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5 Statistics Related to the Quality of Science and Mathematics Teaching As noted in previous chapters, the supply and demand for teachers of mathematics is brought into equilibrium in the short term by adaptations in the selection criteria for teacher or teaching quality. Thus a school system unable to hire science and mathematics teachers at a preferred quality level will have to lower its minimum quality requirements. Conversely, school systems facing a supply of teachers of acceptable quality in excess of the number they need will be able to choose those at the top of their quality scale, thus ending up hiring teachers of higher quality than suggested by their minimum criteria. While this comprises a generally accurate description of school system hiring practices, it does not tell us anything at all about what factors go into quality teachers or quality teaching. It is to that topic that we now turn. It should be recognized from the beginning that we do not have very precise notions about what constitutes teacher or teaching quality, and thus we cannot provide definitive prescriptions as to types of data that need to be obtained in order to monitor either the level of teacher quality that exists or changes over time in quality. The problem is that assessment of quality is an extraordinarily difficult enterprise, and existing research does not go very far in identifying the factors that determine quality. It is the panel's view that the right dimensions of teacher or teaching quality are factors that produce a positive influence on student outcomes that is, higher quality in our view should be defined to mean better student outcomes, given the influence of other forces besides teachers or school system factors that influence student outcomes. Perhaps the best way to summarize the current state of knowledge on this topic is to note two sets of facts that come from existing studies of teacher quality. 116

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STATISTICS RELATED TO QUALITY 117 1. Teacher quality matters a good deal to student outcomes, in the sense that it is possible to identify teachers who have produced well below average outcomes. In this context, i~lentib simply means that specific teachers can be shown to produce relatively good outcomes, and other specific teachers can be shown to produce relatively poor outcomes (Contra and Potter, 1980~. 2. If one tries to describe what factors are associated with teachers who produce good outcomes or bad outcomes, one finds very little associa- tion between particular characteristics of teachers and the resulting student outcomes. That is, better formal credentials, better preparation in terms of course work more years of teaching experience, better scores on standard tests of teacher qualifications, etc., do not generally show up as teacher characteristics that are strongly related to better or worse outcomes (Druva and Anderson, 1983; Hanushek, 1986, 1989~. It has often been found that teacher verbal ability is positively related to better student outcomes, but the relationship is not exceptionally strong; most other factors do not show up at all (Darling-Hammond and Hudson, 1986~. In sum, we know that there must be characteristics of teachers or of classroom situations that produce better student outcomes, and qualities or characteristics that produce worse student outcomes, but we do not know what these characteristics or qualities are with any degree of assurance. Although it may be surprising to some readers that so little is known about what factors are related to teacher or teaching quality, a little re- flection suggests that it is not so unusual that the state of knowledge is so limited. If one were to ask whether some people are more effective social workers and others less effective, whether some people turn out to be very successful business executives and others less so, or whether some people are very successful at doing survey research interviews and others are less successful, the answer in all these cases will surely be that there are very large differences in the degree to which people are successful or unsuccessful in particular kinds of professional activities. If one goes further to ask what factors are associated with success in being a social worker, a business executive, or a survey research interviewer, the answer will commonly be that very little is known about why some people succeed and others fail. The probable reasons are that the factors making for success are complicated, that personal characteristics and characteristics of the particular environment interact and may be idiosyncratic to particular situations or types of work environments, and that success has a lot to do with motivation, energy, striving for success, interpersonal skills, and

