




AP Calculus: Evolution of a Calculator Policy

  The College Board and Educational Testing Service (ETS) had been under pressure from some mathematics educators since the early 1980s to allow calculators on their standardized tests.
The myriad uncertainties of introducing calculators seemed to be too numerous to risk pioneering this effort on such highvolume assessments as the SAT®, so they asked the AP Calculus Development Committee what they thought about allowing calculators on the AP Calculus Exams. The Committee, aware of the capabilities of the scientific calculators available at the time, conjectured that they would not make much difference one way or the other. They therefore agreed to allow students the optional use of scientific calculators on the AP Exams in 1983 and 1984.
Calculators certainly were making a difference. At the 1983 AP Reading (scoring of the freeresponse questions), it became apparent that the calculators certainly were making a difference but not in a positive direction. Students who clearly knew the calculus were being led into mistakes by the unwise use of their (obviously unfamiliar) calculators. Since the calculators were not even required, this introduced an unfortunate confounding factor into the measurement of calculus proficiency, the intended outcome of the exam. The experiment continued for a second year but only because there were no effective means for calling it off. It had failed from the start in the only way that had mattered.
The calculator question came up again in 1989 under highly different circumstances. Calculators by that time could sketch graphs of functions, run programs, and store significant quantities of data. The NCTM Standards were calling for the regular use of graphing calculators in all classes beyond grade 10, and the early architects of calculus reform, with graphing technology in mind, were stressing the graphical representations of calculus as much as the traditional analytic representations. The AP Calculus Development Committee saw the potential for the new graphing machines to enhance the teaching and learning of calculus, but their previous experiment with calculators had shown them the dangers of introducing them into the testing process without first assessing their probable impact. They had also learned that optional calculator use confounded the measurement process, so the decision this time would have to be either to disallow them or to require them  and requiring them meant writing questions for which they would be needed.
The College Board funded a carefullydesigned "calculator impact study" in April of 1990 that led to a 100page report from ETS measurement specialists, notably Rick Morgan, Joe Stevens, and longtime ETSAP liaison, Chan Jones. A distinguished panel of experts from ETS, the College Board, and various mathematical societies then gathered with the Committee in October to analyze that report and suggest a course of action. Their eventual recommendation was to require scientific calculators for the 1993 and 1994 exams  a temporary measure  but to move the AP Program toward graphing calculators with an eye toward requiring them in 1995. Three former chairs of the Committee were among the university mathematicians who contributed at that historic meeting, but the calculator decision and many other transitional details over the next four tumultuous years would be communicated to AP teachers by one of their own: Dan Kennedy of Baylor School in Chattanooga. It was at that meeting that he became the first high school teacher to chair the AP Calculus Committee in 35 years.
No reasons for delaying implementation. In 1993 the Committee surveyed colleges and secondary schools across the country to assess the acceptance and availability of graphing calculators. As the results of the survey turned up no reasons for delaying implementation, the first "graphingcalculatoractive" exams were given in June of 1995, right on the predicted schedule. Sage observers had cautioned the Program to be prepared for a slow growth year due to the dramatic transition, yet 1995 surprisingly produced an unusually large jump in the number of AP Calculus Exams administered. While not all those students were successful, the feeling was universal that the calculator experiment was. Granted, lessons have been learned in that year and every subsequent year about how to ask and answer calculus questions in a calculator environment, but nobody who has scored the students' responses has doubted whether the questions are testing the actual understanding of calculus.
Preparing teachers to accept and utilize the graphing calculator. The meticulous planning behind exam development was only one factor in the successful introduction of technology into AP Calculus; there was also the matter of preparing teachers to accept and utilize the graphing calculator  not as a novelty but as an integral component of their calculus courses. With its national curriculum and its wellestablished program of workshops and Summer Institutes, the AP Program became the mechanism to spread the message nationally. A highly successful initiative called TICAP (Technology Intensive Calculus for Advanced Placement) conceived and directed by John Kenelly, John Harvey, and Wade Curry, the former College Board director of AP, showed the way. Before the NSF funding had run out, 125,000 AP students were learning calculus with graphing calculators in their hands. TICAP is now considered a model for achieving the goals of education reform.





