Just take the data! It works!

Left to their own devices, novice physics students get easily intimidated by laboratory.  They concern themselves so much with the precision of each measurement that they lose sight of the overall purpose of the lab.  How do we get students to just freakin' measure, for goodness' sake?

Sports analogy time:  I'm a baseball umpire.  When I work a game with players and coaches who have never seen me, they're sizing me up, figuring out what's a ball and what's a strike.  

Now, I generally work high school JV and 8th grade games.*  I call a wide strike zone -- a tight zone at a level where the pitchers can only aim the ball within a steradian or thereabouts leads to walk after walk, which is no fun for anyone.  So how do I establish this strike zone?

I don't talk about it.  I just call it and smile confidently.

Sure, I get a lot of stares some bad body language, even a few verbal complaints in the first few innings.  But it's amazing how quickly everyone sees what I'm doing.  They adapt.  By the fifth inning, the batters are swinging more often; they aren't turning around when I call a strike on the outside corner.  And if they see me in a game a week later, they know what to expect right away.  I get a fun, action-packed, fast-paced game with few if any complaints -- all because I weathered the initial storm to establish my strike zone. 

* By choice, much of the time -- I've done varsity games, but at varsity they expect you to start perfect and get better.  The participants and fans at a lower-level game are so happy to see someone who seems relaxed but serious and competent that they don't complain or argue with me.  I've had even losing fans repeatedly thank me for my work as I'm leaving... that never happens at the varsity level.  

I start establishing the physics laboratory equivalent of the strike zone on the first day of class in conceptual physics.  We measure angles of reflection and refraction with a ray box, a protractor, and a mirror.  I call students to the front of the room to make the measurements and record data on the board; everyone else is in a seat making a graph as the measurements show up on the board.  Easy stuff, but we're learning:  we're learning that angles are measured from the normal, we're learning how to use a protractor, we're learning to graph as we go in lab... we're learning not to think too hard, but just to make the measurements and move on.

Then in the first student-run lab exercise, they measure angles of refraction in a plastic block with a ray box and protractor.  I go from group to group, cracking the figurative whip.  "Why are you arguing?  Just record the data point and move on."  "Why is there no graph?  No, you're not allowed to 'just graph it later,' graph it now."  "If he's so slow at making the measurement, change roles; you do the measuring, you make the graph."  "You've done fifteen measurements for angles less than 20 degrees.  How 'bout some large angles?" "You've just spent three minutes deciding between 29 degrees and 30 degrees?  Just pick one and be done with it."  

Okay, I freely admit -- *I'm* intimidating the students a bit.  A bit of fear won't hurt.  They're more afraid of me telling them they're doing something silly than they are of the scary lab equipment.  I'm so loud, too, that telling one group something that they can improve means the whole class hears.  Of course, I'm not a jerk here... groups find abundant and loud praise when their data starts looking good.  "Hey, what a great-looking graph!  See what happens when you just take the data quickly?"  I always maintain a smiling face, but I move things along with no tolerance for baloney.

Most of the class figures out by the end of the 90 minute lab period what makes me bark, and what makes me wag my tail.  I hand out candy to the group with the best graph; we deconstruct as a class what we're looking for during a data collection session.  Everyone leaves with a smile, and a bit of relief that loud guy is done shouting.

But then the second week... I don't have to shout at all.

We do the lens experiment shown in the picture above, in which students graph image distance vs. object distance for real images in a converging lens.  For the most part, they don't make the same mistakes they made in the first week; those who do start doing something silly often hear from their classmates before they hear from me.  Data collection is so fast that they're all working on the homework well before the end of the lab period.  

It all starts with weathering the storm in the stressful first lab session.  The same thing worked well in AP physics; so much so, that by mid-year I could just describe the experiment and then sit at my desk while the class got on with their data collection.  

Justifying answers in 9th grade physics

The phrase "justify your answer" appears on AP physics exams all the time... and I would contend that this phrase should be a staple of everyone's physics classes.  Students usually struggle to understand just what depth of justification is necessary; often they even struggle with the idea that a justification isn't simply a restatement of the question.

