Use unlined paper for problem sets in honors / AP physics

I do a lot of posting about what has worked for my class.  Today I post about an idea I had that didn't work like I expected.

About a year ago, I redesigned my problem sets for honors students.  For over a decade, I had simply assigned end-of-chapter-style problems via email, and required students to answer each on a fresh page of unlined paper.  I changed the assignments so that each problem was typed out on the front and back of a page, AP free response style, with space to answer under each part.  These new problem sets looked like worksheets, not end-of-chapter problems.

The theory was, I wanted to get better attention to the meaning of the answers, and specifically to each step in the problem solving process.  By asking the question in stages, each of which couldn't be ignored, I thought I'd set students up for success, minimizing the helpless feeling of "I don't know where to start."  Furthermore, I figured I'd be able to grade more quickly and accurately, because I could turn directly to the part of a question that I most wanted to see answered.  No more hunting through a poorly-presented page of work!

In general, my "theory" was proven correct.  Grading was quicker, I got fewer students trying to hide the fact that their work was incomplete, I got full sentence answers to direct questions like "justify the reasonability of your answer to (c) by comparing it to speeds with which you are familiar."

It was the unintended consequences that proved dastardly.  Primarily, the perception of the homework as a worksheet to be filled out damaged the collaborative culture of the course.  

Students would check their answers to part (d) with each other.  But if they found that their answers were different because of an issue earlier on in part (b), they would not take the time to deconstruct part (b).  Previously, when the problem had been presented on a blank canvas, everyone saw the problem as a whole (even if the original text on a different page used parts (a) (b) (c) ) -- and so they discussed their whole solutions. 

I asked a lot of "place a check by one of the following, and justify your answer."  Students would verify with each other that they had checked the correct box, but would not discuss their justifications (figuring, I guess, that they had "collaborated" by looking to see that the right box was marked).  Without the checkbox and the space for answers, I used to get too-long essays as justifications; but the students communicated with me in writing, and with each other both in writing and in face-to-face discussions.  That's what I wanted. 

Yes, grading was quicker and less intellectually taxing,  because I could quickly find the student's response to each part of the question.  The unintended consequence was that collaboration became less intellectually involved, too, because the students never had to read each other's work.  When using a blank page, I often saw students going line-by-line through each others' solutions, trying to find mistakes or common ground.  (And I saw their presentation get better as not only I but also their peers criticized sloppy and haphazard solutions.)  When I dictated presentation style through my worksheets, student-to-student discussions became nasty, brutish, and short.

Note that I've been very happy with worksheet-style assignments in regular physics, and I'm going to use that style in conceptual next year.  In those classes, though, most students aren't ready right away for substantial multi-step, creative problem solving.  

I had wanted to move to the AP worksheet-style homework assignments for years, and only recently found the time to write the worksheets.  Turns out, that effort was essentially wasted.  Next time I teach honors or AP, I will be back to requiring a full page of unlined paper for each problem.

Rewriting Problem Sets for Honors / AP Physics

Above is an example of the layout style I'm applying to
problem sets.  Every problem will require both verbal
AND mathematical response.  See this link for a
google docs example:
projectile problem on google docs

Traditionally in my algebra-based AP-level physics course, I've assigned about two homework problems per night.  When I began teaching AP, I selected these problems from the textbook.  All textbooks seem to label their end-of-chapter problems by difficulty:  level I or * means easy, level III or *** means hard.  In every major textbook, the problems at the middle level of difficulty tended to be approximately on target for AP.

Now, there's much more to learning college-level physics than solving end-of-chapter problems.  Although textbooks are trying to improve, still their problems are heavily calculational.  Conceptual questions requiring verbal responses are shunted off into another section, rather than integrated into every problem.  That's not how an AP exam is structured. 

An AP free response question will have 3-5 lettered parts.  Some of these parts will likely require calculation; some parts will require explanation.  It is rare nowadays that a single free response item does not include BOTH verbal and mathematical sections.  I want to mimic this style in my own nightly assignments -- partially as a tool to prepare for an AP-style exam, but primarily because I think it good pedagogy to integrate verbal and mathematical questions.

