds of problems, even if she doesn't get the exact right answers. Help her keep focus on the big picture of all the things she's done well -- both in and out of physics class -- and don't engage with Chicken Little talk.

It's very likely that, by year's end, she'll start making connections and improve dramatically. I've had a number of students making Cs this time of year who ended up with 4s and 5s on the AP exam. Things often click after long-term exposure to physics.

It's also possible that she pulls a C for the year. That's okay, too. I have struck out every at-bat for four games in a row; I've earned Cs on tests and in classes. Those strikeouts and Cs no more define me than they should define your daughter. 

29 December 2016

Start Teaching Newton's 2nd Law Without Numbers or Equations

You've gone through a unit on motion; your students know the difference between velocity and acceleration.  (Or, at least some of them do, some of the time.) Now you're ready to introduce F = ma.  What do you do first?

I think most physics teachers, and certainly most textbooks, recognize the necessity of diving into free body diagrams right away.  Somehow, you must show the difference between an individual force and the NET force.  I concentrate on getting students to write out the object applying and experiencing the force; this helps avoid including fictitious forces (like "force of motion"), and it makes a future discussion of the third law child's play.

But, what do you do with those free body diagrams, other than make them?  

(1) Some books and teachers jump to a mathamatical treatment of F = ma.  Practice problems in which the free body is used to determine the value of the net force, use the second law to determine acceleration, then use kinematics to get something like the initial or final speed of an object, or its time in motion.  Then you can do the reverse -- use motion information to calculate net force, and then the amount of an individual force.

(2) Others go from the free body diagram to a semi-quantitative treatment of F = ma.  That is, show mathematically and experimentally that at constant mass, a larger net force yields a larger acceleration; for constant acceleration, a larger mass demands a larger net force.  Linear graphs can be created to verify the second law relationship.  

While I get to both (1) and (2), I don't start there.  I start merely with free body diagrams and the direction of motion.

But Greg, you say.  Free body diagrams have nothing to do with the direction of motion.  

Yes.  That's the point.

Before I do any work with the relationship F = ma, I ask every possible question I can think of about how the object is moving.  Here we're considering motion in a line only; circular and projectile motion are for later on.  

For example: This cart experiences a 3 N force to the left, and a 2 N force to the right. 

* Which way is the net force on the cart?  (Left, because the greater forces act to the left.)

* Which way is the cart's acceleration? (Left, because net force is always in the direction of acceleration, and we just said net force acts left.)

* Which way is the cart moving? (No clue.  Acceleration and motion aren't simply related.  The cart could be moving left and speeding up, or moving right and slowing down.)

* Could the cart be moving to the right?  (Sure -- if the cart is slowing down.  Note that the most common answer which is utterly unacceptable is "Yes, if another object applied another 2 N force to the right.")

* Could the cart be moving left at 1 m/s?  (Sure, as long as its speed a moment later is greater than 1 m/s.  NOT "Yes, as long as its mass is 1 kg.")

* Could the cart be moving left at a constant speed of 1 m/s?  (No way.  The cart experiences a net force, so the cart has an acceleration, so the cart's speed must change.)

It's useful to let students play with the phet simulation "force and motion basics."  In class, I have students do a series of experiments in which they predict the force necessary to cause an object to speed up or slow down.  We don't worry about the actual value of acceleration, just the directions of motion and acceleration.  

Once my students are rolling their eyes at these sorts of questions, answering with the same voice that my son uses when I remind him to wear a jacket to school on a cold day... well, then you're ready to move on to lessons (1) and (2) above.