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Appendix Tables
List of Appendix Tables Educational attainment of the civilian labor force (percent distribution) Population of 18- to 24-year-olds High school dropouts among 18- and 19-year-olds (percent distribution) Enrollment rates of 18- to 24-year-olds in institutions of higher education A2.5 Enrollment rates of 25- to 34-year-olds in institutions of higher education A2.6 Bachelor's degrees conferred by institutions of higher education A2.7 Undergraduate enrollment in institutions of higher education A2.8 Persistence rates for 1980 high school graduates A2.9 Anticipated college major (percent distribution) A2.10 Numbers and attainment rates of masters and doctoral degrees for selected fields, 1971 to 1985 A3.1 Attitudes of 8th and 12th grade mathematics students toward mathematics, 1981-1982 school year Average SAT scores in mathematics, 1970 to 1987 A3.3 Average ACT scores in mathematics, 1970 to 1988 A3.4 Average NAEP scores in mathematics, 1973 to 1986 A3.5 Enrollments in selected mathematics courses in colleges and universities (in thousands) A3.6 Enrollments in undergraduate mathematical sciences departments by type of institution (in thousands) A3.7 Mean number of semester credits completed by bachelor's degree recipients, by major and by course area: 1972 to 1976 and 1980 to 1984 A4.1 Number of mathematical sciences degrees awarded, 1950 to 1986 A4.2 Comparison of actual versus expected number of mathematical sciences bachelor's degrees Anticipated college major and probable career occupation (percent distribution) A4.4 Number of education and mathematics education degrees for selected years A4.5 Full-time graduate students in doctorate-granting institutions for selected fields, 1975 to 1986 A4.6 Enrollments in doctorate-granting institutions for mathematical sciences by sex, 1975 to 1986 Source of major support for full-time mathematical sciences graduate students in doctorate-granting institutions, 1986 A4.8 Type of major support for full-time graduate students in doctorate- granting institutions for selected fields, 1986 A4.9 1986 enrollments in graduate mathematical sciences programs A4.10 Number of mathematical sciences master's degrees awarded by subfield 91 91 92 92 92 93 94 94 95 96 97 98 98 99 100 100 101 102 103 103 104 105 106 107 107 108 109 89
A Challenge of Numbers A4.11 Attainment rates of master's and doctoral mathematics degrees by sex, 1970 to 1986 A4.12 Characteristics of new doctorates in mathematical sciences, 1974 to 1986 A4.13 Primary sources of support of doctorate recipients in the physical sciences, 1977 and 1986 A4.14 Number of doctorate recipients in broadly interpreted mathematical sciences, 1976 to 1986, awarded by U.S. universities A4.15 Total number and distribution of new mathematical sciences doctorates by subfield and sex, 1960 to 1982 A4.16 Number of doctorates awarded in selected fields, 1970 to 1985 A5.1 Number of employed scientists and engineers A5.2 Selected employment characteristics of scientists and engineers, 1986 AS.3 Number of scientists by field and type of employer, 1976 and 1986 AS.4 Field of employment for recent (1984/85) mathematics degree recipients, 1986 (percent distribution) A5.5 Primary work activities for recent (1984/85) mathematics degree recipients, 1986 (percent distribution) A5.6 Median annual salaries by field and type of degree of recent (1984/85) graduates, 1986 A5.7 Demand and supply of new teachers in elementary and secondary schools, 1970 to 1992 (in thousands) Numbers of faculty members by types of institutions for selected years Mathematical sciences and computer science enrollments per full-time equivalent (FTE) of faculty A5.10 Age distribution of full-time mathematical sciences faculty in 1985 in four-year colleges and universities Age distribution of full-time mathematical sciences faculty in 1985 in two-year colleges A5.12 Employment status of new doctorates awarded by U.S. and Canadian mathematical sciences departments A5.13 Mathematical sciences faculty salaries by type of institution (in 1985 constant dollars) A5.8 A5.9 90 109 110 110 111 112 113 113 113 114 115 115 115 115 116 117 117 118 118 119
Appendix Tables _ TABLE A2.1 Educational attainment of the civilian labor force (percent distribution) Years of school 1965 1975 19842000 (new jobs) Less than 4 years of high school 42.5 29.3 19.514.0 High school (4 years) 35.5 39.6 40.735.0 College (1-3 years) 10.5 15.5 19.022.0 College (4+ years) 11.6 15.7 20.930.0 Median number of years in school 12.2 12.5 12.813.5 SOURCES: Bureau of Labor Statistics (BLS, 1987, p. 98) and Bureau of Labor Statistics (BLS, 1985, p. 164). TABLE A2.2 Population of 18- to 24-year-olds Race or ethnic group 1970 1975 . 1980 1985 1990 1995 2000 2010 Total (in millions)24.728.030.328.725.8 23.7 24.6 27.7 Hispanic originaaa2.32.4 2.5 2.8 3.6 White21.524.025.621.618.9 16.9 17.2 18.6 Black2.83.54.04.13.8 3.5 3.8 4.6 Other races0.40.50.70.80.8 0.9 1.0 1.1 Total (percent distnbution) 100100 100 100 100 Hispanic origin 89 11 11 13 White 7573 71 70 67 Black 1415 15 15 17 Other races 33 4 4 4 a Persons of Hispanic origin were included in white, black, and other races during 1970 to 1980. SOURCES: Bureau of the Census (BOC, 1982; 1986, p. 14~. 91
