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1 Introduction In recent years a number of studies have expressed concern about current and prospective shortages in the nation's available supply of pre- college science and mathematics teachers. Some studies claim that severe shortages currently Ernst; other studies find that, while current shortages are not severe, future shortages are likely; and still others find that, although there is no quantitative shortage, there is a gap between the quality of current teachers of science and mathematics and the quality needed to ensure effective instruction. Most, but not all, of the studies have focused on teachers at the secondary level, for which more information by discipline is available. Although the panel is not charged with determining whether a shortage of precollege science and mathematics teachers either exists now or is likely in the future, the mandate to specie types of data needed to understand that issue requires the panel to examine the demographic and employment patterns affecting supply and demand in particular labor market areas. Thus we are concerned about the forces associated with changes in precollege enrollments in science and mathematics courses, including both changes in the demographic configuration of children in the relevant age ranges and changes in state or district requirements specifying the number of science and mathematics credits needed for high school graduation. We also look at the principal determinants of the total supply of teachers, including the demographics of the teacher corps. A major concern is to understand the appropriate characteristics of teacher qualifications and teaching quality, since supply and demand for teachers come into equilibrium through adjustments in quality. Quality cannot be monitored unless the characteristics associated with it can be specified. Thus, our basic concern is to identify the types of data needed 14 -

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INTRODUCTION 15 to understand quality in order to evaluate how it is changing. In the course of the effort we examine some of the available data that have led many to conclude that the quality of science and mathematics training in the United States is not satisfactory. Specifically, we examine data on student performance from studies carried out under the aegis of the International Association for the Evaluation of Educational Achievement and from the National Assessment of Educational Progress~ata that have raised questions about the quality of teaching in that country. Finally, we have considered the relationship between teacher~training and preparation, teacher instructional activities in the classroom, and stu- dent outcomes. Although it is certainly true that unsatisfactory outcomes in terms of student understanding of important concepts and topics in science and mathematics can be due in part to deficiencies in the academic back- ground or pedagogical training of science and mathematics teachers, it does not follow that poor outcomes can be attributed squarely to deficiencies in these areas. Many factors could contribute to poor student understanding. Unsat- isfactory outcomes could be due to the structure of the science or mathe- matics curricula; they could be due to insufficient emphasis on science and mathematics topics in the allocation of time during the school day; they could be due to the manner in which schools and classrooms are organized with respect to opportunities for interchange among teachers, the amount of time available to teachers for planning and preparation, the availability of inservice training opportunities, and so on. Poor outcomes could also be due to the fact that children receive less time and attention from par- ents in home environments than was true in the past, or due to changes in parents' expectations, beliefs, and behaviors related to learning science and mathematics that influence children's developmental outcomes. It is thus the panel's conviction that to understand the supply and demand for precollege science and mathematics teachers, and to understand the quality characteristics of teacher supply, we must go beyond a narrow mandate to examine the adequacy of the available data from which teacher supply and demand models could be constructed. However, the panel's mandate is not so broad that it requires us to prescribe policies whose effects might be to change either supply, demand, or quality. THE MEANING OF SHORTAGE In everyday parlance, when most people speak of a shortage of precol- lege science and mathematics teachers, they are likely to mean that they are dissatisfied with the quality of people teaching science and mathematics, rather than to mean that there are insufficient numbers of teachers to staff science and mathematics courses. In technical terms, it is hardly possible to

