A Challenge of Numbers People in the Mathematical Sciences (1990) / Chapter Skim
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From page 87... ...
Appendix Tables
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From page 89... ...
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)
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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)
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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)
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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.
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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.
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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.
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NOTE: NA means not available. SOURCE: Cooperative Institutional Research Program (CIRP, 1987b, p.
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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.
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From page 97... ...
. 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.
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. 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)
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Those average scores are given above, including the ones extrapolated for 1973. SOURCE: Educational Testing Service (ETS, 1988)
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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.
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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.
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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.
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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.
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. SOURCES: National Center for Education Statistics (NCES, 1984; 1987a)
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~ ' ~ _ , ~_ _ 106 Do a, _ - oo ~ oo oo o o ~ ~o ~ U ~o C~ ~o ~ ~o ~ ~o _ _ = ~_ - ~ d- - oo ~ ~ _ - .
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. 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)
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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.
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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)
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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.
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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)
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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)
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From page 113... ...
. 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.
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~ O O O C O O O C O O ~ ~~D ~ =, _ O O O O O O oo _ r~ ~ ~ ~ O ~ _ C O O O O O oc oc X ~ \0 O O O O .
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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)
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From page 116... ...
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.
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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)
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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.
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From page 119... ...
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.
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