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2 Determining Teacher Demand In this chapter we are concerned with the demand for new teachers, specifically teachers new to a particular job. Projections of the demand for new teachers require the projection of a minimum of three data ele- ments: student enrollment, pupil-teacher ratios, and teacher attrition rates. Demand projections for segments of the teacher population, such as sec- ondary school teachers of mathematics and science, require the projection of these data elements for the specific segments. For example, projecting the demand for mathematics teachers requires, at a minimum, projections of enrollment in mathematics classes, the expected size of mathematics classes, and the attrition rate of mathematics teachers. The necessary data for teacher demand projections vary in availability and reliability. Pupil-teacher ratios vary with staffing patterns, class sizes, teaching loads, course requirements, and course-taking patterns in science and mathemat- ics. Meaningful projections of the consequences of course-taking patterns or teacher attrition are typically less available than are projections of future student enrollment. Statewide enrollment projections are more reliable than those for local school districts. In general, the smaller the subset projected, the lower the reliability. STUDENT ENROLLMENT The two main topics discussed in this section describe methods of projecting student enrollment, based on either public-school enrollment data or population data. The main features and limitations of both sources of data are discussed. We then turn to the other key components of estimating demand for teachers pupil-teacher ratios and attrition. 37

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38 PRECOLLEGE SCIENCE AND MATHEMATICS TEACHERS Enrollment Projections Based on Student Enrollment Data Projections Of student enrollment, one of the three elements neces- sary for projecting the demand for new teachers, are the easiest. K-12 enrollment projections are widely available. Most states and many local districts produce enrollment projections, particularly for the public schools, although some states produce them for both public and private schools. These projections typically follow a standard "cohort survival" methodolog I, which uses observed enrollment ratios between grades to move ("survive") classes ("cohorts") forward to the next level. If the state or school system has low or constant levels of migration, then reliable projections by grade are produced. The National Center for Education Statistics (NCES) produces one- year projections by state and nationwide projections for 10 years into the future. Until 1988, NCES projected enrollments were for the public schools only; projections for private schools began in 1989. NCES employs a mixed model in which participation rates for kindergarten, grade 1, and special and ungraded classes are calculated by applying recent public school enrollment data, collected in its annual survey of the states, to age-specific population estimates produced by the Census Bureau. The resultant rates are then applied to projected populations of the appropriate ages (e.g., 5-year-olds for kindergarten, 6-year-olds for first graders) to arrive at levels of future enrollment for those grades and classes. Retention or grade progression rates from the NCES annual survey are used to calculate grades 2 through 12. The NCES method of projecting enrollments is described more fully in Part III of the panel's interim report (National Research Council, 1987c), which discusses the components of the NCES model and those of six states. The sources of data used by NCES are also described in the Guide to Sources portion of the Digest of Education Stai~si~cs (National Center for Education Statistics, l9~b:358-3803. Enrollment-based changes in the demand for public school teachers below the national level are usually better obtained directly from actual enrollment projections for the state or locality in question than from pro- jections of the school-age population. The reason for preferring enrollment projections at the subnational level is the difficulty of projecting internal and foreign migration for subnational populations. Although birth and death data for population projections are quite accurate, migration esti- mates are less certain, especially as they must be allocated by age. Both the uncertainty and the effect of migration are greater for subnational aggre- gations than for the entire country, yet no data are collected for interstate or intrastate movement. Enrollment projections, however, are typically based on annual cen- suses of the school population that are taken for administrative purposes,

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DETERMINING TEACHER DEMAND 39 including the allocation of state support. The bases for enrollment projec- tions are therefore firm, and the grade progression ratios can be updated annually as circumstances change. The changing circumstances include net migration, which is picked up by the grade progression ratios. Geographic Differences in Projected K-12 Enrollment There are great differences among regions of the United States, and the localities within those regions, in prospective public school enrollment change over the next 10 to 20 years. The nationally projected growth, and expected eventual decline, in the 5- to 13-year-old population and the current nationwide decline and subsequent slow growth in the 14- to 17- year-old population are far from evenly distributed among states or within states. A well-known compendium of individual state enrollment projections that shows the dramatically different demographic expectations among states is produced by the Western Interstate Commission for Higher Ed- ucation (WICHE) in cooperation with Teachers Insurance and Annuity Association and the College Board. WICHE produces projections of num- bers of high school graduates using K-12 enrollment data provided by the states and a cohort survival methodology. The authors do not attempt to integrate the individual state projections into a valid national projection by making explicit assumptions about migratory movements among the states, although they do sum the projections into regional and a national totals. However, recent migratory movements are embedded in the observed pro- gression ratios for each state, which are used to move the enrollments forward into the future. The WICHE projections illustrate the potential for sharply divergent demographic futures in the different regions of the nation and within states between 1986-91 and 2003-4. In WICHE's 1988 set of projections (WICHE, 1988) the number of high school graduates nationally has formed a "roller coaster" pattern since the late 1970s, a pattern that will continue through the next decade. The general roller coaster pattern reflects past birth patterns in the United States, but it differs from region to region and from state to state. The regional differences, the document's foreword explains, are due to "the mobility of the population, varying economic conditions, and growth in minority populations." The number of high school graduates is projected to decline for the North Central and Northeast states, while the West, South, and South Central regions are projected to have little decline in the mid-199Os and then will experience substantial growth Cables 2.1 and 2.2~.

