MATHEMATICS: A CASESTUDY

Administrative Committee onAcademic Affairs

October 16, 2001

Adapted from presentation at Summer Institutes, July 2001, NASH/Education Trust

A NATION AT RISK

“WE ARE AT RISK OF BECOMINGA NATION DIVIDED BOTH

ECONOMICALLY AND RACIALLYBY KNOWLEDGE OF

MATHEMATICS.”

Source: National Research Council, Everybody Counts: A Report to the Nation on the Future ofMathematics Education, National Academy Press: Washington, D.C., 1989.

“By the year 2000, United Statesstudents will be first in the world in

mathematics and scienceachievement.”

--National Education Goal #5

ACHIEVEMENT INK-12

Source: NCES 1999-081R, Highlights From TIMSS

Nations’ Average MathematicsPerformance Compared With the US

Nations Scoring

12

7

7

14

5

720

2

14

0%

100%

Grade 4 Grade 8 Grade 12

Below the US Same as the US Higher than the US

Source: NCES, TIMSS, Pursuing Excellence: A Study of U.S. Twelfth-Grade Mathematics and Science Achievement inInternational Context, 1999.

Average Advanced Mathematics Performance ofAdvanced Mathematics Students in All Countries

Nations Scoring

5

11

00%

100%

Grade 12

Higher than the US

Same as the US

Below the US

*U.S. students with pre-calculus, calculus, analytic geometry or AP calculus instruction,representing about 14% of the U.S. cohort. Of the higher-performing countries, all but fourinclude more of their age cohort in this category.

ACHIEVEMENT INHIGHER EDUCATION

Source: USDOE, NCES, National Adult Literacy Survey, 1992, in Literacy in the Labor Force: Results from the NALS, September 1999, p. 61.

Many College Graduates DemonstrateWeak Quantitative Literacy Skills

Grads:2 Yr. Colleges

Grads:4 Yr. Colleges

Level 5: High 5 13

Level 4 30 40

Level 3 44 40

Level 2 17 10

Level 1: Low 4 3

Description:Quantitative Literacy Level 3

• CAN Determine correctchange usinginformation on a menu

• CAN Use informationstated in news article tocalculate amount ofmoney it takes to raise achild

• CAN’T Determineshipping and total costson an order form foritems in a catalog

• CAN’T Use informationin news article tocalculate difference intime for completing arace

Source: USDOE, NCES, National Adult Literacy Survey, 1992, in Literacy in the Labor Force: Results from the NALS,September 1999, p. 61.

Math Proficiency Gaps Persist:College Graduates

288282

328

250

275

300

325

350

Mea

n M

ath

Pro

fici

ency

African American Latino White

Source: US Department of Education, National Center for Education Statistics. Adult Literacy in America. (p. 36)Washington, DC: US Department of Education, 1992.

“Mathematics and science educationwill be strengthened throughout the

system, especially in the earlygrades.

--National Education Goal #5, Objective 1

CURRICULUM:K-12

Quality of Mathematical Contentof 8th Grade Lessons

87

13

0

13

57

3040 37

23

0

20

40

60

80

100

Pe

rce

nt

U.S. Japan Germany

Low Medium High

Source: TIMSS : unpublished tabulations, Videotape Classroom Study, UCLA, 1996, in Pursuing Excellence: A Study of USEigth-Grade Mathematics and Science Teaching, Learning, Curriculum and Achievement in International Context, 1997.

Average Grade Level of Content in 8th GradeLessons, by International Standards

9.1 8.7

7.4

0

1

2

3

4

5

6

7

8

9

10

U.S. Japan Germany

Gra

de

Lev

el O

f C

on

ten

t

Source: NCES, “Pursuing Excellence: A Study of U.S. Eighth-Grade Mathematics and Science Teaching, Learning,Curriculum, and Achievement in International Context”, 1997.

Math Emphasis Favor SkillsOver Understanding

24

60

96

10

20

40

60

80

100

Pe

rce

nt

Goal =Mathematicalthinking

Goal = Learnskill/formula

Practice routineprocedures

Invent newsolutions andproofs

Source: Pursuing Excellence: A Study of US Eighth-Grade Mathematics and Science Teaching, Learning, Curriculum andAchievement in International Context, 1997.

United States 8th Grade Math Teachers

High School Graduates TakingMore Mathematics

0

20

40

60

80

1982 1987 1990 1994 1998

Per

cen

t ta

kin

g s

elec

ted

mat

h c

ou

rses

Calculus

Pre-calculus

Algebra II

Geometry

Algebra I

Source: HS&B, HSTS, NELS data, in NCES Digest of Education Statistics, 2000, Table 140.

