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Calculus in High School Too much
of a good thing? David Bressoud, Past-President Mathematical Association of America; DeWitt Wallace Professor of Mathematics Macalester College
PowerPointavailableatwww.macalester.edu/~bressoud/talks
MAA
BaylorUniversityWaco,TexasOctober6,2011
210,000 students entered four-year undergraduate programs with the intention of majoring in engineering, a physical science, mathematics, or statistics.
In the Fall of 2010:
About half will succeed.
Students in college or university Calculus I:
mean score on SAT Math: 652 75% earned 610 or higher (top 23%)
mean score on ACT Math: 28.5 75% earned 26 or higher (top 16%)
MAAsurveyof700instructors,over14,000students,alltypesofcollegesanduniversiJesacrossUS,Fall,2010
Students in college or university Calculus I:
68% studied calculus in high school 68% of them studied AP Calculus
half of them took the AP Calculus exam and earned 3 or higher (22% of all students in college Calculus I)
MAAsurveyof700instructors,over14,000students,alltypesofcollegesanduniversiJesacrossUS,Fall,2010
Me and AP:
1968 took AP Calculus exam
1990–1991 taught AP Calculus at State College Area High School
1993–2007 AP Reading (Reader, Table Leader, Question Leader)
1999–2005 AP Calculus Development Committee (Chair from 2002 to 2005)
The Chronicle of Higher Education January17,2010
TheRockyTransi/onFromHigh‐SchoolCalculus
hOp://chronicle.com/arJcle/High‐School‐Calculus‐The‐E/63533/
0
50
100
150
200
250
300
350
FallEnrollmentsinCalculusIversus
APCalculusExams(thousands)
4‐yearcolleges 2‐yearcolleges APexams(AB&BC)
CBMSandCollegeBoarddata
About650,000studentsarestudyingcalculusinhighschoolthisyear,over1/3ofthe1.8millionwhowillgodirectlyfromHStocollege.
2011:341
2000:171
1990:78
1980:28
NCES&USCensusdata
0.0%
0.2%
0.4%
0.6%
0.8%
1.0%
1.2%
1.4%
1.6%
1.8%
2.0%
Math‐intensiveBachelor'sdegreesrela/vetonumberof22year‐olds(degrees÷#of22‐yearolds)
Engineering PhysicalScience Math&Stat
Gordon Chalmers (right), President of Kenyon College, with Thornton Wilder
1953–55:College Admission with Advanced Standing
Bowdoin,Brown,Carleton,Haverford,Kenyon,MIT,Middlebury,Oberlin,Swarthmore,Wabash,Wesleyan,andWilliams
1956:First Advanced Placement exams administered by College Board
JaimeEscalante
1970’s and 1980’s
1988
RichardRiley,GovernorofSouthCarolinaattheJme,laterSecretaryofEducaJonunderPresidentClinton
1984: South Carolina’s Education Improvement Act
0 10,000 20,000 30,000 40,000 50,000 60,000 70,000 80,000 90,000
AP Calculus
AB exams BC exams Total Calculus exams
1990’s 1995: Graphing Calculators
1998: AB subscore
Today, two-thirds of the exam is calculator-free, one-third allows and may require use of graphing calculator.
Students who do best on both parts of exam have teachers who allow use of calculators ¼ to ½ of time.
0 50,000
100,000 150,000 200,000 250,000 300,000 350,000
AP Calculus
AB exams BC exams Total Calculus exams
NCESdata
2%
3%
4%
5%
6%
7%
8%
9%
10%
11%
AfricanAmericansas%ofTotalBachelor’sDegrees
%oftotaldegrees Engineering MathemaJcs PhysicalSciences
Morgan&Klaric,2007:studyof22collegesanduniversiJesinfall,1994;gradesweightedsothatSATscoresarecomparable
Placedvia averagegradeinCalculusII SATAdjustedgrade
PassedCalculusI 2.43
3onABexam 2.69 2.64
4onABexam 2.90 2.78
5onABexam 3.34 3.15
Placedvia averagegradeinCalculusII SATAdjustedgrade
PassedCalculusI 2.50
3onBCexam 3.00 2.92
4onBCexam 3.45 3.35
5onBCexam 3.46 3.27
BarnardCollege,BinghamtonU.,BrighamYoungU.,CarnegieMellonU.,CollegeofWilliam&Mary,CornellU.,Dartmouth,GeorgeWashingtonU.,GeorgiaInsJtuteofTechnology,MiamiU.(Ohio),NorthCarolinaStateU.,TexasA&M,U.ofCaliforniaatDavis,U.ofIllinoisatUrbana/Champaign,U.ofIowa,U.ofMaryland,U.ofMiami,U.ofTexasatAusJn,U.ofVirginia,U.ofWashington,WesleyanCollege,WilliamsCollege
Keng & Dodd 2008 study with comparable results, University of Texas, Austin, 1998–2001.
Students who earned 3 or higher on AB exam and chose to retake Calculus I did worse in Calculus II then those who went directly to Calculus II.
Caveats: Difference was statistically significant at .05 only 1 out of 4 years.
Not controlled for comparability of ability levels
Phil Sadler Factors Influencing College
Success in Science
Students who study Calculus in HS and do well on AP exam (≥ 3 on AB exam) do significantly better in Calculus I as well as intro Biology, Chemistry, and Physics.
There is little or no discernible benefit from simply taking Calculus in High School.
Ofthehighschoolstudentswhograduatedin2004andearnedcreditfor“calculus”whileinhighschool,17%tookremedialmathema+csincollege.
Ofthehighschoolstudentswhograduatedin1992andearnedcreditfor“calculus”whileinhighschool,31%tookprecalculusincollege,andafurther32%tooknocalculusincollege.
Ofthehighschoolstudentswhograduatedin2004andearnedcreditfor“calculus”whileinhighschool,17%tookremedialmathema+csincollege.
Ofthehighschoolstudentswhograduatedin1992andearnedcreditfor“calculus”whileinhighschool,31%tookprecalculusincollege,andafurther32%tooknocalculusincollege.
All evidence suggests that calculus in high school works well for most of the roughly 25% who earn college credit.
Those who do not have access to a good calculus program in high school are at a serious disadvantage in pursuing engineering or science.
PowerPointavailableatwww.macalester.edu/~bressoud/talks
We don’t know enough about the other 75%.