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42 PRECOLLEGE SCIENCE AND MATHEMATICS TEACHERS TABLE 2.2 Projected Proportion of United States High School Graduates, by Region, 1986-2004 l South/ Total South North North- United West Central Central east States 1985-86 0.18 0.30 0.27 0.25 1.00 1986-87 0.18 0.30 0.27 0.24 1.00 1987-88 0.19 0.30 0.27 0.24 1.00 1988-89 0.19 0.31 0.27 0.23 1.00 1989-90 0.19 O.31 0.27 0.23 1.00 1990-91 0.19 0.32 0.27 0.22 1.00 1991-92 0.20 0.32 0.26 0.22 1.00 1992-93 0.20 0.32 0.27 0.22 1.00 1993-94 0.21 0.32 0.26 0.22 1.00 1994-95 0.21 0.32 0.26 0.21 1.00 1995-96 0.21 0.32 0.26 0.21 1.00 1996-97 0.22 0.32 0.26 0.21 1.00 1997-98 0.22 0.31 0.26 0.21 1.00 1998-99 0.23 0.31 0.25 0.21 1.00 1999-2000 0.23 0.32 0.25 0.21 1.00 2000-01 0.23 0.32 0.24 0.21 1.00 2001-02 0.24 0.32 0.24 0.21 1.00 2002-03 0.24 0.31 0.23 0.21 1.00 2003-04 0.24 0.31 0.23 0.21 1.00 Source: Western Interstate Commission for Higher Education (1988:133. Local-Area Projections The striking differences in enrollment-based demand projections among the states are mirrored within states by differences among localities. Since teacher labor markets have important local components (as the panel's case studies suggest), it would be useful to be able to produce enrollment projections for local areas. One barrier to local enrollment projections is the reliability of small-population projections that are needed to estimate enrollment in kindergarten and the first grade. Fertility patterns can vary locally, and births and deaths may be reported for an area different from

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DETERMINING TEACHER DEMAND 43 school district boundaries. More important, the smaller the population, the greater the potential influence of hard-to-predict migration on future size and distribution. The difficulty of making reliable small-area projections is undoubtedly one reason that few school districts appear to make projections beyond the next year, if that far. However, standard enrollment projection techniques would be adequate to give general magnitudes of change in all but the smallest and least stable districts for 5 to 10 years into the future, longer for the secondary level. State departments of education could make a considerable contribution by encouraging school districts to project their enrollment for 5 to 10 years in the future, providing technical guidance in developing projections and coordinating their efforts. Properly done, such projections could be combined in order to approximate likely levels of enrollment-generated demand within teacher labor markets. Of course, es- timation of attrition-generated demand and subject-specific demand would require additional projection efforts. Population Projections A Proxy for Enrollment Projections Although the cohort survival method of projecting enrollment is widely used in the education community, population projections reveal some highly interesting trends that could influence the demand for teachers. Using Census Population Projections to Estimate K-12 Enrollment Demand At the national level, projections of the population by age provide a very good proxy for enrollment projections, especially if the interest is in total enrollment demand and not just demand for public school teachers. This is particularly true for the population age 5 to 13, which has close to 100 percent attendance, virtually all of it in grades K through 8. Population projections have the advantage of greater simplicity than enrollment projections, since assumptions about movement from grade to grade or from public to private schools do not have to be made. National projections of the population are updated by the Census Bureau every several years, more often if the underlying assumptions prove incorrect. The biggest disadvantage to using population projections as a substitute for enrollment projections is that population projections take no account of possible changes in dropout rates, an important element of enrollment projections for the secondary level. Using population projections as a proxy for K-12 enrollment, in particular for grade 9-12 enrollment projections, makes the implicit assumption that dropout rates will remain constant.