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118 PRECOLLEGE SCIENCE AD ~THE~TICS TRACHEA myriad other factors that come together in subtle ways to produce better or worse outcomes.] Given this state of knowledge, what should be done about the collection of data that relate to teacher or teaching quality? It is the panel's view that, although little is known about what factors are importantly related to quality, something is known about the kinds of factors that probably play some role in determining quality. We should try to collect the best such set of factors, recognizing that the data collected will not be sufficient to do a satisfactory job of explaining student outcomes. Thus in ' this section we discuss a number of types of data that are probably related to quality, although they have not been convincingly shown to be either strongly or systematically reliable indicators of quality. These results may be caused by systematic errors: for example, the better teachers teach higher-order skills, but tests measure primarily lower-order skills, so the quality difference in teaching is not measured. The reader will note that we have talked about quality both in terms of teacher quality and teaching quality. The two are not synonymous. By teacher quality we mean those personal characteristics of individuals that enable them to be more effective in classroom settings: education level, subject matter knowledge, interpersonal skills in working with students, degree of inservice training, formal credentials, etc. By teaching quality we have in mind a somewhat broader notion that encompasses not only teacher characteristics but also the school setting in which classroom teaching takes place. Thus teaching quality includes factors that are beyond the control of the 'individual teacher: disciplinary norms of the school system or of the building principal, support given by principals to teachers, the presence or absence of inse~vice training opportunities or opportunities for interaction among teachers, types of textbooks that are selected for use in the school systems, amount of time allocated to each subject, number of classroom hours taught, and so on. Thus, teaching quality encompasses factors that 1The nature of the problem is illustrated by the example of survey research interviewing. This subject has been studied for many decades, and what we know with certainty are only a few relevant facts, none of which is sufficient to design a test to predict success at survey research interviewing. There are enormous differences in degree of success. Some interviewers achieve close to a 100 percent cooperation rate and have virtually no refusals, collect consistently high- quality data, and do so with relatively few hours expended in the interviewing task and thus have lower costs. Other interviewers have extremely high refusal rates, do not collect consistently high-quality data, and take a great many hours to produce relatively mediocre results. Although we know that these differences exist, it has not been possible to identify personal characteristics that would enable survey research organizations to predict who will be a good interviewer and who will not. Conventional demographic characteristics (educational level, experience, age, etc.) are of virtually no use in explaining success. Although a few personality characteristics seem to have some association with success, the state of knowledge is still relatively crude, despite a great deal of methodological work.

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STATISTICS BELA TED TO QUALITY 119 are not within the control of individual teachers, while teacher quality includes only those factors that relate to the personal characteristics of individual teachers. In examining the quality of mathematics and science teachers, we have in mind a broader notion than assessing the quality of teachers who specialize in mathematics or science. Although some districts employ teachers who specialize in science or mathematics as early as the fourth grade, most teaching in mathematics in grades K-8 is done by teachers in either elementary or middle school who may not be classified as science or mathematics teachers, but rather as teachers who teach science and mathematics. The distinction is important: we are interested in assessing the quality of mathematics and science teaching on the part of teachers who teach those subjects, and many of them probably most- are not specialized in the teaching of either science or mathematics. Moreover, we are also interested in those dimensions of quality that relate to preferences of the school systems for the types of teachers they wish to hire. It is clear enough from our case studies, as well as from extensive discussions with the personnel directors of large city school systems, that mathematics or science teachers are not hired solely for the perceived quality of their mathematics or science teaching. Many school systems have other dimensions of teacher performance in mind when they hire teachers. In some school systems, the ability to fit in with the community is important; in some, the ability to teach other subjects or to direct extracurricular activities is important; in some, the ability to work with the types of students in the school system is perceived to be extremely important. The basic point is simple enough: school systems do not hire teachers to teach science and mathematics solely because of their perceived ability to be effective in classroom settings. Rather, hiring decisions are influenced by a great many other factors, some of which will necessarily result in hiring people who are likely to be less effective in teaching science and mathematics than teachers who were not hired because they lacked other skills or characteristics. In the remainder of this chapter, we attempt to sort out the major ingredients of teaching and teacher quality that call for further data. We look first at school system policies and practices and the school-level condi- tions that can affect teaching quality. Next we look at the qualifications of incoming teachers their college and professional preparation, their level of achievement in science and mathematics, their cognitive abilities, and so on. Finally, we examine other factors that also influence student outcomes but do- not fall neatly under either school system policies and practices or teacher qualifications and characteristics: curriculum and textbook selection issues, time-on-task issues, and issues relating to the home environments of students. All of these do or may influence student outcomes to a substantial

