Maseeh Lecture. Calculus in High School
Transcript of Maseeh Lecture. Calculus in High School
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
PowerPoint available at www.macalester.edu/~bressoud/talks
MAA
Maseeh Lecture Portland, OR May 12, 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:
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)
MAA survey of 700 instructors, over 14,000 students, all types of colleges and universiGes across US, 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
1999–2005 AP Calculus Development Committee (Chair from 2002 to 2005)
1993–2007 AP Reading (Reader, Table Leader, Question Leader)
The Chronicle of Higher Education January 17, 2010
The Rocky Transi/on From High-‐School Calculus
hLp://chronicle.com/arGcle/High-‐School-‐Calculus-‐The-‐E/63533/
CBMS and College Board data
2009: 305
0
50
100
150
200
250
300
350
Fall Enrollments in Calculus I versus
AP Calculus Exams (thousands)
4-‐year colleges 2-‐year colleges AP exams (AB & BC)
Over 600,000 students are studying calculus in high school this year, roughly 1/3 of the 1.8 million who will go directly from HS to college.
2010: 325
2000: 171
1990: 78
1980: 28
NCES & US Census data
0.0%
0.2%
0.4%
0.6%
0.8%
1.0%
1.2%
1.4%
1.6%
1.8%
2.0%
Math-‐intensive Bachelor's degrees divided by number of 22 year-‐olds
Engineering Physical Science 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, and Williams
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!
Jaime Escalante
1970’s and 1980’s
1988
Richard Riley, Governor of South Carolina at the Gme, later Secretary of EducaGon under President Clinton
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
Gasper Caperton, College Board President since 1999
2007: AP Course Audit
Effect of math teacher quality (TQI) on readiness for college of students who have completed calculus in high school (Illinois, 2002).
Percentage ready for college TQI percentile
0–10 11–25 26–50 51-75 76–100
Black students
50% 67% 73% 74% 75%
White students
* 94% 95% 96% 97%
Presley & Gong, Demographics and Academics of College Readiness in Illinois, IERC Report #2005-‐3
24% of Black students were in schools with math teachers in the 0–10 percenGle.
2000’s
Gasper Caperton, College Board President since 1999
2007: AP Course Audit
NCES data
2%
3%
4%
5%
6%
7%
8%
9%
10%
11%
African Americans as % of Total Bachelor’s Degrees
% of total degrees Engineering MathemaGcs Physical Sciences
How effective is AP Calculus?
Morgan & Klaric, 2007: study of 22 colleges and universiGes in fall, 1994; grades weighted so that SAT scores are comparable
Placed via average grade in Calculus II SAT Adjusted grade
Passed Calculus I 2.43
3 on AB exam 2.69 2.64
4 on AB exam 2.90 2.78
5 on AB exam 3.34 3.15
Placed via average grade in Calculus II SAT Adjusted grade
Passed Calculus I 2.50
3 on BC exam 3.00 2.92
4 on BC exam 3.45 3.35
5 on BC exam 3.46 3.27
Barnard College, Binghamton U., Brigham Young U., Carnegie Mellon U., College of William & Mary, Cornell U., Dartmouth, George Washington U., Georgia InsGtute of Technology, Miami U. (Ohio), North Carolina State U., Texas A&M, U. of California at Davis, U. of Illinois at Urbana/Champaign, U. of Iowa, U. of Maryland, U. of Miami, U. of Texas at AusGn, U. of Virginia, U. of Washington, Wesleyan College, Williams College
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.
Of the high school students who graduated in 2004 and earned credit for “calculus” while in high school, 17% took remedial mathema4cs 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 mathema4cs 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.
Those who do not have access to a good calculus program in high school are at a serious disadvantage in pursuing engineering or science.
High teacher quality is essential for an effective AP Program, especially for minority students.
We need to screen students to ensure that they are prepared for calculus in high school, and we need strong alternatives to calculus for those
students whose precalculus skills are inadequate.
PowerPoint available at www.macalester.edu/~bressoud/talks
We don’t know enough about the other 400,000 students.
All evidence suggests that calculus in high school works well for most of the top 200,000, the top third of the students who take it.