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44 PRECOLLEGE SCIENCE AND MATHEMATICS TEACHERS Since our present discussion is limited to a general overview of the likely forces of change in the demand for teachers, our remarks on the likely contribution of nationwide enrollment change to teacher demand are based on population projections. The national projections for the 5- to 17-year-old age group should prove moderately accurate through the year 2000, as shown in Table 2.3. Reliability declines toward the end of the l990s, when the projections for the age group begin to depend more on projections of births and less on children already born. However, the fertility assumptions used in the projection have been close to actual fertility so far, and there is little reason to expect large changes in the fertility rates in the next few years. The other factor that could lead to the divergence of the actual numbers from those projected international migration is unlikely to cause major discrepancies at the national level in the period and at the ages shown in the table. The size of the U.S. population relative even to high levels of migration, and the typical concentration of migration in the early adult years, dampens the effect on the school-age population, at least in the short and medium run. Interstate migration is, of course, not relevant to national projections. Recent projections by the Census Bureau show 12 percent growth for the school-age population in the United States between the middle l980s and the end of this century (Table 2.3~. The 5- to 17-year-old age group is projected to grow by more than 5 million. However, as a result of past birth patterns, the increase will not be distributed equally across the age group. Until the end of this century, most of the growth will occur at the younger ages and will affect the elementary grades. The number of children age 5 to 13 is projected to increase by nearly 5 million, or 17 percent, by 1999. After 1999 this age group is projected to decline. By contrast, the number of young people age 14 to 17, the secondary school-age group, is projected to decline 12 percent in the 5 years between 1985 and 1990, a reduction of 1.8 million. Thereafter, the number of secondary school-age children will grow slowly but is not expected to regain the 1985 level until 1997. More rapid growth is projected for the early years of the next century. The projected demographic changes in the school-age population will have opposing potential effects on the nationwide demand for teachers, increasing it at the elementary level and reducing it at the secondary level. There could even be a reduction in the absolute number of secondary school teachers employed over the next few years. However, change in the number of students is only one of the elements in the calculation of demand for teachers. Teacher attrition and pupil-teacher ratios are the other important factors in demand, although pupil-teacher ratios are probably as much dependent on enrollment change as they are an independent factor. The

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DETERMINING TEA ClIER DEMAND TABLE 2.3 Projections of the United States School-Age Population to the Year 2000 (in thousande) Age 5-13 Number (000) Age 14-17 - Index (1985 = 1.00) Number (000) Age 5-17 Index (1985 = 1.00) Number (000) Index (1985 = 1.00) 1985 29,654 1.00 14,731 1.00 44,385 1.00 (actual) 1986 29,922 1.01 14,588 0.99 44,510 1.00 1987 30,358 1.02 14,237 0.97 44,595 1.00 1988 30,954 1.04 13,662 0.93 44,616 1.01 1989 31,523 1.06 13,160 0.89 44,683 1.01 1990 32,189 1.09 12,950 0.88 45,139 1.02 1991 32,777 1.11 12,964 0.88 45,741 1.03 1992 33,400 1.13 13,087 0.89 46,487 1.05 1993 33,900 1.14 13,260 0.90 47,160 1.06 1994 34,193 1.15 13,714 0.93 47,907 1.08 1995 34,435 1.16 14,082 0.96 48,517 1.09 1996 34,598 1.17 14,513 0.99 49,111 1.11 1997 34,681 1.17 14,848 1.01 49,529 1.12 1998 34,668 1.17 15,027 1.02 49,695 1.12 1999 34,566 1.17 15,214 1.03 49,780 1.12 2000 34,382 1.16 15,381 1.04 49,763 1.12 Source: Bureau of the Census (1984a:43-74~. 45 demand for teachers of specific disciplines, of course, depends on student choice (or changing graduation requirements) as well. The Changing Demographic Profile of the School-Age Population Education planners and social observers have devoted considerable attention to the changing demographics of the American population and to projections of large continued changes. The demographic changes referred to are usually changes in ethnic composition and family circumstances, especially increased proportions of children in single-parent families and/or

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46 PRECOLLEGE SCIENCE AND MATHEMATICS T=CHE~ especially increased proportions of children In s~ngle-parent families and/or with working mothers. Increased poverty levels among children are often also at issue. The conclusion, sometimes stated explicitly and sometimes left to the reader, is that these changes require urgent social and political attention. These changes in the relative size of elementary and secondary school-age populations, in racial/ethnic composition, in income and pov- erty- are interesting and relevant considerations attendant on the demand for teachers. They do not emerge from enrollment projections, but rather through population projections. We first tale about broad population fac- tors, demographic trends that influence demand. Then we return to the use of enrollment projections in models of teacher supply and demand. . Projecting Changes in Race and Ethnicit~r. Expected change in the eth- nic distribution of school-age children in America is of interest for our discussion only insofar as youngsters of the different categories may be expected to have differential patterns of enrollment in mathematics and science courses or require different strategies of teaching than are used currently. However, the link between ethnic and racial identity and school- related characteristics or needs is not a clear one, particularly over the long run. Unless there is reason to believe that racial and ethnic groups will retain currently observed particular needs over the long run, projecting the racial and ethnic distribution of the school-age population, or of school enrollment, is of little utility for planning curricular or other change for science and mathematics. Very often, the effect of racial and ethnic change, especially the effect of the projected increases in the proportion of the population of Hispanic and Asian origin, is confounded with the effects of migration for example, an increase in the number of students with limited ability to speak English or from families with the low educational levels characteristic of Latin America and much of Southeast Asia. This confusion is bemusing in a country that has seen the children and grandchildren of poor, illiterate immigrants from Southern and Eastern Europe people viewed as forever unassimilable 75 years ago-become thoroughly assimilated Americans. Changes in racial and ethnic distribution per se may be the least reason for expectations of changed enrollment patterns in science and mathematics or for planning changes in curricular and teaching strategies. However, because of the great public interest in ethnic change, we explore the feasibility of racial and ethnic projections and consider the results of recent projections. As noted earlier, standard population projections require a base popu- lation and assumed rates of fertility, mortality, and migration for each age. The decennial census counts the black population with reasonable accuracy,

