Re: [Phys-L] problems with the teaching of algebra

[Ze'ev Wurman <zeev@ieee.org>]

On 10/24/2014 10:39 AM, Philip Keller wrote:
> Hello All,
>
> As I mentioned, I have been working on a project related to how we teach
> algebra.  My goal is to present the material both differently and earlier
> than a traditional algebra 1 approach.  For example, I don't see why we
> wait until algebra 2 or precalc to teach about functions.

I will not start a discussion when it is appropriate to start teaching 
*formally* functions and, in particular, how much focus they ought to 
get in the first formal algebra course. Nevertheless, it is an 
interesting and important topic.


> And I am always
> troubled by students who see algebra as a set of procedures rather than a
> language.

This is the part that baffled me. I don't see the (traditional) algebra 
simply as "a set of procedures," but I can hardly think of a more 
wrong-headed  way than seeing it as a "language."

Don't get me wrong -- algebra today does have a language. But algebra 
200 years back, or 1200 years back, or even 2000 years back, had a 
completely different language yet anyone looking closely will recognize 
it as "algebra." Saying that algebra is a language is akin to saying 
that Shakespeare works are "English."

A brilliant mathematician recently suggested that algebra is simply the 
set of procedures used/needed to solve "the inverse problem." Clearly, 
one can limit it further by saying what those procedures *cannot* use 
such as calculus or analysis, but even without it I think this is one of 
the better definitions of algebra I have ever seen.

Ze'ev