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16 PRECOLLEGE SCIENCE AND MATHEh[4TICS TEACHERS have either a shortage or a surplus of particular kinds of precollege teachers, or indeed of teachers generally, since school systems typically have neither classes without teachers to teach them (excess demand/short supply) nor employed teachers without classes to teach (excess supply/short demand). Thus a quantitative shortage fewer teachers teaching science and mathe- matics than there are science and mathematics classes to be taught will not be observed except in those cases (which may be frequent but not well documented by data) in which a course or class is cancelled because a teacher cannot be found with the appropriate credentials/qualifications. What actually takes place is an equilibrating process that is expressed in the short run by quality adjustments in the criteria for hiring next year's teachers. In the long run, salary is the equilibrating factor for supply and demand. While the quantity of people teaching science and mathematics will almost always be equal to the quantity of science and mathematics teaching offered, tendencies toward either surplus or shortage will surface as adjustments in quality. In planning for the next school year, if there are not enough applicants with science and mathematics credentials to teach science and mathematics classes, a district will either undertake aggressive recruiting or a teacher will be drafted from inside (or hired from outside) and provided with emergency certification to teach the course. If there is a potential surplus, qualified science and mathematics teachers will end up either teaching some other subject or not teaching at all. In the fanner case, if school systems do not recruit aggressively, they may have to dip down far into the pool of teachers less experienced or qualified in science and mathematics to fill the available positions. If the premise is true that quality is positively associated with experience and training, their average quality will tend to decline.1 In the latter case, depending on institutional rules or practices, only the best qualified (or the most senior) science and mathematics teachers will get the available science and mathematics classes, and other teachers will have to go elsewhere or teach something else. If the available classes go to the best qualified teachers, on average the quality will tend to increase. However, if the available classes go to me most senior teacher, which is the policy in most systems, the erect on quality is difficult to assess. 1 Some economists define commodities By listing their attributes, of which quality is one. This way of thinking about commodities, however, is a very special usage. In fact, in the situation described the district did not get first-rate mathematics and science teachers, and therefore experienced a shortage of such teachers. But it is rare that this would be revealed through questionnaire responses, since questions ask only whether the district found people who were certified in the relevant field to fill a vacancy. The dimensions in which equilibrium takes place, including quality, are relatively unobservable. The concept of shortage does not suggest a strategy for measuring shortage. Although we could refer to a "shortage of teachers of desired quality" throughout the report, for simplicity we have chosen simply to refer to a "shortage."

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INTRODUCTION 17 While these observations are straightforward and almost self-evident, they do account for the fact that some studies of the supply-demand bal- ance in precollege science and mathematics have concluded that there is a considerable shortage of teachers, while others have concluded that no shortage Busts at all. The former type of studies have defined shortage as the absence of sufficiently qualified teachers to staff the relevant classrooms and have judged that many classrooms are staffed by inadequately qualified teachers (as examples, see National Education Association, 1988; Weiss, 1987; Akin, 1986~. The latter type of studies, asking whether schools have been unable to hire teachers to teach science and mathematics courses, have found that school systems are able to hire such teachers (as ex- amples, see National Center for Education Statistics, 1985a; Feistritzer, 1988b). Thus the importance of the general proposition that, although quantitative gaps between supply and demand are not generally identified, quality adjustments ensure that supply and demand are equal is that un- derstanding both the quantitative and the qualitative dimensions of teacher supply and demand is essential to understanding the supply and demand for teachers. 1b do otherwise is to miss a significant part of any potential problem. FACI ORS AFFECTING DEMAND A data system able to track changes in the demand for precollege science and mathematics teachers must as a minimum be able to assess demographic factors, which include changes in student enrollment, in the ratio of male to female students in science and mathematics courses, and in the proportions of minority students in science and mathematics courses, as well as changes in policy variables, such as graduation requirements mandated by the state, entrance requirements of colleges and universities, and changes in acceptable pupil-teacher ratios. Demand also depends on the number of vacancies resulting from the creation of new positions and from teacher attrition. All these factors affect the demand for classes in science and mathematics. As noted in the panel's interim report, the most accurate data used in current supply and demand models are probably the demographic data for projecting demand. For the precollege student population, projections of the total will be extremely reliable for all K-12 grades for at least five years into the future, since students starting kindergarten will already have been born about five years ago. Thus, even birth rate projections have only a small influence on demand projections, unless the projections go out further than five years. And total enrollments in grades 7-12 (the point at which specialized science and mathematics courses typically begin to be

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18 PRECOLLEGE SCIENCE AND AL4THE~4TICS TEACHERS 50 40 en 30 o . _ ._ 20 10 o _ Grades K-12 Grades K-8 Grades 9-12 Projected 1972 1977 1982 1987 1992 1997 Year FIGURE 1.1 Enrollment in grades K-12 of public schools, with projections: Fall 1972 to 1997. Source: National Center for Education Statistics (1988g:14~. Offered) are known at least 12 years in advance since the children have already been born. The demographic base for projecting demand is not quite so solid as the above paragraph suggests, even at a national level. Both in-migration and out-migration occur among school-age children in the United States as a whole. But at the more relevant regional, state, or local level, there is obviously some migration of school-age children that must be taken into account statistically. Thus, even very good national models need to be substantially augmented with accurate subnational migration data to produce useful demand projections at the relevant school district level. School enrollment itself is projected to rise somewhat during the next half-decade. For example, from 1978 to 1987, enrollment in public secondary schools (grades 9-12) fell from about 14 million students to about 12 million; but from 1988 to 1995 secondary enrollment is projected to increase to about 13 million. Over the same period, elementary school enrollment is projected to increase from a little over 28 million students to about 31 million (see Figure 1.1~. A number of forces currently under way suggest the need to track more refined characteristics of the demographics and to add to them data relating to mandated state requirements.For example, a potential exists for greater

