Don’t let high school students revise – make them start from scratch

Greetings from the NSTA conference in Chicago.  Today’s post sprung forth after I attended a session about “chickenology” – two Ohio science teachers who are also chicken farmers use the creation of a gravity-fed chicken feeder as an engineering design project.  They bring their chickens into school to test the designs.  Fantastic.  I attended the workshop alongside Abbie Mills, Woodberry’s engineering teacher, and we got to talking about the design process in the high school classroom – how the chickenologists approached design, how Abbie does, how my wife Shari the ceramics professor does… and how I do in physics class at the smallest scale.

I’ve written already about how my test correction process became optimized when I stopped showing students their original test.  They now get only a blank version of the test, with indication of the parts for which they didn’t get full credit.  They are forced to look at every problem anew, without any indication of how they first tried to solve the problem.  Sure, some students try to reconstruct what they did originally… but they realize pretty quickly that they’re on a fool’s errand.  They just start from scratch.

Why don’t I let them see they’re original answers?  “Please can I see, so I don’t make the same mistakes again?” goes the reasonable request.  But chances are, this student won’t make the same mistake again, if they start anew with a fact or equation straight off our fact sheet, especially if they first have a conversation with a friend about the correct starting point.  And then if they do screw up again, they’re ready right now! for me to show them the conceptual error they’re making.  

But more importantly… students are unhealthily wedded to their first attempt at anything.  Having their original answer in front of them changes the exercise from “solve the problem correctly” to “see if I can explain why I was right, or at least partly right.”  Interestingly, Abbie and Shari independently have come to a similar conclusion about larger-scale design processes.  And both of them were high-level practitioners of engineering/ceramics already before they entered the classroom to teach those subjects.  They know.

Abbie holds a discussion after their first project with stick towers.  Whatever design they start with, she says, the students never, ever just tear it down and start over.  Even when their internal group discussion comes to a consensus conclusion that their design isn’t gonna work. So the post-project discussion becomes, “When did you figure out that your design wasn’t going to work?  Oh, like three class periods ago?  Why, then, did you continue to try to patch it up rather than just redesign?”  Good lesson, eh?

Yes, good meta-lesson, one that I’m glad is being taught.  Yet, I want to focus on the physics lesson at hand, not the meta-lesson.  I want to skip the whole three-day process of using hope and duct tape to finish, and instead force the student to begin anew.  For the long-term goals of my class, I want students to develop confidence in the correctness of their solutions so that they can scaffold their understanding to more and more complicated physics problems.  So I never ask students to revise anything at all.

Understand that this penchant for sticking with the first approach to a school project until death do us part is not unique to physics or engineering!  Shari faces the exact same issue with art students.  They are quite resistant to improving a project that needs more work – they want to be finished.  But if she takes the first attempt away and makes them start over, they produce an improved piece every time.  Same thing goes, she thinks, for her English teaching days: she was so, so frustrated that students “revised” an essay only by making small cosmetic changes in response to direct input from the teacher.  She thinks that had she taken the first draft completely away, made general comments, and demanded a new essay from scratch, her students’ writing would have been much improved.

As always, I’m transparent with my pedagogy.  As students bring me responses to check – lab predictions, test corrections, in-class problem solving exercises, anything – I either stamp them off as correct, or ask students to redo from scratch on a blank sheet.  The first time I place a student’s incorrect response in the garbage can, I see horrified faces: omg, that’s so harsh!  They see quickly that my calm, smiling, polite explanation of why, pedagogically, they need to start from scratch is in no way harsh.  They see that other students meet the same fate, such that my objection to their wrong physics is in no way personal.  And over the weeks they see how quickly they’re improving their physics understanding… to the point that the students themselves begin to trash partially correct responses without any intervention from me.  

Lab always takes longer than you think...

I just finished this year's Conceptual Physics Summer Institute.  It's always fun to share laboratory ideas, especially the "come and show me" exercises that form the ground state of my courses.  

