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15 November 2016

Don't be afraid to ask an open-ended question; but make your students answer it.

A man of mass 80 kg stands on a scale in an elevator.

Think of all the questions that can be asked in this situation.  I'll give some typical questions... but look at the end to see my crazy open-ended versions.

The scale reads 750 N.  What is the magnitude and direction of the man's acceleration?

Good start.  Your student has to recognize that the acceleration is the NET force divided by the mass, not any old force.  And has to know that 80 kg means a weight of 800 N, making the net force (800 N - 750 N) = 50 N.  Acceleration is in the direction of the net force, so downward.

The biggest misconception here, though, isn't about the relationship between net force and acceleration -- it's the relationship between net force and motion.  Try this one:

The elevator moves upward and slows down.  Is the reading in the scale greater than, less than, or equal to 800 N?

Half of your class will say the scale reading is greater than the 800 N weight of the man, because they assume that net force and acceleration must always be in the direction of motion.  Aarrgh!  No, net force is in the direction of acceleration; when an object slows down, its acceleration is opposite the direction of its motion.

No matter how good you are at disabusing folks of this misconception, getting 100% of a class to answer this question correctly is a neigh-impossible task.

That said, questions that directly address the misconception and then require students to explain their reasoning are a bigly step toward busting the misconception.  Yes, your students will get this wrong; but fewer and fewer will get it wrong as the year goes on and as you ask similar questions again and again.

I phrase some of these questions in an even more open-ended style:

The scale reads 750 N.  Which way is the elevator moving?

Even better!  Now the students have to recognize and articulate for themselves that the question is unanswerable, and why it's unanswerable.  Acceptable answers include "we don't know because we only know the direction of acceleration, not motion" or "if the elevator is speeding up, it's moving upward."  The important point of this style of question is, the answer can't easily be gamed by the good test-takers taking clues from the phrasing.  Even including choices such as (A) up (B) down (C) it can't be determined gives a clue.  A physics student who has truly attained a masterful understanding of the relationship between force and motion will not have any difficulty with this question.

Now, this approach doesn't work if students habitually ask questions during a quiz, or if they come straight to the teacher for help on homework before answering.  "Wait, teacher, you didn't give us enough information to solve the problem, what are we supposed to do?"  Whatever you say, you're sunk; the student AND HIS CLASSMATES have just heard the game-the-question clue they wanted.  

So you must establish from the start of your class that these sorts of open-ended questions will be asked; and that they must be answered without any attempt to drag hints out of the teacher.  Don't tolerate whining like "that's not fair, it's a trick question."  There are no trick questions.  Success in physics comes when the class stops looking for the tricks and starts answering confidently with reference to physics facts.  Physics is, at its heart, about understanding the universe.  And Mother Nature is generally unsympathetic to complaints that the problems she poses are too tricky and open-ended.

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