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OCR for page 53
~ Mathematical Scientists in the Workplace
Threefourths of those with mathematical sciences degrees are not classified as
working as mathematical scientists.
The number of persons identified as working as mathematical scientists almost
tripled in the past decade.
Onefourth of those with a bachelor's degree, onethird of those with a master's,
and threefourths of those with a doctorate begin work in educational institutions.
White males currently dominate employment, and there is an increasing
dependence on foreign nationals.
The current supply of faculty depends heavily on persons from outside the United
States, and the expected future supply will be insufficient to replace retirees.
· Shortages of qualified school mathematics teachers have developed, and various
projections on needed replacements are alarming.
Introduction
Standard U.S. labor market data do not tell much about
where persons with mathematics or statistics degrees work
or what they do. Over the past 40 years, approximately
525,000 persons have been awarded baccalaureate degrees
in mathematics or statistics, 110,000 have received mas
ter's degrees, and 24~000 have been granted doctorates.
Current estimates place the number of mathematical scien
tists in the work force at between 100,000 and 150,000,
about onefourth of what would be expected based on the
number of degrees conferred.
Three factors accountformuchofthis discrepancy. The
title of mathematician has not been generally regarded as
a professional title but is gaining recognition as one; statis
tics has been regarded as a profession only in recent years,
but workers with the title of statistician may not hold
college degrees in mathematics or statistics. Persons with
degrees in mathematics work under various job titles;
statistician, computer specialist, engineer, analyst, and
actuary are common. And many such persons are secon
dary school teachers who are not usually classified as
mathematical scientists.
The lack of info' citation about the employment of people
with mathematical sciences degrees reflects a separation
between academic mathematical sciences and the nonac
ademic labor force. As the transition from high school
mathematics to college mathematics is troublesome, so
also is the transition from college to the workplace. The
difficulty in making the latter transition is less understood,
and building a better match between mathematical sci
ences education and the expectations and needs of the
workplace is a major problem that is receiving increased
attention.
Although general labor market data are of limited use in
analyzing how mathematical sciences degrees are utilized,
some trends are clear. The number of identifiable mathe
matical scientists in the work force has increased dramati
cally in recent years and is expected to continue to do so.
A larger proportion of these degree holders are working in
53
OCR for page 53
A Challenge of Numbers
science and engineering fields. And mathematical scien
tists depend much more heavily on academic employment
than does any other group in science and engineering.
Approximately 50,000 mathematical scientists are
employed by college and university mathematical sciences
departments, but only half of these are fulltime faculty.
This relatively small work force plays an essential part in
educating much of the collegeeducated work force, espe
cially students in science and engineering. The employ
ment market for this faculty is unusual because there is no
pool of readily available and wellqualified reserve candi
dates, and supply and demand have little effect on employ
ment conditions. Proper balancing of the supply and
demand has been difficult; currently there are mild short
ages of candidates for the mathematical sciences faculty,
and serious shortages are forecast. Obviously the condi
tions of supply and demand could resolve shortages, but
planning and commitment will be necessary to maintain
and enhance the quality of mathematical sciences educa
tion.
There continue to be shortages of secondary school
mathematics teachers, and many who teach have inade
quate preparation. Projections of the number of replace
ments needed by the year 2000 are alarming, in light of
current trends and employment conditions.
As is true for the study of mathematics in colleges and
universities, relatively few women, blacks, and Hispanics
work in mathematicsbased occupations. Their numbers
are extremely low on college and university faculties
where doctoral degrees are held by most of the members.
Among secondary school mathematics teachers, the repre
sentation of women has improved significantly in recent
years to about onehalf.
General Characteristics and Trends
National labor statistics show that mathematical scien
tists account for less than 3% of the nation's total science
arid engineering work force, and the science and engineer
ing work force constitutes about 4% of the total labor force
of 120 million. In the last decade the science and engineer
ing work force increased at an annual rate that was more
than triple the rate for the general labor force, 7% versus
2% The number working as mathematical scientists
almost tripled in the decade ending in 1986. This was the
largest increase for any science and engineering field, with
TABLE ~.1 Estimates of the number of mathematical scientists by National Science Foundation (NSF), Bureau of Labor
Statistics (BLS), and Conference Board for Mathematical Sciences (CBMS)
NSF
(1986)
Employed in science and engineering
Educational institutions
Business and industry
Federal government and other
OtherC
Total
a Includes faculty only, not graduate assistants.
b Includes mathematicians (20,000), statisticians (18,000), and actuaries (9,400~.
c Includes nonS/E employed under NSF and operation researchers and analysts under BLS.
SOURCES: National Science Board (NSB, 1987), Bureau of Labor Statistics (BLS, 1988a), and Conference Board of the
Mathematical Sciences (CBMS, 1987).
BLS
(1986)
103,000
52,800
35,600
10,700
27,100
131,000
76,600
29,000
37,700b
9,900b
38,000
114,600
CBMSa
(1985)
40,000 (25,000 full time)
54
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Mathematical Scientists in the Workplace
.
the exception of computer science (see Appendix Table
A5.11. This increase in demand is expected to continue: 90
from 1986 to 2000 the increase in demand for scientists,
engineers, and technicians is projected to be 36%, and for
mathematical scientists, 29C%o. This compares with a pro
jected 19% increase in demand for the general labor force.
Estimates of the number of people working as mathe
matical scientists in the United States today range from
114,000 to 131,000, while the count of mathematical
scientists employed in U.S. educational institutions ranges
from 29,000 to 53,000. Some counts include only faculty
members in mathematical sciences departments, whereas
others include workers and faculty members in other
departments. Moreover, the definition of mathematical
scientists can vary. For comparison, three mathematics
organizations (AMS, MAA, and SIAM) have a combined
membership of approximately 46,000 people, and the two
statistical societies (ASA and IMS) have a combined
membership of approximately 17,000 (see Box 3.1~. Table
5.1 gives estimates from three sources of the number of
people working as mathematical scientists.
None of the estimates given in Table 5.1 appears to
count elementary and secondary school mathematics teach
ers among the mathematical scientists. Estimates of their
numbers vary, but the range is approximately 125,000
certified secondary school teachers plus 20,000 certified
elementary and middle school mathematics teachers (NSB,
1985) to 300,000 public and private school mathematics
teachers. In any event, there appear to be at least as many
secondary school mathematics teachers as there are total
mathematical scientists in the reported counts of science
and engineering personnel. Clearly these teachers are not
included as mathematical scientists, although many have
the equivalent of a bachelor's degree in mathematics and
work 90% of their day in mathematics. On the other hand,
many persons with bachelor's degrees in science or espe
cially in engineering are included in the counts.
