An example of a question that *must* be written as multiple coice

The best teacher I've ever met, Matt Boesen, teaches US history and constitutional law.  Debate tournaments have turned because his students can instantly remember and use facts from his classes.  I have every intention of sitting in on the constitutional law class at some point in the future.

Importantly, Matt and I are very DISsimilar in some aspects of our teaching.  The most glaring example is what a typical class looks like:  Matt facilitates discussion while sitting with his students around an elliptical table, while (on the occasions when the students aren't themselves experimenting) I perform live demonstrations on a table elevated above rows of students.  Partly that's a function of our personalities; primarily the difference is one of history vs. physics.  Good physics teaching looks different from good history teaching.  Not even all good physics teaching looks alike...

One point on which Matt and I actively disagree is the utility of multiple choice items on tests.  His own take is that multiple choice is the creation of the devil, the lazy teacher's way of finding out which students are good test takers regardless of which students understand the course content.  I certainly see his point within the teaching of history, where a better alternative to multiple choice is always available.  Recall of facts can be tested more authentically with identification questions that don't give hints to the answer ("What were the provisions of the fugitive slave act?").  Higher-order thinking about history requires writing; not necessarily five-page essays, but paragraphs making connections between concepts ("Explain the political circumstances that led representatives from free states to support the fugitive slave act").  

But physics is different.  Well-designed multiple choice questions *can* authentically test understanding. The advantage then is that the short response time*  allows a test to cover a broad swath of topics in a variety of contexts.  Moreover, some physics questions are best phrased as a multiple choice item.  For example, here's a question from my recent 9th grade conceptual test:

* since there's no writing necessary, you can reasonably give one question per two minutes or less

Ball A is dropped from rest and falls for 2 s.  Ball B is also dropped from rest, but falls for 4 s.  How far does ball B travel?

(A) one-fourth as far as ball A

(B) four times as far as ball A

(C) twice as far as ball A

(D) half as far as ball A

(E) the same distance as ball A

The incorrect answers are not chosen arbitrarily -- I could go through each incorrect choice to explain the misconception or mistake that would lead the student to choose that answer.  In that sense, the item is an authentic test of reasoning with the equation d=(1/2)at².

But this question doesn't work well at all without the choices!  In response to just the prompt "How far does ball B travel," a student might try to plug in numbers to answer "19.60 m," in which case the question is evaluating a very different skill, the skill of plugging and chugging.  Okay, so suppose I rewrite the stem to read "How much farther does ball A travel than ball B?"  A reasonable answer:  "14.7 m", which is the difference between ball A's 4.9 m and ball B's 19.6 m.  Still, this is a different response than I wanted.

Rewriting again, maybe I say "How many times farther then ball A does ball B travel?"  Or "What is the ratio of the distance ball B travels to the distance ball B travels?"  Now the student's answer might be "4 meters."  Aarrgh... you meant "ball B travels 4 times farther than ball A," but that's not what you said.  Or, perhaps the student rounded weirdly to get "4.0816:1." That's not a physically useful answer.  Grrr.

So on one hand I write this question as multiple choice because the choices frame the style of answer required.  But it's more than that.  The manner of the phrasing of the choices firmly defines the physical meaning of the answer. Any other phrasing I can think of can encourage a student to perform a mathematical manipulation.  Upon doing test corrections, I don't want someone who missed this problem just to figure out how to do the math right to get "4"; the choices emphasize that the question asks about a performable experiment.  I'm not likely to get an argument that "Look, if you play with the equations THIS way you get 2, like I did, so I should get credit."  In the rare case someone tries to argue points with me, I don't engage; I just say, "okay, let's do the experiment."  

Of course, like any teaching tool, multiple choice questions have to be used correctly in order to be useful.  The questions must be well-written, so that it's highly likely that a correct answer comes not from gaming the test, but from good physics knowledge.  Other forms of test questions must be used in concert with the multiple choice in order to get a complete picture of a student's ability.  (An easy way to add variety and higher-order thinking to a test is to ask a multiple choice question, then say "Justify your answer.")  And if you're going to test with multiple choice questions, students have to be used to seeing multiple choice questions on homework and quizzes; I'd say about half my general physics problem set questions are multiple choice with "justify your answer."  

