Buy that special someone an AP Physics prep book: 5 Steps to a 5: AP Physics 1

Visit Burrito Girl's handmade ceramics shop, The Muddy Rabbit: Yarn bowls, tea sets, dinner ware...

14 October 2016

Mail Time: Why do we have to memorize facts in 9th grade conceptual physics?

In conceptual physics, I don't use a textbook.  Instead, the reference material for the class is contained in our "fact sheets."  These facts are handed out piecemeal to the class, about three to six sentences at a time as they're relevant to the current content.

You can see all the facts from the full conceptual course here; feel free to use these in your own class.

I ask students to learn the facts by heart.  We have occasional fill-in-the-blank quizzes in which they have to recall the important words in a fact; on homework, students are required to write these facts nearly word-for-word as the first step in responding to any physics problem (though they have access to notes for all homework). 

I got an email from Keri, who is using these fact sheets for the first time in her conceptual class.  She's encountered an unusual problem: her freshmen are complaining about having to memorize these facts.  How should she justify to students, parents, and administrators why a physics class requires remembering words?

Keri has three proposed responses: 

(1) Since she's giving students a formula sheet, they don't need to memorize formulas.  It's more important to memorize facts; and those facts won't be available during an exam.

(2) Paraphrasing the facts generally isn't enough, because it's too easy for a new student to miss something important in the paraphrase

(3) Facts should be instant-recall, not thought processing, so students can focus instead on the reasoning involved with each problem.  

Keri, that's a really interesting and unusual complaint. The vast majority of complaints that I get, and that other physics teachers report to me, are of the form "but I learned the facts and equations, I can spit them back, why aren't I getting an A?" Now, your students are saying, hey, don't make me memorize anything, THAT'S too hard, too! I suppose they're suggesting that we all just sit here and watch videos for a year? My cynical mind and experience as a baseball umpire draws the conclusion that people will kvetch about teachers regardless of what we do. Everyone thinks they can do a better job than we can, everyone's a critic. 

I've never been asked this particular question, but it deserves a good answer. You've given an excellent three-pronged argument. I'll elaborate on each prong.

 I love your answer #1. I'd add that memorizing facts is what allows students to deal with problems that aren't merely recitation of facts. How is anyone supposed to interpret a position-time graph if they can't remember that the steepness (or slope) determines the object's speed? 

In terms of paraphrasing, note that our daily quizzes don't say "Write fact #3 about velocity-time graphs word for word." They say, "on a velocity-time graph, the speed is determined by _____." If you can't tell me that's the vertical axis, you don't understand velocity-time graphs.  Now, I generally accept "y-axis" or something that's pretty danged close. My colleague Curtis, who taught me about this style of quiz, insists on word-for-word terminology pretty much because he wants the class using the same language as each other, and he wants quick recall not processing (which is your point #3 above). 

With ninth graders especially, we start by asking them to copy these facts by hand into a notebook. Then they can use their personally handwritten notes on some of the quizzes. For example, we'll give a quiz with notes the day after they get the facts. Then, after they've used the facts for a day or two, we give a later quiz without notes. There's so much repetition in our class -- via quizzes, writing on homework, writing on in-class exercises -- that student draw confidence and comfort from the rote knowledge of the facts that they develop.

And finally, remember that a lot of the whining you're hearing comes from a position of ignorance. You as a physicist know when a substitute word is truly a synonym, and when a substitute word changes the meaning. In the example above, "y-axis" and "vertical axis" have the same meaning, even to a first year student. But my students have written, "on a velocity-time graph, the speed is determined by the velocity." "Oh, come on, the vertical axis is velocity, so you know I meant that velocity is the vertical axis!" No, sorry. That doesn't make sense. I've chosen my words very carefully on those fact sheets so that learning the facts leads to understanding. 

Physics is already a difficult subject -- it becomes EASIER, not harder, when students learn the facts by rote. There's gotta be trust in you as the teacher, just as we trust the musician who tells her students to practice scales. You, not your students, not your parents, are the physics teaching expert. When your students have a physics degree and a job in your school teaching physics, then they can decide what is a correct fact of physics. That was your final point in the email: "because I said so!"