Participation in the labor force and other selected
employment characteristics for mathematical scientists
were similar to those for all scientists and engineers in
1986. Most scientists and engineers, including mathemati
cal scientists, are in the labor force, and the majority are
Master's
75
45
30
15
O
Bachelor's
1976 1986
1976 1986
FIGURE 5.1 Percent of recent mathematics degree holders
employed in a science or engineering job, 1976 and 1986.
SOURCE: National Science Board (NSB, 1987~.
working in science anden~ineeringfields. The unemploy
ment rates are low between 1.1 and 2.4% (see Appendix
Table A5.2~.
Primarily a mental discipline, mathematical sciences is
considered to be a field well suited to those with physical
disabilities. However, only a small portion of mathemati
cal scientists ( 1,600 of 13 1,000, or 1.2%) report a disabil
ity, compared with the 2% of all scientists and engineers
who perceive themselves as disabled (NSF, 1988d). Dis
abled persons are distributed among the various fields at a
rate similar to that for all scientists and engineers. Little
information is available concerning working conditions
for disabled people in the mathematical sciences, but the
general impression is that there are fewer barriers in mathe
matics than in otherfields. Advances in computertechnol
oay are expected to further increase opportunities and
provide links for the disabled in all science and engineering
fields (NRC, 1989~.
The vast majority (85%) of science and engineering
graduates find employment in a science and engineering
field. The major employers include business and industry,
educational institutions, and the federal aovemment. One
half of all scientists work in business and industry, but only
onethird of mathematical scientists do, whereas fewer
55
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A Challenge of Numbers
than one in three scientists work in an academic setting, but
half of mathematical scientists do (see Appendix Table
A5.31. At the doctoral level, about threequarters of
mathematical scientists work in educational institutions;
this fraction drops to about oneth~rd at the master's level
and to onefourth at the bachelor's level.
Over the past ten years, the percentage of mathematics
degree recipients employed in science and engineering
fields has increased dramatically, from 46% to 74 37c for
bachelor's degree holders and from 62% to 90~c for mas
ter's degree holders (Figure 5.1~; for all mathematical
scientists, the percentage is 79%. The current employment
pattern for mathematicians resembles that for computer
scientists, physical scientists, and engineers, replacing the
previous pattern, which resembled those in the life and
social sciences, for which the percentages of bachelor's
degree holders employed in science and engineering are
somewhat lower (NSB, 19871.
Employment of Recent Graduates
Analyses of the employment patterns of recent recipi
ents of mathematical sciences degrees reveal varied and
improving opportunities that are related to the level of
education achieved. Generally, the employer type shifts
from business or industry to academe as the degree level
rises from the baccalaureate to the doctorate. Exceptions
are the recipients of doctorates in statistics or some applied
mathematics fields; larger fractions of these people work in
business or industry.
A survey of 1984 and 1985 bachelor's and master's
degree recipients conducted by the NSF in 1986 showed
that about half of all recent graduates at both degree levels
worked in business or industry (NSF, 1987a). About one
in four bachelor's degree recipients taught in educational
institutions, presumably high schools. Onethird of recent
master's degree recipients taught in educational institu
tions, some in high schools, and others in colleges. Ac
cordin~ to a 1986 NRC survey ofthose new doctoral degree
holders with employment plans (NRC, 1987), three of four
planned academic work, one of five planned to work in
business or industry, and fewer than one in ten plaImed to
work in government (Table 5.2)
The majority of mathematicians with doctorates are
members of college and university faculties, which are
discussed in later sections of this chapter. This section's
description of primary work activities and salaries pertains
to master's and bachelor's degree recipients only. Al
though specific job titles and descriptions are not available,
information on primary work activities and fields of em
ployment sheds some light on what these workers do.
About 16% of the 1984 and 1985 bachelor's degree
recipients surveyed in 1986 were enrolled fulltime in
graduate school, and another 13% were enrolled parttime.
Fulltime graduate students were excluded from the em
ployment data. At both the master's and bachelor's degree
levels, the major fields of employment were mathematics/
statistics, computer science, and, to a lesser extent, engi
neenng (Figure 5.2~. A few mathematics graduates found
employment in the fields of psychology and economics.
As many bachelor's degree recipients found employment
in computing science as in a mathematics or statistics field.
About three of five master's degree recipients were work
ing in a mathematics or statistics field; of the remaining
TABLE 5.2 Type of employer of mathematical scientists by degree level, 1986
All Math.
Bachelor's Master's Doctorates Scientists All Scientists
Educational institutions 26% 37% 73% 51% 29%
Business and industry 55% 48~o 20% 34% 48%
Government and other 20% 15% 8% 15% 24%
SOURCES: National Science Foundation (NSF, 1987a) and National Research Council (NRC, 1987~.
56
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Mathematical Scientists in the Workplace
Enalneenna
Computer
Science
40~o
Psychology
To
Mathematics/
Statistics
42%
Englneenng
17~c
Computer
Science
15%
Psychology
6% .


Mathematics/
Statistics
62%
FIGURE 5.2 Field of employment for recent mathematics degree recipients, 1986. Left: Bachelor's degree holders. Right:
Master's degree holders. SOURCE: National Science Foundation (NSF, 1987a).
two, one was working in an engineering field and the other
in computer science.
Information on what nondoctoral mathematical scien
tists do in the workplace is very limited. Broad descriptive
categories, such as primary work activities, field of em
ployment, and type of employer, are available for the
nondoctoral decree holder, but these broad categories offer
little insight into what specific opportunities are available
to these mathematics graduates. This type of information
is needed to smooth the transition from college to the
workplace for these graduates and to better meet the needs
and expectations of business and industry.
A few colleges have information about what their
mathematics and statistics graduates are coin,, but local
market conditions determine to a tar ,e extent what oppor
tunities are available. Thus such information is not gen
eral, but rather only illustrative of opportunities. These
opportunities include positions in educational, financial,
governmental, religious, business, and industrial institu
tions. In educational institutions positions include mathe
matics teacher, coordinator for dropout prevention, guid
ance counselor, school principal, college instructor, and
college professor. Some of the financial and business op
portunities for mathematics graduates have included posi
tions such as actuary, computer systems analyst, program
mer, banker, bond specialist, insurance analyst, operations
research analyst, financial analyst, financial accounting
supervisor, pension consultant, employee education man
ager, and forecasting analyst. Other positions include
lawyer, missionary, pastor, designer/draftsman, meteor
ologist, energy policy specialist, and marketing manager.
Some of these positions require schooling beyond the
bachelor's degree, but many do not. Contrary to many
students' views of mathematics as too specialized for the
workplace, students who have majored in mathematics are
engaged in a wide variety of jobs with diverse work
activities at different types of institutions.