Next time colleagues or administrators challenge your use of multiple choice items, enthusiastically take them aside and show them a few well-designed physics questions which cry out for the multiple choice format.  Show them this post.  Go into a detailed discussion of the pedagogical philosophy of articulating physics concepts, not just solving math problems.  Generally, you'll get one of two responses... virtually every non-physicist you attempt to engage in this discussion will (figuratively) run screaming rather than try to understand how physics teaching actually works.  

Sometimes, though, you'll get the Boesens who enthusiastically listen, recognizing the differences among individuals and disciplines.  These are the colleagues to treasure, because chances are you'll learn as much by listening to them as they learn by listening to you.

GCJ

Teaching acceleration in conceptual physics

In conceptual physics, I define acceleration with one sentence that we repeat ad nauseum:

Acceleration tells how much an object’s speed changes in one second.

Then we talk separately about the direction of acceleration:

When an object speeds up, its acceleration is in the direction of motion.

When an object slows down, its acceleration is opposite the direction of motion.

In Regents-level and Honors physics, I used to define acceleration via the slope of a velocity-time graph and via the equation a = Δv/Δt.  The conceptual class used neither of these, yet seems to understand acceleration better than my Regents-level folks ever did.  (As of about 2014, I've used this verbal approach at all levels.)

In terms of the magnitude* of acceleration, since all of our problems involve constant acceleration, I ask them to use their mathematical instincts:

* Though I never use the term "magnitude"... I say the "amount of acceleration." 

An eastward-moving roller coaster slows from 25 m/s to 15 m/s in 5 s.  What is the amount of the roller coaster's acceleration?

Using the fundamental definition, student can reason:  "Acceleration tells how much an object's speed changes in one second.  The roller coaster changed speed by 10 m/s in 5 s.  So every second, the coaster lost 2 m/s of speed.  The acceleration is 2 m/s per second."

It helps that I have insisted on everyone writing the full relevant fact of physics in answer to every problem.  When someone struggles, I ask him to repeat the definition of acceleration, and I can guide him to the correct answer.  After doing this a few times, he gets the idea.  And the concept is sticking... since we're not plugging blindly into an equation, I'm having fewer mistakes of the form of "the acceleration is 10 m/s because that's how fast the roller coaster moves."  

Note the unusual statement of units.  Rather than use the mathematical notation of meters per second squared, I'm exclusively writing acceleration units as m/s per second.  When students have to write that out on every problem set, they continue the process of internalizing the meaning of acceleration.

As for the direction of acceleration:  that's pretty easy for the class, given that we've practiced all year justifying from facts of physics.  "When an object slows down, its acceleration is opposite the direction of motion.  This coaster is moving east and slowing down, so its acceleration is west."  

The only tricky part here is that I've had to stamp out the phrase "acceleration is moving west."  Acceleration doesn't "move."  Acceleration simply "is."  My students initially complain when they lose points for saying the acceleration moves west.  Then I show them a classmate's reply in which he says "This coaster is moving east and slowing down, so the roller coaster must be moving in the opposite direction of motion, so is moving west."*  I explain that the language in the explanation is as important as the answer.  (And, they know from experience that those points ain't comin' back, no one in the class has any sympathy for their loss of points, so they might as well just do things my way and get the physics right.)

* Not making this up.

The last fact I teach regarding acceleration is that object in free-fall gain or lose 10 m/s of speed every second.  The next post will discuss quantitative and qualitative demonstrations relating to acceleration and free-fall.

Do you want a set of handwritten solutions to Tipler volume 4?

I'm cleaning out my office in preparation for the move to the new Manning Science Building.  I'm excited -- the science department is being released from the dungeon and paroled to the palace.  

I'm throwing away a large collection of Physics Today and The Physics Teacher.  I'm throwing away an enormous collection of American Journal of Physics.  Thing is, I can get all of these online, now, and I don't have the shelf space in my new office to waste on hard copy.

One of the few things I can't bring myself to toss is a thick binder with my solutions to many Tipler volume 4 problems.  (This is a widely-used edition of a terrific calculus-based physics text.)  Anyone want this binder? Send me an email with your address, and it's yours.

GCJ

Edit:  Claimed by Staci Babykin.  

