David Bressoud Macalester College, St. Paul, MN

TeachingUndergraduateMathema1csMSRI,Berkeley,CAMay11,2009

PowerPointavailableatwww.macalester.edu/~bressoud/talks

MAA

AdvancedMathema1csandScienceCoursetakingintheSpringHighSchoolSeniorClassesof1982,1992,and2004.NCES2007‐312

CBMSdata

1985 1990 1995 2000 2005

precollege 482 724 800 763 964

introductory 294 361 415 396 501

calc&advanced 113 140 142 117 120

0

200

400

600

800

1000

1200

Fallenrollments(thousands)in2‐yearundergraduateprograms

0.00%

0.50%

1.00%

1.50%

2.00%

2.50%

3.00%

1985 1990 1995 2000 2005

Percentageofstudentsin2‐yearundergraduateprogramsenrolledin

mathema:csatlevelofcalculusorabove

1985 1990 1995 2000 2005

precollege 251 261 222 219 201

introductory 593 592 613 723 706

calculuslevel 637 647 538 570 587

advanced 138 119 96 102 112

0100200300400500600700800

Fallenrollments(thousands)in4‐yearundergraduateprograms

CBMSdata

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%

1985 1990 1995 2000 2005

Percentageofstudentsin4‐yearundergraduateprogramsenrolledin

mathema:csatlevelofcalculusorabove

1985 1990 1995 2000 2005

Math 13171 13303 12456 10759 12316

Math+MathEd 15738 16419 17285 15750 15685

MathSciencestotal 16718 18472 19701 18565 18441

0

5000

10000

15000

20000

25000

Bachelor’sDegreesinMathema:calSciences

CBMS data

1985 1990 1995 2000 2005

Math 1.33% 1.22% 1.07% 0.87% 0.86%

Math+MathEd 1.59% 1.50% 1.49% 1.27% 1.09%

MathSciencestotal 1.69% 1.69% 1.70% 1.50% 1.29%

0.00%

0.20%

0.40%

0.60%

0.80%

1.00%

1.20%

1.40%

1.60%

1.80%

MathMajorsasPercentofTotalDegrees

CBMS data

0

50

100

150

200

250

30019

80

1982

19

84

1986

19

88

1990

19

92

1994

19

96

1998

20

00

2002

20

04

2006

20

08

FallEnrollmentsinCalculusIversus

APCalculusExams(thousands)

4‐yearcolleges

2‐yearcolleges

APexams(AB&BC)

CBMSandCollegeBoarddata

500,000–600,000studentsstudycalculusinhighschooleachyear.160,000–200,000earncollegecreditforthiscourse.

Ofthehighschoolstudentswhograduatedin1992andstudied“calculus”whileinhighschool,31%tookprecalculusincollege,andanother32%tooknocalculusincollege.

From the transcript analysis of the National Education Longitudinal Study begun in 1988.

0

20

40

60

80

100

120

1980 1985 1990 1995 2000 2005

FallEnrollments,CalculusII(thousands)

4‐yearcolleges

2‐yearcolleges

0

20

40

60

80

100

120

1980 1985 1990 1995 2000 2005

FallEnrollments,CalculusIII&IV(thousands)

4‐yearcolleges

2‐yearcolleges

CBMSdata

APCalculusABhasamuchbroadersyllabusthanthetypicalCalculusI.

About1/3ofstudentsdowellenoughtobereadyforCalculusIIorhigher.

Remainder(300,000–400,000)runintoproblemswhenenteringthecollegecurriculum.

Manystudentsearncreditforcalculusinhighschoolandavoidtakinganymathema[csincollege.Weneedcoursesthata]ractandengagethem.

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

50000

2002 2003 2004 2005 2006 2007 2008

nu

mb

er

year

Calculus Before Grade 12

AB Calc < grade 12 BC Calc, < grade 12

College Board data

0

10

20

30

40

50

60

1990 1995 2000 2005

en

rollm

en

t (t

ho

usa

nd

s)

year

Calculus II, fall enrollment (thousands)

Research Univ Comprehensive Univ Undergrad College 2-year College

Since1995,therehasbeena22%decreaseinthenumberofstudentstakingCalculusIIintheFalltermatcomprehensiveuniversi[es,undergraduatecolleges,and2‐yearcolleges.

CBMSdata

1985

1990

1995

2000

2005

R²=0.98146

150

160

170

180

190

200

210

220

230

240

80 85 90 95 100 105 110 115 120

totalFallcalculusen

rollm

ent(tho

usan

ds)

prospec:veengineers(thousands)

#ofprospec:veengineersagainsttotalfallcalculusenrollmentsinresearchuniversi:es

CBMSandCIRPdata

Thenumberofenteringfirst‐yearstudentsintendingtomajorinEngineeringincreasedby31%over1995–2005.

ThishaskeptCalculusIIenrollmentsfairlystable.

Thetrendlineforprospec[veengineersisdownward.

TheAmericanFreshman,CIRPdata

0.0%

2.0%

4.0%

6.0%

8.0%

10.0%

12.0%

1980

1982

1984

1986

1988

1990

1992

1994

1996

1998

2000

2002

2004

2006

2008

Frac:onofIncomingFreshmanIntendingtoMajorIn...

Engineering

BioSciences

PhysicalSciences

ComputerScience

Mathema[cs

Weneedcoursesthatarerelevanttoanda]ractpoten[albiologymajors.

Weneed:

• moreinforma[onaboutwhathappenstostudentsinthetransi[onfromhighschooltocollege,

• moreeffec[vemeansofa]rac[ngfirst‐yearstudentstoandkeepingtheminterestedinmathema[cs,

• coursesthatrecognizetheirstrengthswhileaddressingtheirweaknesses,preparingthemforhigherlevelcoursesinmathema[cs.

“Themathema[csprofessionasawholehasseriouslyunderes[matedthedifficultyofteachingmathema[cs.”

RameshGangolliMERWorkshopMay31,1991

PowerPointavailableatwww.macalester.edu/~bressoud/talks