The primary work activities of recent mathematical
sciences degree holders have been separated into research
and development, management and administration, teach
ing, productionfinspection, reporting/statistical/comput
ing activities, and other activities (Figure 5.3~. As would
be expected for graduates only two years out of college,
fewer bachelor's than master's degree recipients were in
management and administration positions in 1986, and
more master's decree holders were teaching.
In 1986 the median annual salariesforrecentmathemat
ics degree recipients at both the master's and bachelor's
degree levels were just slightly below the average for all
science and engineering fields (Figure 5.4~. The median
annual salary for a bachelors recipient was $24,100 and
for a master's recipient, 531,500. For both groups the
57
OCR for page 53
A Challenge of Numbers
.
Reporting/Statistics/ \
Computing Activities \
Other Research arid
Development
~16%
34~c Production/Inspection
6%
Other
11%
Reporting/Statistics/ /`
Management and Computing Activities / ~~
Administration 15% /
3%
f Teaching Production/Inspection
24% lo
Research and
Development
_ 17%
 ~ Management and
Administration
15%
Teaching
34%
FIGURE 5.3 Primary work activities of recent mathematics degree recipients, 1986. Left: Bachelor's degree holders. Right:
Master's degree holders. SOURCE: National Science Foundation (NSF, 1987a).
salaries were higher than those for physical, er~viron
mental, social, and life scientists but somewhat lower than
those for engineers and computer scientists.
Secondary School Mathematics Faculty
The combined decrease in the number of both teachers
and mathematicians graduating from colleges in the period
from 1970 to 1985 (39% for mathematics arid 50% for
education) has already resulted in a shortage of qualified
mathematics teachers to staff the nation's schools. And
Psychology
Life Science
Social Science
Environmental Science
Total Science
Physical Science
Mathematical Science
Total, Science and
Engineering
Computer Science
E. .
n,e!lneenug
more severe shortages are projected.
The decrease duIin:, the past decade in the number of
college students planning to become teachers and an in
crease in the number of teachers approaching retirement
predict shortages of teachers of all kinds. And losses from
teachers leaving the profession in the middle stages of
careers may further reduce the supply (OTA, 1988b, pp.
5457~. The general shortage of mathematical scientists to
gether with the resulting demand across the work force
adds to the prospects for too few secondary school mathe
matics teachers.
Psychology
Life Science
Social Science
Environmental Science
Total Science
Physical Science
Mathematical Science
Total. Science and
En~ineenng
Computer Science
Englneenn~
$0 $ 1 0,000 520~000 $307000
$0 $12 000 S94.000 536.000
FIGURE 5.4 Median annual salaries of recent science and engineering graduates. Left: Bachelor's degree recipients. Right:
Master's degree recipients. SOURCE: National Science Foundation (NSF, 1987a).
58
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Mathematical Scientists in the Workplace
Approximately 11% of all secondary school teachers
are mathematics teachers. The actual number of mathe
matics teachers in secondary schools is somewhat elusive
but was estimated to be 126,300 in 1984 (NSB, 1985~.
Science teachers were estimated to number 115,600. 200
Another estimate numbered the total teaching force of iso
mathematics and science teachers at 200,000 in 1984 and ~00
estimated the number of new mathematics and science
in
teachers needed by 1995 to be 300,000 (RAND, 1984~.
Thus, by the latter reckoning, the estimate of the new
mathematics and science teachers needed in less than a
decade exceeds the total current force. Other estimates of
the current number of school mathematics teachers range
as high as 300,000.
As the counts of mathematics secondary school teach
ers vary widely, so do estimates of shortages. However,
most who have assessed the situation agree that future
demand will be greater than current supplies, that the
academic abilities of those attracted to education need to be
elevated, that the most academically able are the most
dissatisfied with teaching as a career, and that attrition is
highest among the most able.
Demand for both secondary and elementary school
teachers is projected to increase steadily from 1988 to the
early 1990s. The supply of new teacher graduates is
projected, at an intermediate projection level, to decrease
slightly from 1988 to the early 1990s, leaving a deficit of
25,000 to 72,000 teachers each year (Figure 5.51.
The current shortages are not evenly distributed geo
graphically or across disciplines, and the fields of mathe
matics and science have been particularly hard hit. In 1985
a low estimate of the shortages of mathematics teachers
was 3,700 and of science teachers, 2,800 (NBC, 1985~. If
teachers currently assigned but not qualified were to be
replaced at a modest rate of 5% of all teachers in the field,
then the forecast of annual shortages would increase to
9,200 in mathematics and 8,000 in science. In 1987,
according to opinions of teacher placement officers sur
veyed by the Association for School, College, and Univer
sity Staffing, Inc., considerable shortages of mathematics
teachers were reported in all regions of the country except
the Northwest and the Rocky Mountain states (ASCUS,
thousands
300
250
\~\` ;~0 ~· Demand
~it_  ~ '~9 ~ A ~
_
ARC

o
1970 1974 1978 1982 1986 1990
i I I , I I , / I ~, , I I , i, I I i I I
o Supply
FIGURE 5.5 Supply and demand of new elementary and
secondary school teachers, 1970 to 1992.
SOURCE: National Center for Education Statistics as re
ported in National Science Board (NSB, 1987~.
1987~. These shortages have been classified as consider
able (having been assigned values of between 4.25 and
5.00 ore a scale of 5.00) each year for the period from 1982
to 1987.
The Report of the 198586 National Survey of Science
and Mathematics Education by Iris Weiss (RTI, 1987)
gives some characteristics of the mathematics teaching
force. The mathematics teaching force closest to college
and university mathematics programs is the high school
teaching force, which is the focus of this section of the
report.
In the decade ending in 1986 the fraction of men on
senior high school mathematics faculties dropped from
twothirds to only about onehalf. Currently the vast
majority (94%) of such faculty are white, 3% are black, 1%
are Hispanic, and 1% are Asian. The average age is 40 and
the average number of years of teaching experience is 14.2.
A high school mathematics teacher is slightly more likely
than not to have earned a degree beyond the bachelor's.
Approximately onequarter of high school mathematics
teachers do not have a degree in a mathematics or mathe
matics education field, but only 15 % report teaching courses
that they are not certified to teach This compares with 16%
of science teachers with a degree in a field other than
science or science education, and 20~o of science teachers
who reported teaching courses that they are not certified to
59
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A Challenge of Numbers
.
Rococo
1 6~000
8.000
4~000 1
o
24.800
10.000
IZ~500 8~0
Jr...........
.. ... .......
....... it. .....
Fouryear
Colleges
81lWa~#~
',uuv
1
~ unlversl~les ~
~.
1970 1975 1980 1985
1 s7s 1 980 1 sss
FIGURE 5.6 Left: Number of fulltime mathematical sciences faculty members at colleges and universities. Right: Number
of parttime mathematical sciences faculty memher~ at ~11~ ~nrl ~laiv~r~;ti~c ~T Tl) If. r~ A D_ Ad! 4~ ~ ~ I
matical Sciences (CBMS, 1987~.