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DETERMINING TEACHER DEMAND 47 at least for most public policy analysis purposes. Vital statistics are virtually universally collected by race, including birth and death records. Estimating migration by race is more troublesome, but sufficient data exist to develop estimates of base populations by race between censuses and to develop assumptions for projections. It is feasible to project the black population and the white population, although, as with all subcategory projections, such projections will tend to be somewhat less reliable than projections of the total population. Other racial groups are more difficult to estimate because of small numbers and, in the case of Asians, very high- rates of foreign migration. Projections of nonracial ethnic populations are more difficult. On the whole, ethnic identity has been gathered only sporadically in either the census or in vital statistics. Even were a group to arrive all at once, thereby providing a clear base population, and subsequently maintain accurate birth and death records, the accuracy of any long-range projection would be in doubt because of the likelihood of intermarriage and the lack of an agreed- on definition of ethnic identity for the children. The reasons underlying the questionable feasibility of ethnic projections also raise the question of their meaningfulness for social or educational policy planning. Because of the interest in the rapid increase in population from Mexico and Central and South America, numerous projections of the Hispanic pop- ulation have been produced. The Census Bureau first asked respondents to identify themselves as Hispanic or non-Hispanic in the 1980 census. The states with the bunk of the U.S. Hispanic population began to ask Hispanic identity for birth and death certificates around 1980 as well. The data collection efforts since 1980 provide a base population for projecting Hispanics, as well as fertility and mortality rates. Migration estimates can also be made, although with only very modest reliability. Given the im- portance of migration for determining the size of the Hispanic population, this is a decided disadvantage. More problematic for long-range projection purposes is the lack of a socially agreed-on ethnic identity for the children of marriages in which only one partner is identified as Hispanic. Results of Racial and Ethnic Projections. The following discussion ex- amines the results of ethnic and racial estimates and projections for the national population by age. In the last two decades, the proportion of American youngsters from non-Hispanic white backgrounds has decreased nationwide and the proportion from Hispanic and from nonwhite back- grounds has risen. This shift is projected to continue, although, as shown in Table 2.4 and described below, the change will be relatively modest at the national level. In 1970 the census recorded that 13.5 percent of the population age 5 to 17 was black The proportion rose to 14.8 percent in 1980 and by

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DETERMINING TEACHER DEED 49 which are real but less dramatic nationally than might be supposed from the level of popular interest. Providing an adequate education for immigrants and their children is a crucial concern for the schools, especially in areas of heavy influx. It is less clear how important the ethnic shifts, in and of themselves, will be to the schools in the future. Family Structure and Changes in Poverty Rate for Children. Other shifts in the characteristics of school-age children may be of far more importance to science and mathematics enrollment, as well as to the curriculum that teachers should be prepared to teach, than changes in racial and ethnic distribution. These include changes in family structure, specifically the increase in the proportion of children in single-parent families, and the increase in the proportion of children living in poor families. Data as of 1985 showed that 16 percent of all white children, 43 percent of all black children, and 40 percent of children of Spanish origin were reported to be living in poor families (Bureau of the Census, 1986: 22~. The rate of family poverty among all children rose during the 1970s and early 1980s, wiping out gains made in the 1960s. The poverty rate for children was 20.1 percent in 1985, compared with a low of 13.8 percent in 1969 (Bureau of the Census, 1986:22~. During roughly the same period 1970 to 198~Current Population Reports revealed that the percentage of children living in single-parent families doubled (Bureau of the Census, 1984b:4~. In 1984, 22.6 percent of children under 18 were living with one parent, compared with 11.9 percent in 1970 (Bureau of the Census, -1984b:4~. In 1984, over half of all black children lived with only one parent, compared with one-sixth of all white children. Among children of Spanish origin, one of every four lived with one parent. As has been relentlessly demonstrated in innumerable studies, poor children, so many of whom live in one-parent families, are at risk of school failure because of multiple disadvantages, which may include the lack of adequate housing, or any housing at all; frequent moves from school to school; less than sufficient food; inferior medical care; a total lack of dental care; exposure to criminal behavior in deteriorating neighborhoods; and the stress that accompanies the struggle of the adults in the family to survive. Projections of the proportion of children living with one parent can be made with moderate reliability using current data; the proportion liv- ing in poverty requires assumptions about the economy as well and are therefore less easy to construct, or at least less easy to construct with any reliability. The nature of the effect of family poverty and family structure on academic achievement and, more specifically, on the demand for science and mathematics instruction is less well understood. The subject is of great social importance, given the large numbers of children involved, and we

