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~ Mathematical Scientists in the Workplace Three-fourths 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. One-fourth of those with a bachelor's degree, one-third of those with a master's, and three-fourths 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 one-fourth 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

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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 full-time faculty. This relatively small work force plays an essential part in educating much of the college-educated 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 well-qualified 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 mathematics-based 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 one-half. 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 non-S/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 one-third 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 three-quarters of mathematical scientists work in educational institutions; this fraction drops to about one-th~rd at the master's level and to one-fourth 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. One-third 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 full-time in graduate school, and another 13% were enrolled part-time. Full-time 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

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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. 54-57~. 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 1985-86 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 two-thirds to only about one-half. 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 one-quarter 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. ..... Four-year Colleges 81lWa~#~ ',uuv 1 ~ unlversl~les ~ ~-. 1970 1975 1980 1985 1 s7s 1 980 1 sss FIGURE 5.6 Left: Number of full-time mathematical sciences faculty members at colleges and universities. Right: Number of part-time 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 self-evaluation 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 one-fourth 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 student-related 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.

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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 high-demand 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 9-month salary is translated to a 1 2-month basis, the 1975 average salaries for teachers and employees in private industry were essentially the same. By 1986, however, even the 12-month 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 two-thirds of the 25,000 full-time faculty members are tenured. Balancing the supply arid demand for faculty members has been difficult because there have been no candidates in reserve-there 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 part-time members. This small but / W/: ~/ \ ~Private I. , , 1 9701 975 Two-year 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 four-year college and university mathematical sciences faculty Mathematic s -S tall stic s Public four-year 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 four-year 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 Asian-Americans. 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 two-year or four-year 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 one-course 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 four-year colleges and universities and in the 20 to 30 range at private institutions. Introductory classes are generally larger and advanced classes smaller. On aver

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$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 two-year colleges, 100 per semester in public four year colleges, and 70 per semester in private four-year 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 30-39 40-49 50-59 260 Age Category 1975 1985 FIGURE S.9 Age distribution of full-time mathematical sciences faculty in four-year 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 two-year colleges, the CBMS questionnaire did not ask the question summarized in Table 5.3 for four-year colleges and universities. The survey of two-year colleges asked for the percent of faculty ending in certain profes TABLE 5.4 Professional activities of two-year college mathematical sciences faculty . 1975 1980 1 As Attending at least one professional meeting per year Taking additional courses during year Attending mini-courses 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 1985-1986 CBMS Survey results Number showed that a maximum of 13% of the two-year 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 low-level, 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, full-time or part-time employment, subject Greats) taught, and research activity. The following subsets are useful in analyzing faculty characteristics and employment markets: Doctorate full-time faculty members in four-year col leges and universities (FT-D-FYCU) number approxi mately 16,000, with 6,500 in doctoral-degree-granting departments and 9,500 in master's-degree- and bachelor's soo Two-year College ~1 _ --- ll'8@~: ~ in Academe _ (1987) it. ~ i: . New U.S. Ph.D.'s (1987) at= _ me_ ~Four-y~ ~u ~ ~ ~ I 1986- 1993- 1998- 2003- 2008 1992 1997 2002 2007 2012 New Ph. D 's FIGURE 5.10 Estimated number of retirements of full-time college and university mathematical sciences faculty. SOURCE: Adapted from Conference Board of the Mathe- matical Sciences (CBMS, 1987) and American Mathematical Society (AMS, 1987~. degree-granting 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 four-year colleges arid universities, the bulk being at the universities. Non-doctorate full-time faculty members in four-year colleges and universities (FT-ND-FYCU) number ap- proximately 4,500, with 500 in the doctoral-degree-~rant- ing departments and 4,000 in the others. Part-time faculty members in four-year colleges and universities (PT-FYCU) of whom there are approximately 7,000, not including graduate teaching assistants. Full-time two-yearcollegefaculty members (FT-TYC), a component that includes approximately 6,500 members; 13% have doctorates. Part-time t~vo-yearcollegefaculty members (PT-TYC), who number approximately 7,500. Graduate teaching assistants (GTA), a group with approximately 8,000 members (all in doctoral and master's de,ree-granting 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.~. Non-academic l employment 7% 3 Miscellaneous 13% Another two-year college faculty 6% Non-academic employment 8% ',~ ... .. , : ..... .................. , ..,j ; ,., : , .......... . .. a , ., , . ~ . ..... .... ....... .. ~ 111 Parr-time facula at same institution 25% Another two-year college faculty \ 15% . ~ Four-year 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 two-year college full-time faculty in mathematical sciences. Bottom: Destina- tion of departing mathematical sciences two-year 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 full-time and part-time fac- uIty members by category of institution over the period from 1970 to 1985 reveals little or no increase in full-time faculty members even though enrollments increased dra- matically. In fact at universities the number of full-time 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 part-time faculty members to meet the demands of in- creased teaching loads, and this part-time 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 full-time faculty members has increased. An analysis of hiring for the period 1 983 to 1988 is given in the section titled "Four-year College and University Doctor- ate Faculty." The increase in part-time 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- andfour-yearcol- 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 part-time faculty and in enrollments per faculty member, have apparently been reversed in the 1980s. The heavy use of part-time faculty members was viewed by many as a serious prob- lem, as reflected in the 1985-1986 CBMS Survey (CBMS, 19871. The need to use temporary and part-time 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 FT-D-FYCU 13,200 1,5001,300 16,000 FT-ND-FYCU 3,750 50700 4,500 PT-FYCU 3,950 503,000 7,000 FT-TYC 5.600 200700 6,500 PT-TYC 6,450 250800 7,500 GTA 6,250 1,7500 8,OOO Estimated FTE 27,600 2,3004,000 33,900 NOTE: Each part-time faculty member is considered one-third of FTE and each GTA is considered one-quarter 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 four-year college mathematics departments, 42% of the private four-year college mathematics depart- ments, and 61% of the two-year 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 full-time and part-time- became available. Universities were much more likely to have a separate computer science department than were the four-year or two-year 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 full-time faculty in universities while four-year full-time 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 doctorate-granting 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 full-time 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