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INTRODUCTION 19 demand for science and mathematics training for female children in the K-12 age range, simply because of persistent changes in attitudes toward appropriate sex roles for men and women and the associated changes in the career aspirations of young women. It is already evident that more young women are planning to enter science and engineering fields than was true 20 years ago. In fact, the number of undergraduate women majoring in science and engineering has risen dramatically since the mid-1970s. For example, the physical sciences showed an increase from 30,900 women in 1976 to 38,100 in 1984, then decreased to 36,500 in 1986 (National Center for Education Statistics, 1988b:167~. Similarly, in 1976, 28,800 women majored in engineering. This number increased to 74,800 by 1984 and declined slightly to 71,200 in 1986. Though trends have attenuated for the present, it is important to monitor the enrollment of women as science and mathematics majors at the postsecondary level. Currently, 28 percent of all physical sciences majors are female; because of the potential for further increase, female enrollment in science and mathematics should be monitored. Similarly, it seems likely that the movement toward equal opportunity will generate an increased demand for science and mathematics training on the part of minority youngsters. The evidence here, some of which is shown in Tables 1.1 and 1.2, is not easy to interpret. For students who were high school seniors in 1980, the 1980 data indicate that blacks actually took more semesters of mathematics than whites, and only Chicanos and Native Americans (especially the latter) are markedly lower than average. For science, black seniors were well below whites in number of semester hours in 1972, but in 1980 black seniors had nearly caught up with whites, while all the other minority groups except Asian-American and Puerto Rican students were below whites. These data are for seniors, and high school dropout rates are much higher for minority students than for whites. Moreover, the data noted above do not standardize for the level of science and mathematics courses. Minorities other than Asian-Americans are historically more likely to be found in remedial mathematics than in the more challenging mathematics courses and in general science courses than in physics and chemistry (Office of Technology Assessment, 1988:45~. A recent report by the Educational Testing Service (ETS) drawn from a research paper on course-taking patterns in the 1980s by Goertz (1989), compares students' course-taking patterns in 1982 and 1987, using data from the High School and Beyond study by the National Center for Education Statistics (NCES) (1982 graduates) and the High School Transcript Study by Westat, Inc. (1987 graduates). This report (Educational Testing Service, 1989:20) finds significant gains in course-taking by black and Hispanic students between 1982 and 1987. Some of the gains were impressive, others modest. For example, 29 percent of black graduates in 1982 had

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22 PRECOl.~.EGE SCIENCE AND M'4THEMi4 TICS TEACHERS taken geometry; by 1987, 44 percent had taken geometry, compared with 64 percent of whites. In calculus, gains were slight for blacks, from 1 percent in 1982 to 2 percent in 1987, compared with 6 percent for whites. The percentage of Hispanic graduates who had taken algebra I rose from 55 to 77 percent between 1982 and 1987, and by 1987 they were nearly even with whites (at 78 percent). Minority gains in science course-taking were similarly notable. However, blacks and Hispanics still lag behind whites and Asians in their enrollments in the higher-level mathematics and science courses. In addition, school districts have changed their graduation require- ments to include more science and mathematics training or credits required for graduation from high school. In 1985, NCES surveyed a sample of 565 districts and asked for math and science requirements for high school grad- uation in 1982, 1985, and the expected requirements in 1988. Between 1981-82 and 1984-85, for example, nationally the average number of years of course work required for graduation from public high schools increased from 1.6 to 1.9 for mathematics, and from 1.5 to 1.8 for science (see Able 1.3~. The National Commission on Excellence in Education (1983) recommended 3.0 years for both science and mathematics. In response to changes in the graduation requirements of districts, states, and even in the entrance requirements of colleges and universities, increased enrollments in high school science and mathematics courses have been documented (Educational Testing Service, 1989~. The years between 1982 and 1987 have seen strong gains in science and mathematics course- taking, except in physics and calculus, for which gains were modest or nonexistent. To the extent that new state course requirements exceed those already in place in the districts, the result can be a stronger demand for science and mathematics training, given the same student population. However, when local school district requirements already exceed new state requirements, which they often do, new demand for teachers may not result. Therefore it is important to monitor changes in course requirements at both the state and district level to assess the effects on the demand for teachers. In addition to changes in course requirements, a number of other policy-related factors influence the demand for new science and mathe- matics teachers. Changes in pupil-teacher ratio can result in changes in demand. And a number of policy-related factors at the school, district, or state level can influence the ratio-changes in budgets, class size policies, or course requirements, for example. These changes should be monitored in any data system that tracks changes in demand for science and mathematics teachers. Another major component of demand models is the pattern of attri- tion for science and mathematics teachers-due both to retirement and