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so PRECOLLEGE SCIENCE AND MATHEAL4TICS TEACHERS hope that the links will be better understood in the future. However, at present, not enough is known to be useful in constructing projections of demand for science and mathematics teachers. 1b summarize, there are interesting and relevant trends that emerge from population projections, which should be included in any statistical description of the changing demand for teachers. However, for purposes of projecting demand for precollege science and mathematics teachers, the education community generally finds enrollment-based projections more useful Research Areas Related to Student Enrollment Methods employed in current teacher demand models, specifically the cohort survival methodology used to project enrollments, are relatively reliable. However, for longer-term projections, particularly at the high school level, and for specific subjects within science and mathematics fields, enrollment projections are less reliable due to the impact of changes in the behavior of students, parents, and school systems. The utility of demand models for addressing-policy issues concerning science and mathematics education over the long term would be greatly enhanced by the development of more dynamic, behaviorally responsive models. We discuss three types of behavioral responses that need to be understood to develop more useful models of teacher demand. They are determinants of course selection by students, determinants of parental and student preferences for public and private schooling, and changes in dropout rates that can be expected in response to social, economic, and educational changes. We discuss them in the order of their priority as we assess the relative importance of each topic to teacher demand projections and the relative gains that could be expected from research. As the panel's interim reported stated (National Research Council, 1987c:49), research on the determinants of course selection by students is critical to the development of useful projections for broad subject cate- gories, including science and mathematics, at the high school (and possibly middle school) level. This is an area about which we know very little. Many factors can influence students' choice of courses, including high school grad- uation requirements, college entrance requirements, government (including federal and state) support for science and mathematics education that mo- tivates schools to encourage enrollment in these subjects, and fashions or tastes on the part of students and their parents and peers for certain subjects. Given that most current models focus on public school demand (al- though the National Center for Education Statistics model develops sep- arate public and private school projections), another important area for

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DETERMINING TEACHER DEMAND 51 research concerns the determinants of parental and student preferences for private and public schooling (National Research Council, 1987c:49~. Nationwide, private elementary and secondary school enrollment was 11.5 percent of the total in 1980, but had grown to 12~5 percent by fall 1987 (NCES, 1988b:9~. Changing preferences for private school enrollment, a topic about which almost nothing is known, can importantly affect public school demand. Particularly in today's educational climate, when private schools are perceived by some parents to offer a more attractive educational environment than public schools, research into the factors that influence the choice of type of school is needed. One type of response that affects demand projections at the high school level is the dropout rate (National Research Council, 1987c:50~. We know a good deal from previous research about why students drop out of school. Work is needed, however, on changes in dropout rates that can be expected in response to a variety of social, economic, and educational changes. For example, the changing ethnic composition of the school-age population in many areas of the country may dramatically affect dropout rates in those areas. Increased high school graduation requirements may increase dropout rates as a side effect of raising educational levels for those who stay in school. PUPIL-TEACHER RATIOS Enrollment change does not translate immediately into a corresponding proportional change in the demand for teachers. As a recent RAND report assessing teacher supply and demand explained, "adjustments are made to pupil-teacher ratios to smooth the effects of rapid enrollment changes, to accommodate established school staffing patterns and budgets, and to take into account existing contractual agreements with teachers, in the case of enrollment declines" (Haggstrom et al., 1988:37~. A small change in pupil-teacher ratio can cause a significant change in the projected demand for teachers. Changes in pupil-teacher ratios can be caused by a number of factors at the school, district, or state level: changes in school budgets; staffing patterns, class sizes, or teaching loads; graduation or program requirements; and course offerings. A layering of school, district, and state policies may add to the complexity of factors that change the ratio and the demand for teachers. Even though these factors are complex, they should be identified and discussed briefly as components of teacher demand (Haggstrom et al, 1988:37-38~.

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52 PRECO' [FETE SCIENCE AND MATHEMATICS TEACHERS Components of Teacher Demand and Related Data Changes in school budgets can cause changes in staffing practices, class sizes, and teaching loads. The district's allocation of its budget among its many needs for staff, materials, and services affects the pupil-teacher ratio generally as well as specific programs or subjects. In one of the panel's case studies of a school system in a western state, the district filed for bankruptcy following a teachers' strike. This led district officials to make conservative estimates of the number of students expected to be enrolled- and hence the number of teachers needed. An overestimated enrollment could cost the district roughly $1,000 per student, it was thought. The tendency to underestimate enrollment and therefore the number of teaching positions has had various effects: raising pupil-teacher ratios, straining teaching loads, or eliminating such support as department chairmanships or resource teachers in disciplines such as mathematics. Implementation of a school finance formula that changes a district's proportion of local discretionary resources can also affect pupil-teacher ratios. The panel's case studies found that, although some school districts in a southeastern state had enough local discretionary funds to hire additional teachers (part time or full time) in computer science or other subjects, other districts in the state had very little. Local discretionary money if the district knew the amount far enough in advance-could be used to sign an early contract with a talented candidate for a mathematics resource teacher or an elementary science teacher, for example. Loss of that opportunity could mean leaving the position unfilled. These examples suggest how the budget can directly affect the ability to hire and can substantially affect the pupil-teacher ratio for certain subjects, and ultimately general pupil-teacher ratios. Changes in stations pattems, class sizes, or teaching loads may be pro- mulgated by a district rule or policy change, by state policy-or by both, as when a district rule extends beyond a state requirement. These can cause an immediate change in pupil-teacher ratios and in the demand for teachers. A district requirement to employ a full-time guidance counselor in every elementary school, without full additional funding to do so, could strain staffing patterns elsewhere in the school and indirectly push up the pupil-teacher ratio. The Schools and Staffing Survey (SASS), recently ini- tiated by NCES and first fielded in 1988, collects information on staffing patterns, class sizes, and teaching loads. The second SASS survey will be conducted in 1991 and at regular intervals thereafter. As a time series of data becomes available, it will be possible to monitor changes in these variables over time. SASS includes a teacher demand and shortage ques- tionnaire for public school districts and private schools, as well as a school administrator questionnaire for public school principals and private school