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120 PRECOLLEGE SCIENCE AND MATHEMATICS TEACHERS degree, and none is likely to be under the control of either the teacher or the school principal. SCHOOL SYSTEM POLICIES AND PRACTICES The assignment of a teacher to courses and pupils appropriate to the individual's educational background, certification status, and experience is crucial to quality instruction in precollege mathematics and science. But district personnel policies, budget constraints, and other external factors can impede the ability to achieve the most effective match. A policy maker with the specific goal of higher~uality instruction often finds that it is difficult to change many of the policy variables that affect the quality of instruction. District policies exist in a complex web of competing goals and pressures. Even if the central goal is quality teaching, the policy maker must also consider school system policies and union contract provisions regarding recruitment, initial assignment, and transfer and retention of teachers. A given set of policy guidelines can have quite different effects depending on whether enrollment is stable, growing, or declining. For example, seniority rules for assignment or transfer have different effects in environments in which enrollments are rising or declining. Personnel policies are also affected by the enrollment size of a particular school system, the enrollment size of a high school, the extent to which the curriculum is taught by specialists, and the match among educational background, teaching assignment, and teacher and student cultures. Recruitment and Hiring Practices Certain policies set by the school district, teacher organization, or state school finance plan can have deleterious effects on the ability to hire the most talented teachers. The examples given here apply not only to science and mathematics teachers but probably also to teachers in general. Discussions with personnel offices of large school systems suggested that recruitment of new teachers by large districts with diverse student pop- ulations was often hindered by the fact that recruiters could not specie the school to which the applicant would be assigned. Many persons would find such a school system desirable only if they could teach in a given section of the school system or in a specified school. Since recruiters could not make such commitments, or could not make those commitments early enough in the recruitment period, candidates were lost to the school system. This problem stemmed from district policies related to the timing of hiring, in- te~viewing, and specific placement. District policy in some systems requires

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STATISTICS RELATED TO QUALITY 121 the applicant to be interviewed 'only by the district administrator; subse- quent assignment is a central office decision. Other district administrators screen applications and refer promising candidates directly to principals, who conduct the interviews. The uncertainty of initial assignment also seemed to be exacerbated by seniority rules of internal transfer. In one medium-sized school district in a western state that participated in our case study analysis, internal transfer rules took months to implement. With a tendency for junior high science and mathematics teachers to request high school positions, and for elementary teachers to request junior high positions, the process of considering all transfer applications and then determining which positions were actually vacant continued well into the summer. Job offers could not be made until August. Since other districts could make job offers in March and April, this district was left with candidates who had not obtained positions elsewhere. In some circumstances, the problems stemming from seniority rules become especially severe when combined with rehiring rights after teachers have been laid off due to enrollment decline or financial constraints. In such circumstances, district rules, regulations, and practices rather than pro- fessional judgment often seemed to determine the match between teacher and classroom assignment. For example, seniority rules may restrict new hires to the least desirable schools in the district. These rules may drive teachers not only from the school system but also from the profession. Se- niority rights may also prevail when teachers are transferred among schools. When vacancies occur, the teacher with the greatest longevity in the school system may have first choice. When enrollment declines, teachers with higher longevity in the school system, the school, or a teaching field may have rights to bump less senior teachers. The length of the waiting period before opening vacancies to outside applicants greatly affects the district's ability to sign on talented applicants. Many officials said they lose good annlicants to cipher districts whose rules or budgets allowed them to hire err -^ -^ sooner. Enrollment size and composition also influence district policies. The hiring restrictions of one large urban school system in the West contrasted starkly with the innovative practices for meeting future needs employed by a small suburban school system in the same region. The suburban superintendent, in conjunction with a nearby college, recruited well-trained graduates to fill projected vacancies. The smaller enrollment size and relative wealth of the suburban school system, as well as the homogeneity of the student population, accounted for the differences in practices between the suburban and the urban systems. In another suburban school system in the East, a teacher who attracted high school students to advanced science classes had been allowed to develop his own teaching assignment. Such

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122 PRECOLLEGE SCIENCE AND 1~4THEMi4TICS TEACHERS flexibility is less likely in a larger school system concerned with uniform course offerings among schools. One of the reasons for more rules, and sometimes less flexible ones, in larger school systems is the need to adhere to goals of equity among staff members in conditions of employment. Factors external to the school district can also affect local hiring prac- tices. Increases in state-mandated graduation requirements for mathematics or science can cause the district to fill vacancies in those fields with teach- ers not yet certified in the particular subjects, in order to meet the state requirement. As noted in Chapter 2, 42 states have added requirements in science or mathematics since 1983. The Center for Policy Research in Education (CPRE), which has surveyed the states' graduation requirements, has found that in schools affected, about 27 percent of students are taking an extra mathematics course and 34 percent an extra science course (CPRE 1989:33~. Many of these student are middle- to low-achieving, the CPRE study relates (p. 35~. CPRE inquired as to the nature or level of the additional courses. In many instances the added courses were remedial or lowerlevel science and mathematics courses (p. 35-36~. The increased requirements undoubtedly have changed schools' staffing patterns and course assignments and have probably affected hiring practices for science and mathematics teachers. State-mandated minimum competency test scores and state school- finance formula constraints on local funds for laboratory equipment and supplies, computers, teacher aides, or teacher salaries are other external factors that local personnel officials must take into consideration in hiring teachers. An unintended consequence of decisions made under these conditions may be a loss in teacher or teaching quality. Of course, not all rules act to restrict supply or make the task of matching persons and assignments more difficult; certain rules may benefit some school systems. When there is a potential for future growth in high school enrollments, teachers in a school system may pursue advanced study so that they can move from elementary school or junior high to high school. Other teachers may be attracted to begin their career in the district with a thought toward future advancement. Without seniority rules, there would be no such encouragement, as new hires might occupy newly created positions in high schools. Data are needed to better describe the incidence of these and other policies and practices that affect the ability to hire and place the most promising candidates to assure instruction of high quality. The Schools and Staffing Survey (SASS) does not yet provide data related to most of these areas. In-depth conferences with a sample of SASS districts on a regular basis are recommended (see Chapter 6) to gain more accurate insights into the use of such policies and practices.