Percentage of High School GraduatesCompleting Algebra II, 1998

56.0%

70.0%

48.0% 47.0%

65.0%

0%

50%

100%

African American Asian Latino Native American White

Source: HS&B, HSTS, NELS data, in NCES, Digest of Education Statistics, 2000.

Percentage of High School GraduatesCompleting Pre-calculus, 1998

14.0%

41.0%

15.0% 16.0%

25.0%

0%

50%

African American Asian Latino Native American White

Source: HS&B, HSTS, NELS data, in NCES, Digest of Education Statistics, 2000.

Percentage of High School GraduatesCompleting Calculus, 1998

7.0%

18.0%

6.0% 6.0%

12.0%

0%

50%

African American Asian Latino Native American White

CURRICULUM:Higher Education

UNDERGRADUATE MATHEMATICSCOURSE ENROLLMENT

✔ENROLLMENTS IN MATHEMATICALSCIENCES COURSES HAVE DOUBLED INTHE LAST 20 YEARS, BUT THE INCREASESHAVE ALL BEEN AT THE LOWER LEVELS,WITH REMEDIAL ENROLLMENTS LEADINGTHE WAY.

Committee on the Mathematical Sciences in the Year 2000, A Challenge of Numbers:People in the Mathematical Sciences. National Academy Press: Washington, D.C.,1990.

Many Freshmen Must TakeRemedial Math Courses, 1995

All institutions 24%

Public 2 year 34%

Public 4 year 18%

High MinorityEnrollment

35%

Low MinorityEnrollment

21%

Source: USDOE, NCES, PEQUIS, Remedial Education at Higher Education Institutions in fall 1995 (1996), in The Condition of Education 1999, p. 88

COLLEGE MATHEMATICSENROLLMENT

�Two thirds of all college mathematicsenrollments are below the level of calculus.

�96% of all college mathematics enrollments arein courses also taught in High School.

�In America today, the profile of mathematics inhigher education is not that much different fromthat of mathematics in high school.

Source: National Research Council, Moving Beyond the Myths: Revitalizing Undergraduate Mathematics, NationalAcademy Press: Washington, D.C., 1991.

1995 FALL ENROLLMENT INMATHEMATICS COURSES

0

800

Remedial Precalculus Calculus Advanced

En

roll

men

t 10

00's

Four-Year Colleges Two-Year Colleges

Source:

“The number of teachers with asubstantive background in math

and science will increase by 50%”

--National Education Goal #5, Objective 2

TEACHERS: K-12

How Far Have We Come?Percentage Public High School Math Teachers With

a Major or Minor in Field

Source: Richard M. Ingersoll, "The Problem of Underqualified Teachers in American Secondary Schools," EducationalResearcher, Vol. 28, Number 2, March 1999

72 69 72

0

20

40

60

80

100

Per

cent

Mathematics

Middle School Math Students MostLikely to have Underqualified Teachers

0%

20%

40%

60%

80%

100%

7th 8th 9th 10th 11th 12thGrade Level of Class

Percent of public secondary students taught by teachers without major of minor in math

Source: Richard M. Ingersoll, "The Problem of Underqualified Teachers in American Secondary Schools,"Educational Researcher, Vol. 28, Number 2, March 1999

Math & Science Classes With a High Percentage ofMinority Students Are More Often Taught by

Underqualified Teachers

54%

86%

42%

69%

30%

90%

90-100% Non-White 90-100% White

Certified in Field B.A. or B .S. in Field

Source: Jeannie Oakes. Multiplying Inequalities: The Effects of Race, Social Class, and Tracking on Opportunities to Learn Mathematics andScience (Rand: 1990)

0

10

20

30

40

Level 1 Level 2 Level 3 Level 4 Level 5

teachers other BA

Math Literacy of TeachersVersus Other BAs

Source: ETS, Barbara A. Bruschi and Richard J. Coley, “How Teachers Compare: The Prose, Document andQuantitative Skills of America’s Teachers”, Princeton, NJ, 1999, p. 6.

Description:Quantitative Literacy Level 3

• CAN Determine correctchange usinginformation on a menu

• CAN Use informationstated in news article tocalculate amount ofmoney it takes to raise achild

• CAN’T Determineshipping and total costson an order form foritems in a catalog

• CAN’T Use informationin news article tocalculate difference intime for completing arace

Source: USDOE, NCES, National Adult Literacy Survey, 1992, in Literacy in the Labor Force: Results from the NALS,September 1999, p. 61.

TEACHERS:Higher Education

WHO IS TEACHING REMEDIALMATHEMATICS?