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DETERMINING TEA ClIER DEMAND 53 heads. It also includes a teacher questionnaire and a teacher-follow-up survey: a one-year follow-up survey of the sample teachers who have left teaching and some who have remained. This ongoing, integrated survey ef- fort has been designed to provide the most comprehensive data on teacher demand and supply available to date. Although we mention the survey frequently as a potential data source, as with all new surveys, the extent to which it will live up to its expectation cannot be known until policy makers and the research community have used the data in a variety of analyses. Course requirements in science and mathematics for graduation- (usually established by the state) clearly affect pupil-teacher ratios. As an example of such policies and responses that can cause changes in pupil-teacher ratios, most states and school districts have increased their graduation requirements since 1980 (NCES, 1988c), often adding additional science and mathematics course requirements. The Center for Policy Research in Education (CPRE) reports that since 1983, 42 states have added course credit requirements in science, mathematics, or both (CPRE, 19894. NCES has found, through its Fast Response Survey System, that the state re- quirements are often exceeded by the requirements of individual districts (personal communication, M. Papageorgiou, NCES, June 7, 1989~. Unless more teachers are assigned or hired to teach science and mathematics, the pupil-teacher ratio for these subject areas clearly increases. Some nationally collected data on high school graduation requirements are available on a regular basis. The Education Commission of the States (ECS) and the Council of Chief State School Officers publish information periodically on state-mandated high school graduation requirements. They track mathematics and science as general categories, however, listing only the number of courses or years of science and mathematics that are required for graduation. SASS includes an item in the teacher demand and shortage question- naire for public school districts on high school graduation requirements, by subject (physical and biological sciences, mathematics/computer science). It asks for changes in these requirements between 1987 and 1988. Future SASS results will reveal changes in requirements over longer time spans. Course offerings and enrollments also influence pupil-teacher ratios. Whereas requirements clearly help determine what courses high school students take and the demand for teachers of those subjects an impor- tant constraint is whether the required courses are actually offered. For example, only a few schools offer a complete range of college-preparatory mathematics and science courses; a physics course might be offered only every other year. And very few students are enrolled in the most advanced courses. Course offerings and enrollments by school, school system, and state emerge as an important variable. Course offering data could serve as an

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54 PRECOLLEGE SCIENCE AND MATHE~4TICS TEACHERS excellent indicator of science and mathematics demand by either students or state requirement. Course offerings and enrollments would contribute toward indicating change in demand over time, by size of school and school system, by other relevant school district characteristics, and by state, especially when state graduation requirements for science and mathematics courses have changed. Course offerings and enrollment would also permit analysis of the degree of school response in terms of teacher assignment. The extent to which teachers need to teach more than a single subject could be noted. Some data related to course offerings and enrollments by school system and school are being gathered nationally. The 1985-86 National Survey of Science and Mathematics Education (Weiss, 1987) provides the most recent comprehensive data on course of- ferings. Data on course offerings are also included in (1) the longitudinal study High School and Beyond, (2) in the National Educational Longitudi- nal Study of 1988 (NELS:88) (for middle schools and junior high schools), and (3) for students age 9, 13, and 17 in the National Assessment of Educational Progress (NAEP) in those years when science or mathematics achievement are assessed. While data from these surveys are disaggregated by specific subject areas, they are conducted infrequently. The data on course offerings and course enrollments are "plagued with inconsistencies," according to a recent report on elementary and secondary science education (Office of Technology Assessment, 1988:42~. Course titles often are not a reliable basis for comparisons among schools, states, or years. Moreover, some advanced courses are offered not by the high school but by the community college, and there are no national data available on this practice. National data do not show how often a physics course is given. Nor do we know how many sections of a given course are taught. These data may change, as well, from year to year in a single school. NELS:88 asks middle schools and junior high schools for data on nu- merous courses and whether they are offered. In a more detailed format, questions on course offerings are included in the SASS teacher question- naire. Given a probability sample of teachers by fields (as is the case for the teacher sample), it should be possible to estimate the prevalence of course offerings and trends in course offerings (including science and mathematics offerings) at national and regional levels. Finally, course offerings could serve as a basis for drawing samples to test for varied working conditions, recruitment patterns, and range of initial assignments possible among school systems. Vacancies matched to schools classified by offerings might indicate conditions of low retention. The SASS questionnaire of local education agencies (LEAs) asks district administrators for the total number of positions that are either vacant, filled