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STATISTICS RELATED TO QUALITY 123 Misassignment of Teachers Teacher assignment is critical to quality instruction in all subjects, es- pecially so for science and mathematics. Misassignment of science teachers can occur when a vacancy in a science specials is filled with a certified science teacher who is unfamiliar with that particular field. High schools may be too small to have a full-time chemistry or physics teacher or even a full-time biology teacher.2 In 1986-87, only 13 percent of teachers who taught physics in secondary schools had teaching assignments in physics alone. Almost two-thirds of the teachers who taught physics had their primary concentration of classes in chemistry, mathematics, or general and physical science (American Institute of Physics, 1988:17~. There may be a need for one but not two science teachers. The same type of misassign- ment can occur in mathematics, when a teacher is trained to teach areas of mathematics other than that assigned or some other subject altogether. In many states, it is legal to assign a teacher to teach part time in an area in which the teacher is not certified, under a practice called out-of-field teaching as opposed to "misassignment" (Robinson, 1985~. Estimates of the prevalence of misassignment based on data from the early 1980s collected by the National Center for Education Statistics (NCES) and the National Education Association (NEA) vary considerably. In a preliminary report on indicators of precollege education in science and mathematics, the National Research Council (NRC) notes the erosion of the quality of the existing teaching pool by misassignment of newly certified teachers. This report cites NCES findings that, among bachelor's degree recipients in 1979-80 who were teaching elementary or secondary 2 In one of the case studies, the employment of a full-time chemistry teacher by a school system was mentioned. This condition was treated as rare for the school systems studied. Such employ- ment can be seen as unusual for the United States by examining some necessary conditions. If one assumes that a teacher teaches 5 classes and that a class has between 25 and 30 students, then to teach a single subject at the same grade level requires 125 to 150 students per grade level. For a 4-year high school this means a school enrollment size of 500 to 600. For a 3-year high school, it means an enrollment size of 375 to 400. In 1982-83 9.5 percent of secondary students attended schools below the latter size criterion. An additional 10.5 percent of secondary students met the former criterion. If only half of the students take a chemistry course, then slightly more than half of the students, 53.3 percent, attend such secondary schools. If only a third of the students take a chemistry course, then only slightly more than 10 percent of secondary students (13.4 percent) attend schools of that enrollment size (ACES, 1986:68~. That only a third of secondary students are likely to take a chemistry course can be garnered from the fact that 65.4 percent of public secondary school students take natural science (p. 41), and the average number of Carnegie units (a standard of measurement that represents one credit for the completion of a one-year course) in natural science is 1.9 (p. 44~. Expanding the ranges of possible courses in natural science to include two courses in chemistry or chemistry and physics would indicate that only 3.9 percent of schools, that is, the schools with larger enrollments that enroll 13.4 percent of the students, would be able to hire a full-time chemistry or physics teacher.