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24 PRECOLLEGE SCIENCE AND MATHEMATICS TEACHERS especially to leaving earlier in one's teaching career. It is essential for an effective data system to be able to monitor attrition rates by subject as well. Finally, research Is called for to identify other behavioral factors that influence the demand for teachers: for example, patterns of dropping out of high school, parents' choice of private over public schools, and the timing of that choice. FACTORS AFFECTING SUPPLY Teacher supply can be examined in terms of retention rates for the present stock of teachers, the flow of newly certified teachers from colleges and universities, and the flow of returning teachers who have been absent from the labor market, laid off during the past decade due to declining en- rollments, or have come from other occupations or alternative certification routes. As with demand, these factors include both demographic charac- teristics (the age distribution of current teachers) and policy variables. In our interim report, we noted that most of the existing supply models focus on the flow of new graduates of education degree programs, despite the fact that most of the new hires during recent years have come from other sources. The existing data, most commonly from the states and from periodic surveys at a national level, should be examined in greater detail to estimate future declines in the supply of available teachers, both for precollege science and mathematics and for precollege teachers generally. 1b what extent will there be a substantial decline in the overall teacher retention rate, arising from the fact that large numbers of teachers will be entering the age and experience combination at which teachers have often retired in the past? One of the best-established relationships in the teacher supply literature is the U-shaped relationship between age/experience and teacher retention: in the early years, attrition rates are high either because many entering teachers find that the occupation is not what they had thought, have adverse experiences that result in withdrawal from the teacher corps, or find more attractive employment opportunities. At the other end of the spectrum, where the older and more experienced teachers are located, attrition rates rise as retirement approaches. Thble 1.4 illustrates this pattern for the state of New York. Both early and late attrition estimates will be important factors affecting the supply of science and mathematics teachers. The current composition of the teacher corps is concentrated in an age/experience cohort in which there will be many retirements starting in the late 1990s. For example, the 1985-86 Survey of Science and Mathe- matics Education conducted for the National Science Foundation (Weiss, 1987) found some indication that the science and mathematics teaching

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26 PRECOLLEGE SCIENCE AND AL4THEAL4 TICS TEACHERS force is aging but did not predict an unusually large wave of retirees in the near future. Monitoring relevant statistics related to factors associated with choosing to stay or choosing to retire is crucially important for un- derstanding future teacher supply, as is monitoring the effects of incentive programs designed to encourage continuation and discourage retirement (or vice versa). One sign of an impending shortage of new teachers has been a decline in the number of education degrees awarded. For example, the number of bachelor's degrees in education fell from 108,000 in 1980-81 to 87,000 in 1985-86 (National Center for Education Statistics, 1986:134; 1988b:196~. The number of master's degrees in education also declined, from 99,000 in l9SO-81 to 76,000 in 1985-86. Among those enrolled as teacher candidates in secondary education programs, the proportion majoring in mathematics education held steady at about 25 percent between 1985 and 1988. How- ever, the proportion of students majoring in science education has declined from 21 percent of all enrolled in 1986 to 16 percent in 1988 (AACTE, 1989~. The shortage issue is complicated, since new teacher supply can be fairly quickly adjusted as opportunities are perceived to arise. Conventional teacher training institutions are not the only source of new supply. In recent years new supply has come mainly from a broader source of teachers that includes (1) graduates of other institutions who enter the teacher supply with temporary credentials and later certification; (2) the so-called reserve pool: past graduates of teacher training or other institutions who did not enter teaching when they graduated but could be attracted to teaching careers with the right incentives; and (3) former teachers who return to teaching from another occupation or activity. In short, monitoring the basic demographics of teacher age/experience, as well as the potential supply of new graduates and returnees from other occupations, will be crucially important to understanding the probable evolution of teacher supply over the next decade. QUALITY ISSUES IN SUPPLY AND DEMAND Much of the impetus for concern over the supply, demand, and quality of precollege science and mathematics teachers arises from the continuing evidence that U.S. students do not appear to know as much science and mathematics as their age peers in other countries. The most widely cited such data come from the International Educational Assessment program (IEA) and from the National Assessment of Educational Progress (NAEP). The IEA administered science tests to fifth-grade and ninth-grade students and to twelfth-grade students who were studying biology, chemistry, or physics in the terminal grade in school in 17 countries in 1983 (1986 for the United States). The results of these tests tend to show U.S. students'