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DETERMINING TEACHER DEMAND 55 by a substitute, or withdrawn for lack of a suitable candidate; this total is disaggregated by subject. Research on Determinants of Pupil-Teacher Ratios A closer analysis of often interrelated factors that influence pupil- teacher ratios is a rich area for further research. As noted earlier, in most models pupil-teacher ratios are estimated in a relatively-arbitra~y way. But numerous factors operate and interact to cause changes in pupil- teacher ratios for science and mathematics subjects and in general. And we suspect that certain types of dynamics in teacher markets (e.g., declining enrollments or increased school budget) may be associated with declining pupil-teacher ratios. Other conditions (e.g., surging enrollments, budget cutbacks) are associated with rising pupil-teacher ratios. Since that ratio is so critical to an assessment of the demand for teachers, research on its determinants is needed. I-he factors that can change pupil-teacher ratios affect adjustments over both short-term and long-term periods, although short-term adjustments differ from longer-term ones (National Research Council, 1987c:50~. For example, a shortage situation may result in a marked increase in pupil- teacher ratios until the school system has had time to implement responses, such as extended recruitment or hiring teacher aides. A common practice in projecting the demand for teachers is to project the increase in enrollment and to divide it by the current pupil-teacher ratio to calculate the number of additional teachers needed to provide for the enrollment increase (National Education Association, 1987f:14~. But an assumption that using the current, general pupil-teacher ratio reflects accurately the number of teachers is too simplistic; enrollment changes affect pupil-teacher ratios in more indirect ways. For example, research suggests that, when enrollments decline, teacher unions may be willing to forgo salary increases to keep current teachers employed (Cavin et al., 1985; noted in Haggstrom et al., 1988:42~. Despite enrollment declines, school boards may decide not to lay off staff in science and mathematics if they have had difficulty hiring them in the past, or if they feel it will be hard to find qualified teachers of certain subjects in the future (Prowda and Grissmer, 1986:12~. Moreover, supply-demand projections for precollege science and math- ematics teachers will be far more meaningful if both enrollments and pupil-teacher ratios are disaggregated by subject area. In Connecticut, for example, secondary enrollments have been declining, but the demand for secondary science and mathematics teachers is steady or may increase be- cause of increased graduation requirements in these subjects, coupled with

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56 PRECO!:LEGE SCIENCE AND MATHEMATICS TEACHERS decisions made (influenced by budgetary considerations) to decrease class sizes (Prowda and Grissmer, 1986:12~. There is reason to believe that pupil-teacher ratio is a dependent as well as an independent factor in the creation of demand. In periods of enrollment growth and teacher or financial shortages, the ratio (or class size) can be increased. When demand slackens, if all "surplus" teachers are not let go, then the ratio drops. A history of these coping responses would be extremely useful in developing better assumptions about pupil-teacher ratios for demand models than the assumption that the current, general pupil-teacher ratio is adequate. The development of demand models for science and mathematics teachers would require similar information on the history of class size responses to teacher shortages or surpluses within these disciplines, a formidable undertaking but necessary for really well-defined models. In sum, we continue to recommend, as we did in our interim report, that research be conducted on the determinants of pupil-teacher ratios, including research on adjustment lags as enrollments change and on how changes in demand for courses contribute to changes in these ratios and in the demand for teachers of science and mathematics. TEACHER ATTRITION RATES The third major element in the construction of teacher demand models is the rate at which teachers leave their jobs. It should be noted that teacher attrition is largely a supply phenomenon, reflecting the decisions of individual teachers. In Chapters 3 and 4 we treat attrition as a supply variable, but here it is natural to think of it as resulting in a demand for new teachers. One part of the leaving rate-retirement is fairly easy to model, if data on the teaching force by age are available and if something is known about the typical ages at which teachers retire. Rates of attrition for other reasons are much less easy to determine. Some of this information exists in school records, but it must be gathered and put into forms usable by those developing models. In aggregating attrition data gathered from school districts it is important to avoid double counting, since what is attrition to one district might be a new hire to another. The Connecticut model of teacher supply and demand revealed how important age is in estimating attrition rates (Prowda and Grissmer, 1986~: "We have noted high early career attrition rates, low mid-career attrition, and high attrition around 60 and 65 years old" (p.l). It is likely that attrition rates change over time, reflecting the numbers of teachers hired in a given year or period (high attrition rates may be observed soon after). A RAND study of teacher attrition found a similar U-shaped pattern of

