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
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.
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
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
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
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.
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.
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.