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25 March 2015

Need a paragraph-response item for AP Physics 1?

Remember the 2013 AP Physics B problem 4 about a modified-Atwood machine?  A ball was placed on top of the block on the top surface.  That ball became a projectile when the top block hit the edge of the table.  After some good calculational parts, part (d) asked a very carefully targeted descriptive question.  The exam stated that increasing the mass of the ball would cause the ball to land closer to the table... then asked, why?

I'd say a good quarter of the responses globally were something along the line of "since the ball is heavier, it falls faster, and so doesn't have time to go as far while it's in the air."  My personal opinion -- NOT shared by the College Board, at least publicly -- is that readers should be allowed to make a student who gives this response retake the entire test, this time in the presence of flesh-eating ants.  My proposal for this particular adjustment to the rubric was not accepted by the table leaders, because it was too late in the process to make substantive changes.

Every physics teacher I know praised the verbal portion of the question.  It did an outstanding job of rewarding students who could *explain* physics rather than merely solve problems.  On the old AP Physics B exam, a verbal-response item had to be targeted carefully such that students could answer in the time allotted.  The new exam provides plenty of time for such questions.  In fact, one entire question will include a phrase such as "justify your answer in a clear, coherent, paragraph-length response."  I rewrote this 2013 AP B problem as a paragraph-response item.  Here is my version of the problem, followed by some commentary.

1.      (7 points, suggested time about 13 minutes)
A ball of mass m is in a cup of negligible mass attached to a block of mass M that is on a table.  A string passing over a light pulley connects the blocks to a 2.5 kg object, as shown above.  The cup is a vertical distance h off of the floor.  All friction is negligible.
 In Trial 1, the system is released from rest, the block accelerates to the right, and after moving a distance x the block collides with a bumper near the end of the table.  The ball continues to move and lands on the floor at a position a distance d horizontally from where it leaves the cup.  In Trial 2, the mass m of the ball in the cup is doubled.  The system is again released from rest.  The block collides with the same bumper, the ball continues to move, and lands on the floor.
 In trial 2, does the heavier ball land a horizontal distance from the table that is greater than, less than, or equal to d?  Justify your answer in a clear, coherent, paragraph-length explanation.

Since the paragraph-response item doesn't ask for calculations, I eliminated most of the numerical values.  (I left the 2.5 kg hanging mass so I didn't have to make up yet another mass variable.)  In thirteen minutes, a student will have plenty of time for reasoning and writing; so I didn't feel the need to reveal that the ball goes a distance less than d.  

We only have one published example of a paragraph-response rubric, so most of us teachers are on our own to guess how these will be scored.  In my rough rubric, I looked for the following seven elements:

* Recognition that it is necessary to consider the ball's speed after traveling the distance x
* Statement that the ball has a smaller speed after the distance x in trial 2
* Then two steps of reasoning supporting a smaller speed, for example:
       + In F=ma, the net force on the system is the same with larger mass, giving smaller a
       + Smaller acceleration means the block speeds up less in trial 2, or reasoning with v2 = 2ax
* Statement that the ball goes a distance smaller than d
* Then two steps of reasoning supporting a smaller distance, for example:
       + Kinematic justification that the ball is in the air for the same time either way
       + Linking the horizontal distance to the initial horizontal velocity through x = vt

You might come up with a completely different rubric.  That's fine.  I merely chose several elements of reasoning that I expected to see, which allowed me to award partial credit to those who had a reasonable but incomplete understanding of the problem.

When I gave this item on my trimester exam, I found my seniors knocked it out of the park.  The continual writing practice we've been doing this year paid off big time.  The majority of the class earned full credit.  A few people said the ball would go the same distance either way, but they earned partial credit by correctly explaining the projectile portion of the problem -- they didn't understand the modified Atwood part of the problem.  My 9th graders didn't do as well, because they have a lot more trouble expressing their understanding in words.  They would have performed equivalently or better to the seniors on the original, calculation-heavy 2013 AP Physics B problem.  But the seniors have so much more facility with the written word that they dominated the freshmen on this one.  Of course, that's fodder for a future post.

Please feel free to use this question in your class.  Let me know if you have tweaks, either for the question or for the rubric.  And feel free to send your paragraph-response items!


16 March 2015

Two Confusing AP Physics 1 Learning Objectives: Waves

A friend asked about two of the new AP Physics 1 learning objectives.  He's (rightfully) confused about how to present them to his class.  They are:

6.A.4.1: The student is able to explain and/or predict qualitatively how the energy carried by a sound wave relates to the amplitude of the wave, and/or apply this concept to a real-world example.