(Of course, feel free to hide behind me, too -- "Hey, it's not me, these were written by this AP physics reader who's published five books and a blog. Feel free to take your complaints to him." :-) )

Good luck, Keri, and to all using these fact sheets.  They work.  

01 October 2016

Teaching the qualitative-quantitative translation: Why our students use common sense instead of calculation.

Today's question: Planet X has three times the free-fall acceleration of Earth. 

(a)          A ball is thrown vertically upward with the same initial velocity on Earth and on X.  How does the maximum height reached by the ball on X compare to the maximum height on Earth? 

(b)          Next, a ball is thrown vertically upward on X with three times the initial velocity of an identical ball on earth.  How does the maximum height reached by the ball on X compare to the maximum height on Earth?

The newbie physics student generally doesn't want to learn how to approach a physics problem.  He or she wants to get to an answer.  Usually the unsuccessful path to the answer takes one of two forms:

(1) Common sense.  "Obviously, more gravity means smaller max height, and three times more gravity means three times less height.  And in (b), three times more speed cancels out the three times more gravity, so the same height for each."

(2) Trying to find the one weird trick. "In class, I remember you asked a question like this.  Since the equation has a square in it, three times the gravity means nine times less height.  And in (b), the square terms cancel to give the same height."

(If you've been teaching for more than a month, you've seen these sorts of answers.  Let me know if you haven't seen one, and I'll buy a beer for you in anticipation of when you do.)

Why do our students say these things rather than just do the calculation?

In many of our students' minds, good, smart boys and girls know the answer.  The thought of "figuring out" the answer from first principles isn't part of their skill set.  You don't "figure out" the 3rd person plural present active indicative of cupio; you remember that -io verbs take -iunt in this form.  And if you don't remember, you should, 'cause you've been taught that.  So take a guess, knowing that -nt is a typical 3rd person ending.  You'll at least get close.  

There's your common sense approach in (1) above.  Since of course smart students should know the answer, they take a reasonable guess based on their instincts and previous experience.  Those instincts have been good in previous classes, especially math class; so guesses like this should work in physics, too.

The next step for students is to try to mimic what they see in class, what they read in the textbook.  When they recognize that common sense approaches don't work, they despair -- "oh, physics is impossible, every question has a trick to it."  So find the trick.  Note the language used in response (2) above, referring to "the equation".  WHAT EQUATION?  I want to shout.  Shouting is useless, of course... 

The student looking for one weird trick doesn't remember that in class I showed how to determine the correct relevant equation, then to solve it for the height of the ball in terms of the other variables.  

The student does remember that I got the answer.

The student assumes that I already knew the answer, and only went through the calculations for form's sake, like a prosecutor painstakingly presenting evidence that Jack Ruby shot Lee Harvey Oswald.

The student takes away, then, that HE is supposed to know the answer, too.  He shows his work only because I insist on it for silly teachery reasons.

How do we train students to use quantitative reasoning when answering these sorts of questions?

Understand that we're fighting a war of attrition.  There's no one weird trick for teachers that will suddenly cause enlightenment.  Chip away at the class, getting one student at a time to use quantitative reasoning properly.

Begin the battle by modeling good qualitative-quantitative translation skills.  Model an organized approach, in which you solve for the desired quantity in variables.  Use numbers too, not only variables -- early in the year, most of your class will not yet be comfortable looking at variables with squares and square roots, but they're easily able to compare 9 meters to 3 meters.  As the year goes on, you can help everyone transition to using variables only.  

Next, do an experiment to demonstrate your results.  Okay, you can't travel to planet X for the problem I've posed here.  But you can show that doubling a block's initial speed will quadruple its stopping distance on a track.  You can show that dropping from twice the height does not double the time a ball is in the air.  Emphasize that we're making physical predictions, not merely doing abstract mathematics.

And finally, demand to see a quantitative approach.  Look how I've rephrased these same questions below, to emphasize that we're looking for a multiplicative factor.  

For the students who still don't do the calculations -- yes, that means about 1/4 of my class -- make them do the problems again with even more explicit instruction, like "Pretend the initial speed is 10 m/s.  Use kinematics to calculate the height on X and on Earth."  Eventually, they'll get it.  Just be patient yet persistent.

The question, rephrased: Planet X has three times the free-fall acceleration of Earth. 