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DETERMINING TEACHER DEMAND 57 attrition in Illinois, Michigan, New York, and Utah (Grissmer and Kirby, 1987:36-38~. Higher attrition rates were found among newly hired teachers than among other groups, including those eligible to retire. In addition to reflecting age or years of experience, calculating attrition for mathematics and science teachers requires gathering the necessary data by specific field, a considerably more demanding task than obtaining the data for the entire teaching force. There are studies that have gathered discipline-specific data (Murnane and Olsen, 1989a, l990b; Grissmer and Kirby, 1987), but these data have not often, if at all, been used in the development of teacher demand models (or supply models in which they would also be of use). As part of the fifth follow-up of participants in the National Longitudinal Study of 1972, completed in 1986, a Teaching Supplement Questionnaire was sent to sample members who were teach- ers, former teachers, and those who had been trained to teach but had not taught. Information from the survey included detailed professional and personal histories that could be used for analyses of attrition patterns during the early part of their careers, from 1977 to 1986. Heyns (1988) analyzed the data, but results were not reported by field of discipline. The SASS questionnaires were designed to provide national data on teacher at- trition by field. The SASS public school questionnaire asks for the number of teachers, by field, who left in the previous year and their destinations. However, due to low response rates for these items, researchers have to de- pend on the SASS teacher follow-up survey of former teachers (conducted in 1988-89) for estimates of attrition by field. NCES staff is exploring alter- native ways of obtaining better attrition data. The follow-up survey, which also asks for the destinations of leavers, is expected to provide national attrition rates by field. Attrition has important demographic elements, in part because so much of it is caused by retirement. Since something is known of the demographic profile of the teaching force, it is possible to estimate the likely general trend of attrition in the future, which is almost certain to be on the rise. In much of the country, low rates of new hires over the past 10 years and reductions in force, with the newest teachers being the ones let go, have left a relatively senior task force. Able 2.5 shows an upward trend from 1976 to 1986 in the proportion of current teachers who are age 40 and over (from 34.6 to 51.3 percent) and who are age 50 and over (from 15.5 to 21.2 percent). A rise in the rate of retirements will, of course, increase attrition. In addition, evidence noted earlier points to particularly high levels of attrition in the early years of teachers' careers. In order to forecast attrition adequately, more information is needed not only on the distribution of teachers by age, but also by disciplinary area and level of preparation, and on the current attrition levels within those categories. It would also be useful to have a better understanding

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58 PRECOLI EGE SCIENCE AND Mi4THEMA TICS TEACHERS TABLE 2.5 Age Distribution of U.S. Public School Teachers, 1961-1986 1961 1966 1971 1976 1981 1986 Years Mean Median 41 36 35 42 39 38 36 33 Under age 30 Age 30 39 a Age 40_49 a Age 50 a 33.9% 37.1% 22.8 22.8 17.5 17.8 and over a 25.8 22.3 39 ~ 41 37 40 37.1% 18.7% 11.0% 28.3 38.8 37.7 19.1 23.1 30.1 15.5 19.4 21.2 a Subgroup data not available. Source: National Education Association (1987e:73~. Of why attrition differs for the different categories, if it does, so that more reliable assumptions can be developed for projection models. These issues are discussed in more detail in Chapters 3 and 4, which focus on supply. SUMP The demand for teachers, as we have indicated, depends on enrollment changes, both generally and in mathematics and science courses. The demand for teachers also depends on changes in pupil-teacher ratios, caused by changes in staffing patterns, class size, teaching loads, course requirements, and course offerings in mathematics and science. In addition, a school district's demand for new science and mathematics teachers in a given hiring season also depends on the number of vacancies in those subjects. The number of vacancies results not only from the creation of new positions, but also from teacher attrition, a component of supply. In general, the panel considers the data available for projecting de- mand to be more adequate than data for projecting supply. The task of projecting enrollment-driven demand for science and mathematics teachers is relatively straightforward.

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DETERMINING TEACHER DEMAND 59 There is a small number of significant gaps, however, in data related to demand, and the panel recommends collecting data to fill these gaps. Forecasting the demand for science and mathematics teachers particularly could be improved by better data on the following variables: Course-taking behavior in high school. Data on state-mandated high school course requirements, collected regularly over time and by science or mathematics subject, could suggest changes in demand for teachers of various types or levels of courses. School district requirements often exceed state requirements, but with both state and district data we could- begin to trace how changes in course requirements stimulate changes in demand for secondary science and mathematics teachers. Changes in course o~enngs in science and mathematics. Changes in course offerings can change the demand for science and mathematics teachers and can identify the need for teachers with special skills,. for example, ability to teach advanced placement physics. Enrollment changes disaggregated into science and mathematics course enrollments. Better data on this aspect of course-taking behavior, in con- junction with changes in course requirements, would strengthen the demand component of projection models. Data on attrition for reasons other than retirement by field. Attrition by retirement is relatively well known. For other types of attrition, further analysis of the NLS-72 follow-up of teachers and former teachers should provide more insight into patterns of attrition during the early years of a teaching career (Heyns, 1988~. The best source for obtaining new nonre- tirement attrition data will be SASS, which has recently experimented with questions on attrition by field, although the item response rate was low. High priority should be given to collecting attrition data because they are essential to both demand and supply models. The panel urges that NCES redesign the SASS questions on attrition and subject them to a thorough pilot test before using them. When combined with other SASS data on teachers, the attrition data could help answer questions such as: Among mathematics teachers and science teachers who leave earlier in their ca- reers, how many had taught advanced courses? Introductory-level courses? In high school or middle school? The demand created by such patterns will thus be better known, and a closer fit may be possible in filling the demand. In addition, research is suggested on the behavioral factors that influ- ence the demand for teachers, particularly teachers of science and mathe- matics in the higher grades, for use in development of improved models for longer-term projections. Among the research areas noted are the behav- ioral determinants behind course selection, factors that influence dropout rates, influences on parents' choice of public versus private schools, and the relationship between demand for certain courses and pupil-teacher ratios.