alt.education

"Herman Rubin" wrote in message
news:frbofq$12u6@odds.stat.purdue.edu...

> ... I read through the entire
> book written by NCTM. I do not believe that they
> understood anything about mathematics; I question
> whether any of them understood concepts as distinct
> from manipulations.

Years ago I attended a NCTM math conference session on the use of"Algebra
Tiles". There's other names for other brands but the concept of
manipulations is the same.

About 1/2 way through the presentation I asked "... how do you make the
transition from the tiles to what's on paper...". The response, "... we'll
get to that ...". Having not been addressed, at the end of the session I
asked again about the transition from the manipulations to paper and pencil.
The response (I'll never forget it): "Don't worry, the students will make
the transition".

I've been in schools that spent (literally) thousands of $$$ on
manipulations. Not to mention the untold hours of in-service for teachers.

I know of very very few (if any) teachers who use them - and those who do
use them tend to be first year teachers who use them because the district
said to use them. They sit on the shelf gathering dust. As for myself,
haven't touched 'em in well over 10 years.

I remember attending a session, much later, and they spent a freakin' hour
about the use of Algebra Tiles in Algebra II !!!

> Concepts make the rest easy,
> and learning manipulations seems to make concepts
> hard, at least in mathematics at any level.

Agree. 100%.

Jerry