~^ ~^ ~ _8 ~8L8~iJ ~_VA ~ ~_VllIC! O11~ Aft U Ul ills 1vl~111~
teach. Most mathematics (84~o) and science (89%) teach
ers are certified in their respective fields. Certification is
determined locally, varies from district to district, and does
not imply a uniform set of qualifications across the states.
The National Council of Teachers of Mathematics
(NCTM) has developed guidelines for the preparation of
mathematics teachers. The guidelines provide lists of com
petencies and recommend courses to develop these compe
tencies for prospective teachers of mathematics. For
instance, at the senior high school level the recommended
courses for mathematics teachers include, among others, at
least three courses of calculus, one of computer science,
and two courses in methods of teachin;, mathematics.
According to the Weiss survey, 36% of high school mathe
matics teachers have not completed three courses in calcu
lus, 27% have not completed a course in computer science,
and 46% have not completed two courses in methods of
teaching.
Perceptions of the quality of mathematics high school
teachers, based on selfevaluation and ratings by princi
pals, reveal that most mathematics teachers enjoy teaching
(95%) and agree that they are "master" mathematics teach
ers (63%~. But their colleagues in science and in social
science and history are more likely to be rated highly com
petent by the principals than are mathematics teachers,
with percentages of 72% versus 67~o. Of those mathemat
60
ics teachers not rated highly competent by the principals,
30~c were considered competent and 3% incompetent.
In the Weiss survey (RTI, 1987), the most frequently
cited factors considered to be serious problems for mathe
matics teachers were student related. Almost onefourth of
senior high school mathematics teachers felt students' lack
of interest in science, inadequate reading, abilities, and
absences were serious problems in their schools. Other
less frequently cited serious problems were lack of mate
rials, insufficient funds, large class sizes, arid inadequate
access to computers.
In addition to studentrelated problems, there are a host
of other sources of discontent that were not included in the
Weiss survey. The Coming Crisis in Teaching reports the
results of a Rand study (RAND, 1984) that queried teach
ers about their views of the workplace. Between 40% and
50% of teachers who had degrees that reflected their area
of teaching were dissatisfied because of a lack of adminis
trative support, bureaucratic interference, a lack of auton
omy, salaries and other working conditions. Education
majors also registered a certain amount of discontent with
these same workin, conditions, but much less frequently
(at percentages ranging from 5% to Arc) than did aca
demic majors. Thus the most academically qualified
teachers were also the most dissatisfied and, because of
this, are more likely to leave teaching.
OCR for page 53
Mathematical Scientists in the Workplace
Many policymakers and educators point to low salaries
as a major stumbling block to both improving the quality
and increasing the number of mathematics teachers. Since
salary schedules are generally the same for teachers re
gardless of the subject, salary levels are more critical in
highdemand areas such as science and engineering. Dif
ferential salary levels are being considered to address
teacher shortages but have not yet been widely imple
mented. In real teens, average annual public school sala
ries fell during the 1 970s and by the mid 1 980s were almost
back to the 1970 level. The mean salary for teachers in
1986 was about $25,000, with wide variations among the
states (OTA, 1988b, p. 571. The average starting salaries
forpublic schoolteachers were $8,233 in 1975 and $16,500
in 1986. These compare to average starting salaries for
college graduate mathematical scientists in private indus
try of $10,980 in 1975 and $23,976 in 1986 (BOC, 1988a).
Public school salaries are generally for 9 or 10 months. If
a 9month salary is translated to a 1 2month basis, the 1975
average salaries for teachers and employees in private
industry were essentially the same. By 1986, however,
even the 12month equivalent of the teacher salary was
about 10% less than the industry salary.
Both a high action rate, 9% in 1983, and a high
retirement rate, estimated to be over 40% from 1983 to
1993, of mathematics and science teachers signal major
replacement problems in the next few years (RAND,
1984~. School districts may have to replace mathematics
teachers with teachers from other fields. Furthermore,
increases in the demand for secondary school mathematics
teachers are likely because of increased high school gradu
ation requirements in mathematics and fewer collegiate
remedial programs in mathematics. If current patterns
persist, then the prospects for a sufficient number of
qualified replacements are dim.
critical work force has fundamental responsibilities for the
education of many U.S. workers, bears the principal re
sponsibility for maintenance and development of the dis
ciplines of mathematics and statistics, and is charged with
educating replacements and additions within its own ranks.
These responsibilities have changed dramatically over the
past 40 years, and there are major challenges projected by
the year 2000.
Approximately three of every four mathematical sci
ences doctoral degree holders and about one of every four
master's degree holders are on these faculties, most of
whose members have their highest degrees in mathemat
ics, mathematics education, or statistics. Among these
faculty members are approximately 10,000 of the nation's
estimated 11,000 research mathematical scientists. Ap
proximately twothirds of the 25,000 fulltime faculty
members are tenured.
Balancing the supply arid demand for faculty members
has been difficult because there have been no candidates in
reservethere are very few postdoctoral positions, and
mathematics is a field people leave rather than move into.
For many years, members of this faculty have come from
other countnes, and that practice has increased since the
early 1970s as the number of U.S. citizens receiving
mathematical sciences doctorates annually has dropped
from over 900 to under 400.
140
~0
100
80
Characteristics of College and University Faculties 60
The colic ,e and university mathematical sciences fac
ulty, which accounts for about 5.5 To of all faculty, numbers
approximately 50,000, including about 8.000 graduate
assistants and 15,000 parttime members. This small but
/
W/:
~/ \ ~Private
I. , ,
1 9701 975
Twoyear
Colleges
Universities
Public Colleges
Colleges
1 980 1 98:
FIGURE 5.7 Mathematical and computer sciences enroll
ments per FTE of faculty. SOURCE: Conference Board of
the Mathematical Sciences (CBMS, 1987).
61
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A Challenge of Numbers
TABLE 5.3 Professional activities of fouryear college and university mathematical sciences faculty
Mathematic s S tall stic s
Public fouryear
Universities
Classroom teaching performance
Published research
Service to department, college,
Or university
Talks at professional meetings
Activities in professional societies
or public service
Supervision of graduate students
Undergraduate/graduate advising
Expository and/or popular articles
Textbook writing
colleges
70 (3)
96 (0)
31 (5)
42 (I)
22 (8)
34 (7)
9 (22)
22 (13)
9 (35)
81 (2)
70 (10)
63 (I)
49 (1 1)
4s (4)
21 (32)
24 (20)
37(14)
17 (3s)
Private fouryear
colleges
96 (4)
26 (39)
66 (0)
13 (28)
33 (9)
39 (12)
14 (40)
11 (58)
Universities
71 (6)
100 (0)
31 (11)
25(11)
31 (6)
81 (0)
21 (21)
14 (19)
12 (50)
NO l lit: lithe first number in each cell is the percentage of departments responding that the activity was very important. The
number in parentheses is the percent of responses that indicated the activity was of little or no importance. The possible
responses were 0,1,2,3,4, or 5 with 0 meaning "no importance" and 5 meaning "very important", and the others indicating
gradations between these. The percentages given above for "very important" represent the 4 and 5 responses while "little
or no importance" represents the 0 and 1 responses. By subtracting the sum of these percentages from 100, one can get the
percentage of 2 and 3 responses.
