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561 FText of a Letter Endorsed by the Governing Boards of the Mathematical Association of America and the National Council of Teachers of Mathematics Concerning Calculus in the Secondary Schools33 TO: FROM: DATE: RE: .~ Secondary School Mathematics Teachers The Mathematical Association of America The National Council of Teachers of Mathematics September, 1986 Calculus in the Secondary School Dear Colleague: A single variable calculus course is now well established in the 12th grade at many secondary schools, and the number of students enrolling is increasing substantially each year. In this letter, we would like to discuss two problems that have emerged. The first problem concerns the relationship between the calculus course offered in high school and the succeeding calculus courses in college. Ibe 33This letter was extracted from Calculus for a New Century: A Pump, Not a Filter, A National Colloquium, October 28-29, 1987 (MAA Notes, Number 8, edited by Lynn Arthur Steen for the Board on Mathematical Sciences and the Mathematical Sciences Education Board of the National Research Council, Mathematical Association of America, 1988).

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562 CONTENT PANEL REPORT Mathematical Association of America (:MAAJ and the National Council of Teachers of Mathematics (NCTM) recommend that the calculus course of- fered in the 12th grade should be treated as a college-level course. The expec- tation should be that a substantial majority of the students taking the course will master the material and will not then repeat the subject upon entrance to college. Too many students now view their 12th grade calculus course as an introduction to calculus with the expectation of repeating the material in college. This causes an undesirable attitude on the part of the student both in secondary school and in college. In secondary school all too often a student may feel "I don't have to study this subject too seriously, because I have already seen most of the ideas." Such students typically have consider- able difficulty later on as they proceed further into the subject matter. MM and NCTM recommend that all students taking calculus in second- ary school who are performing satisfactorily in the course should expect to place out of the comparable college calculus course. Therefore, to verify ap- propriate placement upon entrance to college, students should either take one of the Advanced Placement (AP) Calculus Examinations of the College Board, or take a locally-administered college placement examination in cal- culus. Satisfactory performance on an AP examination carries with it college credit at most universities. The second problem concerns preparation for the calculus course. MAA and NCTM recommend that students who enroll in a calculus course in sec- ondary school should have demonstrated mastery of algebra, geometry, tr~go- nometry, and coordinate geometry. This means that students should have at least four full years of mathematical preparation beginning with the first course in algebra. The advanced topics in algebra, trigonometry, analytic geometry, complex numbers, and elementary functions studied in depth during the fourth year of preparation are critically important for students' latter courses in mathematics. It is important to note that at present many well-prepared students take calculus in the 12th grade, place out of the comparable course in college, and do well in succeeding college courses. Currently, the two most common methods for preparing students for a college-level calculus course in the 12th grade are to begin the first algebra course in the 8th grade or to require students to take second year algebra and geometry concurrently. Students beginning with algebra in the 9th grade, who take only one mathematics course each year in secondary school, should not expect to take calculus in the 12th grade. Instead, they should use the 12th grade to prepare them- selves fully for calculus as freshmen in college. We offer these recommendations in an attempt to strengthen the calcu- lus program in secondary schools. They are not meant to discourage the

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MATHEMATICS teaching of college-level calculus in the 12th grade to strongly prepared students. LYNN ARTHUR STEEN President, Mathematical Association of America JOHN A. DOSSEY President, National Council of Teachers of Mathematics a: 563

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