Discover the unexpected magic of science!
We need to make clear that
math sees patterns of
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.
|"Making measurements, reporting data, and interpreting
one's results are crucial to gaining an appreciation of what science is
"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, + & –
|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.)||
from infancy to science-see
|Balance and mutual reciprocity
EXPLOREPDX's "Have you Noticed..." for March 2003
|"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
has been made by the Physics Education Group at
the University of Washington.