SOURCE: Conference Board of the Mathematical Sciences (CBMS, 1987~.
The mathematical sciences faculty is more than 80%
male and more than 80% white, with half of the others
being AsianAmericans. The age distnbution, skewed by
the heavy hiring in the 1960s, predicts an increased retire
ment rate by 2000. Projected shortages of replacement
candidates and general demographic trends and reform
scenarios indicate even worse shortages.
What Faculty Members Do
Most colleges and universities expect mathematical
sciences faculty members to perform in three areas: teach
ing, service, and research. The definitions of these three
areas vary across institutions, and the boundaries are usu
ally blurred and do not include increasing responsibilities
for planning and reporting.
Teaching usually means having sole responsibility for
62
conducting classes and evaluating student performance,
and the numbers of classes and students vary. Most full
time faculty members in twoyear or fouryear colleges
teach three to five separate classes each semester, consti
tutir~g 12 or more contact hours per week. Most university
faculty members teach one to three separate classes each
semester, with the onecourse load being rare and the lower
loads occurring most frequently at institutions where the
research expectations are higher. Frequently at larger in
stitutions, classes are large, and a faculty member lectures
100 to 300 students and has an assistant for grading,
conducting recitation or problem sessions, and helping
students outside of class. When no such assistance is
provided, class sizes are mostly in the 30 to 50 range at
public fouryear colleges and universities and in the 20 to
30 range at private institutions. Introductory classes are
generally larger and advanced classes smaller. On aver
OCR for page 53
$60,000
$50,000
$40,000
$30,000
$20,000
$10,000
$0
$60,000
$30,000
$40,000
$30,000
$20,000
$10,000
$0
GROUP I
_
~ r
Asst. Prof. Assoc. Prof. Full Prof.
GROUP II
, ~
bit ~ ...............
~_ as.
Asst. Prof. Assoc. Prof. Full Prof.
GROUP III
$60~004
$50~000  .
$40,000 ~ _
$7,O,000
Asst. Prof. Assoc. Prof. Full
$60,000
$50,000
$40,000
$30,000
$20,000
S10,000
$0
$60,000
$50,000
$40,000
$30,00C
$20,00G
$ 10,00G
$0
. Prof.
........
..........
. . .
.......... .
.....
...........
.,'..'.'..
i............
....~..
...........
.......
......
.~ .  . .
_~
$60~000
$50,000
$40.000
S30~000
$20,000
$10,000
~0
~ 1970 ~ 1975 ~ 1980 E3 1985 1
Mathematical Scientists in the Workplace
. . _
GROUP IV (Statistics)
GROUP M
GROUP B
~ ~ ,. ~', .. ~ ~ ~ .~
~ ., ~ .. ~I
l _ I I If. I ~A, ~
Asst. Prof. Assoc. Prof. Full Prof.
FIGURE 5.8 Mathematical sciences faculty salaries, 1970 to 1985 (in 1985 dollars). (See Box 3.2 for explanation of groups.)
SOURCE: American Mathematical Society (AMS, 1976 to 1988); see Appendix Table A5.13.
63
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A Challenge of Numbers

age, faculty members teach about 120 students per semes
ter in twoyear colleges, 100 per semester in public four
year colleges, and 70 per semester in private fouryear
colleges. Other teaching duties include student advising,
cumculum development, coordinating or supervising the
teaching of others, and proposal writing and grant admini 20
stration.
so
Service activities of faculty members include consult
ing, assisting public schools or community groups, institu
tional committee work, recruiting students and faculty
members, and public relations.
The meaning of "research" varies from institution to
institution. At research institutions, especially those with
doctoral programs, the meaning of research in mathemat
ics is usually clear. Research production usually means
publishing new theorems on mathematics in refereed re
search journals or research monographs. In statistics, the
meaning is usually broader, especially for applied statisti
cians. At other institutions, the definition of research
production may be broader and may include textbook
writing and expository writing, but there is no broader
definition that is generally accepted by the academic mathe
matics community.
The CBMS surveys have asked department chairs to
rate the importance of venous professional activities ire
promotion or salary decisions. 'lthe most recent survey
40
30
ck
c
10
<30 3039 4049 5059 260
Age Category
1975
1985
FIGURE S.9 Age distribution of fulltime mathematical
sciences faculty in fouryear colleges and universities.
SOURCE: Conference Board of the Mathematical Sciences
(CBMS, 1987~; see Appendix Table A5.10.
results supported the emphasis on research at universities,
with published research being most frequently cited as a
very important activity (Table 5.3~. At colleges, more
importance was given to teaching activities.
For twoyear colleges, the CBMS questionnaire did not
ask the question summarized in Table 5.3 for fouryear
colleges and universities. The survey of twoyear colleges
asked for the percent of faculty ending in certain profes
TABLE 5.4 Professional activities of twoyear college mathematical sciences faculty
.
1975 1980 1 As
Attending at least one professional meeting per year
Taking additional courses during year
Attending minicourses or short courses
Giving talks at professional meetings
Regular reading of articles in professional journals 47
Wnting of expository and/or popular articles
Wnting research articles
Writing textbooks
47
21
NA
9
NA
15
59
22
NA
15
57
6
NA
10
70
31
31
16
72
6
4
NOTE: Numbers indicate percentage of faculty surveyed indicating participation in activity. NA means "not available."
SOURCE: Conference Board of the Mathematical Sciences (CBMS, 1987~.
64
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Mathematical Scientists in the Workplace
signal activities. The 19851986 CBMS Survey results Number
showed that a maximum of 13% of the twoyear mathe peryear
matical sciences faculty wrote either textbooks orresearch, i'°°°
expository, or popular articles (Table 5.4~.