At the institute, participating teachers did two of these activities - one with motion graphs, one with circuits.  The question I was asked throughout the weekend was, "how long do you spend on these labs in your class?"  And the answer is, for activities that took only minutes for each individual teacher, I generally spend a full week of class.  

Folks were a bit incredulous, I think.  That's a long time for what seem to be simple "worksheets".  Why do they take so long?  I've got two reasons, among others that people can suggest in the comments:

(1) I'm not just expecting students to get answers and experimental results.  For the prediction portion of the lab exercise, I'm expecting thorough justifications in exactly the format and style I've modeled for them.  No shortcuts are allowed - I only allow them to do the experiment once I've checked their prediction for that thoroughness.  

For the experimental portion of the exercise, I expect clear data that stands up to scrutiny.  At least one second of motion detector data that matches the predicted graph.  Properly obtained speeds, masses, or times that match prediction within 20%.  (For most exercises other than resistors-in-series, if they don't match prediction, they redo either the prediction or the experiment.  We don't just say "human error" and move on.  Grrr.)

(2) Teachers - myself included! - oft underestimate the discrepancy between those tasks which we can do on automatic, and those which the students can NOT.  See, even teachers who are unfamiliar with the "come and show me" methodology are familiar with the ideas that underlie the facts and equations used for prediction.  Students are not.  No, not even if you spend 10-20 minutes going over the facts and equations with the students, showing them exactly how they apply to the exact situations they'll be dealing with.  Your class is starting from square one, and the only way for them to advance to [square>1] is through slow engagement.  They must find the right fact - even if sometimes they find the wrong fact and have to try again.  They must use the equation correctly - even if they not only use the equation incorrectly, but they also are using the wrong equation to begin with.

Oh, then consider the data collection process itself!  Making the simple measurements I ask for with motion detectors, photogates, smartcarts, voltmeters, etc. should be a two minute process - 90 seconds to set up, 30 seconds to acquire the data.  I even demonstrate this two minute data collection process for the class.  Yet.  Figuring out the simplest of ideas - like, how do I quadruple the distance this cart travels along a track? - takes forever for an inexperienced student.  Not because they're dumb, not because they're a lazy slacker, but because they are utterly ignorant, ignorant of not just lab equipment uses but of life in general.*  

* My wife found this out the hard way in her ceramics class.  The class had made cylindrical mugs from molds.  She gave everyone string and rulers, and asked them to measure the circumference of the mug so that they could cut a wraparound decoration to the right length.  She was astounded that very few students could even figure out how to make this measurement at all, and that even those who made the measurement got it way wrong.  

I'm in no way intending a negative rant about the danged kids these days!  I'm just making an observation about the reality of our students' practical skills upon entry to our class.  

One of the hoped-for outcomes of a physics (or ceramics) class is that students have gained some kinesthetic experience with how the world works.  Few school courses outside art or science require students to work with their hands.  So don't expect your class to be able to do simple tasks at all quickly.  Everything in lab always, always takes longer than it should.  And that's okay.  It's time well spent.

Teaching stories 1 - Martha's group work

“Okay, boys and girls, get out your notebooks and copy down today’s notes,” Martha pontificated. Oy, her singsong voice sounds worse than fingernails on a blackboard, Alex thought. Wait. My dad used to use that phrase… but I’ve never been in a classroom with actual chalk or a blackboard. Maybe “sounds worse than dry erase markers smell” is the modern version?  Martha’s sharp tone snapped Alex to attention.

“Right, Mr. Alexander?”

“Please?” said Alex.” 

“Please show the class a velocity vector, like I was saying?”

“Gotcha,” Alex replied, as Martha gave him the Stare of Death.  Alex drew an arrow up and to the right, labeling the angle from the horizontal as 30 degrees.

Martha took over Alex’s position at the front of the room as the big-dog takes over little-dog’s spot in line for doggie dinner.  “Now, I draw the horizontal component like this.  In math class we’d use the kohssin to figure out the horizontal component, but here we’ll just measure with a ruler.”

“You mean cosine, Mrs. F?” said the freshman Will Jefferson.  Martha switched the Eye of Sauron from her colleague to her student in the front row.  “No, Will, I mean kohssin.  See: C-O-S-I-N.” Martha wrote the letters on the board. “Kohssin.”

