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21 March 2013

Discussing a daily quiz: explanation first, THEN answer

I've always used a daily quiz to focus the class in the right direction (and to ensure that we start on time). In my junior-senior classes, these quizzes have been a mix of 3-4 question multiple choice quizzes and 5-10 question recall quizzes.  For the 9th grade, I've tried to stick to a standard format of 6-12 questions, each of which can usually be answered with just a few words.  Here's an example of a daily quiz that I used as we were preparing for last month's trimester exam.

Now, I'm not going to grade 40 quizzes every single day.  No, instead, I have the 9th graders trade their papers and grade 'em with the red pens that I hand out.  The answers are generally straightforward enough that we don't have arguments about the rightness of the answer.  They mark each answer right or wrong, then total up and record the score.  The in-class grading process saves me 20-40 minutes per night.

But the purpose of in-class grading goes beyond the logistical, and into the pedagogical.  The desire of a 9th grader for immediate feedback can hardly be overstated.  These folks are desperate, desperate, I say, to know whether they got credit or not.*  Knowing that, consider the subtle but important difference between these two ways of communicating to the class the answer to question 1 for them to grade:

* Notice that I don't say they are desperate to find out whether their answer was right.  No one cares about that.

Question 1: A car moving 30 m/s collides with a mosquito.  Does the car or the mosquito experience more acceleration during the collision?

(a) "The mosquito experiences more acceleration, because acceleration is the change in an object's speed in one second.  During the collision, the car's speed barely changes from 30 m/s.  However, the mosquito goes very quickly from rest to 30 m/s.  The mosquito must have a larger change in speed in the same amount of time, and thus has more acceleration."

(b) "Acceleration is the change in an object's speed in one second.  During the collision, the car's speed barely changes from 30 m/s.  However, the mosquito goes very quickly from rest to 30 m/s.  The mosquito must have a larger change in speed in the same amount of time.  So, the mosquito experiences more acceleration."

I've watched the students while they grade quizzes.  Their red pens hover, waiting for the exact moment when the answer on the paper -- and in their mind -- is confirmed or shot down.  They make a mark the very instant that they hear confirmation of the answer.

Therefore, Don't state the answer right away! 

In explanation (a), I've stated the answer up front.  Thus, I would see the students mark the answers right or wrong, then wait patiently for us to go on to question 2.  Maybe they'd keep marking, with a "good job" or a "nice!" or even a "boux!" for someone who got the wrong answer.  But they wouldn't be listening to me.

But when I use phraseology (b), the class waits breathlessly.  Sometimes, the sharper students jump the gun halfway through the explanation when they can see that their reasoning matches mine.  Most wait attentively until the very last sentence, when I explicitly state the answer.

It takes a serious effort on my part to give an explanation first before saying the answer.  The temptation is to say "Number 6: d=vt," and then move on, only discussing the answer if someone looks puzzled.  The trick is to start with the most basic reasoning, and make the class hear it: "A projectile moves at constant speed in the horizontal direction.  When something moves at constant speed, the equation for distance traveled is d=vt."

GCJ

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