I've written before about crystallizing the elements of an appropriate justification:  it should be written to be understood by an intelligent student at the same level of physics, and should include either an equation, a calculation, or a fact of physics.  

In my 9th grade conceptual class, we're avoiding calculations wherever possible.  And ninth graders are much less savvy than seniors about what might be considered a "fact of physics."  So I've had to adjust my approach a bit.

We use the Phillips Style of teaching ninth grade physics, in which we spend time in class highlighting relevant facts of physics in the text, then we quiz on those facts.  Students are allowed to use notes that they hand-wrote outside of class for some of the quizzes.  This style does two things for me.  For one, my students can tell you pretty quickly that "When light speeds up into a new material, the light bends away from normal."  Their recall of facts is solid.

For another, and more importantly, the statements we highlight in the text define the starting point for justifications.  We never have to go deeper than the facts we've learned; we must always start with one or more of these facts.  

The requirement:  Each justification must include at least two sentences.  The first sentence or two must be facts of physics, stated pretty much word-for-word from our class notes. Then, the facts must be related to the problem at hand with a separate sentence.

Consider a seemingly simple question:

A beam of light travels from air into a liquid.  The index of refraction of the liquid is 1.4.  Will the light bend toward the normal, or away from the normal? 

 

The justification must include two sentences, for example, like:

1. Light travels as fast as fast as it can possibly go in air.  When light enters a material in which its speed decreases, the light bends toward the normal.

2. In this problem, the speed of light in the liquid must be less than in air, so the light must slow down, bending toward the normal.

Or, perhaps:

1. The higher the index of refraction, the slower the speed of light in a material.  When light enters a material in which its speed decreases, the light bends toward the normal.

2. In this problem, the speed of light in the liquid must be less than in air because the liquid has a higher n.  So the light must slow down, bending toward the normal.

Or the equation n=c/v could be used to show that the light slows down -- we put that equation in our notes.

Now, at first I'm being somewhat generous about credit.  I'm giving plenty of credit for reasonable attempts that use facts of physics from the notes; after all, these are freshmen, and I'm pleased at this point if they are not leaving problems blank.  And I'm fine for now if the answer is in the style required, but the logic is incomplete.  All I ask is that everyone write facts from the book, not facts they made up.

And that's fine progress for the first few weeks of general ninth grade physics.  One step at a time.

A clever way to insist on a good initial effort on problems

The two extremes we try to avoid in teaching creative problem solving:

(a) The student who holes up in a quiet place for hours by himself hammering his head on the desk trying to solve a problem that should take all of 20-25 minutes

(b) The student who looks at the problem for 30 seconds, throws up his hands, and turns in a blank page saying "I have no idea, this is too hard."

Somehow we have to convince students to make a serious individual effort, but to stop and seek help when they get truly stuck.  How?  I've got my own techniques, which usually involve rules about how much time students must spend writing down their own ideas before collaborating.  Occasionally I've assigned work due on one day, then on that day granted a reprieve to allow further collaboration.  That works great; except, you can only do it once or twice before students stop doing the individual work, hoping for and expecting a reprieve.

Jen Deschoff, originally a Michiganer but now a North Carolinininian,  created a kick-arse approach to holding students accountable for their individual effort on problem sets.  In my Summer Institute that Jen attended, I pointed out the four essential elements of a well-presented physics problem:

* words

* diagrams

* equations

* numbers

There's hardly a well-solved AP-level problem anywhere which doesn't include at least three of these four elements.  I remember making a throwaway comment that, if I were pressed for time during the school year*, instead of grading a problem set carefully I might just look quickly for these elements in order to assign a grade.  

* Ed. Note: Why use the subjunctive?  You're a teacher.  When school is in session, you are pressed for time by definition.  Might as well say "If Ray Lewis could beat you up, then he wouldn't steal your lunch money, 'cause he's reformed now."

Well, Jen took that comment and ran with it.  She now grades many AP-level problems in two stages:

Stage 1: On the day the problem is due, students give the problem to another student, who looks for each of the four elements.  The students are NOT grading the answer at all!  They're just verifying that words, diagrams, equations, and numbers show up somewhere, and giving a grade for that.  Everyone keeps their original work.  

