Put Calculus in its Right Place
By Alfred Posamentier, Ph.D.

Who 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.

Simply 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 mathematics.  So 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.

In addition, 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 field.  This should be done without the calculus.

The history 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. 

This downward 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 mathematics.  At 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.

Let’s 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.#

Dr. Alfred 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.