(a)          A ball is thrown vertically upward with the same initial velocity on Earth and on X.  How does the maximum height reached by the ball on X compare to the maximum height on Earth?  Justify your answer with both words and kinematics calculations.  Then your answer should state “The ball goes ____ times higher on X.”

(b)          Now, a ball is thrown vertically upward on X with three times the initial velocity of an identical ball on earth.  How does the maximum height reached by the ball on X compare to the maximum height on Earth?  Justify your answer with both words and kinematics calculations.  Then your answer should state “The ball goes ____ times higher on X.”

17 September 2016

A tribute to Clint Alexander

Folks, it's been a rough, rough week for me at Woodberry.  On Thursday the school announced that my great friend and the school's head football coach, Clint Alexander, would not be returning after this season.

What's that got to do with a physics teaching blog?

Know that Clint has been the best academic mentor I've ever known.  He helped me understand how to build relationships with students I hadn't previously connected with.  His willingness to involve me in his program -- as coach for a few years, and as broadcaster for a decade -- gave me the basis for relationships with countless boys who took my class.  

When I have a problem with a student in physics, I go to Clint for help in figuring it out.  He knows nothing of physics.  But he knows everything about teaching.

Below is the short halftime segment I did during the audio broadcast of today's football game.  I will miss him.

-- GCJ

Under Clint Alexander’s reign as coach, football here at Woodberry has become the epicenter for positive leadership in the school.  Our football players are the embodiment of the Woodberry mandate to work hard, build character, and take care of each other.  

That wasn’t always true.  I remember, years ago, pushing a baby stroller (with my baby in it) past the field before a practice.  Some players whom I didn’t even know loudly catcalled from afar.  They succeeded in making me uncomfortable at my own school, my own home.  I questioned my place here.  If *I’m* being treated this way, how would I feel as a new boy?  Especially a new boy who didn’t play football?  

That sort of thing doesn’t happen anymore.  I proudly now live at a kinder, gentler Woodberry.  

Clint’s influence began with the football team, of course.  He convinced them that the depth of their commitment and love for each other would translate both into success on the field, and to lasting friendships.  He was right, as seven graduated classes would attest.  He sold his vision to parents, telling them famously that their boys “will be husbands and fathers far longer than they’ll be football players.”  

But his message of inclusive values permeated the campus, not just the football team.  

I have always known that I’m an outsider here at Woodberry.  I don’t share an ethnic, religious, or cultural background with anyone.  Physicists aren’t generally known for their ability to fit in socially.  Yet, Clint welcomed me, made me feel like I belonged.  Clint has reached out to everyone, not merely the popular, athletic, and large.  He sponsored the Korean barbecue team.  He worked with the smallest of freshmen, and even faculty spouses, in the weight room.  He was the one who took Keith Johnson and Abbie Ryan seriously about coaching football - even though 15 years ago, appointing a grounds staff member or a woman as a football coach simply was Not Done.

“Whatsoever you do to the least of my brothers and sisters, you do to me.”  I’ve heard us read that verse in chapel; I’ve never seen anyone who lives those words more authentically than Clint Alexander.  

I’ll end with a note from Pete Cashwell, longtime play-by-play man for the Woodberry Forest Sports Network -- another of the many outsiders, non-”football people” whom Clint has welcomed as part of his program.   “In the last decade,” Pete says, “no member of the Woodberry faculty or staff has done more than Clint Alexander to help strengthen the school's community on campus and enhance its reputation off campus. I'm saddened that his efforts will not be continuing after this season's end and wish him the best of luck wherever he goes from here.”  

Pete -- word.

08 September 2016

AP Physics 1 mail time: Relative motion, and how do you handle calculus-laden responses?

Hibisca, who was in my Walton High School APSI last June, writes:

1. When do you teach relative motion, if you do at all? I could not find any direct references to it in the course description, but there is a multiple choice question in the 2014 practice exam (#35) about frames of reference. I also did not find any direct references to it in your "info to memorize" sheets or other materials.

I don't formally teach it at all... usually a discussion comes up at some point, though.  That #35 is the one about two balls colliding in a moving train car.  I think of it more as a center of mass question -- the center of mass of the two balls keeps going at constant velocity, whether we're observing inside or outside the train car.  (See, I'm phrasing it so "relative motion" doesn't come into play -- just the terminology causes headaches with students, so I try to get the concept without the terminology.)

