Become a magician

Discover the unexpected magic of science!
Discover real  mathematics!

We need to make clear that math sees patterns of patterns?
Devlin's "fourth-level" of abstraction and Piaget's "formal operational" insight.

Mathematics is many things.

It is measurement, without which science tends to drift into speculation.
It is logical relationships, which when unseen leads the unseer to absurdity.
It is visualization, which leads mathematicians to see math in the real world

"Making measurements, reporting data, and interpreting one's results are crucial to gaining an appreciation of what science is all about."

"Fourth graders scored above the average...  Our 12th graders got the lowest scores in physical science of the 21 nations participating...   What happened between the 4th and 12th grades?"

Ans:  Middle school, where the texts "fail to present what science is all about."

John Hubisz in "Middle-School Texts Don't Make the Grade"
Physics Today, May 2003

visualize numbers,  + &
Math is "magic" because it's a level or two beyond the levels at which we routinely operate. 
The logic of math can be powerful; it can be unseen; it can seem magical. 

Watch the magicians; they will humble you if you realize what they are doing, and they will show you directions to try to go into.

the dimensions of color
as seen by Feynman
Visualization carries our minds across the boundaries of the several levels of abstraction.  (And Feynman was a synesthete.)

visualize measurement
from infancy to science-see
Balance and mutual reciprocity
EXPLOREPDX's "Have you Noticed..." for March 2003
If the textbook authors don't get it right, what can we expect of our students?
"We regularly saw "speed," "velocity," and "acceleration" confused.  Often writers referred to the gravitational acceleration, 9.8 m/s2, as "gravity" or "the force of gravity."  Cause and effect were frequently backwards as in "an acceleration is a change in velocity that results from speeding up, slowing up, or changing direction."  Note the use of "change in velocity" instead of the correct "change in velocity with respect to time."  That imprecision was a common error.  One text reported that an object is a force, rather than exerts a force."
from "Middle-School Texts Don't Make the Grade"
by John Hubisz, Physics Today, May, 2003, pp 50-54
The above link is dead (June 2005): try the link below, instead.
Middle School Physical Science Resource Center

Substantial progress toward solving these problems
has been made by the Physics Education Group at
the University of Washington.