A Challenge of Numbers TABLE A2.3 High school dropouts among 18- and 19-year-olds (percent distribution) Race or ethnic group1970 1975 1980 1985 - Total16.2 16.0 15.7 14.3 Hispanic origin- 30.1 39.0 30.6 White14.1 14.7 14.9 13.8 Black31.2 25.4 21.2 17.3 NOTE: High school dropouts are considered to be those not enrolled in school and not high school graduates. SOURCE: National Center for Education Statistics (NCES, 1987a, p. 861. TABLE A2.4 Enrollment rates of 18- to 24-year-olds in institutions of higher education Race or ethnic group 1970 1975 1980 1985 1986 Enrollment as a percent of 18 to 24 year olds Total 25.7 26.3 25.6 27.8 Hispanic origin 20.4 16.1 16.9 White 27.1 26.9 26.2 28.7 Black 15.5 20.7 19.2 19.8 Enrollment as a percent of high school graduates Total 32.7 32.5 31.6 33.7 34.0 Hispanic origin - 35.5 29.8 26.9 29.4 White 33.2 32.4 31.8 34.4 34.5 Black 26.0 32.0 27.6 26.1 28.6 SOURCES: National Center for Education Statistics (NCES, 1987a, p. 155; 1988b, p. 14). TABLE A2.5 Enrollment rates of 25- to 34-year-olds in institutions of higher education Race or ethnic group 1976 1980 1984 1986 Enrollment as a percent of high school graduates Total 9.6 8.9 8.6 8.3 Hispanic origin 10.9 9.2 9.9 10.4 White 9.2 8.7 8.4 8.0 Black 11.9 9.6 8.1 7.8 SOURCE: National Center for Education Statistics (NCES, 1988b, p. 14). 92
Appendix Tables TABLE A2.6 Bachelor's degrees conferred by institutions of higher education Major19711975198019851971 to 1985 (% change) Total839,730922,933929,417979,47717 Agriculture and home economics23,83934,30041,21333,66241 Business and management114,865133,010185,361233,351103 Computer and information sciences2,3885,03311,15438,8781,528 Education176,614167,015118,16988,161-50 Engineenng and engineering technologies50,04646,85268,89396,10592 English/letters64,93348,53433,49734,091-47 Fine arts30,39440,78240,89237,93625 Health sciences25,19048,85863,60764,513156 Humanitiesa44,74153,11254,17665,61847 Life sciences35,74351,74146,37038,4458 Mathematics24,80118,18111,378- 15,146-39 Physical sciences21~41220,77823,41023,73211 Social sciences and psychology193,116186,153145,481131,272-32 Professionalb17,33639,93150,66042,492145 OtherC14,31228,65335,15636,075152 Total (percent distribution)100100100100 Agriculture and home economics3443 Business and management14142024 Computer and infonnation sciences0114 Education2118139 Engineenng and engineering technologies65710 English/letters Fine arts Health sciences Humanitiesa Life sciences 8 s 4 4 4 4 3 5 5 6 6 7 4 6 5 4 Mathematics 3 2 1 2 Physical sciences 3 2 3 2 Social sciences and psychology 23 20 16 13 Professionalb 2 4 5 4 OtherC 2 3 4 4 a Includes area and ethnic studies, communications, foreign languages, philosophy, religion, and theology. b Includes architecture and environmental design, communication technologies, library and archival sciences, military sciences, parks and recreation, protective services, and public affairs. c Includes law, liberal/general studies, and multi/interdisciplinary studies. SOURCE: National Center for Education Statistics (NCES, 1987a, p. 190~. 93
A Challenge of Numbers TABLE A2.7 Undergraduate enrollment in institutions of higher education Race or ethnic group 1976 1978 1980 1982 19841986 Total(in millions) 9.50 9.80 10.60 10.90 10.6010.80 Hispanic origin 0.36 0.39 0.44 0.49 0.500.57 White 7.80 7.90 8.60 8.70 8.508.60 Black 0.95 0.98 1.00 1.00 1.001.00 Total (percent distnbution) 100 100 100 100 100100 Hispanic origin 3.7 4.0 4.1 4.5 4.75.3 White 82.2 81.4 81.0 80.5 80.079.2 Black 10.0 10.0 9.7 9.4 9.49.2 NOTE: Figures include nonresident aliens. SOURCE: National Center for Education Statistics (NCES, 1988b, p. 12~. TABLE A2.8 Persistence rates for 1980 high school graduates From AY Summer AY Summer AY Summer AY From high 80-81 1981 81-82 1982 82-83 1983 83-84 start school Total 93.3 92.5 87.3 93.3 96.4 95.1 84.2 54.3 15.7 Gender Male 94.1 93.1 86.5 93.5 96.4 95.9 85.1 55.7 15.4 Female 92.5 91.9 88.1 93.1 96.4 94.4 83.4 53.0 16.0 Race or ethnicity White 93.4 93.1 87.7 93.6 96.7 95.5 84.3 55.6 16.9 Black 91.7 89.9 83.8 90.4 93.0 92.1 81.3 43.5 11.6 Hispanic 90.6 83.0 85.6 92.3 96.6 92.2 80.1 42.3 6.5 Asian 99.4 91.8 90.1 90.8 98.5 93.4 88.6 60.9 27.1 Socioeconomic quartile Low quartile 91.7 90.4 79.9 91.3 94.9 86.4 84.2 41.7 6.1 High quartile 95.9 93.5 90.8 93.6 96.9 97.0 84.3 60.4 31.9 Type of college 9J80 Public 4-year 93.1 92.3 87.6 93.2 96.2 93.8 82.9 52.5 a Private 4-year 93.6 92.8 86.8 93.3 96.8 97.5 86.6 57.6 a a Not computed. SOURCE: National Center for Education Statistics (NCES, 1989). 94
