Re: [Phys-L] The Make-Believe World of Real World Physics

[John Denker <jsd@av8n.com>]

On Jul 30, 2013, at 2:15 PM, I wrote IN PART:
> > > "Taking the average does not commute with taking the inverse"

On 07/30/2013 12:04 PM, jbellina wrote:
> Common now John, seriously, would you say this to a middle school
> student, or even an average high school student and expect any real
> response?

Come on, yourself.  Try reading what I wrote IN CONTEXT,
including the part where I said

> I'll bet there
> are a lot of students who have never heard the expression "Taking 
> the average does not commute with taking the inverse" and could 
> not explain what it means.  I'll bet there are lots of students
> who blissfully average the speeds, and don't understand why it's
> not always the right thing to do.

It's like most other math topics:  They're "supposed" to know
the concept, but they don't.  The definition of "commutative"
is on the common core standards for *third grade* but that
doesn't mean students actually understand it or retain it.