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

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

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.