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Calculus & The Reform Movement

Genesis of the Calculus Reform Movement
AP Calculus and the Reform Movement

Genesis of the Calculus Reform Movement
The calculus curriculum for college undergraduates first came under friendly national fire in June of 1983 at a Sloan Foundation-sponsored conference at Williamstown College. The organizers of that conference felt that the modern applications of mathematics, particularly those inspired by computer programming, had created a need for more finite mathematics in the core undergraduate curriculum and that calculus was consequently too narrow a focus for the first two years of college study. While the idea of replacing calculus with discrete topics was not widely accepted at that time, the challenge to the status quo did inspire the defenders of calculus to admit that their own house needed serious cleaning. The result was another Sloan conference in 1986, this one at Tulane University, to discuss the creation of a "lean and lively calculus" to meet the needs of the twenty-first century. It was that conference that kicked off the calculus reform movement that continues unabated (albeit not unchallenged) today.

All 25 participants at the Tulane Conference were prominent mathematicians, drawn to that historic discussion by their common concern for undergraduate mathematics education. One of them, Katherine Layton, was a high school teacher. Her credentials for inclusion in that group were many, including membership on the Mathematical Sciences Education Board of the National Research Council. But the journey that led her to that college table had begun at her high school desk some 20 years earlier when she started teaching AP Calculus. In addition to Katherine Layton, there were six other participants who had some involvement with the AP Program along the way, and two of them (John Kenelly of Clemson University and Thomas Tucker of Colgate University) had even chaired the AP Calculus Development Committee.

The follow-up to the Tulane conference was a national colloquium on Calculus for a New Century, held in Washington, D. C. under the joint sponsorship of the National Research Council and the Mathematical Association of America. There were more than 600 participants at that meeting, and AP teachers were again a significant presence, contributing several papers to the proceedings. It was apparent from the beginning that AP Calculus would have its own role to play in the reform movement, although only a few (and perhaps only John Kenelly) would have predicted in those early stages how significant that role would be.

AP Calculus and the Reform Movement In some sense AP Calculus has been a reform movement from the very beginning, founded as it is on the once-revolutionary premise that high school students really can learn calculus.

Does the AP Program effect change?
Some reform enthusiasts have been dismayed that the AP Program has not played more of a leadership role in fomenting change on a national scale (something which it is almost uniquely positioned to do), but they tend to underestimate the dilemma that is created by the AP mission itself, which is predicated on the supposition that the high school AP courses are equivalent to the college courses they emulate. Given the pace of change in the colleges and universities, particularly when measured on a national scale, this has had an obviously tempering influence on the extent to which the AP Program can effect change.

AP Quickly Reflects Change
On the other hand, this phenomenon is nicely balanced by how quickly the AP Program can reflect change. The AP Calculus Development Committee is composed of three secondary and four college mathematicians who have been chosen from a national pool of very dedicated and highly competent teachers. Each typically serves for three years, infusing the Program with fresh ideas and a great deal of hard work, influencing the dedicated and highly competent teachers of the AP students who eventually show up as the best and the brightest in every university's classrooms. If a reform project is working, there is no more fertile ground in which the idea can be planted than the AP community. So even though the calculus reform movement began as a college-level phenomenon, there has been nothing passive about the AP involvement. Decisions made by the AP Calculus Development Committee have influenced calculus reform, and ideas from the calculus reform projects have influenced the Committee.

Putting Recommendations into Practice
When the college community formed the Committee on the Undergraduate Program in Mathematics (CUPM) and charged them to design the curriculum for the first two years of college mathematics, the textbook authors took note of their recommendations as expected. But who first put them into use on a national scale? The AP Calculus program, with the course descriptions we know today as Calculus AB and Calculus BC. And when the 1986 Tulane Conference challenged the mathematics community to reform undergraduate calculus courses, they discussed a timetable of pilot programs and textbook development that they hoped could produce significant national change by 1990. Less than four months after the conference, Thomas Tucker and the AP Calculus Development Committee had drafted a position paper that envisioned concomitant changes in AP Calculus as college reforms would gain acceptance. "Although it is not the role of the AP Program [AP Calculus] to lead this reform," the paper noted, "we must be ready to anticipate changes and respond to them."

The Committee did indeed watch and anticipate for a while, but in 1989 it began moving toward a decision that would, at least in one significant area of reform, put AP Calculus in the lead.

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