Stage 2: The NEXT day, everyone just turns in the problem, and Jen grades it for correctness as well as for the four problem solving elements.  

This approach fosters discussion among students -- they grade each other's initial work, and so I'm sure they comment on the correctness of the solution.  Someone who was previously stuck will likely see the hint he needs.  And now the guy who writes nothing because "it's just too hard" stands naked* before the class, seeing that he could have, should have, earned credit just by going through the problem solving motions.  (Jen says she has thrown** blank papers back to students.)  Next time, when he does go through those motions, he'll be surprised to find that physics isn't as hard as he thought.  

* figuratively

** literally

Graph paper link, and setting up a graph for conceptual physics

Above picture from
free online graph paper

Wednesday is our first day of class.  New students arrived here on Sunday, so we're in the midst of two days of orientation and partying.*  I've spent the past week making final preparations for teaching 9th grade conceptual physics -- no wonder I haven't posted much.

*Unfortunately, the skee-ball machine is delayed, so probably won't be at my house for my advisee group's get-together tonight.  I'll have to use it for physics classes, instead.

In the first class session, we will set up a mirror and ray box.  Students will take turns using a protractor to measure angles of incidence and reflection.  Each student will make a graph of angle of incidence on the horizontal, and angle of reflection on the vertical.  The point here is to establish context for reflection and refraction, and to be sure we all know how to use a protractor before the first true laboratory exercise on refraction.

In a 12th grade course, I'd have students figure out how to scale the graph.  Dealing with a range of 0-90 degrees, when the graph paper has seven major ticks and 70 minor ticks on the horizontal axis, is a serious skill that I try to teach, and which takes significant patience and practice.  However, for 9th graders I'm happy if they can plot points accurately at all.

So I've gone to this link for free online graph paper.  This page is particularly nice because you can choose from common templates (e.g. 1 inch major with 1/10 inch minor gridlines), OR you can customize the weight of the line, number of lines per inch, etc.

For that first class session, I can bring the class to understand that we need to scale each axis from 0-90 degrees.  Making that scale will be easy as pi, because I've printed out customized paper that has nine major gridlines across the page, and five minor gridlines per major gridline.  The class can see quickly that each major line will represent 10 degrees, so each minor line will represent two degrees.  And the graph will take up the whole page.

GCJ

Wolfram calculators, and a conceptual physics kinematics possibitily

I've been using Wolfram Alpha scripts regularly as I prepare conceptual physics questions.  I need to know, say, the critical angle for light traveling from Lucite to water.  I'm more than competent to use a scientific calculator to figure that out; however, getting up to fetch the calculator* is more trouble than it's worth.  I just go to wolframalpha.com, type in "critical angle calculator," and input values. Voila.  

* and not finding the calculator, and swearing mildly, and looking somewhere else, and... honestly, I've got no grounds to complain about students, Burrito Girl tells me.

In conceptual physics, I don't want students doing any plug-and-chug problems that truly require a calculator.  They can find the speed of a mass dropped from rest after 3 seconds:  add 10 m/s of speed each second.  But they can't find the maximum height for a ball shot upwards at 4.8 m/s.  

That said, by the time we get to kinematics, I *do* want my students to be able to fill in known and unknown variables in a chart, with appropriate signs.  With no calculation, students can recognize that  "maximum height" means final velocity equals zero; that initial velocity and acceleration must have opposite signs; and that the problem is solvable with three of the five kinematics variables.

The final skill I'd like to teach is recognizing the reasonability (or unreasonability) of the answer.  We can develop a feel for how fast 4.8 m/s is -- that's a bit more than 10 mph, so we can all throw a ball much faster than that.  If someone tells me that the ball will go 120 m, I know that's silly: no matter how hard I throw, I cannot get a ball to reach the top of a skyscraper.  But the (correct) answer of 1.2 m is reasonable, 'cause that's a bit higher than a meterstick, and I can certainly throw higher than that.

Now, Wolfram Alpha will, in fact, spit out kinematics answers given input values, just like it spit out critical angles.  But the script for kinematics is not neat and clean.  Look up speed under constant acceleration on wolfram to see what I'm talking about.  I can easily get to an answer, but it often takes three clicks to choose the right input format, and then much sorting through a wide variety of output formats (e.g. 480 ms and .48 s and such). That's too complicated for freshmen.

