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

Grade for college Calculus I:

22% A

28% B

23% C

27% D, F, or Withdrew

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

A quick History of AP Calculus

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

0

2,000

4,000

6,000

8,000

10,000

12,000

14,000

16,000

year

AP Calculus

AB Calc BC Calc total Calc

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

2000’s

GasperCaperton,CollegeBoardPresidentsince1999

2007:APCourseAudit

NCESdata

2%

3%

4%

5%

6%

7%

8%

9%

10%

11%

AfricanAmericansas%ofTotalBachelor’sDegrees

%oftotaldegrees Engineering MathemaJcs PhysicalSciences

How effective is AP Calculus?

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%.