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10 August 2016

Secret to AP Physics 1: Build *gradually* from calculations to verbal-response

Last year, I swore a blood oath that I would never teach juniors and seniors again.  I loved so much my 9th graders' growth mindsets, their puppyish enthusiasm, their enduring trust in an expert teacher who cared about them.  I could not have been happier teaching the conceptual and the AP 9th grade course.

Well, um... sometimes the Patriots need Troy Brown to switch from reciever to defensive back; sometimes the Yankees need Alex Rodriguez to play third base rather than his natural shortstop.  And, needs must in the physics department, too.  I've gotta pick up the junior-senior AP Physics 1 class this year.  Unless I'm mercifully struck by lightning for breaking my blood oath, anyway.

The good news is, I've made and learned from a bunch of mistakes in teaching this course a couple of years ago.  See the series of three posts (starting here) from April 2015.  

You've heard over and over that AP Physics 1 requires deep understanding and verbal reasoning.  I've told you, the College Board has told you.  The released free response require zero -- ZERO! -- numerical calculations over four exams.

Yet, my problem sets through the first several months require calculations.  My first test in September is constructed based on old AP Physics B items, which require numerical calculation.  Even my mid-February test includes two Physics B-style free response questions along with a paragraph response item.

Of course, these problem set and test items are hardly just "find the right equation and plug in numbers" questions.  They include "justify your answer" parts, qualitative-quantitative translation, "explain what would change", and all sorts of questions that probe understanding beyond just calculation.  But they start with calculation.  Why?

Because I learned the hard way how fixed-mindset juniors and seniors approach this new and intimidating subject.

My students are used to math class, where the method is subordinate to the answer.  Explaining how to solve a problem is less important than clever use of various routines to get to the answer.  The test of whether a problem is done sufficiently is simple -- compare the student's answer to the teacher's or textbook's answer.  Black and white, right or wrong.

Yet, in their writing classes, much is negotiable.  Style is personal, both to the student and the teacher.  Is this piece of literature referencing Homer's Oddyssey?  Very likely a clever student can make a resonable argument, however tortured, which will -- if phrased with good grammar and big words -- earn high marks.*  My wife the English teacher tells of pointing students to clear rules in grammar books, only for the students to tell her that the rule doesn't apply to their particular paper, or that the rule itself is wrong.

* The teacher may give these high marks as much to avoid the inevitable protracted lawyerly discussions about why the marks should have been higher as because the paper actually deserved high marks.

The skills required for AP Physics 1 are far closer to those used in English than in math.  A problem is similar to a page-long essay.  The explanation is as important as the conclusion itself, as is demonstrated by the released free-response rubrics which award little credit for answers in the absence of clear justification.

And therefore, veteran students revert to English class mode.  I can't tell you how many quasi-confrontations I had with upperclassmen:  

"What's wrong with this answer?"  

"Well, as we discussed in class, you've gotta connect the conclusion that the distance increases to the fact that the mass is in the denominator with all else constant, and thus is inversely related to distance." 

"I said that."  

"No, you just said 'distance increases because of the mass.'"  You have to explain the connection between mass and distance with reference to the relevant equation."

"Yeah, I know, that's what I did.  Now what's wrong with that?"

"Who's on first?"

Start the year with calculation in order to avoid these frustrating converstaions; and in order to build the skills that will allow for better and better explanations throughout the year.  When I assign calculational questions, no one ever asks "what's wrong with this answer?"  They know: the numerical result doesn't match my numerical result.  Instead, they ask, why didn't I get the right answer?  That discussion is usually extremely productive.  And, I can follow up those discussions with a targeted quiz question about how a common error led to a wrong answer.  

Point is, instead of blaming me for their own inadequacies, students who get numerical calculation questions wrong tend to be willing to hear about the source of their own misunderstanding.  The process of correcting their work, of identifiying common errors, teaches the very skills that AP 1 demands.

By March, I can give exclusively AP Physics 1 items, with no calculations whatsoever.  That's because I've weaned the class off of numbers as a crutch, or of numbers as a way to avoid an unproductive argument about points.  After months of exposure to physics problem solving and laboratory work, my students understand the point: not to earn points, not even to get the right answer... but to explain how the natural world works based on the facts and relationships we've studied.  

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