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Calculus in High School

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David Bressoud, Macalester CollegeRandolph Lecture, Rochester, NYOctober 20, 2007This PowerPoint will be available atwww.macalester.edu/~bressoud/talksHigh school graduates, 2007: 3,232,0002006 high school graduates who entered college withina year: 1,850,0002004 Bachelor’s degrees: 1,400,000engineering & eng. technology: 78,200biological sciences: 61,500computer & information science: 59,500physical sciences: 18,000math & stat: 13,300 230,500Dept. of Ed, NCES dataCBMS datayear % majoring in math 1975 2.03% 1980 1.23% 1985 1.33% 1990 1.22% 1995 1.07% 2000 0.87% 2005 0.86% CBMS dataCBMS and College Board dataAP Calculus currently growing at>14,000/year (about 6%)AP Calculus currently growing at>14,000/year (about 6%)Estimated # of students takingCalculus in high school (NAEP,2005): ~ 500,000Estimated # of students takingCalculus I in college: ~ 500,000(includes Business Calc)High School Calculus breakdown:380,000 take AP Calculus (College Board estimate)50,000 take IB or Dual Enrollment100,000 take another course with “Calculus” in the titleHigh School Calculus breakdown:380,000 take AP Calculus (College Board estimate)276,004 took AP exam; AB: 211,693, BC: 64,311High School Calculus breakdown (2007 numbers):380,000 take AP Calculus (College Board estimate)276,004 took AP exam; AB: 211,693, BC: 64,311AB exam: credit-AP BC exam: 79%-73%5: 44,500 84%-77% 28,0004: 39,600 82%-64% 11,5003: 40,400 60%-39% 12,1001–2: 92,500 12,700Percentages from 2002 nationwide random sample for The CollegeBoard by Karen Morgan, N = 435 (AB), = 139 (BC)Based on the estimates by Morgan, of 276,000 whotook the AP exam in 2007, roughly 145,000 receivecollege credit for calculus, roughly 125,000 of themuse this credit to go directly to the next math class.Fall of 1991Boston College, Brigham Young University, Carnegie Mellon University,Clemson University, College of William and Mary, Cornell College (IA),Cornell University, Duke University, Michigan State University, PennsylvaniaState University, Stanford University, Tulane University, UC-Davis, UC-Irvine,University of Georgia, University of Illinois, UNC-Chapel Hill, UT-Austin,University of Utah, University of Virginia, Yale UniversityMorgan & Ramist, 1998Average grade in Calculus II:Took Calc I at that university: 2.523 on AB exam and used AP: 2.674 on AB exam and used AP: 2.795 on AB exam and used AP: 3.23Fall of 1991Boston College, Brigham Young University, Carnegie Mellon University,Clemson University, College of William and Mary, Cornell College (IA),Cornell University, Duke University, Michigan State University, PennsylvaniaState University, Stanford University, Tulane University, UC-Davis, UC-Irvine,University of Georgia, University of Illinois, UNC-Chapel Hill, UT-Austin,University of Utah, University of Virginia, Yale UniversityMorgan & Ramist, 1998Average grade in Calculus III:Took Calc II at that university: 2.873 on BC exam and used AP: 3.114 on BC exam and used AP: 2.745 on BC exam and used AP: 3.321996–99University of Texas at AustinDodd et al, 2002Average grade in Calculus II:Took Calc I at that university: 2.553–5 on AB exam and used AP: 2.98Non-AP students chosen so thatSAT scores are comparable forboth sets of studentsFall of 1994Barnard College, Binghamton U., Brigham Young U., Carnegie Mellon U.,College of William and Mary, Cornell U., Dartmouth College, GeorgeWashington U., GA Institute of Technology, Miami U. (OH), NC State U.,Northwestern U., Stanford U., Texas A&M, UC-Davis, UC-LA, U. of FL, U. ofIL-Urbana, U. of IA, U. of MD, U. of Miami, USC, UT-Austin, U. of VA, U. ofWA, Wesleyan College, Williams CollegeMorgan & Klaric, 2006Average grade in Calculus II: SAT-adjustedTook Calc I at that university: 2.433 on AB exam and used AP: 2.69 2.644 on AB exam and used AP: 2.90 2.785 on AB exam and used AP: 3.34 3.15Fall of 1994Barnard College, Binghamton U., Brigham Young U., Carnegie Mellon U.,College of William and Mary, Cornell U., Dartmouth College, GeorgeWashington U., GA Institute of Technology, Miami U. (OH), NC State U.,Northwestern U., Stanford U., Texas A&M, UC-Davis, UC-LA, U. of FL, U. ofIL-Urbana, U. of IA, U. of MD, U. of Miami, USC, UT-Austin, U. of VA, U. ofWA, Wesleyan College, Williams CollegeMorgan & Klaric, 2006Average grade in Calculus III: SAT-adjustedTook Calc II at that university: 2.503 on BC exam and used AP: 3.00 2.924 on BC exam and used AP: 3.45 3.355 on BC exam and used AP: 3.46 3.27Classes of 1990 & 1991College of William & MaryDavid Lutzer, private communicationPercentage taking next math class (SAT-adjusted)≥ 4 on AB or ≥ 3 on BC: 60%Took Calculus I at W&M: 61%Percentage that eventually majored in Mathematics(SAT-adjusted)≥ 4 on AB or ≥ 3 on BC: 3%Took Calculus I at W&M: 8%Conclusion:Students who take AP Calculus in high school and dowell on the exam generally are as well prepared for thenext class as those coming out of the comparablecollege courses.But, this is a very large group (about 145,000) of verytalented students. Are the colleges and universitiesdoing all they can and should to entice these students tocontinue mathematics and to prepare them formathematically intensive majors?2007: 64,311CBMS & College Board dataCollege Board dataBC exam,8,818 in 200215,533 in 200776% increaseCollege Board dataAmerican Math Competition survey, spring 2007,3516 high schools1582 reported at least some students take highest levelof calculus offered before senior year.1114 reported that at least some of these students takeno mathematics in their senior year. In 203 of theseschools, more than 50% of these students take nomath in their senior year.Reasons:•Taking AP courses in other subjects - 580•Intended major doesn’t require any more math - 458•No courses available - 245Conclusion:Students completing calculus before their senioryear are the best of the best, and their numbersare significant. What can colleges anduniversities do to encourage them to continuetheir study of mathematics?Roughly 130,000 took AP exam, did not earn orchose not to accept credit. Morgan data suggests thatabout 2/3rds plan on retaking calculus in college.Those who take calculus in high school but notreceive college credit for it consist of:~100,000 take generic “calculus”;~105,000 take AP calculus but not the exam;105,000 take AP exam and score less than 3;~30,000 score 3 or better on AP exam but do notreceive credit or elect not to use itAbout 340,000 studentsarrived at college this fallhaving taken


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