2. How do you handle students who give answers/explanations with calculus? I can't imagine that would be a common issue on the AP exam, since there aren't any calculations, but I did have an issue on their last quiz where I asked students to determine the final position of an object based on a v-t graph. All of the students except for one used the formula for a triangle; one student set up an integral instead. Do you emphasize the need to approach everything algebraically, or do you give full credit to students who correctly use calculus?

They get full credit, as long as the calculus is clearly communicated.  As you say, the AP question would be "explain how you could determine", and if the student says, "we need to know how far the ball went from its initial position, that's the integral of the velocity function with limits 2 s and 5 s, that works out to 10 m, so add that to the initial position of 1 m to get 11 m final position" that's beautiful.

If you're worried that such a student might not truly understand what he or she is doing, or if the student uses calculus without words and gets huffy when you don't count it right... then the next quiz question might be "explain how to determine the final position of the object" rather than "determine the final position of the object." 

Not that you shouldn't have asked them to "determine the final position of the object."  I start there, too.  But then after I'm comfortable that everyone can do the calculation, I insist on the AP Physics 1-level explanation.

More questions about your physics classes?  Send 'em via email, and I may publish as a Mail Time.

29 August 2016

A letter to my forthcoming AP Physics 1 class

School starts for me in a couple of days.  I've got a wonderful first-world problem to deal with: I have more students signed up for my AP Physics 1-equivalent course than I have desks in my very large classroom.  

We're going to eventually deal with this issue by moving in more desks.  But first, I want to be sure that these prospective students know what they're getting into.  I'm more than willing to teach an enormous class -- as long as everyone in the class is there for the right reasons.  

Below is a letter I've sent to everyone who's currently enrolled.  Note that I've attempted to communicate my personal excitement and investment in the material -- those of you who read my blog know all about that, but students who don't know me well aren't familiar with my eccentricities.  See the part where I reassure both first-time and second-time physics students that this course is for them.  No calculus nor previous physics required, though previous physics doesn't mean you'll be bored.

And finally, note the direct approach to issues of mindset, pedagogy, and reasons for enrolling.  I've heard from large numbers of good physics teachers who are similarly direct and transparent with their classes, especially because AP Physics 1 is so fundamentally different from most any class my students have ever taken before.The advice I got was, manage expectations, plea repeatedly for students to have patience with me and with themselves... and then I'll be likely to have a great and exciting year because success will come sooner than the students expect rather than later.


Hey, all... I have you signed up for Honors Physics 1.   I wanted to give you some background information about what this class is all about.

The course itself is exciting, with lots of hands-on laboratory work.  You'll learn in tremendous depth the rules that govern how objects move, how circuits work, how waves propagate.  I've been studying physics for more than a quarter century, and I still discover new and exciting things each year.  Physics is the best.

Honors Physics 1 is a college-level introduction to physics.  We will prepare you to take the AP Physics 1 exam in early May -- based on past history, you're likely to do well, almost always well enough to earn college credit.  When you take an actual college physics course, your experience here will make you the natural leader of your class.  You'll be the one explaining physics to your friends, often with enthusiastic hand gestures and quick experiments that you make up on the spot.  

Now, that said, I'd like you to consider your reasons for taking this course.  Success in physics cannot be attained by merely "hard work".  You will need to enter into this year with a growth mindset, willing to dive headfirst into learning new skills.  Homework, test, and quiz problems will NOT be essentially identical to the ones we did in class; every physics problem represents a new situation, a new puzzle to be figured out.  We will do extensive experimental work, in which you will not be given a list of instructions, but rather a task to accomplish in a creative way.

Are you taking physics for the first time?  That's fantastic.  Though some members of the class will have taken conceptual physics previously, I assume that you have no prior knowledge of physics -- nor any mathematical skills beyond algebra 1.  Honors Physics 1 can be a perfect introduction to rigorous college physics.  By the end, you'll know exactly how to learn physics, such that you can advance to the next level of physics in college; or such that you acquire a serious background in the subject even if you know that you never want to take another physics class.  First-timers are in the right place.