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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). 30-39 40-49 50-54 55-59 60-64 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 four-year 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 two-year college faculty =12% ~/=:ly Graduate school 3% No full-time employment 21~c - Secondary teaching, 37% FIGURE 5.12 Source of two-year college part-time 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 four-year institutions. Mathematics topped all the sciences in the proportion (35%) of full-time 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 doctorate-granting to master' s-granting to bachelor's- granting institutions, faculty members are not as well compensated today as they were 15 years a go (Figure 5.8~. Four-year 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 four-year colleges and universities, except

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Mathematical Scientists in the Workplace Graduate school Institutions outside U.S. 7% Non-doctorate [acuity receiving doctorate To Nr~n_~r~H-mir employment Institutions outside U.S. ~ J Another / college/university faculty 42% Non-academic 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 AMS-MAA 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 four-year college and university faculty members were 40 to 55 years old, as were more than half of the two-year college faculty members. The two-year 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 four-year 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 two-year 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 1984-1985 (CBMS, 1987~. Early retirements from this faculty are apparently popular, as there was TABLE 5.7 Full-time mathematical sciences faculty by ethnic origin and sex, 1985 Asian Black Hispanic Native American Men Women All four-year colleges 7.1% 3.5% 3.4% 0.1% 85% 15% All two-year colic Yes 3~c 4% 4% 1 % 69% 31 To Statistics University mathematical sciences Public four-year mathematical sciences Private four-yea 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 full-time mathe- matical sciences faculty (CBMS, 1987~. The representa- tions of women on the faculties et four-year colleges (15%) and at two-year 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. Two-Year College Faculty Mobility The 1985-1986 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 two-year colleges had previously taught in secondary schools, whereas the survey for 1985 showed that most new full-time hires came from either graduate school or from the part-time 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 part-time faculty, a major feeder of the full-time faculty. For 1985 the major sources of 7,500 part-time two-year colleges mathematical sci- ences faculty were secondary school teachers and industry employees (Fi~ure 5.12~. Four-year College and University Doctorate Faculty The number of doctorate faculty in the mathematical sciences in four-year 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~. Four-Year College and University Nondoctorate Faculty In 1987 there were approximately 4,500 nondoctorate full-time faculty members in four-year 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 part-time faculty and the two-year 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 three-fourths 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 four-vear colleges and universities, 1982 to 1987 - Net Flow Graduate schools Non-doctorate faculty Non-academic employment Non-U.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 full-time fac- ulty assumed more responsibility for teaching. 71

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