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INTRODUCTION 27 science performance declining from a middle position in fifth grade to quite low by twelfth grade (IEA, 1988~. In science, U.S. 10-year-olds were eighth among 15 countries ranked? U.S. 14-year-olds were fourteenth among 17 countries ranked, and of 13 countries ranked for twelfth-grade students who were taking science courses, U.S. biology students were thirteenth, chemistry students eleventh, and physics students ninth (Table 1.5~. In general, although U.S. students did relatively poorly overall, they did worse at the higher grades and better at the lower grades. This may be explained in part by cross-nationa1 differences in science curricula. The science curricula in the other countries participating in this study generally require more years of science than are required in the United States. The U.S. results for grade 12 generally correspond to student achievement near the end of their second year of the subject; students in the other countries generally would have completed three years of the science by grade 12 (Jacobson and Doran, 1988~. U.S. twelfth-grade college-preparatory mathematics students fared poorly against their peers in both developed and less-developed countries of the world in performance on mathematics achievement tests (McKnight et al., 1987~. For example, for high school seniors taking mathematics, U.S. students' scores ranked in the lowest quarter of the countries in three cate- gories (number systems, algebra, and geometry) and were below the median in the other three (sets and relations, elementary functions/calculus, and probability/statistics). Eighth-grade students in the United States ranked somewhat higher, scoring at the median in arithmetic, algebra, and statis- tics; at the 25th percentile in geometry; and below it in measurement. The mathematics data are shown in Bibles 1.6 and 1.7. In the IEA mathematics study, the method used by the United States, England, and Wales to obtain a sufficiently large number of cooperating school districts, namely requesting participation of twice as many school districts as were needed with the expectation of a 50 percent cooperation rate, might be expected to produce a bias in achievement scores. However, no evidence of bias has been found (Garden, 1987:133~. Neither of the international comparisons is without its problems and ambiguities. For example, it is not clear whether the student populations tested in the IEA science study are fully comparable across countries. Furthermore, it is sometimes argued that the tests themselves are biased, since the U.S. curriculum in science and mathematics may be different from the typical curriculum used elsewhere, and the tests may be heavily weighted with items that are not covered in U.S. curricula. Data from the IEA study on test validity and test relevance, however, do not support that proposition (IEA, 1988:88-95~. A similar picture is presented by the NAEP data on achievement scores, which indicate that large fractions of U.S. students do not appear

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28 PRECOLLEGE SCIENCE AND MATHEMATICS TEACHERS TABLE 1.5 Rank Order of Countries for Science Achievement at Three Levele of Schooling 10-Year 14-Year Grade 12/13 -Old~, -Olds, Science Students a Non Grade Grade Science 4/5 8/9 Biol- Chem- Phys- Students ogy istry ice Australia 9 10 9 6 8 4 Canada 6 4 11 12 11 8 (English speaking) England 12 11 2 2 2 2 Finland 3 5 7 13 12 Hong Kong 13 16 5 1 1 Hungary 5 1 3 5 3 1 Italy 7 11 12 10 13 7 Japan 1 2 10 4 4 3 Korea 1 7 Netherlands - 3 Norway 10 9 6 8 6 5 Philippines 15 17 Poland 11 7 4 7 7 Singapore 13 14 1 3 5 6 Sweden 4 ~8 9 10 Thailand - 14 U.S.A. 8 14 13 11 9 - Total Number of Countries 15 17 13 13 13 8 a Students taking biology, chemistry, or physics in the terminal grade in school. Source: International Association for the Evaluation of Educational Achievement (1988:3~.

