Issues of the Transition to

College Mathematics MAA Retiring Presidential Address

David Bressoud Macalester College, St. Paul, MN

Joint Math Meetings New Orleans, LA January 8, 2011

PowerPointavailableatwww.macalester.edu/~bressoud/talks

MAA

“… our work does not end with a high school diploma. For decades, we led the world in educational attainment, and as a consequence we led the world in economic growth … But in this new economy, we've come to trail other nations in graduation rates, in educational achievement, and in the production of scientists and engineers.”

Remarks by President Obama at the National Academy of Sciences, April, 2009:

1.  Evidence of a problem in the preparation of mathematicians, scientists, and engineers.

2.  The effect of AP Calculus on this problem.

3.  Components of the solution:

a)  Gather better information about the problem.

b)  Work on PreK-12 mathematics education.

c)  Work on first-year college mathematics.

0

10,000

20,000

30,000

40,000

50,000

60,000

70,000

80,000

BachelorsDegrees,math‐intensivemajors

Engineering PhysicalScience Math&Stat

NCESdata

0%

1%

2%

3%

4%

5%

6%

7%

8%

Math‐intensivemajorsas%ofBachelorsDegrees

Engineering PhysicalScience Math&Stat

NCESdata

0.00%

0.05%

0.10%

0.15%

0.20%

0.25%

0.30%

0.35%

BachelorsDegrees,math‐intensivemajors,as%of20–24year‐olds

Engineering PhysicalScience Math&Stat

NCES&USCensusdata

CBMSdata

0

200

400

600

800

1985 1990 1995 2000 2005

Fallenrollments(thousands),Calculusandabove,4‐yearundergraduateprograms

0%

1%

2%

3%

4%

1985 1990 1995 2000 2005

Fallenrollments,Calculusandabove,aspercentageof20–24year‐olds

CBMS&USCensusdata

0

100

200

300

400

500

1985 1990 1995 2000 2005

Fallenrollments(thousands),Calculusandabove,4‐yearundergraduateprograms

ResearchUniversiPes undergrad/comprehensive

CBMSdata

Increasingly, the students who do not have to take mathematics, don’t.

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

Math&StatsMajorsbyGender

Men Women

NCESdata

2%

3%

4%

5%

6%

7%

8%

Hispanicstudentsas%ofBachelorsDegreesinselectedfields

%oftotaldegrees Engineering MathemaPcs PhysicalSciences

NCESdata

2%

3%

4%

5%

6%

7%

8%

9%

10%

African‐Americansas%ofBachelorsDegreesinselectedfields

%oftotaldegrees Engineering MathemaPcs PhysicalSciences

There were 1,089 Bachelors in Math or Stat earned by African-Americans in 1997. By 2008, that number was down to 818.

NCESdata

186,000 students entered four-year undergraduate programs with the intention of majoring in engineering, a physical science, mathematics, or statistics.

In the Fall of 2009:

Approximately 600,000 of the entering students passed a class in calculus while in high school.

CBMSandCollegeBoarddata

2009:305

0

50

100

150

200

250

300

350

FallEnrollmentsinCalculusIversus

APCalculusExams(thousands)

4‐yearcolleges 2‐yearcolleges APexams(AB&BC)

Over600,000studentsstudiedcalculusinhighschoolthisyear,roughly1/3ofthe1.8millionwhowillgodirectlyfromHStocollege.

2010:325

2000:171

1990:78

1980:28

Slightlyover150,000ofthesestudentsearnedandusedcreditforCalculusI.

0

20

40

60

80

100

120

1980 1985 1990 1995 2000 2005

FallEnrollments,CalculusII(thousands)

4‐yearcolleges

2‐yearcolleges

CBMSdata

All evidence suggests that calculus in high school works well for most of the roughly 25% who earn and use their college credit.

What about the other 75%?

Those who do not have access to calculus in high school are at a serious disadvantage.

Ofthehighschoolstudentswhograduatedin2004andstudied“calculus”whileinhighschool,17%tookremedialmathema+csincollege.

Ofthehighschoolstudentswhograduatedin1992andstudied“calculus”whileinhighschool,31%tookprecalculusincollege,andafurther32%tooknocalculusincollege.

Ofthehighschoolstudentswhograduatedin2004andstudied“calculus”whileinhighschool,17%tookremedialmathema+csincollege.

Ofthehighschoolstudentswhograduatedin1992andstudied“calculus”whileinhighschool,31%tookprecalculusincollege,andafurther32%tooknocalculusincollege.

SOLUTIONS:GatherbeberinformaPon

What happens to those who take calculus in High School?

What are the strengths and weaknesses of incoming students?

How well are existing placement programs and courses serving our students?

Of students who took pre-calculus and • Their declared major required at least one semester of calculus, and • They earned an A in pre-calculus,

43% chose not to enroll in calculus.

Pat Thompson, lead author

Arizona State University study of student data, 2001–06

During the period fall 2001 through fall 2006,

43% of engineering majors, 54% of mathematics majors,

51% of physical science majors, and 50% of technology majors

who enrolled in Calculus I at ASU and whose intended majors required Calculus II never earned credit for Calculus II.

Pat Thompson, lead author

Arizona State University study of student data, 2001–06

During the period fall 2001 through fall 2006,

43% of engineering majors, 54% of mathematics majors,

51% of physical science majors, and 50% of technology majors

who enrolled in Calculus I at ASU and whose intended majors required Calculus II never earned credit for Calculus II.

Pat Thompson, lead author

Arizona State University study of student data, 2001–06

The point is that ASU gathered this information, and they are now doing something about it.

Phil Sadler Factors Influencing College

Success in Mathematics

Controlling for socio-economic factors, what aspects of high school mathematics prepare students for success in Calculus I?

Bressoud, Carlson, Pearson, Rasmussen: Characteristics of Successful Programs in College Calculus

College factors that influence success in Calculus I and case study analysis of successful programs.

MAA

SOLUTIONS:ImprovePreK‐12Math

Intel Math: Mathematics Professional Development for K-8 Teachers

Bill McCallum

SOLUTIONS:ImprovePreK‐12Math

Jim Lewis

NJ Partnership for Excellence in Middle School Mathematics

Amy Cohen

SOLUTIONS:ImprovePreK‐12Math

SIGMAAonCircles

SOLUTIONS:Improvefirst‐yearcollegemathemaPcs

Bernie Madison

Place students in appropriate courses.

SOLUTIONS:Improvefirst‐yearcollegemathemaPcs

Use online resources to address individual student weaknesses.

Alison Ahlgren

SOLUTIONS:Improvefirst‐yearcollegemathemaPcs

MA 103: Mathematical Modeling and Introduction to Calculus. The course lays the foundation for calculus and differential equations through difference equations

This course has now been in place for twenty years. A similar course at Macalester is over 5 years old.

SOLUTIONS:Improvefirst‐yearcollegemathemaPcs

MTBI supports the development of students through educational, research and mentorship activities from the undergraduate to the postdoctoral level.

Carlos Castillo-Chavez

PowerPointavailableatwww.macalester.edu/~bressoud/talks

With thanks to Susanna Epp for preserving this quote.