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## 21 September 2012

The phrase "justify your answer" appears on AP physics exams all the time... and I would contend that this phrase should be a staple of everyone's physics classes.  Students usually struggle to understand just what depth of justification is necessary; often they even struggle with the idea that a justification isn't simply a restatement of the question.

I've written before about crystallizing the elements of an appropriate justification:  it should be written to be understood by an intelligent student at the same level of physics, and should include either an equation, a calculation, or a fact of physics.

In my 9th grade conceptual class, we're avoiding calculations wherever possible.  And ninth graders are much less savvy than seniors about what might be considered a "fact of physics."  So I've had to adjust my approach a bit.

We use the Phillips Style of teaching ninth grade physics, in which we spend time in class highlighting relevant facts of physics in the text, then we quiz on those facts.  Students are allowed to use notes that they hand-wrote outside of class for some of the quizzes.  This style does two things for me.  For one, my students can tell you pretty quickly that "When light speeds up into a new material, the light bends away from normal."  Their recall of facts is solid.

For another, and more importantly, the statements we highlight in the text define the starting point for justifications.  We never have to go deeper than the facts we've learned; we must always start with one or more of these facts.

The requirement:  Each justification must include at least two sentences.  The first sentence or two must be facts of physics, stated pretty much word-for-word from our class notes. Then, the facts must be related to the problem at hand with a separate sentence.

Consider a seemingly simple question:

beam of light travels from air into a liquid.  The index of refraction of the liquid is 1.4.  Will the light bend toward the normal, or away from the normal?

The justification must include two sentences, for example, like:

1. Light travels as fast as fast as it can possibly go in air.  When light enters a material in which its speed decreases, the light bends toward the normal.
2. In this problem, the speed of light in the liquid must be less than in air, so the light must slow down, bending toward the normal.

Or, perhaps:

1. The higher the index of refraction, the slower the speed of light in a material.  When light enters a material in which its speed decreases, the light bends toward the normal.
2. In this problem, the speed of light in the liquid must be less than in air because the liquid has a higher n.  So the light must slow down, bending toward the normal.

Or the equation n=c/v could be used to show that the light slows down -- we put that equation in our notes.

Now, at first I'm being somewhat generous about credit.  I'm giving plenty of credit for reasonable attempts that use facts of physics from the notes; after all, these are freshmen, and I'm pleased at this point if they are not leaving problems blank.  And I'm fine for now if the answer is in the style required, but the logic is incomplete.  All I ask is that everyone write facts from the book, not facts they made up.

And that's fine progress for the first few weeks of general ninth grade physics.  One step at a time.