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INTRODUCTION 29 TABLE 1.6 Mathematics Achievement Comparisons: Twelfth Grade United States and International, 1981-82 (Percentage of Iteme Correct) United States Pre International (15 Countries) calcu- Calcu- 25th 75th lus lus Percen- Percen Topic Classes Classes Total tile Median tile Sets & relations 54 64 56 51 61 72 Number systems 38 48 40 40 47 SO Algebra 40 57 43 47 57 66 Geometry 30 38 31 33 42 49 Elementary functions/ calculus 25 49 29 28 46 55 Probability/ statistics 39 48 40 38 46 64 - Source: McKnight et al. (1987:23) to meet minimal standards of literacy in science and mathematics. The NAEP Science Report Card of September 1988 indicated that, despite gains over the past four years, particularly among minorities, a majority of high school students "are poorly equipped for informed citizenship and productive performance in the workplace" (National Assessment of Educational Progress, 1988b:5~. A problem with both NAEP and the IEA tests is the limited extent to which they assess higher-order skills. Although some test materials administered by NAEP and IEA involve hands-on exercises, much more research and development activity is needed to construct free-response materials and techniques that measure skills not measured with multiple choice tests. Current improvements in mathematics and science curricula are focused on learning of "conceptual knowledge, process skills, and the higher-order thinking that scientists, mathematicians, and educators

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30 PRECOLLEGE SCIENCE AND MATHEMATICS TEACHERS TABLE 1.7 Mathematics Achievement Comparisons: Eighth Grade, United States and International, 1981-82 (Percentage of Items Correct) United States (Percentage 25th Correct) Percentile Median Percentile Topic International (20 Countries) -75th Arithmetic 51 45 51 57 Algebra 43 39 43 50 Geometry 38 38 43 45 Statistics 57 52 57 60 Measurement 42 47 51 58 Source: McKnight et al. (1987:21~. consider most important" (Murnane and Raizen, 1988:63~. It is not clear what the relative standing of U.S. students would be on a test that assessed higher-order thinking skills more fully. Despite all the caveats that have been and can be made with regard to these comparisons, the evidence is that U.S. high school students cannot be judged to perform well in science or mathematics by any reasonable standard, or at least not as well as society seems to expect. Evidence from TEA that young people who concentrate heavily in science and mathematics do not perform especially well implies even worse outcomes for the great majority of American youth who take very little science and mathematics in high school. From the perspective of employers, for example, what matters at least as much as the quality of instruction for high school students who are potential scientists and engineers is the quality of technical or quantitative training for the great majority of high school students who will not go on to these types of careers but will enter the work force after graduation. Concern over the ability of young people to function effectively in today's technical environment, given the inadequacy and often the total absence of science and mathematics training with any degree of rigor, looms as a major societal concern and is the subject of numerous recent reports.

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INTRODUCTION 31 Both low test scores and the generally low level of scientific literacy underpin the concern with the quality of science and mathematics training, and with the prospective shortage of qualified science and mathematics teachers. Poor outcomes have thus spurred a deep concern with the quality of teaching and the qualifications of teachers of science and mathematics. Since it is through adjustments in quality that the supply and demand for precollege science and mathematics teachers reach equilibrium in the short run e.g., the next school year an examination of possible statistics to measure quality is of central concern to the panel. At least two different sets of factors are relevant to an assessment of teaching quality. One set relates to the teaching environment and includes school, district, and state policies and practices that enhance or impede one's ability to secure the right teaching assignment and to teach effectively. Such factors include time spent on science and mathematics, teaching burden, textbook use, district decisions about recruiting and hiring teachers, and inse~vice education policies. Another set of factors relates to the background and qualifications of the individual teacher. These include type of certification, relevant courses taken in the past and currently, and measures of cognitive ability. The need for better data on these kinds of factors, both for monitoring supply and demand and for modeling purposes, is discussed in Chapter 5. It should be kept in mind that even if all the comparison data were valid and indicated that U.S. students have low absolute and relative achievement in science and mathematics, it would not necessarily follow that the problem lies solely or even mainly with the training of U.S. teachers of precollege science and mathematics. Educational outcomes are a complex function of student and family inputs, teaching inputs, educational curricula, school and community environment factors, and student behaviors, including student such as doing homework, attitudes toward science and mathematics, and scientific habits such as objectivity, skepticism, and replication of results (Murnane and Raizen, 1988~. Poor outcomes can clearly be due in part to the inadequate training of teachers, but they can also be due to factors that have little or nothing to do with the training and ability of the teacher corps. For example, there has been a continuing dispute among mathematics teachers about curricular issues, which are seen by some as having a strong influence on the level of performance of U.S. students in standardized tests of mathematics skills. It Is alleged that mathematics skills in U.S. schools are typically taught in a layered or "spiral" curriculum, whereby students are taught a number of concepts in grade t, and are then taught slightly augmented but basically similar concepts in grades t+l, t+2, .... It is argued that students are thus introduced to relatively little new material each year through grade 8; that most of what is done constitutes review