An active program of scholarly activities outside of
assigned teaching and service duties is generally accepted 600
as necessary to keep faculty members intellectually alive 400
and abreast of the developments in their discipline and in
their profession. The losses from not having a program Of 200
"continuing education" or faculty development will be
large if the discipline is changing and the curriculum is
responsive to society's needs. The mathematical sciences
are changing very rapidly, and a responsive curriculum
should be a national imperative. When faculty members
spend all of their working time conducting classes, espe
cially lowlevel, routine courses, the losses in their effec
tiveness are accelerated through forgetting, boredom, and
failing to keep up with new developments. A faculty
member teaching for 35 years is likely to teach as many as
8,000 students, and so losses in teaching effectiveness can
affect many students. In effect, intellectual capital (teach
ing potential and effectiveness) is being spent to conduct
classes. Other professionals for example, engineers in
industry~onsider continuing education essential to
maintaining competence. This consideration is gaining
broader acceptance and practice among academic mathe
matical scientists, and new patterns of professionalism are
emerging.
Faculty Members by Duties and Credentials
In this section college and university mathematical
sciences faculty are categorized by type of institution,
academic credentials, fulltime or parttime employment,
subject Greats) taught, and research activity. The following
subsets are useful in analyzing faculty characteristics and
employment markets:
· Doctorate fulltime faculty members in fouryear col
leges and universities (FTDFYCU) number approxi
mately 16,000, with 6,500 in doctoraldegreegranting
departments and 9,500 in master'sdegree and bachelor's
soo
Twoyear College ~1 _
 ll'8@~: ~ in Academe
_ (1987)
it. ~
i: .
New U.S.
Ph.D.'s
(1987)
at= _
me_
~Foury~ ~u ~ ~ ~ I
1986 1993 1998 2003 2008
1992 1997 2002 2007 2012
New Ph. D 's
FIGURE 5.10 Estimated number of retirements of fulltime
college and university mathematical sciences faculty.
SOURCE: Adapted from Conference Board of the Mathe
matical Sciences (CBMS, 1987) and American Mathematical
Society (AMS, 1987~.
degreegranting departments.
· Research faculty members publish traditional original
research results regularly, and most have research as a
designated part of their jobs. The size of this component is
estimated at 10,000, constituting more than 90% of the
nation's mathematical sciences researchers. Almost all are
doctorate faculty at fouryear colleges arid universities, the
bulk being at the universities.
· Nondoctorate fulltime faculty members in fouryear
colleges and universities (FTNDFYCU) number ap
proximately 4,500, with 500 in the doctoraldegree~rant
ing departments and 4,000 in the others.
· Parttime faculty members in fouryear colleges and
universities (PTFYCU) of whom there are approximately
7,000, not including graduate teaching assistants.
· Fulltime twoyearcollegefaculty members (FTTYC),
a component that includes approximately 6,500 members;
13% have doctorates.
· Parttime t~voyearcollegefaculty members (PTTYC),
who number approximately 7,500.
· Graduate teaching assistants (GTA), a group with
approximately 8,000 members (all in doctoral and master's
de,reegranting institutions). Approximately 45% teach
65
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A Challenge of Numbers
~ . _
their own classes, another 40% conduct quiz or recitation
sections, and the remainder perform other duties such as
. . .
tutoring or grading papers.
Another basis for separating the college and university
mathematical sciences faculty is by the fields in which they
teach, notably mathematics, statistics, or computer sci
ence. (Although some faculty members work in other
areas such as operations research, no finer classification
will be made in this report.) The subsets of faculty given
Graduate school ~
30~o 4.~.
Nonacademic l
employment 7% 3
Miscellaneous
13%
Another twoyear
college faculty
6%
Nonacademic
employment
8%
',~
... .. , : .....
.................. , ..,j ; ,., : ,
.......... .
.. a , ., , . ~
. ..... .... ....... ..
~ 111
Parrtime facula at same institution
25%
Another twoyear college faculty
\ 15%
. ~ Fouryear college faculty
3%
~ ..
Secondary teaching
13%
Deaths or
retirement
~50%
Secondary teaching college faculty
9% 14%
FIGURE 5.11 Top: Source of new hires of twoyear college
fulltime faculty in mathematical sciences. Bottom: Destina
tion of departing mathematical sciences twoyear college full
time faculty. SOURCE: Conference Board of the Mathe
matical Sciences (CBMS, 1987~.
66
above separate into these disciplines approximately as
given in Table 5.5.
The category "computer science" in Table 5.5 does not
include faculty members in computer science departments,
but only those in mathematical sciences departments.
Also, although Table 5.5 includes many departments of
statistics, there are units in statistics in other academic
departments that are not included in this summary for
mathematical sciences departments.
Comparing the number of fulltime and parttime fac
uIty members by category of institution over the period
from 1970 to 1985 reveals little or no increase in fulltime
faculty members even though enrollments increased dra
matically. In fact at universities the number of fulltime
mathematical sciences faculty in 1985 was 14% less than
ire 1970 (Figure 5.6; see Appendix Table A5.89. This
represents a loss in both the mathematics faculty and the
statistics faculty. Colleges and universities employed
parttime faculty members to meet the demands of in
creased teaching loads, and this parttime sector of the fac
ulty more than tripled from 1970 to 1985 (Figure 5.61.
However, this trend has reversed; since the early 1 980s the
hiring of fulltime faculty members has increased. An
analysis of hiring for the period 1 983 to 1988 is given in the
section titled "Fouryear College and University Doctor
ate Faculty."
The increase in parttime faculty members was not
enough to keep pace with enrollments. From 1970 to 1985
enrollments per FTE of faculty member increased, espe
ciallyduring 1970 to 1980. Atbothtwo andfouryearcol
leges, enrollments per FTE appeared to level off, but at
universities the number of enrollments per FTE steadily
increased until 1985 (Figure 5.71. The data are combined
for mathematical sciences and computer science in the
CBMS reports, but the data for mathematics alone yield
even higher numbers of enrollments per FTE.
These two trends, steady increases in parttime faculty
and in enrollments per faculty member, have apparently
been reversed in the 1980s. The heavy use of parttime
faculty members was viewed by many as a serious prob
lem, as reflected in the 19851986 CBMS Survey (CBMS,
19871. The need to use temporary and parttime faculty
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Mathematical Scientists in the Workplace
TABLE 5.S Numbers of mathematical sciences faculty members by teaching area and type of institution, 1987
Mathematics
StatisticsComputer Science Total
FTDFYCU 13,200 1,5001,300 16,000
FTNDFYCU 3,750 50700 4,500
PTFYCU 3,950 503,000 7,000
FTTYC 5.600 200700 6,500
PTTYC 6,450 250800 7,500
GTA 6,250 1,7500 8,OOO
Estimated FTE 27,600 2,3004,000 33,900
NOTE: Each parttime faculty member is considered onethird of FTE and each GTA is considered onequarter of FTE.
Distribution of the faculty members is partially determined by the distribution of teaching responsibilities among the three
disciplines. See "Faculty Members by Duties and Credentials," p. 65, for explanation of acronyms.