6.D.4.1: The student is able to challenge with evidence the claim that the wavelengths of standing waves are determined by the frequency of the source regardless of the size of the region. 

I'd say, it's not worth looking this closely at the curriculum framework.  A College Board speaker last year at the AP reading emphasized that straight-up teaching to the learning objectives could lead to disappointment.  She said that a number of teachers to the redesigned biology course had hammered their students with practice tasks and questions narrowly tailored to each learning objective, only to find that the students had trouble handling the broader free response items.

But you have the right general idea about using the curriculum framework to figure out what aspects of waves you need to present to your class.  Try looking not at the learning objectives, but instead at the "essential knowledge" statements.  They state the aspects of each topic that must be covered.  The learning objectives are hyper-specific about skills and "science practices."  Learning objectives are, in my mind, only useful to those asked to write test items; the true outline of the course comes from the essential knowledge statements.  

For the specific topics in your inquiry:

Essential knowledge 6.A.4 merely states the fact that energy carried by a mechanical wave depends on amplitude; and reminds us that examples should include sound waves.  (Not light waves -- that's in AP Physics 2.  We're talking waves on a string, waves in water, sound waves, etc.)  That's easy enough to teach, demonstrate, and explain.  I based a multiple choice question in my book around a stone thrown into a calm pond: the stone creates a wave on the waver's surface.  That wave would carry more energy per meter to a close-by shoreline than a far away shoreline.  And, sure enough, the amplitude of this wave would be higher near the close-by shore than the far away shore.

Essential knowledge 6.D.4 says "The possible wavelengths of a standing wave are determined by the size of the region to which they are confined," which is a highfalutin' way of describing the classic pictures of standing waves.  In language tied to the demonstrations my students have seen, I'd say that the length of a string or pipe must be just right to fit a whole number of standing wave "humps."  This essential knowledge statement goes on to remind us that changing the boundary conditions or the length of the string will change the possible wavelengths.

To me, this just means "teach standing waves."  Now, some folks think of "teaching standing waves" as simply memorizing the equations for fundamental and harmonic frequencies and wavelengths.  No, teaching about standing waves means showing demonstrations and experiments,  It means explaining why standing waves do or do not form.  It means being able to explain with diagrams and words how standing waves in an open pipe differ from those in a pipe closed at one end.  It means relating the relevant equations to those diagrams and words.  

When your students can answer any question about standing waves, including descriptive and experimental questions, you have taught them the necessary background for not just LO 6.D.4.1, but for the AP Physics 1 exam in its entirety.


09 March 2015

Video Documentary: The US Invitational Young Physicists Tournament

Woodberry Forest's second place 2015 Physics Team
Woodberry Forest School hosted the US Invitational Young Physicists Tournament in January 2015. The school hired Kirby Martin to make a documentary video.  The documentary focuses on Woodberry's team and our research program; it also discusses the structure and benefits of the USIYPT.

I encourage you to take a look here at the documentary.  If you'd like to become involved in the tournament, send me an email; you can take a look at the problems for the 2016 tournament here.  

And in the world of crazy youtube algorithms:  The first follow-up video that youtube played for me after the USIYPT documentary was four hours of footage from day 3 of an NCAA Bowling invitational tournament.  


05 March 2015

Does a "paragraph response" in AP Physics 1 require sentences? Or are bullet points enough?

One of my friends who's a bloody awesome College Board physics consultant has a follow-up question to the "white paper" about paragraph response free-response items on the new AP 1 and 2 exams.  She says she's had several teachers ask "hard and fast" if the CB need the answers in complete sentences, paragraph style; or if a numbered list or bullet points would suffice.

Thing is, I don't know for sure, because grading an AP Physics paragraph response item is new to pretty much everyone in the world.  I can make a well-educated guess, based on the scoring guidelines on the published practice exam.  Nothing in these guidelines says anything about complete sentences; it talks about a "coherent argument".  My instinct is that if I got bullet points that addressed the correct issues and formed a logically-connected, coherent argument, I'd be fine with that, even if some of the entries weren't complete sentences.  

That said, bullet points that DON'T make an obvious coherent "argument" won't work.  Saying "*potential energy mgh, kinetic energy 1/2mv^2 -- both blocks, momentum conserved, energy shared, move both ways" doesn't cut it.  "Oh, but I addressed each of the points in the rubric," says the student.  No, you didn't -- you didn't COMMUNICATE.  The response must make sense on first reading; the reader is not going to make connections for the student, the student must make connections for the reader.