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32 PRECOLLEGE SCIENCE AND MATHE3L4 TICS TEACHERS of materials previously taught, and that as a result students become bored with the constant repetition and never really master many of the key ideas involved in the development of mathematical skills. It is also judged by people who hold this view that part of the problem is that mathematics textbook producers try to widen the appeal of their product to as many school systems as possible; they end up including small segments on a varieW of topics and intensive treatment of few, if any, of these topics. Since the basic text is the primary resource used by most precollege mathematics teachers (Weiss, 1987:31, 39), and since the text usually favors breadth and facts over depth (Office of Technology Assessment, 1988:30-34), the result is that a significant fraction of students master few if any of the topics. A different line of argument, which could in principle be resolved more easily and might make a substantial difference to outcomes, is that U.S. students have inadequate skills in science and mathematics simply because teachers, especially elementary school teachers, do not spend much classroom time on science and mathematics topics. Research indicates a great deal more time is devoted to reading than to mathematics (Cawelti and Adkisson, 1985; Weiss, 1987~. Observations of actual classroom time spent on mathematics also have found very large differences between students in Minneapolis, Minnesota, and those in Taipei, Taiwan, or Sendai, Japan (Stevenson et al., 1986~: U.S. students spend far less time on mathematics than do Asian students. To the extent that the performance of U.S. students on science and mathematics tests and the level of their skill in these areas is simply due to the emphasis on language arts found in U.S. classrooms and/or to the smaller amount of time spent either in school or in school-related activities at home, both the interpretation of the problem and the solution are relatively simple provided school systems can be encouraged or induced to change the structure of their curricula. But if that is the basic problem, then the issue again is not one of inadequacy of preparation or academic training on the part of teachers of science and mathematics in the United States, but simply one of relative emphasis within the curriculum. In that case, the question should be raised as to why fewer hours are spent on science and mathematics in American classrooms. Of course, it is possible that one reason U.S. students spend less time on science and mathematics is that many U.S. elementary school teachers are much less comfortable in teaching science and mathematics than in teaching language arts, and that part of the reason for the curricular emphasis is a preference on the part of teachers and/or administrators derived in turn from their own training. It appears unlikely that specialist teachers of mathematics in the early grades would be motivated to shorten class time spent on mathematics, and use of such teachers is more common in Japan, China, and Taiwan than in the United States in the early grades.

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INTRODUCTION 33 There also appear to be differences in the nature of the pedagogical training given to U.S. and Japanese mathematics teachers. The IEA math- ematics study (McKnight et al., 1987) reported that among mathematics teachers at the eighth- and twelfth-grade levels, the U.S. teachers had taken more mathematics courses and fewer mathematics pedagogy courses than their Japanese counterparts (p. 64~. American teachers also have much less nonteaching time scheduled during the day, compared with their Asian counterparts (Stevenson, 1987:32~. And the degree of teacher autonomy is different: U.S. teachers are often on their own after the first year, while in Asian classrooms younger teachers are typically under the tutelage of a senior teacher for a number of years (Lee et al., 1987; Stevenson et al., 1988; Stigler et al., 1987; Stevenson and Bartsch, in press). Home environment is another factor that affects student outcome. There is considerable evidence that learning and training for young children take place in the home as well as in the school, and that the relative importance of training in the home is much greater when children are young. The home environments in which children are being raised in the United States are considerably different now from the way they were several decades ago. The proportion of children raised in single-parent households is much larger now than in the past, and the proportion of mothers who work full- or part-time is much higher now than in past decades. These realities can create problems for children, especially for minority children, many of whom are raised in single-parent households for a substantial portion of their developmental years (Hill et al., 1987~. Although we cannot be certain that the amount of time and attention parents pay to young children's development is necessarily less because there are fewer "parent hours" available in the aggregate, it is certainly plausible to suppose that fewer total parent hours will result in fewer developmental hours spent by parents on children. There is some evidence that working mothers largely trade off leisure time and sleep for work hours, not for time spent with their children (Hill and Stafford, 1985~. In any event, demographic characteristics have a potentially serious influence on the process of skill development in young children, and part of understanding educational outcomes is surely to understand how these home environment factors relate to these outcomes. In addition to the demographic differences in home environments, there also appear to be substantial differences in the practices, beliefs, and expectations of parents in American households compared with those in other countries. Again, the best-documented evidence comes from a comparison of American and Asian households. As a generalization, Asian mothers are less satisfied with the school performance of their children than American mothers (despite the fact that their children are generally doing better), they are more likely to attribute success in school to hard