“Mrs. F!  That’s pronounced “cosine!” the freshman Will Jefferson said.  “It’s a natural consequence of projecting a vector quantity along the line of a second vector using the “cross product,’ aka the ‘scalar product.’  The cross product of vectors A and B is represented by AB cosine theta, where theta is the smallest angle measure between the two vectors.”

While Will’s lungs audibly refilled to continue the lecture - Will had asthma, every intake or outtake of breath was audible to the surrounding congressional district - Martha frowned, folded her arms, and tapped her feet.  Will wasn’t taking the hint.  “And so,” he said, “---”

“Mr. Jefferson, you are, of course, 100 percent correct.”  Twenty-one sets of eyes snapped to Alex.  “Although, you’ve conflated the technical term ‘cross product’ with ‘dot product.’  That’s an easy enough mistake to make, no worries.  Thing is, Mr. Jefferson, right now I’m happy for our class just to understand how to draw and measure a vector component with a ruler.  No trigonometry necessary.”  Alex put on his biggest smile.  “If you, or anyone else, would like to stick around after school one day this week, I’d be happy to show you some advanced vector operations and how they apply to physics beyond this course.  

“Right now, though, y’all take a look at my diagram here.  This is all we need for today.  Watch what I do so you can do it on the homework assignment.” 

As Alex turned to draw on the board, he registered a gaggle of open mouths among the students.  Except for the freshman Will Jefferson.  His eyes were wide, but his mouth was closed.  The rest of the students seemed stunned.  Alex heard a whisper somewhere in the back: “Woah! Will shut up!  How’d that happen?”

***

“Will sure is smart,” Martha mentioned to Alex conversationally.  All students had filed out, and Alex was sprawled in his desk chair.  “Yup,” Alex replied.  He was tired.

“He’s too smart, I think,” said Martha.

“How is he ‘too smart?’ I mean, isn’t that our job to help students get smarter?”

“I mean, he’s way ahead of the class, and that’s not good for him or for overall class morale. And he needs to learn when to speak, and when to keep quiet. Let’s put Will in a group tomorrow to help some other students who aren’t as smart as he is.”  

Alex frowned. Martha’s tone sounded ominous, as if a soundtrack were playing a scary string crescendo over her words.  But Alex didn’t have the mental energy to discuss further.

***

“Good morning, boys and girls!” Alex cringed, outwardly as well as inwardly.  He couldn’t help it.  Why does Martha have to address the class that way?  Why not “folks,” or “everyone,” or even “class?”  Calling 14 year olds “boys and girls” is guaranteed to breed resentment; it preemptively destroys relationships. 

“You have today’s lab sheet on your desk.  We are measuring the circumference of circular things with a string, and the diameter with a meter stick.  Please graph circumference on the vertical axis and diameter on the horizontal.  Your groups are listed on the screen.  I’ll give a score for the accuracy of your data, for your ability to work together as a group, and for the analysis.  One graph per group.  Okay…. Go!”

“Dammit!”  said Lindsay, sotto voce but not so sotto that her friends couldn’t hear her voce.  “Why do *I* have Will in my group?”  The students surrounding Lindsay laughed.  Most of them, anyway.  

Will hung his head.  But then he fixed a smile, sat next to Chris and Wilson, and grabbed the lab sheet.  “Hi, Christopher, Hello Wilson.  Here, I have four strings so that we can divide the measuring work.  Here is the graph paper; let’s each mark our data points on the graph ourselves, does that sound good?”

Chris and Wilson grunted noncommittally.  They were both eyeing Lindsay surreptitiously as she flounced toward their table.  “Ugh.  So you’ve already given us our orders, right, Will?  You’re so smart and diligent, aren’t you.”  Eye roll.

“Lindsay, I made a suggestion about optimizing our efforts so that we can be done quickly and accurately.  You don’t have to agree with me, of course - do you have an alternative suggestion about the division of labor in this enterprise?”  Lindsay said nothing, just sat still and defiant.  