I've taught kinematics for years using a five-entry chart, always in the same order, for each problem:  initial velocity, final velocity, displacement, acceleration, and time.  I'd like to see a script somewhere that takes these exact inputs in this exact order, and that spits out the missing values.  

Now, the simplest solution is to use the TI-83 calculator.  My colleague Alex Tisch actually programmed something like this.  But I've tried to move away from that evil, expensive, and complicated calculator.  Among other things, I don't want to have to teach the class the five buttons to press just to enter the program.  Instead, I want a simple app on a smartphone or on a computer.  (I'm getting ipads for use in class this year, and here would be a great use for them.  Plus most of the students have smart phones that they can use on dorm.)

Such an app cannot be that difficult to program... in fact, if you give me an Apple 2c or a TRS 80, I could still, now, create such a program.*  Thing is, I don't know how this dagburn newfangled technology works. Can someone point me to such a script?  Or, could someone program such a script?  If you do, I will send you a can of skyline chili upon request.

GCJ

* 

10 print "Nachos!";

20 goto 10

30 tell teacher computer is broken

40 wait to hit "ctl-c" until she's called three different colleagues for help

50 I never actually did this, but I had several teachers who deeply deserved it.

Conceptual physics lab: refraction without using Snell's law

We're starting the year in conceptual physics with geometric optics.  On the very first day, we'll set up a mirror and a ray box.  The class together will measure a bunch of angles of incidence and reflection, and we will together graph θr vs. θi.  We'll set up both axes from zero to ninety degrees, and show that we get a straight line.  We'll show from the graph that, say, doubling the incident angle also doubles the reflected angle.  No slopes, no calculations, just graphical experimental evidence for the law of reflection.

The next week, we'll use the ray box to shoot light into a plastic block.  We'll set up the same axes, and this time graph refracted vs. incident angle for light refracting in the block.

Now, in AP physics, we'd make a new graph of sin θi vs. sin θr; the slope of that line would be the index of refraction of the plastic.  But this year I'm not teaching AP physics.  This is ninth grade conceptual physics.  So what are we doing?  And why are we doing it?

Well, I will certainly spend about five minutes asking students to predict what the θr vs. θi graph might look like.  I'd be happy if anyone recognizes that the data won't ever approach 90 degrees on the refracted angle axis.  But prediction is not really the essential issue.  My goals for this experiment are:

(1) Establish norms for data collection.  This is a simple experiment.  I showed my nine-year-old how to do it just once, and he collected data without my help.  So there's no reason we shouldn't be able to acquire data quickly, accurately, without asking a bazillion questions.  I will go around the class and hurry them along, teaching them not to second-guess data, not to be overly precise... and importantly, to collect data rather than argue with the partner.  It's also a good experiment with which to establish the rule that since no one is leaving early or doing work for another class, we might as well take as many data points as humanly possible.

(2) Practice graphing data as it is collected.  I recognize that many freshmen will struggle with a skill as simple as graphing data by hand.  So I use this straightforward experiment with axes scaled identically on the vertical and horizontal to start practicing.  Each partnership will graph data as it is acquired, one graph per group; then I'll show them where they need to collect more data in order to define the shape.  When they're done collecting, I'll give them a homework sheet, part of which will ask them to regraph their data on axes that I've prepared.  The homework is one graph per person.  This way, a partnership can split duties efficiently during lab, but nevertheless everyone will have to physically make a graph.

(3) Make a first stab at interpreting graphs.  A novice physics student might think it "stands to reason" that since the angle of incidence vs. reflection was a straight line, the angle of incidence vs. refraction should also be straight.  That's not the case.  One of the homework questions will ask whether doubling the angle of incidence doubles the angle of refraction as well... just looking at the graph shows that the angle of refraction does not quite double in this case* -- no use of Snell's Law is required at all.

*Okay, for small enough angles, doubling θi does in fact double θr as well.  If someone is actually astute enough to point out the small-large angle difference, I'll be pleased, but I'm not expecting that level of analysis.