Have you had conceptual or general physics before?  That's also fantastic.  We will cover some of the same topics you've already seen, but at a much deeper level conceptually, mathematically, and experimentally.  You'll get a chance to answer some of those burning "why" questions that your teacher told you were beyond the scope of your first course.  We'll talk about motion, force, energy, momentum, waves, and circuits, but also rotation and universal gravitation.  Honors Physics 1 can be a great follow-up that prepares you well for (or, on the contrary, can exempt you from) college physics.  Second-year physics students are also in the right place.

But please think carefully.  Are you taking this course mainly so that you can pad your college resume or your GPA?  Is a primary motive that honors physics will make your transcript more impressive?  That you're more likely to advance your GPA above some target if you're in an additional honors course?  If so, this is definitely not the course for you.  It's not that my students' grades are ever really bad -- most everyone tends to get As and Bs, with Cs rare.  It's that if you're not exited about and intrinsically interested in the course content, the effort necessary to earn those grades will not be worth it.  You'll find yourself angry and resentful at a subject that can't be conquered by sheer force of will.

Think how you will react when a test asks you about kind of situation or experiment that you've never seen before in class.  If you'll say, "you didn't cover that, that's not fair, how did you expect us to know", this physics class is not for you.

But if you'll say, "cool, here's my best shot, I hope Mr. Jacobs lets us try this in lab next week to see whether I'm on the right track", then you are perfectly placed in honors physics.

I'm always ready to talk about physics.  Feel free to call or email.

Thanks!  Can't wait to do some physics on Wednesday.


19 August 2016

The five-foot rule: one approach to encouraging effective collaboration

We all want our students to collaborate effectively on problems.  Problem is, there's a very fine line between working together to solve a difficult problem, on one hand; and simply copying another student's work, on the other.  And, no matter how obvious the difference may be to us, students don't necessarily get it.

It took me a while to learn about this disconnect between my own academic experience, my expectations, and those of my students.  At a previous school I became very frustrated and angry with students who seemed like they were copying each others' homework solutions.  And, they were copying, without question.  In their minds, though, they were merely reporting together the results of their effective collaboration -- that same collaboration that I had encouraged so strongly.  So they weren't happy with me for being unhappy with them for following my own instructions.  If you follow.  

The most important step I took toward resolving this difference of understanding was to re-cast the issue so it wasn't about academic integrity.  I couldn't say "don't copy and don't cheat" if the students and I had such good-faith but widely varying ideas of the definitions of "copy" and "cheat."  Rather, I had to find a way to give clear guidance to define the line between collaboration and copying, without invoking the emotionally charged language of academic integrity.

What I came up with, and what has served me well for decades now, was the Five Foot Rule.  My syllabus states*: 

The Five-Foot Rule
We encourage students to help each other.  You may even verbally guide a friend step-by-step through his solution to a problem.  However, do not under any circumstances just give someone your solution “to look at later”.  A friend may, in your presence, look briefly at your work to start himself in the right direction, but no one should ever be using another student’s written solution as a detailed reference.

Thus, when you are actually writing something to be turned in, you must be located at least five feet from any other physics student.  Do not do your homework while sitting next to someone; rather, sit well apart from one another in a dorm or conference room; or, have a discussion, then separate yourselves to write up your solution.

* Remember, I teach at a boys' school, so my use of gendered language is deliberate.  Please don't flame me.

Students who obey the five-foot rule are hardly likely to be copying, unless they have x-ray vision.  The point is for all students to explain the result of collaborative discussion in their own words.  

Then, when inevitably you find two identical problem sets, you can avoid making accusations of dishonesty or cheating.  You can simply discuss the obvious violation of the five-foot rule, and ask that this rule be adhered to.  If the violations continue, and you have to get parents or administrators involved, you are likely to get support.  

Accusations of cheating or copying carry harsh implications. Parents instinctively defend their children, logic be damned.  Administrators question whether it's worth their political capital to engage in a fight over small-scale homework copying -- especially when you expressly encouraged collaboration!

But you're not accusing anyone of cheating, no, not at all.  You're merely asking for cooperation in enforcing and adhering to a straightforward class rule.  Just as students are expected to treat laboratory equipment carefully, just as they're expected to show up on time with their homework finished, they're expected to sit five feet from anyone else when they write work to be turned in.  That's a reasonable enough procedure to follow that students look like idiots if they protest. 