Appendix Tables TABLE A2.9 Anticipated college major (percent distribution) Major 1966 1970 19751980 1985 Total 100 100 100100 100 Agnculture 1.9 2.0 3.92.9 2.0 Business 14.3 16.2 18.921.3 24.8 Computer science NA NA 1.Oa2.5 2.3 Education 10.6 11.6 9.97.7 7.1 Engineering 9.8 8.6 7.911.8 10.7 English 4.4 3.0 1.00.9 1.0 Fine arts 8.4 9.2 6.25 3.S Health sciences 5.3 7.4 7.39.2 8.9 Humanities 4.7 3.5 2.12.1 2.1 Life sciences 3.7 3.5 6.33.7 3.4 Mathematical sciences 4.5 3.3 1.10.6 0.8 Physical sciences 3.3 2.3 2.72.0 1.6 Social sciences NA 8.9 6.24.7 5.2 Other or undecided 29.1 20.5 25.525.6 26.3 a Data for 1977, which is first year data available. NOTE: NA means not available. SOURCE: Cooperative Institutional Research Program (CIRP, 1987b, p. 901. 95
A Challenge of Numbers TABLE A2.10 Numbers and attainment rates of master's and doctoral degrees for selected fields, 1971 to 1985 Degrees awarded for specified period Atrairunent rate B.S.M.S.M.S./B.S. (1971tol983)(1973tol985)(2-yearlag) Engineenng659,101219,70033% Life sciences594,78581,22114% Physical sciences289,78372,61425% Mathematical sciences212,46044,76421% Field Degrees awarded for specified period Attainment rate M.S. Ph.D. Ph.D./M.S. (1971tol980) (1976tol985) (5-yea}lag) Engineenng 158,970 27,035 17% Life sciences 65,037 34,947 54% Physical sciences 57,808 32,501 56% Mathematical sciences 41,399 7,439 18% Field Degrees awarded for specified period Attainment rate B.S. Ph.D. Ph.D./B.S. (1971tol978) (1978tol985) (7-yearlag) Engineenng 345,122 21,633 6% Life sciences 374,732 28,158 8% Physical sciences 171,757 25,729 15% Mathematical sciences 154,146 5,760 4% SOURCE: Adapted from National Center for Education Statistics (NCES, 1987a, pp. 190-192). 96
Survey statement Appendix Tables TABLE A3.1 Attitudes of 8th arid 12th grade mathematics students toward mathematics, 1981-1982 school year . . . . . . . . Percent giving a high rating 8th grade 12th grade . _ . . I usually understand what we are talking about in class 75 I really want to do well in mathematics 87 91 I feel good when I solve a mathematics problem by myself 78 91 My parents really want me to do well in mathematics 86 89 It does not scare me to have to take mathematics 71 81 Mathematics is easier for me than for most persons 56 76 If I had a choice, I would learn more mathematics 66 76 Mathematics helps me think logically 64 85 There is usually a rule to follow in mathematics 82 67 Percent of 8th grade students Percent of 12th grade students giving a high rating to: giving a high rating to: ImportanceEaseLikes ImportanceEaseLikes Memorizing843622 Equations947171 Measures835243 Checking907829 Checking797225 Memorizing854618 Equations785344 Calculators809585 Decimals765644 Word problems782629 Estimating 68 68 49 Function graphs 69 64 37 Charts and graphs 67 74 57 Probability 66 34 37 Ratios and proportions 67 45 35 Charts and graphs 62 80 42 Word problems 66 39 28 Complex numbers 62 52 37 Tables 61 49 37 Denvatives 56 37 34 Geometric figures 60 45 38 Limits 55 42 30 Calculators 54 86 75 Sequences and series 53 43 33 Inequalities 50 35 25 Proofs 52 20 18 Sets 47 57 38 Vectors 48 41 30 Drawing figures 46 55 42 Integrals 46 26 25 All subtopics 66 55 40 All subtopics 66 50 37 SOURCE: As reported in National Science Board (NSB, 1987, pp. 193-194). 97
~ of Numbers TABLE A3.2 Average SAT scores in mathematics, 1970 to 1987 1970 1975 1980 1985 1987 All students 488 472 466 475 476 Male 509 495 491 499 500 Female 465 449 443 452 453 AmencanIndian - 420 a 426 428 432 Asian-Amencan 518 a 509 518 521 Black 354 a 360 376 377 Mexican-American 410 a 413 426 424 Puerto Rican - 401 a 394 409 400 White _ 493a 482 490 489 a Average scores for 1976. SOURCE: College Entrance Examination Board (CEEB, 1987, pp. iii, v). TABLE A33 Average ACT scores in mathematics, 1970 to 1988 - 1970 1975 1980 1985 1986 1987 1988 All students 20.0 17.6 17.4 17.2 17.3 17.2 17.2 Male 21.1 19.3 18.9 18.6 18.8 18.6 18.4 Female 18.8 16.2 16.2 16.0 16.0 16.1 16.1 SOURCES: American College Testing Program (ACT, 1989) and Bureau of the Census (BOC, 1988a, p. 137). 98
Appendix Tables . TABLE A3e4 Average NAEP scores in mathematics, 1973 to 1986 1973 1978 1982 1986 Nine-year-olds Total 219.1 218.6 219.0 221.7 Male 217.7 217.4 217.1 221.7 Female 220.4 219.9 220.8 221.7 White 224.9 224.1 224.0 226.9 Black 190.0 192.4 194.9 201.6 Hispanic 202.1 202.9 204.0 205.4 Thirteen-year-olds Total 266.0 264.1 268.6 269.0 Male 265.1 263.6 269.2 270.0 Female 266.9 264.7 268.0 268.0 White 273.7 271.6 274.4 273.6 Black 227.7 229.6 240.4 249.2 Hispanic 238.8 238.0 252.4 254.3 Seventeen-year-olds Total 304.4 300.4 298.5 302.0 Male 308.5 303.8 301.5 304.7 Female 300.6 297.1 295.6 299.4 White 310.1 305.9 303.7 307.5 Black 269.8 268.4 271.8 278.6 Hispanic 277.2 276.3 276.7 283.1 NOTE: The NAEP has summarized trends in average mathematics proficiency on a common scale ranging from 0 to 500. This is a composite of the student performance on the five content areas. It takes the form of the score on a hypothetical 00-item test composed of questions reflecting the proportional weighting of the subareas. Those average scores are given above, including the ones extrapolated for 1973. SOURCE: Educational Testing Service (ETS, 1988) 99
