issues of the maa transition to university mathematics
TRANSCRIPT
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Issues of the Transition to
University Mathematics
David Bressoud Macalester College
St. Paul, MN
University of British Columbia Vancouver, BC January 17, 2011
PowerPointavailableatwww.macalester.edu/~bressoud/talks
MAA
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“… 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:
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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.
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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
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0%
1%
2%
3%
4%
5%
6%
7%
8%
Math‐intensivemajorsas%ofBachelorsDegrees
Engineering PhysicalScience Math&Stat
NCESdata
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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
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CBMSdata
0
200
400
600
800
1985 1990 1995 2000 2005
Fallenrollments(thousands),Calculusandabove,4‐yearundergraduateprograms
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0%
1%
2%
3%
4%
1985 1990 1995 2000 2005
Fallenrollments,Calculusandabove,aspercentageof20–24year‐olds
CBMS&USCensusdata
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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.
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0
1000
2000
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6000
7000
8000
9000
Math&StatsMajorsbyGender
Men Women
NCESdata
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2%
3%
4%
5%
6%
7%
8%
Hispanicstudentsas%ofBachelorsDegreesinselectedfields
%oftotaldegrees Engineering MathemaPcs PhysicalSciences
NCESdata
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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
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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.
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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.
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20
40
60
80
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1980 1985 1990 1995 2000 2005
FallEnrollments,CalculusII(thousands)
4‐yearcolleges
2‐yearcolleges
CBMSdata
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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.
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Ofthehighschoolstudentswhograduatedin2004andstudied“calculus”whileinhighschool,17%tookremedialmathema+csincollege.
Ofthehighschoolstudentswhograduatedin1992andstudied“calculus”whileinhighschool,31%tookprecalculusincollege,andafurther32%tooknocalculusincollege.
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Ofthehighschoolstudentswhograduatedin2004andstudied“calculus”whileinhighschool,17%tookremedialmathema+csincollege.
Ofthehighschoolstudentswhograduatedin1992andstudied“calculus”whileinhighschool,31%tookprecalculusincollege,andafurther32%tooknocalculusincollege.
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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?
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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
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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
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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.
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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?
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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
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SOLUTIONS:ImprovePreK‐12Math
Intel Math: Mathematics Professional Development for K-8 Teachers
Bill McCallum
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SOLUTIONS:ImprovePreK‐12Math
Jim Lewis
NJ Partnership for Excellence in Middle School Mathematics
Amy Cohen
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SOLUTIONS:ImprovePreK‐12Math
SIGMAAonCircles
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SOLUTIONS:Improvefirst‐yearcollegemathemaPcs
Bernie Madison
Place students in appropriate courses.
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SOLUTIONS:Improvefirst‐yearcollegemathemaPcs
Use online resources to address individual student weaknesses.
Alison Ahlgren
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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.
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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
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PowerPointavailableatwww.macalester.edu/~bressoud/talks
With thanks to Susanna Epp for preserving this quote.