SOURCES: These data are based on Conference Board of the Mathematical Sciences (CBMS, 1987) and American
Mathematical Society (AMS, 1976 to 1988~.
members was classified as a very important problem by
35% of the responding university statistics departments,
42% of the university mathematics departments, 44% of
the public fouryear college mathematics departments,
42% of the private fouryear college mathematics depart
ments, and 61% of the twoyear college mathematics de
partments.
The development of computer science was a contribut
ing factor to faculty hiring practices in mathematical sci
ences departments in the period from 1970 to 1985. As
computer science enrollments and the number of majors
increased rapidly, positions fulltime and parttime
became available. Universities were much more likely to
have a separate computer science department than were the
fouryear or twoyear colleges. Thus, especially from
1970 to 1982, many faculty members were hired to teach
computer science, not mathematics or statistics, which
would partially account for the decline in the number of
fulltime faculty in universities while fouryear fulltime
faculties were growing, albeit slowly. Although verifying
data are not available, it is likely that the number of full
time faculty members teaching mathematics declined sig
nificantly in the period from 1970 to 1982, with the growth
of computer science more than absorbing the new faculty
. .
song.
The Research Faculty
Most of the active mathematics and statistics research
ers in the United States are in the doctorategranting
programs in universities. The 1984 David Report esti
mated the mathematical sciences research community at
10,000, with 9,000 of these being faculty members in edu
cational institutions and having research as their primary or
secondary activity (NRC, 1984~. Of the 9,000 researchers
in academia, the David Report estimated that 5,500 pub
lished regularly, 4,000 frequently, and 2,600 on a highly
productive schedule. Extrapolating those estimates to a
larger faculty yields approximately 1 1,000 active research
ers in 1987.
A 1986 NSF survey (NSF, 1986a) of top research insti
tutions, which yielded responses from 105 mathematical
sciences departments, showed an average per department
of 40 fulltime faculty, up 7% from an average of 37 in a
similar 1974 survey and up from an average of 36 in 1980,
again reflecting the increased hiring in universities after
67
OCR for page 53
A Challenge of Numbers
TABLE 5.6 Age distribution of mathematical sciences faculty members in 105 research universities, 1980 and 1986
<30
1980
1986
7.9~c
6.7%
SOURCE: National Science Foundation (NSF, 1986a).
3039 4049 5054 5559 6064 2 65
37.0%
25.8%
1980. The percent of faculty with a recent doctorate
(received in the previous seven years) In the responding
departments cropped from35% in 1974to22% in 1980 and
to 21 To in 1986. At research institutions, some 5.5% of the
doctorate faculty in the mathematical sciences were aged
60 or over in 1980; 8.6% were in that age category in 1986
(Table 5.6~. Except for computer science, this was the
lowest percent of faculty aged 60 and over for the 22 areas
of science and engineering, surveyed.
The 1986 NSF survey also showed that the number of
women on the faculties of research universities was about
half that on the faculties of all fouryear colleges and
universities, but their representation improved slightly
from 1980 to 1986, from 7.1% to 8.5% of the total faculty
(NSF, 1986a). In 1986 women constituted 5.1~o of the
senior doctoral degree holders, 11.5% of those with recent
doctorates, and 48.9% of the nondoctoral degree holders.
Blacks and Hispanics were also poorly represented on
Another twoyear
college faculty
=12% ~/=:ly
Graduate school
3%
No fulltime
employment
21~c

Secondary
teaching,
37%
FIGURE 5.12 Source of twoyear college parttime faculty in
mathematical sciences. SOURCE: Conference Board of the
Mathematical Sciences (CBMS, 1987~.
68
31.2% 10.9% 7.5%
36.4% 12.6% 9 9%
3.8%
6.5% 2.1%
1.7%
these faculties, but the representation of Asians was about
the same overrepresentation, in terms of their percentage of
the total U.S. population, as for all fouryear institutions.
Mathematics topped all the sciences in the proportion
(35%) of fulltime assistant professors with foreign bacca
laureates. Only mechanical and electrical engineering had
larger proportions, and both of those were 1lnder 40%.
Physics was the second highest of the sciences at about
25% (NSE, 1987c).
Faculty Salaries
Generally, wages increase as the demand for workers
increases and as the supply decreases, but this is not so in
the college and university mathematical sciences faculty.
Normal economic analyses do not apply. In the period
from 1970 to 1985, compensation decreased as the number
of faculty candidates fell and the teaching responsibilities
increased. In constant dollars, professors (assistant, asso
ciate, and full) were earning lower salaries in 1985 than in
1970. Across the board, almost without exception, from
doctorategranting to master' sgranting to bachelor's
granting institutions, faculty members are not as well
compensated today as they were 15 years a go (Figure 5.8~.
Fouryear
college faculty
3% Ages of Faculty Members
lIeavy hiring in the 1960s of relatively young faculty
members resulted in a faculty with more than half its
members under age 40 in 1975. Decreased hiring since the
1970s has resulted in an older faculty (see Figure 5.93.
Similarities exist in the age distribution for doctorate
mathematical sciences faculty members (Table 5.6) and
for all faculty at fouryear colleges and universities, except
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Mathematical Scientists in the Workplace
Graduate school
Institutions
outside U.S.
7%
Nondoctorate
[acuity receiving
doctorate
To
Nr~n_~r~Hmir
employment Institutions outside U.S. ~
J Another
/ college/university
faculty
42%
Nonacademic
employment
16%
Deaths or retirement
18%
~~
LO
\ Another
\ college/university
\ faculty
~ 636?;o
FIGURE 5.13 Left: Source of new hires of doctorate faculty in mathematical sciences, 1983 to 1988. Right: Destination of
departing mathematical sciences doctoral faculty, 1983 to 1988.
SOURCE: Consolidated from AMSMAA annual surveys (AMS, 1983 to 1988~.
for a significantly larger fraction ~ 18.5% in 1986) over the
age of 55 at research institutions. In 1985 half the fouryear
college and university faculty members were 40 to 55 years
old, as were more than half of the twoyear college faculty
members. The twoyear college mathematical sciences
faculty also had a very large fraction (24%) of its members
in the 40 to 44 age bracket.