A Challenge of Numbers TABLE A3.5 Enrollments in selected mathematics courses in colleges and universities (in thousands) Subject 196519701975198019851965-1985 (% increase) Arithmetic end generalmath 29 23 32 63 45 55 High school algebra and geometry 60 78 109 179 202 237 College algebra, tngonometry 262 301 259 345 352 34 Total math enrollment 1,005 1,215 1,252 1,525 1,619 61 SOURCE: Conference Board of the Mathematical Sciences (CBMS, 1987, p. 21~. TABLE A3.6 Enrollments in undergraduate mathematical sciences departments by type of institution (in thousands) 1960 1965 a 1970 1975 ~ 1980 1985 Two-year colleges Remedial NA 109 191 346 441 482 Pre-calculus NA 92 124 149 175 182 Calculus NA 46 69 76 91 103 Other NA 91 171 266 218 133 Computer/data processing NA 5 13 10 95 98 Statistics NA 5 16 27 28 36 Total NA 348 584 874 1,048 1,034 Four-year colleges and universities Remedial 96 89 101 141 242 251 Pre-calculus 349 468 538 555 602 593 Calculus 180 315 414 450 590 637 Advanced 92 133 162 106 91 138 Total 717 1,005 1,215 1,252 1,525 1,619 Total undergraduate enrollments in mathematical sciences departments Remedial NA 198 292 487 683 733 Pre-calculusb NA 661 862 1,007 1,118 1,042 Calculus NA 361 483 526 681 740 Advanced NA 133 162 106 91 138 Total NA 1,353 1,799 2,126 2,573 2,653 Undergraduate enrollments in statistics Elementary 4 11 57 99 104 144 Advanced 16 32 35 42 43 64 Total 20 43 92 141 147 208 a 1966 data used for two-year colleges, since 1965 data are not available. b Includes other, computer/data processing, and statistics at two-year colleges. NA Data not reported or not applicable. SOURCE: Conference Board of the Mathematical Sciences (CBMS, 1987, pp. 18, 31, 1201. 100
Appendix Tables . TABLE A3.7 Mean number of semester credits completed by bachelor's degree recipients, by major and by course area: 1972 to 1976 and 1980 to 1984 Selected Course areas college Total Bus. Comp. Educ. Eng. Math. Bio. Phys. Social Other majors sci. sci. sci. sci. 1972 to 1976a Mean, all majors 124.0 7.8 1.0 9.7 2.3 7.4 7.6 9.0 30.3 48.8 Business and management 124.4 41.2 2.3 0.5 0.4 10.2 2.5 4.8 30.4 32.0 Computer science 133.3 6.6 33.5 0.4 5.3 22.4 1.9 7.8 20.6 34.8 Education 126.4 0.9 0.3 40.2 NA 5.0 5.5 4.3 23.9 46.4 Engineering 134.8 1.6 2.0 0.1 50.0 18.2 1.3 20.5 14.0 27.1 English 117.8 0.5 0.1 7.8 0.1 3.2 3.4 3.4 24.2 75.2 Fine arts 124.9 0.3 0.1 6.6 NA 1.3 2.5 2.1 13.6 98.4 Life sciences 122.2 0.4 0.8 1.7 NA 8.4 35.6 26.2 17.8 31.3 Physical sciences 122.7 0.8 1.4 0.9 1.9 16.2 9.6 49.5 13.1 29.2 Psychology 119.1 2.0 0.5 5.9 0.3 5.5 6.2 5.9 56.0 36.9 Social sciences 120.6 3.4 0.4 3.3 0.4 5.3 3.2 4.3 60.3 40.1 1980 to 1984b Mean, all majors 123.5 12.8 3.3 6.2 4.6 8.4 5.3 8.1 27.5 47.2 Business and management 122.8 41.2 4.5 0.6 1.1 8.9 2.2 3.9 27.5 32.7 Computer science 129.3 11.8 27.9 0.3 4.7 21.3 1.8 8.5 19.0 33.9 Education 127.4 0.7 0.3 45.5 0.1 4.4 4.4 3.8 20.8 47.3 Engineering 132.3 1.0 2.3 0.8 52.5 16.2 1.1 20.2 12.3 25.9 English 114.8 1.7 1.5 6.9 NA 2.2 2.1 4.7 21.4 74.4 Fine arts 120.5 1.7 0.6 5.1 NA 1.7 2.7 1.5 14.1 93.1 Life sciences 121.9 0.7 I.5 1.9 0.2 10.1 33.5 22.6 18.1 33.3 Physical sciences 124.3 0.2 4.9 0.1 2.0 14.1 12.9 48.7 11.6 30.0 Psychology 120.7 3.0 2.7 2.1 NA 6.5 5.8 4.2 55.2 41.2 Social sciences 119.2 6.0 1.4 1.0 0.5 5.4 4.4 5.1 52.0 43.3 a Sample survey based on 1972 high school seniors who completed bachelor's degrees by 1976. b Sample survey based on 1980 high school seniors who completed bachelor's degrees by 1984. NA Data not reported or not applicable. NOTE: Because of rounding, details may not add to totals. SOURCES: National Center for Education Statistics (NCES, 1985; 1987a, p. 2201. 101
A Challenge of Numbers TABLE A4.1 Number of mathematical sciences degrees awarded, 1950 to 1986 l Bachelor's degrees Total Men Women Master's degrees Total Men Women Doctoral degrees Total Men Women 1950 6,382 4,942 1,440 974 784 190160 151 9 1952 4,696 3,374 1,322 802 663 139206 195 1 1 1954 4,O78 2,717 1,361 706 579 127227 213 14 1956 4,646 3,128 1,518 898 719 179235 225 10 1 958 6,905 4,943 1 ,962 1 ,234 994 240247 232 1 5 1 960 1 1 ,399 8,293 3, 1 06 1,757 1 ,422 335303 285 1 8 1962 14,570 1O,331 4,239 2,680 2,179 501396 372 24 1964 18,624 12,656 5,968 3,597 2,91 1 686596 567 29 1966 19,977 13,326 6,65 1 4,769 3,769 1,000782 725 57 1968 23,513 14,782 8,731 5,527 4,199 1,328947 895 52 1970 27,442 17,177 10,265 5,636 3,966 1,670-1,236 1,140 96 1971 24,801 15,369 9,432 5,191 3,673 1,5181,199 1,106 93 1972 23,713 14,454 9,259 5,198 3,655 1,5431,128 1,039 89 1973 23,O67 13,796 9,271 5,O28 3,525 1,5031,068 966 102 1974 21,635 12,791 8,844 4,834 3,337 1,4971,031 931 100 1975 18,181 10,586 7,595 1976 15,984 9,475 6,509 1977 14,196 8,303 5,893 1978 12,569 7,398 5,171 1979 11,806 6,899 4,907 4,327 3,857 3,695 3,373 3,036 2,905 2,547 2,396 2,228 1,985 1.422 1,310 1,299 1,145 1,051 975 865 110 856 762 94 823 714 109 805 681 124 730 608 122 1980 11,378 6.562 4,816 2,860 1,828 1,032 724 624 100 1981 11,078 6,342 4,736 2,567 1,692 875 728 614 114 1982 11,599 6,593 5,006 2,727 1,821 906 681 587 94 1983 12,453 6,995 5,458 2,837 1,858 979 698 582 116 1984 13,211 7,366 5,845 2,741 1,791 950 695 569 126 1985 15,146 8,164 6,982 2,882 1,874 1,008 699 590 109 1986 16,306 8,725 7,581 3,159 2,047 1,112 742 618 124 - SOURCE: National Center for Education Statistics (>JCES, 1988a, p. 237~. 102
