Calculus in High School Too much of a good thing?

Transcription

1 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 MAA Baylor University Waco, Texas October 6, 2011

2 In the Fall of 2010: 210,000 students entered four-year undergraduate programs with the intention of majoring in engineering, a physical science, mathematics, or statistics. About half will succeed.

3 Students in college or university Calculus I: mean score on SAT Math: % earned 610 or higher (top 23%) mean score on ACT Math: % earned 26 or higher (top 16%) MAA survey of 700 instructors, over 14,000 students, all types of colleges and universijes across US, Fall, 2010

4 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 universijes across US, Fall, 2010

5 Grade for college Calculus I: 22% A 28% B 23% C 27% D, F, or Withdrew

6 Me and AP: 1968 took AP Calculus exam taught AP Calculus at State College Area High School AP Reading (Reader, Table Leader, Question Leader) AP Calculus Development Committee (Chair from 2002 to 2005)

7 The Chronicle of Higher Education January 17, 2010 The Rocky Transi/on From High School Calculus hop://chronicle.com/arjcle/high School Calculus The E/63533/

8 : 28 Fall Enrollments in Calculus I versus AP Calculus Exams (thousands) About 650,000 students are studying calculus in high school this year, over 1/3 of the 1.8 million who will go directly from HS to college. 1990: : : year colleges 2 year colleges AP exams (AB & BC) CBMS and College Board data

9 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 rela/ve to number of 22 year olds (degrees # of 22 year olds) Engineering Physical Science Math & Stat NCES & US Census data

10 A quick History of AP Calculus

11 : College Admission with Advanced Standing Bowdoin, Brown, Carleton, Haverford, Kenyon, MIT, Middlebury, Oberlin, Swarthmore, Wabash, Wesleyan, and Williams Gordon Chalmers (right), President of Kenyon College, with Thornton Wilder 1956: First Advanced Placement exams administered by College Board

12 AP Calculus 16,000 14,000 12,000 10,000 8,000 6,000 4,000 2,000 0 year AB Calc BC Calc total Calc

13 1970 s and 1980 s 1984: South Carolina s Education Improvement Act Jaime Escalante 1988 Richard Riley, Governor of South Carolina at the Jme, later Secretary of EducaJon under President Clinton

14 AP Calculus 90,000 80,000 70,000 60,000 50,000 40,000 30,000 20,000 10,000 0 AB exams BC exams Total Calculus exams

15 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.

16 AP Calculus 350, , , , , ,000 50,000 0 AB exams BC exams Total Calculus exams

17 2000 s 2007: AP Course Audit Gasper Caperton, College Board President since 1999

18 11% African Americans as % of Total Bachelor s Degrees 10% 9% 8% 7% 6% 5% 4% 3% 2% % of total degrees Engineering MathemaJcs Physical Sciences NCES data

19 How effective is AP Calculus?

20 Morgan & Klaric, 2007: study of 22 colleges and universijes in fall, 1994; grades weighted so that SAT scores are comparable Placed via average grade in Calculus II SAT Adjusted grade Passed Calculus I on AB exam on AB exam on AB exam Placed via average grade in Calculus II SAT Adjusted grade Passed Calculus I on BC exam on BC exam on BC exam Barnard College, Binghamton U., Brigham Young U., Carnegie Mellon U., College of William & Mary, Cornell U., Dartmouth, George Washington U., Georgia InsJtute 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 AusJn, U. of Virginia, U. of Washington, Wesleyan College, Williams College

21 Keng & Dodd 2008 study with comparable results, University of Texas, Austin, 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

22 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.

23 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.

24 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.

25 Those who do not have access to a good calculus program in high school are at a serious disadvantage in pursuing engineering or science. All evidence suggests that calculus in high school works well for most of the roughly 25% who earn college credit. We don t know enough about the other 75%. PowerPoint available at