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.