Appendix Tables TABLE A4.2 Comparison of actual versus expected number of mathematical sciences bachelor's degrees First year full-time Anticipated major Expected number Actual numberRatio, enrollments mathematics/statsistics of degrees of degreesactual/ (in thousands) (percent) (4 years later) (4 years later)expected 1967 1,335 4.2 56,070 24,8010.44 1968 1,471 4.0 58,840 23,7130.40 1969 1,525 3.5 53,375 23,0670.43 1970 1,587 3.3 52,371 21,6350.41 1971 1,606 2.7 43,362 18,1 ~ 10.42 1972 1,574 2.2 34,628 15,9840.46 1973 1,607 1.7 27,319 14,1960.52 1974 1,673 1.4 23,422 12,5690.54 1975 1,763 1.1 19,393 11,8060.61 1976 1,663 1.0 16,630 11,3780.68 1977 1,681 0.8 13,448 11,0780.82 1978 1,651 0.9 14,859 11,5990.78 1979 1,706 0.6 10,236 12;4531.22 1980 1,749 0.6 10,494 13,2111.26 1981 1,738 0.6 10,428 15,1461.45 1982 1,688 0.6 10,128 16,3061.61 1983 1,678 0.8 13,424 - 1984 1,613 0.8 12,904 1985 1,602 0.8 12,816 - SOURCES: Adapted from Cooperative Institutional Research Program (CIRP, 1987b, p. 90) and National Center for Education Statistics (NCES, 1987a, pp. 130, 207~. TABLE A4.3 Anticipated college major and probable career occupation (percent distribution) 1966 1970 1975 1980 1985 1987 Anticipated college major Education 1 0.6 11.6 9.9 7.7 7. 1 8.9 Mathematics 4.5 3.3 1.1 0.6 0.8 0.6 Probable career occupation Elementary education Secondary education 7.6 14.1 8.0 11.3 3.0 3.8 3.8 3.5 2.2 2.4 5.0 3.1 SOURCES: Cooperative Institutional Research Program (CIRP, 1987a; 1987b, pp. 90, 94). 103
A Challenge of Numbers TABLE A4.4 Number of education and mathematics education degrees for selected years - 197119811983198419851986 Bachelor's degrees Education, total176,614108,30997,99192,38288,16187,221 Mathematics education2,2177986727751,0271,259 Percentage of total education degrees1.30.70.70.81.21.4 Master's degrees Education, total88,95298,93884,85377,18776,13776,353 Mathematics education 372439416426444 Percentage of total education degrees 0.40.50.50.60.6 Doctoral degrees Education, total6,4037,9007,5517,4737,1517,110 Mathematics education 3024322932 Percentage of total education degrees 0.40.30.40.40.5 . . SOURCES: National Center for Education Statistics (NCES, 1984; 1987a) and unpublished data. 104
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Appendix Tables TABLE A4.7 Source of major support for full-time mathe- matical sciences graduate students in doctorate-granting institutions, 1986 Source of major supportMenWomenTotal Total, all sources8,5993,16811,767 Federal808184992 Institutional5,9112,2718,182 Other outside support484103587 Self support1,3966102,006 Percent distribution Total? all sources100100100 Federal Institutional Other outside support6 Self support 9 6 8 69 72 70 3 16 19 17 SOURCE: National Science Foundation (NSF, 1988a, p. 49). TABLE A4e8 Tvpe of major support for full-time graduate students in doctorate-granting institutions for selected fields, 1986 Total, MathematicalPhysical Total,science end Type of major supportsciencessciencesErlg~neenngsciencesengineering Total11,76727,07459,925200,055259,980 Fellowships8711,8994,92918,51623,445 Traineeships13647785213,04813,900 Research assistantships1,01210,84720,40745,15365,560 Teaching assistantships6,89711,32910,97349,95460~927 Other types of support2,8512,52222,76473,38496,148 Total (percent distribution)100100100100100 Fellowships77899 Traineeshipsl2175 Research assistantships940342325 Teaching assistantships5942182523 Other types of support249383737 SOURCE: National Science Foundation (NSF, 1988a, p. 50). 107
A Challenge of Numbers TABLE A4.9 1986 enrollments in graduate mathematical sciences programs ~ . ~ _. . u.6i. citizens Other/ White Black Hispanic Asian Unknown To~U.S. Foreign Total Doctorate granting 8,198 301 248 571 85710,1755,50315,678 Full-time 5,587 191 168 416 443 6,805 4,962 11,767 Part-time 2,611 110 80 155 414 3,370 541 3,911 Master's granting 1,277 147 57 156 659 2,296 405 2,701 Full-time 259 51 14 53 81 458 231 689 Part-time 1,018 96 43 103 578 1,838 174 2,012 Total 9,475 448 305 727 1,516 12,471 5,908 18,379 Full-time 5,846 242 182 469 524 7,263 5,193 12,456 Part-time 3,629 206 123 258 992 5,208 715 5,923 Percent distribution, U.S. Doctorate granting 88.0 3.2 2.7 6.1 100 Full-time 87.8 3.0 2.6 6.5 100 Part-time 88.3 3.7 2.7 5.2 100 Master's granting 78.0 9.0 3.5 9.5 100 Full-time 68.7 13.5 3.7 14.1 100 Part-time 80.8 7.6 3.4 8.2 100 Total 86.5 4.1 2.8 6.6 100 Full-time 86.7 3.6 2.7 7.0 100 Part-time 86.1 4.9 2.9 6.1 100 - SOURCE: National Science Foundation (NSF, 1988a, pp. 51, 53, 57, 59, 135, 175~. 108
