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17 July 2010

No one ever went broke underestimating students' calculational skills

Look, physics isn't about math.  We have to get that message across as many times and in as many ways as possible early in a high school physics course. 

I have already detailed my first salvo against the preconception that math is what makes physics hard.  In sum, I suggested using the minimal algebra skills necessary for AP physics B as a recruiting tool.  The two skills necessary are (1) solving simultadous equations, and (2) knowing the definitions of the three major trig functions.  "You know these things cold," I say.  "I promise, there will be no more complicated math, regardless of what you might be covering in your algebra II or precalculus class."

I received a note with an interesting idea from Matt Swanson, recently of my Kennesaw State AP Summer Insitute.  Matt says:

"I read your blog post about pre-tests and I agree with your advice. However, I was toying around with the idea of giving one on the first day of school anyway. I was thinking about giving them a two question quiz that consisted of your recruiting questions..."

I totally see where Matt is coming from.  He's facing a roomful of nervous AP students whose prejudice is that they're in for a math-style course tougher than the nastiest level of calculus.  He wants to put them at ease about their math skills, while at the same time establishing the daily quiz routine.  My initial reaction was that this might be a good idea in Matt's situation, though I would not use it myself. 

On further thought, though, I realized that such a first day quiz might easily backfire.  Why?  Because I'll bet that a significant fraction of the class would get the very basic questions WRONG.

Quick side story:  When I first started teaching Universal Graviataion, I set up the calculation of the force of the earth on the moon.  I wrote the numerical values of each term on the board, and asked the class to plug into their calculators.  Why?  I knew that a very common mistake in such a calculation is to forget to square the denominator.  My hope was that everyone would get an answer within about 45 seconds, that 17 of 20 students would get the right answer, while the other 3 would forget to square the denominator.  We could have a nice teaching moment (Don't forget GMM/r SQUARED!)  and we'd move on.

Veteran teachers are likely laughing at me in the voice of Emperor Palpatine.  (YOUNG FOOL... ONLY NOW DO YOU UNDERSTAND....)  Of course this didn't work.  It took 3-4 minutes for most of the class to get answers.  Of 20 students, I saw 17 different answers.  I tried again the next year - same result.  Okay, I said, I give up -- I'm going to teach order of magnitude estimation in class, and let the students play futilely with their calculators on their problem sets. 

I've seen similar crazy difficulty with the most basic of quiz questions involving recall or basic arithmetic skills.  As the year goes on, students learn not to fret about occasional dumb mistakes - when an AP exam only requires 65% of the available points to earn a 5, and when the final numerical answer is wholly subordinate to the physics reasoning behind that answer, who cares if a student said that 2 divided by 5 is 0.6. 

My worry about Matt's opening day quiz is that, no matter how simple the algebraic exercises, SOME WILL GET THEM WRONG.  And then the whole point of Matt's opening gambit -- look how easy the math is, you can do it! -- -will have blown up brutally.  All it would take is a few students saying, "Geez, he says that quiz was easy, but I still ran out of time and got it wrong.  I'm failing already on the first day."

Don't worry -- if you do physics from the first day of class, integrating mathematics only where necessary, students will get good at doing the math.  And, if YOU model the correct attitude that mathematical crunching is subordinate to physical understanding, the students will pick it up.

GCJ

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