Re: [Phys-L] foundations of physics: special relativity

["John Clement" <clement@hal-pc.org>]

Of course in grade school students do NOT learn how to add vectors
geometrically without reference to frame or vector basis.  Indeed this is
not learned in MS or HS.  Vectors are very difficult for students to
understand, and most physics teachers just teach the math of adding
components using a table, without really imparting any meaning.

Hake's method of teaching vectors starts with displacements.  I personally
think that it needs to be taught only when it can no longer be avoided, so
it is motivated.  The vast majority of students never really understand
vectors in the conventional physics course.

Actually I did not encounter vectors until HS, so the editoral you probably
does not apply to most people on this list.

John M. Clement
Houston, TX


> In grade school, you learned to add vectors geometrically, 
> tip to tail, without reference to any reference frame or vector basis.
>
> This leads to a style of reasoning that helps keep you out of 
> trouble.  That is, find a way of saying whatever needs to be 
> said using /manifestly/ invariant expressions.  For example, 
> talking about the dot product of physically-relevant vectors 
> is manifestly invariant.  In contrast, talking about the 
> components in this-or-that frame is not.