Appendix Tables TABLE A4.10 Number of mathematical sciences master's degrees awarded by subfield 1981 1983 1984 1985 1986 Percent diet., 1986 Total Mathematics, general Actuarial sciences Applied mathematics Pure mathematics Statistics Mathematics, other 2,567 1,890 NA 179 NA 467 31 2,837 1,924 27 259 21 459 147 2,741 1,846 18 253 25 471 128 2,882 1,892 23 284 27 490 166 3,159 2,057 28 367 23 478 206 100 65 12 1 15 6 SOURCE: National Center for Education Statistics (NCES, 1984; 1987a, p. 187) and unpublished data. TABLE A4.11 Attainment rates of master's and doctoral mathematics degrees by sex, 1970 to 1986 Percentage of master's/bachelor's degrees (2-year lag) Percentage of doctoral/master's degrees (5-year lag) Percentage of doctoral/bachelor's degrees (7-year lag) Yeara 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 15-year average 10-year average Total Men 19 21 20 23 20 23 19 21 18 20 20 21 21 23 22 24 26 24 23 24 21 23 24 24 25 25 28 29 27 27 28 24 Women Total 15 16 16 15 ~5 17 18 18 20 18 19 21 19 18 19 17 Men Women 16 16 15 17 19 Total Men Women 18 21 23 24 29 24 26 29 32 37 20 7 19 18 8 8 21 7 24 9 10 12 11 14 4 4 4 5 s 6 4 6 s 6 6 7 8 9 1 2 2 2 3 19 24 9 4 5 1.5 a Refers to the year in which higher-level degrees were awarded; the lower-level degrees were awarded 2, 5, or 7 years earlier. SOURCE: Adapted from Table A4.1. 109
A Challenge of Numbers . . TABLE A4.12 Characteristics of new doctorates in mathematical sciences, 1974 to 1986 1974 1976 1978 1980 1982 1984 1986 Total number 1,211 1,003 838 744 720 698 730 Percent men 90.5 88.7 85.7 87.2 86.7 83.5 83.4 Percent women 9.5 11.3 14.3 12.8 13.3 16.5 16.6 Percent AmencanIndian 0.2 0.0 0.1 0.0 0.1 0.5 0.2 Asian 13.3 12.0 13.4 15.6 16.4 21.5 24.0 Black 1.9 0.8 1.9 2.0 1.8 1.2 1.8 Hispanic 0.7 1.5 3.2 2.3 3.6 5.8 6.0 White 84.0 85.7 81.3 80.1 78.1 71.1 68.0 U.S. citizens 72.3 74.6 73.9 69.9 63.6 58.3 50.3 PerTnanent visas 5.9 5.5 5.6 8.3 5.7 5.2 4.9 Temporary visas 18.5 18.2 18.5 18.7 26,7 33.2 37.3 SOURCE: National Research Council (NRC, 1987, p.66~. TABLE A4.13 Primary sources of support of doctorate recipients in the physical sciences, 1977 and 1986 Personal 1977 1986 University 1977 1986 Federal 1977 1986 Other 1977 1986 Total, all fields 36.1 42.1 41.9 44.8 16.1 7.2 5.8 6.0 Physics and astronomy 9.8 7.5 75.8 84.0 10.2 4.4 4.2 4.1 Chemistry 9.8 10.3 74.6 81.4 11.7 5.2 3.9 3.1 Earth/atmospheric/manne sciences 17.3 18.9 56.4 70.9 19.4 6.1 7.0 4.1 Mathematics 17.7 14.0 64.1 74.2 11.8 5.3 6.4 6.5 Computer science 45.0 25.6 55.0 58.2 0.0 4.1 0.0 12.1 NOTE: The primary support of mathematics doctoral students is by their universities, and principally as graduate teaching assistants. The above chart from the 1986 ARC Survey Report shows the changes over 10 years and comparisons with the other physical sciences. (Numbers are percent of total with given source of support.) SOURCE: National Research Council (NRC, 1987, p.28). 110
Appendix Tables TABLE A4.14 Number of doctorate recipients in broadly interpreted mathematical sciences, 1976 to 1986, awarded by U.S. universities 1976 1977 1978 1979 1980 1981 19821983198419851986 Total, mathematics 696 664 605 563 569 535 533540496540576 Applied mathematics 105 113 108 111 102 118 108125108116136 Algebra 116 88 87 88 78 56 6055655546 Analysis and functional analysis 141 153 118 111 91 105 9876718381 Geometry 23 26 22 25 35 29 3244273538 Logic 34 17 24 21 24 18 1721253023 Number theory 26 32 18 17 28 24 2819271820 Probability (AMS Survey) 42 33 33 27 30 22 2522193926 Topology 72 70 56 61 57 55 4544423534 Mathematics, general 94 88 92 80 83 77 84867885125 Mathematics, other 43 44 47 22 41 31 3648344447 Total, computing 267 255 252 313 293 319 303381364381486 Computing theory and practices 148 101 55 25 13 16 1112131510 Computer and information science 31 121 210 218 232 220 286 295 310 399 Computer eng~neenng 119 123 76 78 62 71 72 83 56 56 77 Mathematical statisticsab 123 126 135 138 121 141 140 129 162 111 115 Total, statistics 234 242 249 227 218 246 266 250 284 247 238 Eliometrics and biostatistics 46 52 45 44 42 48 59 45 49 40 30 Social sciences statistics 35 35 46 23 33 40 43 47 39 60 65 Econometrics 30 29 23 22 22 17 24 21 27 27 25 Business statistics - 8 7 9 3 Total,operations research 118 118 127 110 104 116 94 102 123 121 129 Mathematics operations research 36 42 43 43 41 36 36 20 27 22 29 Enaineenng operations research 82 76 84 67 63 80 58 44 50 54 54 Business operations research - 38 46 45 46 Total,mathematics education 96 98 57 85 74 62 50 62 64 65 72 a Reported under "Mathematics" in National Research Council (1987). b These numbers are the NRC counts minus the American Mathematical Society counts for probability given above. It is noted that the AMS counts of doctorates in statistics are considerably higher than these NRC counts. The ARC counts in probability and statistics are approximately the AMS counts for statistics alone. SOURCES: National Research Council (NRC, 1987, pp. 60-63) and American Mathematical Society (AMS, 1976 to 1988). 111