Estimates of retirements based on faculty age dis~bu
tior~s indicate serious shortages of replacements by the year
2000 if present trends continue (see Appendix Tables
A5.10 and A5.11) Over the past several years, the full
time mathematical sciences faculty at fouryear colleges
and universities has been retiring at rates of nearly 1 % per
year. The average number of retirements or deaths among
the doctorate faculty for the five years from 1982 to 1987
was 142 per year, or about 1% per year. It is likely that
these estimates for the period i986 to 1992 are low because
the data already available for 1986 and 1987 indicate a
higher rate of attrition through death and retirement; in
addition, early retirement options are increasing, and other
sources of data give larger percentages for the population
aged 60 and over. For example, NSF data give this
percentage as 10%. For twoyear college faculty, the
estimate of retirements for the period 1986 to 1992, based
on the ages of faculty in 1985, is much lower than the 217
retirements or deaths reported in the CBMS survey for the
one year 19841985 (CBMS, 1987~. Early retirements
from this faculty are apparently popular, as there was
TABLE 5.7 Fulltime mathematical sciences faculty by ethnic origin and sex, 1985
Asian Black Hispanic
Native
American
Men
Women
All fouryear colleges 7.1% 3.5% 3.4% 0.1% 85% 15%
All twoyear colic Yes 3~c 4% 4% 1 % 69% 31 To
Statistics
University mathematical sciences
Public fouryear mathematical sciences
Private fouryea mathematical sciences
90%
89%
81%
85%
10%
11%
19%
15%
SOURCE: Conference Board of the Mathematical Sciences (CBMS, 19871.
69
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A Challenge of Numbers
considerable attrition in the group aged 50 to 60 between
1980 and 1985. The current level of production of U.S.
Ph.D.s falls far short of the expected needed replacements
of retiring faculty members in coming years (Figure 5.10~.
Women and Minorities on the Faculty
Table 5.7 shows the fractions of women, blacks, and
Hispanics on the college and university fulltime mathe
matical sciences faculty (CBMS, 1987~. The representa
tions of women on the faculties et fouryear colleges (15%)
and at twoyear colleges (31 %) are very near their current
representations in the recipients of new doctorates and new
master's degrees. Among the various categories of insti
tutions, universities have smaller fractions of each of
women, blacks, and Hispanics on their mathematical sci
ences faculties.
TwoYear College Faculty Mobility
The 19851986 CBMS Survey (CBMS, 1987) reported
theresults of a 1979 survey (McKelvey,Albers, Liebeskind,
and Loftsgaarden) showing that more than 60% of all
mathematics faculty in twoyear colleges had previously
taught in secondary schools, whereas the survey for 1985
showed that most new fulltime hires came from either
graduate school or from the parttime faculty at the same
institution (Figure 5.1 1~. The bulk (nearly 50%) of the
outflow was due to deaths and retirements.
To explain the 1979 survey's finding that 60% of the
faculty had previous experience in secondary teaching, one
needs to look at the source of parttime faculty, a major
feeder of the fulltime faculty. For 1985 the major sources
of 7,500 parttime twoyear colleges mathematical sci
ences faculty were secondary school teachers and industry
employees (Fi~ure 5.12~.
Fouryear College and University Doctorate Faculty
The number of doctorate faculty in the mathematical
sciences in fouryear colleges and universities was ap
proximately 16,000 in 1987 (CBMS, 19875. This faculty
70
expanded from approximately 13,000 in 1975 and from
14,000 in 1980, reflecting a much faster rate of increase
during the 1980s when institutions finally began to address
the additional faculty needs brought on by increased en
rollments. Various counts over the past years have in
cluded computer science faculty in computer science
departments and in mathematical sciences departments.
The count of 16,000 in 1987 did not include faculty from
computer science departments, but it did include some
faculty members (approximately 1,300) who taught com
puter science in mathematical sciences departments.
The number of new hires in this faculty has been in the
range of 1,200 to 1,300 in recent years, with 500 to 600 of
these being persons who have switched from one institu
tion to another within this same faculty. Taking out this
internal movement, the principal source of new hires into
this faculty has been graduate school, and the principal
reasons for leaving have been death and retirement and
nonacademic employment (Figure 5.131.
The net result of the inflows and outflows to and from
the mathematical sciences doctorate faculty since 1982 has
been an average increase of about 400 members per year.
The average net flow into this faculty can be organized into
six categories, but five of the categories sum to zero,
leaving the net increase as essentially the number hired
from graduate schools (Table 5.8~.
FourYear College and University Nondoctorate Faculty
In 1987 there were approximately 4,500 nondoctorate
fulltime faculty members in fouryear colleges and uni
versities. This is essentially the same number as reported
five years previously in 1982. Almost all of these faculty
members were in the institutions granting master's and
bachelor's degrees, with only about 400 reported as being
in doctorate~rantin~ departments.
In recent years the number of hires in this faculty has
been 500 to 600 (AMS, 1987~. About 20~%o of these have
been persons switching institutions. The principal source
for additions to this faculty has been graduate school,
which has provided 60% of the new hires in the past five
years. The other 40 37c have come from various sources,
Or =
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Mathematical Scientists in the Workplace
.
including the parttime faculty and the twoyear college
and high school faculties. The principal reasons persons
left this faculty were to return to graduate school for
doctoral work ( 19%), to move to the doctorate faculty after
earning a degree and not moving (18~o), and because of
death and retirement (23%~. There has been a small net
outflow (a 1982 to 1987 yearly average of 19) from this
faculty to nonacademic employment and a small net inflow
(a 1982 to 1987 yearly average of 8) from institutions
outside the United States.
Summary
Although about threefourths of the people with college
degrees in the mathematical sciences are not identified as
mathematical scientists in the labor force, mathematical
scientists are becoming more visible in the workplace. The
number of workers so identified has tripled in the past
decade, and the fraction of those working in science and
engineering fields has increased dramatically. Still, al
though nonacademic employment is increasing, three
fourths of those with doctorates in the mathematical sci
ences begin work in an educational institution. These
fractions are lower for applied mathematicians and statis
tlclans.
Although white males dominate employment as mathe
matical scientists, particularly on the college and univer
sity faculty, there is an increasing dependence on foreign
nationals. These situations leave the supply vulnerable to
predictable shifts in demographics and unpredictable shifts
in U.S. foreign relations.
TABLE 5.8 Estimate of average annual net flow into doctoral
faculty at fourvear colleges and universities, 1982 to 1987

Net Flow
Graduate schools
Nondoctorate faculty
Nonacademic employment
NonU.S. employment
Miscellaneous/unlcnown
Deaths and retirements
Total
400
70
50
50
100
150
420
SOURCE: Consolidated from American Mathematical
Society (AMS, 1976 to 19881.
there are currently shortages of secondary school
mathematics teachers, and these shortages are expected to
worsen in the future. Moreover the quality of teacher
education is of great concern. The collegiate mathematical
sciences faculty is aging and is of uncertain vitality. If
present trends continue, and as retirements increase over
the next decade, qualified replacements for both the ele
mentary and secondary school and collegiate faculties will
be in short supply. If the system were to be charged with
the intent of improving the quality of mathematics instruc
tion and scholarship, the shortages would be dramatic. For
example, shortages would increase if teaching loads were
reduced, more research support became available for gradu
ate fellowships and postdoctoral salaries, or fulltime fac
ulty assumed more responsibility for teaching.
71
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