Mail Time: "Normal force", "Flex force," or what?

Elizabeth Pate posted a comment asking about the reactions of AP readers:

I have a question about FRQ scoring. I use modeling instruction in my classroom so a few vocabulary terms that I use are different from a traditional physics course. For example, my students would call the normal force a flex force and the net force an unbalanced force. I do teach them both terms but I find they usually prefer flex and unbalanced force to Fnet and Fn, will these cause a problem for graders reading their FRQ's?

Reading AP exams is kind of how I learn about new trends in physics education.  Last year I learned about a commercial device with two (visible) lasers and photoreceptors; when the beams are broken by a moving object, the device calculates speed.  I'd call it a visible photogate.  I forget what it's actually called, but enough students used this device on their lab problem that I found out about it.

So, "flex force," eh?  That makes sense.  Never heard it before.  How would I react to it as an AP reader?  It depends on the rubric, and how the problem is phrased.

When the test simply asks for a labeled free body, we are usually quite generous about those labels.  My quintessential example was a few years back when students had to label a buoyant force, the force of water on a cup.  We accepted "buoyancy."  Then we accepted the misspelled "boyance".  Then we accepted "bouncy," because it made sense in context.  A rumor was spread that someone accepted "Beyoncé," but that's unconfirmed.  :-)

So would I accept "Fflex" on a labeled free body?  Possibly, especially now that I've heard from you that "flex force" is modeling vocabulary for "force of a surface on an object, acting perpendicular to the surface."  

I always train the students to define their labels.  Don't just say "Fn" -- say "force of the road on the car" or "force of the scale on the boy."  Then even if someone misreads the label, or if the label is unintentionally ambiguous, there's no issue.  

For example: we've never accepted "G" as a bare label for the gravitational force, even though some texts and teachers may teach that.  Why not?  Because "G" has a well defined conventional meaning: it's the universal gravitation constant, 6 x 10^-11 N*m^2/kg^2.  

But a student who labels the diagram with "G" and then says "G: force of the earth on the car" earns full credit.  Oh, and he can deal well with Newton's Third Law, too, but that's for a different post.  :-)

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.  

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.”