Issues of the Transition to College Calculus David Bressoud Macalester College, St. Paul, MN PowerPoint available at www.macalester.edu/~bressoud/talks MOMATYC Columbia, MO April 1, 2011 MAA
1. Data on graduation rates in mathintensive majors. 2. Data on high school and college mathematics enrollments. 3. The effect of calculus in high school. 4. What needs to change in our colleges and universities.
¾ Algebra II ⅓ Precalculus Advanced Mathema-cs and Science Course taking in the Spring High School Senior Classes of 1982, 1992, and 2004. NCES 2007 312
350 300 250 Fall Enrollments in Calculus I versus AP Calculus Exams (thousands) 2009: 305 Over 600,000 students studied calculus in high school this year, roughly 1/3 of the 1.8 million who will go directly from HS to college. 2010: 325 200 150 100 1990: 78 2000: 171 Between 150,000 and 200,000 of these students earn and take advantage of credit for Calculus I. 50 0 1980: 28 4 year colleges 2 year colleges AP exams (AB & BC) CBMS and College Board data
120 Fall Enrollments, Calculus II (thousands) 100 80 60 40 4 year colleges 2 year colleges 20 0 1980 1985 1990 1995 2000 2005 CBMS data
Calculus II, fall enrollment (thousands) 60 enrollment (thousands) 50 40 30 20 10 0 1990 1995 2000 2005 year Research Univ Undergrad College Comprehensive Univ 2-year College Since 1995, there has been a 22% decrease in the number of students taking Calculus II in the Fall term at comprehensive universi]es, undergraduate colleges, and 2 year colleges. CBMS data
Fall enrollments (thousands) in 2 year undergraduate programs 1200 1000 800 600 400 200 0 1985 1990 1995 2000 2005 precollege 482 724 800 763 964 introductory 294 361 415 396 501 calc & advanced 113 140 142 117 120 CBMS data
800 700 600 500 400 300 200 100 0 Fall enrollments (thousands) in 4 year undergraduate programs 1985 1990 1995 2000 2005 precollege 251 261 222 219 201 introductory 593 592 613 723 706 calculus level 637 647 538 570 587 advanced 138 119 96 102 112 CBMS data
Calculus enrollments (thousands) by type of insdtudon 250 200 150 100 50 0 1990 1995 2000 2005 Research Univ 193.4 160 182 210 Comprehensive Univ 71.9 72 73 51 Undergrad College 107.4 105 96 98 2 year College 90 95 84 81
800 Number of students (thousands) in 4 year undergraduate programs enrolled in mathemadcs at level of calculus or above (Fall term) 600 400 200 0 1985 1990 1995 2000 2005 CBMS
500 Number of students (thousands) in 4 year undergraduate programs enrolled in mathemadcs at level of calculus or above (Fall term) 400 300 200 100 0 1985 1990 1995 2000 2005 Research Universi]es undergrad/comprehensive CBMS
Fall enrollments, Calculus and above, as percentage of 20 24 year olds 4% 3% 2% 1% 0% Increasingly, the students who do not have to take mathematics in college, don t. 1985 1990 1995 2000 2005 CBMS & US Census data
80,000 Bachelors Degrees, math intensive majors 70,000 60,000 50,000 40,000 30,000 20,000 10,000 0 Engineering Physical Science Math & Stat NCES data
8% Math intensive majors as % of Bachelors Degrees 7% 6% 5% 4% 3% 2% 1% 0% Engineering Physical Science Math & Stat NCES data
2.0% 1.8% 1.6% 1.4% 1.2% 1.0% 0.8% 0.6% 0.4% 0.2% 0.0% Math intensive Bachelor's degrees as % of 22 year olds Engineering Physical Science Math & Stat NCES & US Census data
Math & Stats Majors by Gender 9000 8000 7000 6000 5000 4000 3000 2000 1000 0 Men Women
60% Women as % of Total Degrees 55% 50% 45% 40% 35% 30% 25% 20% 15% all bachelor's degrees Engineering Mathema]cs Physical Science NCES data
Hispanic American as % of Total Degrees 9% 8% 7% 6% 5% 4% 3% 2% % of total degrees Engineering Mathema]cs Physical Sciences NCES data
11% African American as % of Total Degrees 10% 9% 8% 7% 6% 5% 4% 3% 2% There were 1,089 Bachelors in Math or Stat earned by African-Americans in 1997. By 2009, that number was down to 876. % of total degrees Engineering Mathema]cs Physical Sciences NCES data
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?
Numerous studies (Sadler and others) that control for ability (SAT/ACT) and socio-economic factors (e.g. parental education): Students who study Calculus in HS and do well on placement 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.
MAA 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.
Random sample of 12,000 mainstream Calculus I students at all types of colleges and universities across the US (out of about 250,000): 61% took a calculus course in high school 54% of these took an AP Calculus exam 60% of those who took the AP Calculus exam earned a 3 or higher (94 students in the sample earned 5 on the BC exam) 10% are taking calculus in college for at least the second time
Of the high school students who graduated in 1992 and earned credit for calculus while in high school, 31% took precalculus in college, and a further 32% took no calculus in college. Of the high school students who graduated in 2004 and earned credit for calculus while in high school, 17% took remedial mathema-cs in college.
Of the high school students who graduated in 1992 and earned credit for calculus while in high school, 31% took precalculus in college, and a further 32% took no calculus in college. Of the high school students who graduated in 2004 and earned credit for calculus while in high school, 17% took remedial mathema-cs in college.
Arizona State University study of student data, 2001 06 Pat Thompson, lead author 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.
Arizona State University study of student data, 2001 06 Pat Thompson, lead author 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.
Arizona State University study of student data, 2001 06 Pat Thompson, lead author 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 The point is that ASU gathered this information, and they are now doing something about it. who enrolled in Calculus I at ASU and whose intended majors required Calculus II never earned credit for Calculus II.
SOLUTIONS: Improve first year college mathema]cs Alison Ahlgren Use online resources to address individual student weaknesses.
SOLUTIONS: Improve first year college mathema]cs MA 103: Mathematical Modeling and Introduction to Calculus. The course lays the foundation for calculus and differential equations through difference equations and dynamical systems. This course has now been in place for twenty years. A similar course at Macalester is over 5 years old.
SOLUTIONS: Improve first year college mathema]cs Carlos Castillo-Chavez MTBI supports the development of students through educational, research and mentorship activities from the undergraduate to the postdoctoral level.
With thanks to Susanna Epp for preserving this quote. PowerPoint available at www.macalester.edu/~bressoud/talks