1

12

87

26

12

62

0

20

40

60

80

100

Tenured/Eligible Other Full Time TA/Part Time

Research Univ. College

Source: Fall 1995 Conference Board Mathematical Sciences Survey

WHO’S TEACHING FRESHMANMATHEMATICS IN RESEARCH

UNIVERSITIES?

1

18

62

5449

19

0

10

20

30

40

50

60

70

Remedial Precalculus Calculus

Tenured/tenure eligible Graduate Assistants

Source: Fall 1995 Conference Board Mathematical Sciences Survey

GRADUATE TEACHING ASSISTANTS

• Approximately half of the graduate mathematicsstudents in the United States are nonresidentforeigners.

• “Heavy reliance on the use of graduate teachingassistants, many of whom have limited experienceor training for the responsibilities placed on them,has far-reaching consequences.”

National Research Council, Moving Beyond the Myths: Revitalizing Undergraduate Mathematics, National AcademyPress: Washington, D.C., 1991.

“The number of U.S. undergraduate andgraduate students, especially women and

minorities, who complete degrees inmathematics, science, and engineering, will

increase significantly.”

--National Education Goal #5, Objective 3

Junior/Senior MathematicalSciences Majors Declining

50000

55000

60000

65000

70000

75000

1992 1993 1994 1995 1996 1997 1998 1999

72,000 >> 56,200 = -22%

Source: 1999 Annual Survey of the Mathematical Sciences (Second Report), AMS, Vol. 47, Number 8.

Math Majors Declining

1990-91 1997-98PercentChange,91-98

Bachelor’s degreesawarded inmathematics

15,310 12,328 -19.5%

Percent of totalbachelor’s degreesawarded

1.4% 1.0% -28.6%

Source: HEGIS and IPEDS data, in NCES, Digest of Education Statistics, 2000.

Mathematics Degrees Awarded

0

5000

10000

15000

20000

25000

30000

69-70 74-75 79-80 84-85 89-90 94-95 97-98

BA MA PhD

Source: Tabulated by NSF Division of Science Resource Studies; Data from NCES/IPEDS and NSF/SRS, in Science and EngineeringDegrees: 1966-98.

1997-98 BACHELOR’S DEGREESAWARDED IN MATHEMATICS

4%7%

5%

9%

75%

White

Black

Hispanic

Asian/Pacific-Islander

Non-residents

Source: NCES, Digest of Education Statistics, 2000.

1997-98 MASTER’S DEGREES AWARDEDIN MATHEMATICS

4%

2%

6%

29%

59%

White

Black

Hispanic

Asian/Pacific/Islander

Non-Resident

Source: NCES, Digest of Education Statistics, 2000.

1994-95 DOCTORATES AWARDED INMATHEMATICS

0%1%

8%

45% 46%

WhiteBlackHispanicAsian/Pacific IslanderNon-resident

NCES, Digest of Education Statistics 1997.

MATH TEACHERDEMAND

Shortage of Certified and Fully QualifiedMath Teachers

53.5

7.3

13.2

26

Non-Certified New

Non-CertifiedReturning orTransfering

Certified New

Certified Returningand Transferring

Distribution of middle and high school mathand science positions filled in 1993-94.

Source: NCES, SASS data, in Before It’s Too Late: A Report to the Nation from the National Commission on Mathematicsand Science Teaching for the 21st Century, 2000.

Demand is Far Outpacing Supply

• An estimated 240,000 middle and highschool mathematics and science teacherswill be needed over the next 10 years.

• Of this total, nearly 70% will be newcomersto the profession.

Source: Before It’s Too Late: A Report to the Nation from the National Commission on Mathematics and ScienceTeaching for the 21st Century, 2000.

MATH MAJORS IN THEWORKFORCE

• Mean Salary: $50,902

• (30% above mean for all with BA only)• 15% employed in Education

• 64% in for profit sector

• 3% in non profit sector

• 8% self employed

• 10% government

Source: Andrew Sum, Northeastern University

SOME RECOMMENDATIONS FOR THE ROLE OF ARTSAND SCIENCE FACULTY IN MATHEMATICS

• College faculty must become actively involved in the educationof teachers if the teaching of mathematics in the schools is toimprove significantly.

• Colleges and universities should assign significantly higherpriority to mathematics teacher education.

• All college and university faculty members who teachmathematics or mathematics education should maintain avigorous dialogue with their colleagues in schools, seeking waysto collaborate in improving school mathematics programs and insupporting professional development of mathematics teachers.

MAA, “A Call for Change: Recommendations for the Mathematical Preparation of Teachers of Mathematics,” 1991.