What I'm sure many teachers are concerned about is the silly fifth grade social studies "answer in a complete sentence" meme.  Remember, the end-of-chapter question asked, "What are three major exports from the state of Texas?"  You wrote, "oil, beef, and football."  But your teacher condescendingly marked the answer wrong, saying "You didn't answer in a complete sentence."  Really?  You directly and accurately answered the question that was asked.  Turns out she expected you to restate the prompt in the answer, saying "Three major exports from Texas are oil, beef, and football."  The smart students who eventually became physics teachers considered that this teacher was making idiotic, anti-intellectual, bureaucratic demands that had no relation to the content being developed.

Had the book instead asked, "Based on the reading, describe several features of the Texas economy," then my initial "oil, beef, and football" response could justifiably be ignored.  In that case, *I'm* the idiot for giving a four-word answer to a complex question.  And if the question prompt included direction to answer in a clear, coherent paragraph, then I'm charged with an additional count of "failure to follow directions" on top of impertinence, laziness, and general wrongness.

In a physics context, the essay question will not ask "How fast will the ball go when it hits the ground?"  The test will ask something much more deep, which cannot be justified in one word or one equation.  Communication of complicated concepts will be required, and such complex communication generally requires sentences with subjects and verbs.  No one will be grading your students' grammar.  If they structure their response with bullets, I suspect that's fine... but a good response will *of necessity* include many sentences in those bullets, and those sentences will be logically connected.

Hope that helps.  I'll know more once I'm at the reading.  I'm a table leader for Physics 1 or 2... I'd actually love to try the essay question, even though it will make my brain hurt.  :-)

04 March 2015

Open-ended lab exercise: is it constant acceleration?

The College Board has published a set of "Inquiry-Based Laboratory Investigations" for AP Physics 1 and 2.  The downside is that, in order to get to the actual investigations, you have to sort through page upon page of ed-school baloney about "learning objectives" and "building a community of learners" and "exemplifying technology-enhanced interfaces in data-driven schools."*  

* I might have made that last one up with the educational jargon generator.  But check the CB publication to be sure.

The UPside -- and it's a pretty important upside -- is that the investigations themselves include lots of excellent lab ideas from really good physics teachers.  Don't think of these "investigations" as lab guides which you must use verbatim.  Use them instead as a teacher-tested resource to give you good ideas, especially for more open-ended experiments in which students have to design their own procedures.

Now, I'm a big fan of such open-ended exercises, but I only use them in the latter half of the school year.  My students don't come to me with enough basic lab skills to dive straight into even "What factors do and don't affect the period of a pendulum?"  I spend the first part of the year riding herd about collecting lots of data across an entire parameter space, linearizing a graph, using the slope and intercept of a best-fit line to determine physically meaningful quantities, etc.  Once my students begin to see the laboratory process as a bit repetitive, then it's time to give them open-ended challenges.  A couple weeks ago I did "Does a rubber band obey Hooke's Law?"  I submitted this elaborate writeup for the College Board; but in class, I present just the question, and let the students take it from there.  By the time we do this experiment, the principle that they must make a graph and use its best-fit line is well ingrained such that it doesn't even need a discussion.

The very first investigation in the CB's Laboratory Investigations publication put a marble on a track, and asked the student to design and carry out a procedure to determine whether the marble's acceleration was or was not constant.  The experimental setup precluded simply using a motion detector to check for a linear velocity-time graph -- a standard motion detector can't read the marble.  So students have to use stopwatches and metersticks, or video analysis.  In either case, it's a non-trivial exercise requiring significant physics comprehension to explain how to translate from the raw data -- which only show position and time -- to instantaneous acceleration at several locations along the track.

I may come back to this particular exercise in my laboratory later this year.  But for now, I adapted the question as a Direct Measurement Video homework assignment.  This video shows a wind-up toy car speeding up across a table.  I simply ask, "How would you determine whether the toy bus's acceleration is constant? Answer in a clear, coherent, paragraph-length response."  

 I was glad I waited until last week to give this assignment, even though we covered kinematics long ago.  The class had a lively discussion the next day -- a discussion that wouldn't have happened so readily earlier in the year while the class was more answer-focused, while the class was less confident in the difference between acceleration and velocity.  Even those who got the problem wrong on the homework understood their mistakes.  We discussed how to estimate instantaneous velocities at different positions.  We discussed whose method of determining instantaneous velocity was best.  (Early in the year, the question would have been "but is mine right or not?"  Now we have enough experience to understand varying degrees of accuracy in an experimental situation.)  

I'll save the numerous methods of determining whether acceleration was constant for a future post -- feel free to share your idea in the comments.  Or, better yet, give this assignment to your class.  See how they do.  Whiteboard the student-generated results.*  Tell me and other readers your ideas for follow-up questions.  In other words, use the comments to talk shop.

* Sorry, jargon generator again.