Chris grabbed a string and started measuring the circumference of the wall clock above their desk.  Will worked on a table leg.  Wilson started to get up to find something circular. 

Lindsay looked around… no one was paying any attention to her.  

She fixed her face in a determined look, adjusted her blouse, and leaned across the table toward Wilson.  

“Wilson, your headphones have circular ear attachments.  How about we measure those?”  Wilson turned around and stared… he could see directly down Lindsay’s blouse - not exactly into her cleavage, because what was there had already been cleaved and was now hanging straight down like an udder.  Wilson’s mouth was open.  He carefully removed his headphones from his neck, while keeping his eyes stock still.  He passed the headphones ever so slowly to Lindsay, who kept the show open for a long moment.  She sat down and busied herself with her measurement, now pointedly ignoring Wilson.

The Freshman Will Jefferson rose from the table leg.  “6.2 centimeters circumference and 2.0 centimeters diameter, though that diameter is plus or minus a number of millimeters because I can’t put the ruler through the center of the table leg, ha!”  Wilson and Lindsay stared.  Will graphed his data point, and started measuring around the large circular table itself.  

“Ach!  Will, what are you doing close to me?  Stay away!”  Alex turned his head at the shrill exclamation.  Lindsay had backed up as if Will were a skunk.  In truth, contrary to Will’s classmates’ expectations, Will was both cleancut and, well, clean.  Alex knew what it was like to be thought of as the smelly kid.  While Alex himself had been quite a clean, not-smelly 9th grader, he had in fact been a greasy and odiferous 7th grader.  Alex’s classmates hadn’t adjusted to that changing nasal reality for an entire presidential administration.

“Lindsay, I just measured the smallest circumference our group is likely to find; now it is time to measure the largest available circumference.  I’ll only be a moment!”  

“Harumph!” Lindsay said.  When no one noticed her Harumph - except perhaps Wilson, who was still standing still with his mouth open - Lindsay looked around, and made a beeline for a different group.  

Chris, Wilson, and Will settled into the experiment.  Chris put a point on the graph.  After a wistful look at Lindsay’s receding tuckus, Wilson acquired data from his headphones.  Will looked at the graph.  “Okay, if we each get a couple more points in between the table leg and the table, we’ll be good!”  The others were silent, but seemed happy to follow Will’s lead.

Martha strode up to the table.  “This graph is good so far.  Where is your fourth group member?”  

“Mrs. F, our fourth group member has abandoned us, but we are making significant progress in acquiring linear data!” said The Freshman Will Jefferson.  Martha gave the three boys her most condescending frown.

“Well, that doesn’t seem like an appropriately functioning group!  The boys taking over all the tasks and ostracizing the girl!  That is unacceptable.  LINDSAY!  PLEASE COME BACK!”  

Lindsay aimed one last giggle at her friends, then walked meekly back to the table where Martha waited for her.  “Yes, Mrs. F?”

“Lindsay, I’m sorry you felt you needed to leave.  These boys will be inclusive from now on.  Right?  Right?”

Chris and Will stared daggers at Martha.  Will looked angrier by the moment.  He started to say something, but Chris walked in front of him.  “Yes, Mrs. F,” Chris said.  “We understand.”  He looked back at Will, mouthing “it’s okay” with what he hoped was a gentle face.  

“Sure,” said Wilson, “we are very happy to have Lindsay with us!” He looked at Lindsay.  Looked at her chest.  Looked back up at her eyes.  Lindsay smiled evilly.

“Good,” said Martha.  I have taken off 10% from your lab group for this temporary breaking up.  Let’s not allow that to happen again, okay?”  

Chris still had his back to Martha, and was watching Will.  As Will drew his audible squeaky breath, it seemed as if he were a dragon preparing to level a city block.  Chris gently trod on Will’s toes.  “Not now, later,” he mouthed, practically pleading with his eyes.  Will relaxed marginally; his exhalation was a damp squib.  

