Nonpartisan Education Review / Essays

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**Advanced Placement Calculus
is not College Calculus**

W. Stephen Wilson, Professor,

Department of Mathematics and School of Education

Johns Hopkins
University

A while ago I
took a close look at the Advanced Placement (AP) Calculus AB Curriculum
Framework for 2016–2017, the Syllabus Development Guide, and the AB
Practice Exam from the 2014 Administration.

I'm quite fond
of AP Calculus, having signed my high school up for the test and administered
it to myself back in 1964. No doubt it helped me get out of Kansas to M.I.T.

AP Calculus AB
in high school has some serious advantages over Calculus in college. It is a
college semester's worth of material taught over an entire year, usually every
school day, making about 150–180 hours of instruction, often in small
classes compared to college, where the instruction time might well be closer to
50 hours in a large college lecture course. More students take Calculus in high
school than in College.

The AP AB
Calculus curriculum, according to the Framework, "is equivalent to that of a first-semester
college Calculus course... and ... is designed to be taught over a full
academic year." The College Board Administers an associated externally graded
exam. High scores on the exam count for a semester of Calculus credit at many
colleges and universities. This equivalence is an illusion. Calculus at my
university, Johns Hopkins University, could not pass the audit to qualify for
AP Calculus. This is equally true for many other universities and colleges.

I think highly
of most items on the test, have some minor issues with the syllabus, but the
very large flaw is the association of AP Calculus with the graphing calculator.

The graphing
calculator is thoroughly integrated into all aspects of the AP AB course. The
Framework is explicit: "The use of a graphing calculator is considered an
integral part of the AP Calculus courses, and it is required on some portions
of the exams." This statement that the graphing calculator must be an
"integral" part of the course is too extreme for the simple reason that the
graphing calculator is not integral to Calculus. Calculus can be taught and
learned without any technology. The extensive use of the graphing calculator is
also not reflective of college Calculus classes. At the college level, many
professors do not emphasize (or even allow) the use of graphing calculators since
there is no concept in Calculus that requires the technology either to teach or
to assess.

Furthermore, the
graphing calculator is not ideal technology for teachers who may want to use technology
for illustrative purposes. The graphic display is very small and the resolution
poor. Input methods can be time-consuming to learn and to teach, and many
teachers may prefer to focus on the mathematics involved rather than spend time
teaching how to work with graphing calculators. Students who will need
computing technology in the future, will need more sophisticated devices than
graphing calculators. The graphing calculator is an obsolete piece of
electronic equipment that owes its continued existence to the unnecessary AP
Calculus exam requirements.

Although the
problems that are calculator-dependent tend to be real Calculus problems, the
need for the graphing calculator to test the concepts and content knowledge is
completely artificial. These questions do not represent "real world" situations
by any stretch of the imagination. The graphing calculator is used on the exam
to solve completely contrived problems designed so that the graphing calculator
is required. Consequently, either the student's ability to use the graphing
calculator is being tested as content, or the test is testing whether or not
teachers have taught students how to use calculators. The graphing calculator
is not Calculus content and pedagogy should not be tested. There is no justification
for the graphing calculator to be used on the AP Calculus AB Exam.

The Syllabus
Development Guide to AP Calculus AB gives further evidence of the misplaced
emphasis on the graphing calculator. There are 12 scored components in the
curricular requirements. Three of them are about the graphing calculator. To be
an approved AP Calculus AB course, students MUST be taught "to use graphing
calculators" to "help solve problems," to "experiment," and to "interpret
results and support conclusions." None of these are necessary to prepare a
student for a thorough Calculus exam.

The bottom line
is that AP Calculus AB is supposed to be "equivalent" to a first semester
college Calculus course. ** The wrong-headed view that graphing
calculators and Calculus are inseparable means that many, if not most, college
Calculus I courses would not meet the standards of the AP audit to be allowed
to be called AP Calculus.** It is inappropriate for high school Calculus
to attempt to redefine the collegiate version of Calculus. This contradicts the
College Board's intention that AP Calculus is equivalent to college Calculus.

Citation: Wilson, W.S. (2018). Advanced Placement Calculus is not College Calculus,* Nonpartisan Education Review */ Resources. Retrieved [date] from
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