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34 PRECOLLEGE SCIENCE AND MATHEML4 TICS TEACHERS work rather than to native ability, and they are less likely to be satisfied with the way the schools are performing than their American counterparts (Lee et al., 1987~. The implication of the issues just discussed is not that the solution to poor performance on standardized educational outcome tests, and pre- sumptively in the level of skill development in science and mathematics for American students, are to be found in factors other than either the quantity of precollege science and mathematics teachers or the quality of their training characteristics or classroom methods. Rather, it-is that poor student outcomes are not uniquely correlated with, nor necessarily caused by, inadequate quantity or quality, but could easily be due to factors that are largely unrelated to teacher or teaching quality. It would thus be a mistake, in the panel's view, to jump to the conclusion that poor science and mathematics outcomes on the part of students necessarily reflect in- adequacies in the background, training, or ability of their teachers and to seek the remedy for the problem only by enhancing either the numbers or the quality of precollege science and mathematics teachers. That could turn out to be the case, but many other factors, such as the structure of the curriculum, the practices of both K-12 school systems and teacher training institutions, the amount of time spent on science and mathematics topics in schools, and the influence of home environments on development out- comes, all need to be understood before we can expect either to understand the problem or to devise appropriate remedies. TlIE PANEL'S WORK AND ORGANIZATION OF THE REPORT During the course of its work, the panel broadened its understanding of the flow of teachers through school systems by direct contact with 39 public school districts across the country. These school systems ranged from the largest metropolitan systems to the most isolated small school districts and represented a wide geographic range and a variety of labor market conditions. Six of the 39 districts were the subject of in-depth case studies, con- ducted in 1987 and 1988, of supply and demand issues regarding science and mathematics teachers. Two of the districts were in California and near one another geographically: one was a large urban system whose ability to attract talented science and mathematics teachers was affected by a history of budgetary constraints and teacher-organization or school-district provisions, while the other, a small, wealthy district, was able to exercise greater autonomy in attracting and keeping talented teachers. Two other districts one in California and one in Utah both with large enrollments, were selected for their growing populations and rising enrollments. Hiring

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INTRODUCTION 35 in one of them was severely limited by fiscal constraint as well as strong re- ligious and community standards; the other was growing in both enrollment and economic base. Finally, two contiguous school districts in Maryland that were expected to hire from the same labor market were visited a large urban district coping with school closures, leadership changes, and traumatic layoffs as the student population has moved to the suburbs and a medium-sized, stable, semirural school district nearby. The in-depth case studies furnished invaluable context without which statistics portraying supply and demand would be seriously incomplete. Such context showed the role of the individual personnel administrator and his or her ability to maneuver or use informal networks to attract science and mathematics teachers. It showed the effects of competing labor markets, teacher-organization provisions, budgetary constraints, and other external factors. The six in-depth case studies were supplemented by 27 additional mini case studies, conducted by telephone interviews and follow-up question- naires, in order to test the representativeness of the findings. The mini case studies were conducted over the period June through December 1988. Finally, a conference of the chief personnel administrators of seven large metropolitan school districts, representing over 5 percent of the nation's total public school enrollment, was convened in May 1988.2 Issues of supply, demand, and quality of science and mathematics teachers were discussed, and the districts' statistical information systems were examined for data relevant to supply and demand models. Appendix A provides more information about each of these activities. Discussions in the chapters that follow frequently draw on the experiences of the school district personnel administrators who participated in these studies. In the chapters that follow, we further examine the characteristics of demand for precollege science and mathematics teachers (Chapter 2) and issues relating to supply (Chapters 3 and 4~. Chapter 3 reviews projection and behavioral models and the essential behavioral components of effective supply models. It examines individual incentives to teach and school district actions that influence supply decisions and mesh supply with demand. In Chapter 4, data needed to monitor the supply pool along its various stages in the teaching career are discussed. We then turn to the role of quality adjustments in bringing supply and demand to equilibrium. In Chapter 5 we look at the question of measuring teacher characteristics and teaching quality. Chapter 6 contains the panel's conclusions and recommendations: some of the recommendations deal with specific data needed to better understand demand, supply, or quality 2nle number of districts in the three case study activities add up to 40, with one of the large school districts participating in two of the projects.

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36 PRECOLLEGE SCIENCE AND MATHEAL4TICS TEACHERS factors, and other recommendations deal with the types of research needed to better understand the linkages among demand, supply, teacher quality, and student outcomes and ways to facilitate this research.