So they don't protest.  And they follow the rule.  And so they do their own work... often with help, often by rephrasing what a friend told them.  But that's fine -- rewriting in one's own words is a significant step toward deep understanding.

10 August 2016

Secret to AP Physics 1: Build *gradually* from calculations to verbal-response

Last year, I swore a blood oath that I would never teach juniors and seniors again.  I loved so much my 9th graders' growth mindsets, their puppyish enthusiasm, their enduring trust in an expert teacher who cared about them.  I could not have been happier teaching the conceptual and the AP 9th grade course.

Well, um... sometimes the Patriots need Troy Brown to switch from reciever to defensive back; sometimes the Yankees need Alex Rodriguez to play third base rather than his natural shortstop.  And, needs must in the physics department, too.  I've gotta pick up the junior-senior AP Physics 1 class this year.  Unless I'm mercifully struck by lightning for breaking my blood oath, anyway.

The good news is, I've made and learned from a bunch of mistakes in teaching this course a couple of years ago.  See the series of three posts (starting here) from April 2015.  

You've heard over and over that AP Physics 1 requires deep understanding and verbal reasoning.  I've told you, the College Board has told you.  The released free response require zero -- ZERO! -- numerical calculations over four exams.

Yet, my problem sets through the first several months require calculations.  My first test in September is constructed based on old AP Physics B items, which require numerical calculation.  Even my mid-February test includes two Physics B-style free response questions along with a paragraph response item.

Of course, these problem set and test items are hardly just "find the right equation and plug in numbers" questions.  They include "justify your answer" parts, qualitative-quantitative translation, "explain what would change", and all sorts of questions that probe understanding beyond just calculation.  But they start with calculation.  Why?

Because I learned the hard way how fixed-mindset juniors and seniors approach this new and intimidating subject.

My students are used to math class, where the method is subordinate to the answer.  Explaining how to solve a problem is less important than clever use of various routines to get to the answer.  The test of whether a problem is done sufficiently is simple -- compare the student's answer to the teacher's or textbook's answer.  Black and white, right or wrong.

Yet, in their writing classes, much is negotiable.  Style is personal, both to the student and the teacher.  Is this piece of literature referencing Homer's Oddyssey?  Very likely a clever student can make a resonable argument, however tortured, which will -- if phrased with good grammar and big words -- earn high marks.*  My wife the English teacher tells of pointing students to clear rules in grammar books, only for the students to tell her that the rule doesn't apply to their particular paper, or that the rule itself is wrong.

* The teacher may give these high marks as much to avoid the inevitable protracted lawyerly discussions about why the marks should have been higher as because the paper actually deserved high marks.

The skills required for AP Physics 1 are far closer to those used in English than in math.  A problem is similar to a page-long essay.  The explanation is as important as the conclusion itself, as is demonstrated by the released free-response rubrics which award little credit for answers in the absence of clear justification.

And therefore, veteran students revert to English class mode.  I can't tell you how many quasi-confrontations I had with upperclassmen:  

"What's wrong with this answer?"  

"Well, as we discussed in class, you've gotta connect the conclusion that the distance increases to the fact that the mass is in the denominator with all else constant, and thus is inversely related to distance." 

"I said that."  

"No, you just said 'distance increases because of the mass.'"  You have to explain the connection between mass and distance with reference to the relevant equation."

"Yeah, I know, that's what I did.  Now what's wrong with that?"

"Who's on first?"

Start the year with calculation in order to avoid these frustrating converstaions; and in order to build the skills that will allow for better and better explanations throughout the year.  When I assign calculational questions, no one ever asks "what's wrong with this answer?"  They know: the numerical result doesn't match my numerical result.  Instead, they ask, why didn't I get the right answer?  That discussion is usually extremely productive.  And, I can follow up those discussions with a targeted quiz question about how a common error led to a wrong answer.  

Point is, instead of blaming me for their own inadequacies, students who get numerical calculation questions wrong tend to be willing to hear about the source of their own misunderstanding.  The process of correcting their work, of identifiying common errors, teaches the very skills that AP 1 demands.