Martha moved on to harangue another group.  Chris closed his eyes in relief and sat down.  Will’s anger had been turned from medium-high to simmer.  He simply stared at Lindsay.  “Well, I guess we’d better try to get the other 90% of the points,” Will said, keeping his eyes locked with Lindsay.  Finally he broke away and started measuring the knob on the classroom thermostat, on the wall just behind Wilson.   

Wilson and Lindsay smiled at each other, but mischievously, not kindly.  Wilson measured his other headphone.  He put a data point on the graph.  And another data point.  He looked back up at Lindsay, and moved aside so that she could watch the show.

And sure enough, as Will put his next data point on the graph, he gasped.  “What’s this?  Who measured a 10 centimeter diameter and a 60 centimeter circumference?  And this other point, too - that’s not possible!”  Chris shrugged.  Wilson just looked back and forth from Will to Lindsay, alternating between “who, me?” body language and a shit-eating grin.  

“Are you sure of these, Wilson?  Can I see what you measured?  Because these data points don’t make sense!”  

Wilson didn’t say anything.  He just leaned over with his pencil, and put another point on the graph - randomly.  Will’s face contorted.  “You can’t do that!  This isn’t science, this is unethical in the extreme!”  Wilson kept smiling through Will’s increasingly desperate lecture - Lindsay was looking at him with wide eyes, and Wilson felt all tingly from her attention.

When Lindsay and Wilson laughed with each other, while not even looking at or acknowledging Will, Will left.  He started at the wall for a moment, composing himself; and setting himself the most neutral face he could muster, walked to the front of the room.  Alex was helping a group draw a best-fit line.  Martha was sitting at her desk.

Will stated his case to Martha.  “Mrs. F, my partners are not doing what they were assigned to do.  They are falsifying data and making our results inaccurate.” 

Martha looked up from her computer screen.  “Will, in the working world, you will have to learn to cooperate and get along with all types of people.  I’m sorry you’re frustrated with your partners, but you simply must learn to work with others.”

“Ah,” Will said.”  “This is like the working world?  Excellent.  So you are going to fire your useless employees who aren’t doing their jobs properly, right?  You’re not going to finish projects successfully to make the quarterly earnings totals with clowns like them on your staff!”

“Will, that’s enough - we don’t talk like that about our classmates.”

“Are you going to fire them, then?”

“No, Will.  Learn to work together.”

Wheezing intake of breath.  Back to the carefully neutral face.  “Then I’m sending my resume to a competitor, I’m giving my two weeks’ notice, and we are going to drive you out of business.  Furthermore, I will be filing a whistleblower ethics complaint against your company.”  Will gave Martha his gentlest smile.

“Will, I’m assigning two demerits for disrespect to a teacher.  I need you to go take a break, get some water, and come back when you can manage your out-of-control temper.”

“Temper?” Will said, placid as the Lake.  “No, Old Woman F, no temper.  Just returning what’s due with interest.”  He turned his back and walked slowly back to his chair.

Now Martha was visibly angry.  She stood up to continue the argument, but there was Alex. “You know, Martha, he was totally calm, no temper.  He wasn’t even arguably disrespectful to you until after you gave him demerits for disrespect.”  Alex spoke very quietly and gently.  But Martha snapped. 

“He called me ‘Old Woman F!”

“Well, you called them “boys and girls.”

“That’s accurate!”

“Accurate and demeaning.  Exactly like ‘Old Woman F.”

“Goddammit,” Martha hissed.  “It’s your job to back up your teaching partner, not to make excuses for impertinent kids!  Don’t ever do that to me again!”  

Alex didn’t respond - he just walked away to the middle of the classroom, where he saw Bill Clark beckoning to the freshman Will Jefferson.  “Will, come join our group!  We’d be happy to have you over here!”  Will gratefully headed toward Bill’s table before Martha arrived to talk to Will’s former group.  Alex didn’t hear what was said there, but he saw smiling and laughing from Martha as well as from the students.  It was hard to tell who was more uncomfortable - the 13 year old, or the 23 year old.

