My first direct exposure to The Calculus was as a
university freshman in 1966. My intrduction to college
was at the tutalage of an instructor who learned very
well how to wield his power in those turbulent times.
He was a graduate assistant from South Korea who held
unusually strong anti-communist opinions. Our esteemed
instructor knew the power of 'curriculum-as-instrument'
and he wielded that instrument for his own deliberate
purpose in support of America's aggressive war in Viet Nam.
His teaching was intimidating and his testing was aggressive.
Ultimately, only one male student in his class received
a passing grade. Five credit hours of "F" on a beginning
freshman transcript was enough to say, "You're in the Army
now!"
Another significant impact to me in those times was
Jerome Bruner's influence on my career as a young
teacher. In The__Process_of_Education (1960), Bruner
corageously challenged traditional curriculur structures
on the basis of intellectual honesty. He said that "the
foundations of any subject may be taught to anybody
at any age in some form." Second-grade children can
engage in absorbing games governed by the principles
of integration, differentiation, set theory or
approximation without immersing them in the formalisms
associated with college-level Calculus texts. Bruner
advocated a "spiral curriculum" in which all subjects
that are worth knowing should be introduced to all
students at all levels. Calculus need not be the
exclusive domain of career-bound scientists and
engineers to be introduced in high school or college.
The rich mental models that emerge out of honest
child-like inquiry surrounding the infinitesimal can
transform mathematics into a simple expression of
aesthetics that explain our universe in a ways that
fully complement mythology, literature and the fine arts.
In the words of my friend Jim Teslow, "the real world
takes on a smooth, inviting texture--functions become
roller coasters rather than equations; volumes are swept
out by hoops and wands, not mere calculations of base
times height; fluid flow becomes an onslaught of arrows;
and boundaries become approachable asymptotes."
Unfortunately, the Calculus as found in our educational
institutions is too often wielded for purposes of selection,
intimidation and separation. If treated with intellectual
honestly, as Bruner advocated in 1960, it could permeate a
child's curriculum from kintergarten through college.
The Calculus need not take on a formalist structure to be
wielded for any purpose beyond the sheer joy of learning.
Martin R.
> Will all those out there who have become reasonably successful without
> having had a calculus course raise their hands. And then will some one
> suggest why there is pressure on American high schools to require
> calculus courses of high school students?
> Ken Goodman