A Challenge of Numbers TABLE A4.15 Total number and distribution of new mathematical sciences doctorates by subfield and sex, 1960 to 1982 Number of new doctorates Male (%) Female (%) Total Distnbution by sex (percent) MaleFemaleTotal Mathematical sciences, total 18,646 (91) 1,863 (9) 20,509 100100100 Algebra Analysis/functional analysisa Geometry Logic Number theory Probab~lity/math statisticsb Topology Topological algebras Computing theory Computer sciences Operations researche Applied mathematics Mathematics, general Mathematics, other 2,135 (86) 3,538 (93) 559 (91) 489 (91) 468 (88) 2,532 (89) 1,668 (92) 116 (98) 1,534 (94) 922 (89) 326 (91) 2,203 (94) 1,358 (89) 798 (90) 338 (14) 273 (7) 54(9) 46 (9) 63 (12) 310 (11) 136 (8) 2 (2) 106 (6) 111 (11) 33 (9) 136 (6) 162 (11) 93 (10) 2,473 3,811 613 535 531 2,842 1,804 118 1,640 1,033 359 2,339 1,520 891 a This subfield was specified as "Analysis" through 1967; "Functional Analysis" was added in 1968. b "Math Statistics" was deleted from the taxonomy in 1969 but was restored in 1972. c This subfield was deleted in 1967. ~ This subfield was introduced in 1977. e This subfield was introduced in 1973. SOURCE: National Science Foundation (NSF, 1983, pp. 18-19, 22-23, 26-27~. 112 11 18 12 19 15 19 15 3 ~ 3 ~2 3 3 14 9 1 3 3 17 14 7 9 8 6 8 5 6 5 2 2 2 12 7 11 7 9 4 5 4
Appendix Tables TABLE A4.16 Number of doctorates awarded in selected fields, 1970 to 1985 Percent change, Field 1970 1975 1980l9gS 1970 to 1985 - Biological sciences 3,361 3,497 3,8033,771 12 Chemistry 2,238 1,776 1,5381,837 -18 Mathematical sciences 1,225 1,147 744688 -44 Physics end astronomy 1,655 1,300 9831,080 -35 Engineenng 4,434 3,002 2,4793,167 -8 SOURCE: National Science Foundation (NSF, 1988c, pp. 1-5~. TABLE A5.1 Number of employed scientists and engineers Percent increase, 1976 1980 1986 1976 to 1986 All science/engineenng fields2,331,200 2,860,400 4,626,500 98 Physical scientists188,900 215,200 288,400 53 Mathematical scientists48,600 64,300 131,000 170 Computer specialists119,000 207,800 562,600 373 Engineers1,371,700 1,675,900 2,440,100 78 Othera603,100 697,200 1,204,400 100 a Includes environmental, life, and social scientists and psychologists. SOURCE: National Science Board (NSB, 1987, pp. 230-231). TABLE A5.2 Selected employment characteristics of scientists and engineers, 1986 Mathematical Scientists Total Mathematics Statistics Scientists Engineers Total S/E Labor force participation rate 94.6 94.5 95.2 95.3 93.8 Unemployment rate 1.3 1.1 2.4 1.9 1.2 S/E employment rate 79.3 77.7 87.8 76.7 91.9 Underemployment rates 3.3 3.4 3.0 4.3 1.0 Underutilization rater 4.6 4.5 5.3 6.1 2.2 a Those who are involuntarily working either in non-S/E jobs or part-time as a percent of total employment. b Percent of total who are either unemployed or underemployed. SOURCE: National Science Board (NSB, 1987, p. 225). 113
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Appendix Tables TABLE A5.4 Field of employment for recent (1984/85) mathematics degree recipients, 1986 (percent distribution) Field Bachelor's Master's . . . Mathematics and statistics 42 Computer science 40 Erlgineenng Economics Psychology 14 2 61 15 17 2 SOURCE: Consolidated from National Science Foundation (USE, 1987a). TABLE A5.5 Primary work activities for recent (1984/85) mathematics degree recipients, 1986 (percent distribution) Primary work activities Bachelor's Master's Research and development 16 17 Management and administration 3 Teaching Production and inspection 6 Reportin:,/statistical/ computing activities Other 24 34 15 15 34 6 15 11 SOURCE: Consolidated from National Science Foundation (NSF, 1987a). TABLE A5.6 Median annual salaries by field arid type of TABLE A5.7 Demand and supply of new leachers in elemen degree of recent (1984/85) graduates, 1986 tary and secondary schools, 1970 to 1992 (in thousands) S/E field of degree Bachelor's Master's . . Englneenng Computer science Total, science and engineenn:, Mathematics and statistics Physical science Total, science Environmental science Social science Life science Psychology $30,000 $28,000 $25~000 $24,100 $21,400 $21,000 $20,000 $20,000 $17,000 S17~000 $36,000 $36,600 S32,500 $31,500 530,000 $29,000 $27,000 $24,600 $22,000 $23,100 SOURCE: National Science Foundation (NSF, 1987a). Demanda Elementary Secondary Schools Schools Total Supply,b Total Balance 1970 1975 1980 1985 1986 1987 1988 1989 1990 1991 1992 115 101 69 95 114 114 126 126 131 129 129 93 ~5 58 62 56 46 38 47 52 66 80 208 186 127 157 170 160 164 173 183 195 209 76 52 17 - 1 1 -26 -18 139 139 139 138 137 -25 -34 -44 -57 -72 aDemand: Data for 1970 to 1982 are actual new hires. Data for 1983 to 1992 are the intermediate value of three alternate projections. bSupplv: Data for 1984 to 1992 are the intermediate values of three alternate projections. SOURCE: U.S. Department of Education as reported in National Science Board (NSB, 1987, p. 186). 115