*****

Starting off simple: a story about explaining baseball to Germans

At the beginning of the year, students in their first-ever physics class are not ready to deal with the full, unadulterated complexities of the physical universe.  So we cause significant confusion when we discuss complexities.  

When they ask, "what about air resistance?", we can't go into a discussion of the transition from constant acceleration to constant velocity; we can't talk about resistive forces varying as v or v-squared; we can't talk about how even in a vacuum chamber, still some particles of air remain and exert a teeny-tiny resistive force.  

Even though these are all fully correct statements with interesting physical consequences.

Pedagogically, we absolutely must say "air resistance is utterly ignorable within this classroom, and in any simple demonstration I can do.  See here, I drop this 1-kg object and a crumpled-up piece of paper.  They hit the ground at the same time!*  And the kinematics equations make correct predictions in these live experiments I'm doing.  So don't make the world more complicated than it is.

*At least as far as our eyes or a stopwatch can discern.  It's a really, really bad idea to explain that "Well, actually, if we take high-speed video, the 1-kg object hits a very wee bit before the paper."  Every time you're tempted in the first half of your first-year physics course to start a sentence with "actually" or "technically", put $5 in the Swear Jar.

Let me tell you an allegorical story.

In 1995, in the first few weeks of graduate school, I got to know some students who had grown up in Germany.  I very much enjoyed them; they invited me to the official "international student" events*, they invited me later that school year to watch the Champions League final (1.5 decades before I had any clue what a "Champions League" even was).

*I wasn't out of place - my nametag listed my home country as "Kentucky", which was as foreign to most university folks as was Berlin or Cologne.

One day in October, a group of three German students came to me in a panic.  A professor had posed a numerical simulation / programming challenge to their class as a major project:  Consider a baseball game that's going into the top of the 9th inning.  Given the current score and some basic statistics about each team's batters, write a program to estimate the probability of each team winning the game.

To me, this assignment seemed straightforward.  When I was 10, I used dice, playing cards, and the "random number" generator on my TRS-80 to simulate way, way more complicated baseball situations than was posed here.   

But these German graduate students had even simpler questions for me than I had thought about at age 10.  "What's a 9th inning?" for example.

I invited these folks, and a few long-time baseball fans, to my apartment to watch some postseason baseball.  And yes, the Germans appreciated my friendliness and hospitality, and I did help them a bit.  But I realize that I could have helped them so much more if I had understood basic pedagogy.

I should have told them "The batting average gives the probability of reaching base.  As your first pass at the problem, promulgate the probabilities: For each batter after the third who reaches base, count it as a run.  But when three cumulative batters DON'T reach base, end the inning."

That approach is insufficient in a thousand ways.  But it would have given a first-order approximation to their assignment.  It could have given these German students a route to a finished project, and quickly ended their difficult foray into understanding baseball (though they would have learned some basic vocabulary about the game).  It could also have piqued curiosity to encourage them to learn more - for example, if they use the slugging percentage in addition to the batting average, they'd have a probability not just of getting on base at all, but of how many bases a batter might take, improving their simulation.  

Remember, though, that these folks at first did not have the context for me to differentiate between "batting average" and "slugging percentage."  They were still stuck on what, exactly, it meant to "score a run."  

What I *did* was, we all watched a game together while one of them looked at some sort of encyclopedia of baseball they had grabbed from the library.  They asked me questions about the terms in the encyclopedia: "What's a passed ball?"  "What does a 'dropped third strike' mean?"  I answered in simple language, but without getting thorough comprehension.  Responses to follow-up questions made it clear that I was trying to explain complexities of changing planes at O'Hare... to a rural Kansan transplanted in time from 1838.

I was of little help to my colleagues, though I was in fact an expert in baseball statistics.  They would have been better off NOT coming to my apartment.  I only confused them more than they were already confused.

I've internalized my failure from 1995 into my approach to the first weeks of a new physics topic, making the cleanest simplifying assumptions I can.  Speed and velocity are synonyms.  Orbits are circular.  Voltage is defined as "what a battery provides."  Keep physics simple while students wrap their heads around concepts.  Then, you can add complexities, bit by bit over months or years.