A clever way to insist on a good initial effort on problems

The two extremes we try to avoid in teaching creative problem solving:

(a) The student who holes up in a quiet place for hours by himself hammering his head on the desk trying to solve a problem that should take all of 20-25 minutes

(b) The student who looks at the problem for 30 seconds, throws up his hands, and turns in a blank page saying "I have no idea, this is too hard."

Somehow we have to convince students to make a serious individual effort, but to stop and seek help when they get truly stuck.  How?  I've got my own techniques, which usually involve rules about how much time students must spend writing down their own ideas before collaborating.  Occasionally I've assigned work due on one day, then on that day granted a reprieve to allow further collaboration.  That works great; except, you can only do it once or twice before students stop doing the individual work, hoping for and expecting a reprieve.

Jen Deschoff, originally a Michiganer but now a North Carolinininian,  created a kick-arse approach to holding students accountable for their individual effort on problem sets.  In my Summer Institute that Jen attended, I pointed out the four essential elements of a well-presented physics problem:

* words

* diagrams

* equations

* numbers

There's hardly a well-solved AP-level problem anywhere which doesn't include at least three of these four elements.  I remember making a throwaway comment that, if I were pressed for time during the school year*, instead of grading a problem set carefully I might just look quickly for these elements in order to assign a grade.  

* Ed. Note: Why use the subjunctive?  You're a teacher.  When school is in session, you are pressed for time by definition.  Might as well say "If Ray Lewis could beat you up, then he wouldn't steal your lunch money, 'cause he's reformed now."

Well, Jen took that comment and ran with it.  She now grades many AP-level problems in two stages:

Stage 1: On the day the problem is due, students give the problem to another student, who looks for each of the four elements.  The students are NOT grading the answer at all!  They're just verifying that words, diagrams, equations, and numbers show up somewhere, and giving a grade for that.  Everyone keeps their original work.  

Stage 2: The NEXT day, everyone just turns in the problem, and Jen grades it for correctness as well as for the four problem solving elements.  

This approach fosters discussion among students -- they grade each other's initial work, and so I'm sure they comment on the correctness of the solution.  Someone who was previously stuck will likely see the hint he needs.  And now the guy who writes nothing because "it's just too hard" stands naked* before the class, seeing that he could have, should have, earned credit just by going through the problem solving motions.  (Jen says she has thrown** blank papers back to students.)  Next time, when he does go through those motions, he'll be surprised to find that physics isn't as hard as he thought.  

* figuratively

** literally

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.