A Challenge of Numbers TABLE A5.8 Numbers of faculty members by types of institutions for selected years - 1970 1975 198() 109s University Mathematics Full-time faculty6,2355,4055,6055,333 Part-time faculty6156991,0381,044 Statistics Full-time faculty700732610662 Part-time faculty9368132103 Public four-year college Mathematics Full-time faculty6,0686,1606,2647,754 Part-time faculty8761,3392,3193,337 Private four-year college Mathematics Full-time faculty3,3523,5794,1534,762 Part-time faculty9451,3592,0992,706 Total, university and four-year college Full-time faculty16.35515,87616,63218,511 Part-time faculty2,5293,4655,5887,190 Two-year college Mathematics Full-time faculty4,8795,9445,6236,277 Part-time faculty2,2133,4116,6617,433 Total, all institutions Full-time faculty21,23421,82022,25524,788 Part-time faculty4.7426,87612,24914,623 SOURCE: Consolidated from Conference Board of the Mathematical Sciences (CBMS, 1987, pp. 41, 133). 116
Appendix Tables TABLE A5.9 Mathematical sciences and computer science enrollments per full-time equivalent (FTE) of faculty 197019751980 1985 Universities798596 105 Public colleges7887105 100 Private colleges717390 73 Two-year colleges104123134 118 SOURCE: Conference Board of the Mathematical Sciences Surveys (CBMS, 1987, p. 44~. TABLE A5.10 Age distribution of full-time mathematical sciences faculty in 1985 in four-year colleges and universities Percent Retirement years Estimated number of Estimated number of doctorate Age of faculty atage67 retirementsakper year) retirementsb (per year) >60 7 1986-1992 186 138 55-59 8 1993-1997 297 220 50-54 14 1998-2002 520 385 45-49 17 2003-2007 632 468 40-44 19 2008-2012 706 522 35-39 15 2013-2017 - 30-34 14 2018-2022 - <30 6 2023- _ a Based on a total of 18?600 (see Table A5.8~. bAssumes that 74 percent of retirees have doctorate. SOURCE: Adapted from Conference Board of the Mathematical Sciences (CBMS, 1987, p. 57). 117
A Challen:', e of Numbers TABLE A5.11 Age distribution of full-time mathematical sciences faculty in 1985 in two-year colleges Percent Retirement years Estimated number of Age of faculty at age 67 retirementsa (per year) >60 4 1986-1992 36 55-59 7 1993-1997 88 50-54 13 1998-2002 163 45-49 18 2003-2007 226 40-44 24 2008-2012 301 35-39 18 2013-2017 30-34 11 2018-2022 <30 5 2023 a Based on a total of 6,300 (see Table AS.8~. SOURCE: Adapted from Conference Board of the Mathematical Sciences (CBMS, 1987, p. 137~. TABLE A5.12 Employment status of new doctorates awarded by U.S. and Canadian mathematical sciences departments 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 Total 972 952 889 858 904 860 792 789 769 801 845 Doctoral departments 296 280 267 239 235 239 220 192 206 225 202 Master's/Bachelor's depts. 172 160 155 154 157 138 159 175 138 128 141 Other academic units 110 a 84 a 74 68 91 85 60 81 67 72 85 Research institutes - 12 28 26 35 15 22 24 16 28 Government 62 44 34 37 28 24 24 23 14 27 19 Business and industry 136 166 168 167 169 146 105 111 108 109 104 Outside United States 159 182 145 137 172 151 171 153 187 185 201 Other 37 36 34 28 26 42 38 32 25 39 65 These include research institutes. SOURCE: American Mathematical Society (AMS, 1977 to 1987). 118
Appendix Tables - TABLE A5.13 Mathematical sciences faculty salaries by type of institution (in 1985 constant dollars) 1970 1975 1980 1985 Group I Group II Group III Assistant professor $29,400 $25,600 $25,900 $27,700 Associate professor $36,800 $33,200 $32,800 $34,700 Full professor $57,000 $52,300 549,500 $48,800 Assistant professor $30,900 $27,100 $25,400 $27,200 Associate professor $38,300 $33,600 $32,100 $33,200 Full professor $54,700 $48,400 $44,200 $44,400 Assistant professor $30,900 $26,600 $24,500 $26,600 Associate professor $38,500 $33,400 $31,400 $31,900 Full professor $51,500 $44,000 $41,900 S42,400 Group IV (statistics) Assistant professor $30,400 $27,000 $26,400 $28,700 Associate professor $36,800 $35,100 $34,700 $34,600 Full professor $49,400 $50,700 $48,100 $50,000 Group M Group B Assistant professor $29,900 $26,500 $25,100 $26,100 Associate professor $35,500 $32,700 $30,600 $31,600 Full professor $44,600 $39,700 $38,200 $39,200 Assistant professor $28,100 $23,600 $22,400 $24,800 Associate professor $35,000 $28,600 $27,600 $29,400 Full professor 540,800 $35,800 $33,600 S34,700 NOTE: The American Mathematical Society classifies the mathematical sciences institutions by their ranking in the 1982 assessment and by degree programs offered. Of the doctorate-granting institutions, Group I consists of the 39 top ranked, Group II the next 43, and Group III the remaining 73. Group IV consists of the 69 departments (or programs) of statistics that offer doctoral degrees, Group M consists of 273 master's-granting institutions, and Group B consists of 950 bachelor's-granting institutions. (See Box 3.2 for more detail.) SOURCE: American Mathematical Society (AMS, 1986). 119