By March, I can give exclusively AP Physics 1 items, with no calculations whatsoever.  That's because I've weaned the class off of numbers as a crutch, or of numbers as a way to avoid an unproductive argument about points.  After months of exposure to physics problem solving and laboratory work, my students understand the point: not to earn points, not even to get the right answer... but to explain how the natural world works based on the facts and relationships we've studied.  

30 July 2016

Why four rather than five choices on AP Physics 1?

Blog- and AP- reader Barbara sends the question:

Any idea on the rationale for moving from five voices on the MC to four?

Barbara, mainly this was a reading density issue. 

Reading, writing, and understanding English* are inescabable and fundamental parts of learning physics.  Nevertheless, we want the language in questions to be straightforward and minimalist, such that the language doesn't become an obstacle to demonstrating physics knowledge.

* Or another language, of course... but the AP exam is in English. :-)

The College Board and ETS do psychometric** research investigating their exams, and their examination techniques.  For example, they've shown that deducting 1/4 of a point for an incorrect multiple choice answer doesn't differentiate between students any more than just scoring the number of correct answers directly.  At the AP reading, investigations have shown that grading a physics problem holistically*** produces scores indistinguishable from traditional grading.  

** I may have made that word up

*** Meaning something like "2 points for a complete answer, one for a partially complete answer, 0 for a lousy answer" as opposed to assigning each point to a specific element of the response

In terms of five vs. four multiple choice choices, data shows that either approach differentiates students of varying ability appropriately.  (I don't know, 'cause I never asked, whether five-choice questions differentiate better.  The statement I'm remembering is that four-choice produces statistically significant and reliable differentiation.)  

Once the case for the statistical validity of a four-choice exam was made, then it was a shoe-in as the superior option.  Statements from test developers suggested that question authors too often seemed stretched to create four incorrect choices that each made sense -- they got too many questions where some choices could be ruled out on the grounds of "this sounds totally silly and made up."  With only four choices, it's easier to create three incorrect yet plausible responses that directly test student misconceptions.

The bigger issue, though, was the reading burden on the student.  Even for a very well constructed five-choice item, the student still must take the time and intellectual effort to read an extra choice.  The psychometric studies suggested that most students were not, in fact, reading and understanding all five choices; and, that students who DID read all five choices often had to read them multiple times to make a reasonable decision as to the best answer.  

It was clear from the beginning of AP Physics 1 that this new exam would require considerably more verbal expression than AP Physics B did.  So the College Board and ETS made several changes to the format of the multiple choice, with the goal of minimizing the reading comprehension burden:

* Item authors are now required to justify the incorrect choices, explaining how each choice helps differentiate students who understand the physics targeted by the item from those who don't

* The multiple choice section has been reduced from 70 questions to 50 questions, giving students more time to digest the more involved language used in the new exam

* The "roman numeral" question type has been replaced by "multiple correct" items.  (You know, those questions that gave I, II, and III, and THEN gave lettered choice such as "I only" or "II and III, only".  The studies showed that the reading comprehension burden was especially high on these.  However, simply choosing the two out of four correct choices does not require significant additional reading over a standard question.)

* And, as we're discussing... the number of choices was reduced from 5 to 4.

Now that I've taught extensively under both four- and five-choice regimes, I do prefer the four-choice.  My observation is that on the occasional wordy conceptual problem, students can more often than before appropriately eliminate three incorrect choices in preference to identifying the correct answer directly.  I think -- based on no evidence but my own decades-honed instinct -- that with fewer choices the test does zoom in more sharply on my students' physics skills than if those students had to wade through and weigh one more option in every item.  If nothing else, I don't perceive the same level of mental fatigue after a practice test.  And that was kinda the whole goal.


25 July 2016

Justify the ones you missed for homework -- adapting to an every-other-day schedule

It's time for me to adapt to a new ecosystem.  

For the last nineteen years, my classes have met five days a week.  Thus, my assignments and course structure have been adapted to that schedule.  At boarding school, an assignment has been due every day, because students have structured study time each night; at day school, longer assignments were due twice a week, knowing that the students liked to plan to gather about twice a week to do their problem sets together.  In class, I've saved the longer laboratory exercises for my single 90 minute period each week, using the other meetings for quantitative demonstrations and shorter experimental activities.

