in its Right Place
would think that the very course designed to add prestige
to a high school’s curriculum might be one of the causes
for a school’s poor performance on mathematics tests—of
late a great concern for local school districts ever since
the federal “No Child Left Behind” law made testing
the criterion for federal financial support.
Perhaps highest on a school’s boasting list is the number of students
they have enrolled in advanced-placement calculus classes. The very nature of the course requires
teachers with the strongest mathematical background. This effectively removes such teachers from the instructional
pool used to staff the standard courses that the majority
of the students are required to take. Quality
instruction there is crucial in setting a school district’s
overall mathematics performance.
put, the advanced-placement calculus course, if at all
to be offered at the high school level, should be reserved
only for the mathematically gifted youngsters who, by their
own talent, are progressing uncommonly fast through the
curriculum and are “ready” to study this more theoretical course.
Boosting the numbers of advanced placement classes, while
enhancing the school’s status in the community, does
not serve well the majority of youngsters taking the course
who are not mature enough to fully appreciate the abstract
nature of the material. Many,
therefore, require private tutoring just to pass – not
a very motivating experience for winning converts to higher
the strategy backfires in two ways: strong teachers are drained
from the regular mathematics program, and potential math
majors are discouraged from exploring the field further.
the inclusion of this course in the four-year high school
curriculum, which now serves as a gatekeeper for further
study in mathematics, forced out topics from the time-tested
high school mathematics curriculum - such as the study of
three-dimensional geometry. In
contrast, providing a richer (rather than faster) treatment
of high school mathematics would give more students a better
understanding and a more genuine appreciation for mathematics,
thereby motivating them to pursue study in this important
should be done without the calculus.
of mathematics instruction in the schools shows a continuous
progression of moving more sophisticated mathematics instruction
to lower grades. Through much of the 19th century, high
school mathematics focused on arithmetic. The
20th century saw the beginning of a downward shift of mathematics
topics from the college level to the high school. Yet, until the calculus moved to the high school, the courses
did not include the concept of infinity, a topic requiring
a fair amount of mathematical sophistication.
shift continues today, mostly at the middle and lower grades. The New York State Mathematics Standards committee, of which
I was a member, has tried to make the lower grades richer
in their study of mathematics. Although
continuing technological advances enable us to consider mathematics
and its instruction in a different light than previously,
this does not warrant a complete shift of curriculum downward. The
shift can be selective and newly created openings should
be used to enrich the subject matter rather than simply pulling
a college course down to the high school prematurely.
New York State’s new standards for math instruction cover instruction
through the 11th grade and leave the 12th grade open for
local school district option. This
provides an opportunity to create math courses more closely
designed for high school students in preparation for further
study in mathematics as well as other academic endeavors. Let’s
leave the teaching of calculus to the colleges, where students,
by then, ought to be “ready” for this course.
With a greater emphasis on problem-solving skills, drawing relationships
and connections between and among mathematical topics,
as well as the areas beyond mathematics, a richer and better
prepared student is more likely to embark on a study of
a time when we continue to suffer a severe shortage of
math majors (not to mention the catastrophic shortage of
math teachers), we rely on outsourcing mathematical and
technological expertise abroad.
concentrate on making the subject matter exciting, motivating,
and relevant so that we can foster greater pride in achieving
success in mathematics. Perhaps this will finally break the trend of taking pride
in having done poorly in school mathematics. Let’s
get the best math teachers to where they are most needed:
providing instruction to convert the masses to love the subject.#
S. Posamentier is Dean of the School of Education at City
College of NY, author of over 35 books on math, and member
of the NYS Standards Committee on Math.