Making students write facts of physics in every answer

I've discussed how "justify your answer" means to use either a fact, equation, or a calculation to support an answer.  All year in 9th grade conceptual physics, I've handed out printed sheets listing the appropriate facts and equations that can be used for justifications.  Still, a significant subset of students have disappointed me with their justifications: they make up facts, misstate facts, or sometimes just write any old fact, whether or not it has any relevance to the problem at hand.  

I got sick of nagging my students to use facts of physics correctly.  Taking a page out of Jen Deschoff's bag of tricks*, I decided to have the STUDENTS grade assignments for completeness.  Then, the class could have an additional day to check their answers with friends before turning in the final version of the assignment.

* Mixed metaphors are legal in physics blogs

For the past two weeks, I've started class by collecting a problem set and redistributing it to the class.  Each student gets a red pen and is asked to check boxes in a rubric that says:

* Is a fact written nearly word-for-word from our sheet?

* Is the fact relevant to the problem?

* Is there a sentence showing how the fact applies to the problem?

We apply the rubric above to each problem on an assignment.  If even one item is missing on one problem, I take off substantial credit; but I award some credit on each set to those who do everything right.

In the first day or two, lots of students lost credit.  But, it wasn't big bad Mr. Jacobs taking off the points -- their own classmates were the ones checking the facts.  I hold everyone accountable for their grading by asking them to initial the page they grade.  (That means I know who graded what, and I can have a word with someone being too strict or too lenient.)  I'm finding, though, that I don't really have to follow up at all.  The students are more careful about grading than I am.  One even asked, "Do I need to take off for spelling?"  Miracle of miracles, after two days I found everyone writing out facts clearly; also miraculously, everyone was doing better on the problems, because by simply being forced to pay attention to writing a proper fact, the logical connection to the correct answer became more apparent.

Perfect for studying position-time graphs

We spent a week working on just position-time graphs.  The most common issue at the beginning of this unit is a failure to separate the "picture" of the graph and the motion represented by the graph.  For example, students commonly say that a graph with negative slope must represent a cart going down a hill, because the graph looks like a hill.

I only had one student make that mistake this year.  Why?  Because everyone had to start every problem with something like "A position-time graph sloped like a back slash \ means the object is moving away from the detector."  It REALLY takes some serious cognitive dissonance to tell me that the cart is thus rolling down a hill, especially since the problem starts with something like "...the detector is pointing north."  

And velocity-time graphs

After a week, we move to velocity-time graphs.  Usually the abstraction that the graph represents motion on a line is clear by the time we move on; the biggest issue I've had teaching velocity-time graphs is students not frickin' paying attention to whether a graph is position-time or velocity-time.  In past years, I've had people telling me for v-t graphs "the cart moves south because the slope is like this \" even after they've made the same mistake countless times already.

No problems yet this year... because of the student grading.  The second bullet point on the rubric says "Is the fact relevant to the problem?"  I talked to the class ahead of time about how facts for the wrong type of graph are by definition not relevant to the problem.  Meaning, if you use position-time graph facts for a velocity-time graph, I'm not marking you wrong, your friends are; and you're losing not just one point for a "good try, honey," but substantial points for laziness.  

Would student grading for written-out facts work for juniors and seniors?

Not sure.  I've never tried this approach with upperclassmen, because some might see it as busy work, and might rebel.*  But the positive correlation to comprehension is so incredibly strong, that I might suggest giving this sort of approach a try.  Let me know if you do.

* Freshmen, I've discovered, are poor rebels.    

Physics Fights at the Global Physics Department: Wednesday Dec. 5 2012

If you're free this Wednesday night Dec. 5, stop by online at the Global Physics Department.  I presented to the "department"'s weekly meeting back in June.  About 50 people from around the world joined in to see quantitative equilibrium demonstrations.

On Wednesday night at 9:30 PM Eastern time, my students Vinh Hoang and Michael Bauer will be holding a physics fight.  Mr. Hoang will present his 10-minute powerpoint solution to the question "Why do all candles have about the same brightness" - this was one of the problems at the 2012 US Invitational Young Physicists Tournament.   Then, Mr. Bauer will lead a discussion of Mr. Hoang's solution, challenging him to explain each aspect of his research, searching for the truth in the same way that scientists from competing research groups might grill each other at a conference.

You are invited to watch the festivities on Wednesday night.  Just enter the GPD chat room and enjoy.  I think you will love the pedagogy and collaborative yet competitive spirit of the physics fight.

GCJ