This year, though, my class meeting schedule has changed.  My classes will meet for 40 minutes on Mondays... but then two more times in the week for 90 minutes each.  That's less actual meeting time than previously; but I'm not losing much in terms of effective teaching time.  See, 90 minutes straight is much more effective than the two separate 40-minute periods that are being replaced, simply because we don't have to stop working, clean up, and rev up again the next day.

Thus, the way we spend in-class time will hardly change at all.  I already go to great lengths to keep students moving around, focused but relaxed, doing a variety of activities with clearly articulated goals.  Generally, my class already says "aww, crap, can I just finish this real quick?" when I tell them to clean up for departure.  So teaching for 90 minutes straight will be a godsend, not an obstacle.

How I assign homework will have to change, especially in conceptual physics.  The whole theory behind an every-other-day schedule is that without the grind of having to prepare for every class every day, students can pay better attention to engaging intellectually with each night's work.  So, um, that means our faculty have been specifically instructed NOT to simply double the homework we used to assign each night.  I fully support this initiative, as problem solving is a creative process with a law of diminishing returns.  (If you can't lift weights every day in preparation for football season, you can't simply double the number of pounds you're lifting every other day.)

The way I'm thinking now is to divide a night's assignment into two parts.

* The first part is a standard nightly problem set, like I've been assigning for decades.  Remember, a "problem set" is far more similar to an English essay than to a night's worth of math problems.  Written explanations and justifications, not numerical answers, are the dominant feature.

 * The second part begins with a set of multiple choice questions to be done individually.  (The requirement for individual work can be enforced by giving five minutes at the end of class to answer; or, you could use webassign or the equivalent to randomize the questions and the order of the answers, so collaboration would be ineffective.)  I'm going to use socrative to collect student responses electronically.  

Each student will see immediately whether his answer is right or wrong to each question.  The actual assignment, due the next class day, is simply justify the ones you missed.  

Think of the incentive for the students to take these multiple choice questions seriously.  No matter what kind of or how much work you assign, in class or out of class, it is beyond useless unless the students are thoroughly engaged in discovering and understanding the correct response.  Practice doesn't make perfect -- only perfect practice makes perfect.

In this case, the opportunity to avoid doing more homework is what motivates everyone to engage carefully with each multiple choice question.  

Get it right, and it's done and dusted.  

Get it wrong, that's okay.  There's no grade penalty, no disappointed sigh from the teacher, no whipping with a wet noodle.  Every question that's wrong does require some major work to discover, understand, and then write up the correct solution, but that's work that the student knows needs to be done.  After all, he just got the answer wrong, so it's obviously important to figure out how to do it right, right?

08 July 2016

So what does an ohmmeter read when it's directly connected to a non-ohmic bulb?

The previous post describes my students' results showing that a flashlight bulb's resistance varies.  Over the available voltage range of 2 V to 8 V, the resistance (determined by the slope of a voltage vs. current graph) varied from about 50 V to 80 V.

The question was, what does an ohmmeter read when placed directly on this bulb?

Consider how an ohmmeter generally works.  It puts an awfully wee voltage across the bulb, and measures the resulting wee current through the bulb.  Then the meter essentially uses ohm's law to calculate resistance.  (That's why you have to disconnect the bulb from the battery in order to use the ohmmeter.)

In the context of our experimental voltage-vs.-current graph above, the ohmmeter is measuring an out-of-range data point, way off down and to the left of the portion shown.  By extrapolating the curve shown, we could guess that we should get a shallower slope and thus a smaller measured resistance.

Sure enough, the meter measured about 8 ohms, a full order of magnitude less than the resistance in the bulb's operable range.  

Again I caution teachers: this is a cool and somewhat unexpected result.  Nevertheless, it's rather irrelevant to the typical practical analysis of a bulb.  The bulb only glows at all with a volt or two across it; the bulb is only rated to about 6 V, meaning it is likely to burn out over that voltage.  In the operable range, the resistance is reasonably steady.  The resistance only drops by an order of magnitude when the voltage is dinky.

The next question: How can we experimentally extend this graph?

My variable DC supply only goes down to 2 V.  I could get a 1.5 V battery to get one more data point, but that's all I can think of.  Does anyone have a suggestion of a way to explore the parameter space below 1.5 V?