When I began teaching AP, I scoured my textbook for good, level II, end-of-chapter problems.  The assignment would be stated as, "Do chapter 10 problems 29 and 64."  After I had taught the course for a few years, I began to add my own additional parts to the textbook problems, such as "... for problem 64, also describe as you would to a non-physicist the size of the boat."  And in the past few years, I've re-written most problems entirely to phrase them the way I want.

This summer, I've revised my assignments again for the express purpose of integrating verbal and mathematical responses into every problem.  I've typeset the assignments in MS Word, so that each night's assignment takes up a single page, front-and-back, with room for the answers.  You can check out this projectile problem on google docs as an example of the format and style of an assignment.

Why the room for answers after each part?  For a long time now I've observed that students will tend to use whatever space you provide for problem solving -- no more, no less.  If they use their own lined notebook paper, problems are crammed into as few lines as possible.  When I've provided full sheets of blank paper, they use most of the full sheet -- great, but sometimes I get an essay when I wanted a two-sentence response.  My hope is that I will get my class in the habit of giving just the right depth of response by subtly showing them the space that should be filled.

For those of you who are in their first few years of physics teaching, I would suggest you file this post away for future reference.  It takes enough time at first to figure out how to solve and explain the problems; don't worry about whether the problems are perfectly phrased, or well-typeset.  Just get the students in the habit of communicating their solutions.

But if you've been teaching a while, and if you're wondering how to make your assignments shorter yet more effective, I think this style is worth a try.  Make students write verbal responses on every problem, so they see that physics is about so much more than getting the right number. 

You don't want homework to look like this --> .

I only assign about two problems per night, while math classes usually assign 10-30 problems per night. Yet, my physics assignment should take about the same amount of time to finish as a night of math homework. Not only are the physics questions more involved than their math counterparts, physics problems also require enormously more communication.

Without guidance from me, my students’ problem sets will look a lot like the picture to the right. Even with repeated written guidance, oral guidance, examples, threats, and groveling from me, it takes a long time to establish my expectations for problem presentation.

One trick that has helped tremendously is to require all homework to be done on UNLINED paper, with merely one or two problems per page. (One problem per page in AP physics; no more than two per page in general.) Notebook paper seems to constrain a response: all fractions are written on two lines, diagrams are rarely drawn; and if they are, they often fit nicely alongside the lines to the detriment of the communicative power of the diagram. Students schooled in resource conservation and basic economics put as many problems on a single page as they can fit.

A well presented problem usually includes three elements: diagrams, words, and mathematics. In fact, when I’m pressed for time, I will often grade problems cursorily by merely looking for these three elements and the answer. The blank canvas of the unlined paper, along with the mandate to fill up that canvas, seems to free up my students so they are more likely to include all three of the parts of carefully done homework.

It would seem that the cost associated with the benefit of homework on unlined paper would be the necessity for students to purchase expensive paper, along with the associated environmental cost of recycling or trashing the mounds of used homework assignments. I get around this issue by issuing biannual pleas to the school for usable unlined paper that would otherwise be dumped. Sure enough, my class’s needs have been more than met for a decade.

The library has given me their recycle pile, made up mainly of abandoned print jobs that were printed only on one side. (It’s obviously fine for homework to appear on the back of an old English essay, though students are initially hesitant not to present work on a perfectly clean sheet. What do I care about the flip side?) I make a point of keeping the recycling pile in the science department copy room neat, so I can just take it to my room for student use.

But perhaps the most awesome donations I’ve received come from the admissions and development offices. Whenever someone leaves, or whenever a telephone number changes, they must print new stationery. Their attics were full of stacks out-of-date sheets saying the equivalent of “From the desk of President Herbert Hoover.” The folks in these offices now make a point of sending old boxes of stationery to my room, where students love to use the high quality paper.

No one tries to fit lots of work into the corner of a page anymore. On the rare occasion at the beginning of the year when someone does so out of habit, I just remind him what he has to pay for really nice unlined paper.

GCJ