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124 PRECOLLEGE SCIENCE AND MATHEMATICS TEACHERS school full time in May 1981, only 45 percent of science teachers and 42 percent of mathematics teachers were certified or eligible to be certified in the field in which they were teaching (NRC, 1985:52~. More recently, Darling-Hammond and Hudson (1987a:21) reported "estimates that vary depending on who is asked to estimate the degree of misassignment (school administrators versus teachers) and on how misassignment is defined." They reported (1987a:21~: Not certified in area of primary assignment: 9-11 percent by teacher report, 3.4 percent from central office administrators' estimates (NEA, 1982; NCES, 1985a). Not certified for some classes taught: 16 percent by teacher report (NEA, 1982). Less than a college minor in area of primary assignment: 17 percent by secondary school teacher report (Carroll, 1985). The 1985 National Survey of Science and Mathematics Education found higher proportions for science and mathematics 18 percent of grade 7-9 mathematics teachers and 14 percent of grade 10-12 mathematics teachers teach courses for which they are uncertified. For science teachers, the percentages are 25 for grades 7-9 and 20 for grades 10-12 (Weiss, 1987:77-88~. Transfer policies can sometimes lead to a misassignment and thwart a teacher's potential for advancement. In our contacts with school district administrators, a tendency was reported for principals to transfer teachers from subject fields of surplus to subject fields of need. Often, these trans- fers moved the teachers from their primary subject fields to different areas. Transfers of this nature took place due to changes in student demand for subjects under stable enrollments as well as in times of changing enroll- ments. Such transfers also occurred because principals sought teachers able or willing to handle extracurricular tasks such as athletics, the school paper, the yearbook, or student clubs. The extent to which misassignment occurs today in science and math- ematics may be greater than for other subjects. Data on the extent of misassignment for all fields at the school district level will be obtainable from the SASS Teacher Demand and Shortage questionnaire. It will also be possible to estimate misassignment by field by using the SASS teacher questionnaire. This questionnaire obtains courses currently taught by each departmental teacher, the teacher's arrears) of certification, and college major and minor. Estimates of misassignment by field as defined by certi- fication status can be made using these data. Since certification standards vary so much across states, the fact that one was not certified in the field in which one is teaching does not necessarily mean misassignment. To obtain a more complete picture of

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STATISTICS RELATED TO QUALITY 125 misassignment, information on inservice training and actual course-taking preparation should also be analyzed, as Darling-Hammond and Hudson suggest (1987a: 21-22~. The SASS teacher questionnaire represents a promising step forward. It requests data not only on certification status (as above), but also on degrees earned and major and minor fields of study, amount of course work in primary and secondary teaching assignment fields, and, for teachers who teach any science or mathematics courses, the number of graduate and undergraduate courses taken in various categories. These are rich data to examine misassignment and out-of-field teaching. Information from SASS should be analyzed together with state certifi- cation data on the number of emergency certificates issued in science and mathematics; 46 states allow emergency certification. Of these, 30 require university course work in order to renew and work toward full certification (McKibbin, 1988:32~. Supplementary data would include state rules on the extent to which out-of-field assignment is legal. Such information from various sources, when analyzed jointly, will help monitor the extent and trends of misassignment in science and mathematics teaching. Providing for Inservice and Continuing Education Some of the most important district and school practices that affect the quality of instruction are those directed to teachers already in place. maintain quality instruction throughout their careers, teachers require professional support from their schools and districts. This support includes working conditions, facilities such as laboratories, materials and supplies, collegial and administrative support, resources for continuing education, and opportunities to influence decision making (Darling-Hammond and Hudson, 1987a:27-37~. District practices regarding inservice and continuing higher education for teachers in place affect teacher quality directly and can make it more or less attractive for a teacher to continue in a district. School districts have been the primary sponsors of inservice programs, but such programs are highly vulnerable to district budget cuts. Decisions as to what kinds of inservice education to fund with a limited budget affect teaching quality in ways that data alone may be unable to illustrate. In one large, suburban, low-wealth district we studied, much of the staff development budget was geared to weaker teachers. Teachers had little release time during the school year 17 days allotted for each high school. Only about 20 percent of staff development was used for college-level course work. A national commitment to teachers' continuing education appears to be missing. The federal government does support inservice education through the Title II program of the Education for Economic Security

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126 PRECOLLEGE SCIENCE AND M'4THEAL4 TICS TEACHERS Act of the Department of Education and through the National Science Foundation (NSF) Teacher Enhancement Program (Office of Technology Assessment, 1988:69), but funding for both activities is severely limited. Appropriations for the Title II program have been uneven, dropping from $100 million in fiscal year 1985 to $42 million in 1986, then $80 million, $120 million, and $127 million in 1987, 1988, and 1989, respectively (OTA, 1988:123; U.S. Department of Education, 1989~. These are small amounts when viewed on a per-pupil or per-teacher basis. The Office of Technology Assessment notes by comparison that a $40 million education program equates to a spending of $1 per pupil or $20 per teacher (1988:123~. NSF's Teacher Enhancement Program funds a small program of teacher institutes emphasizing teaching techniques in science and mathematics. The institute program is much smaller than it was in the past. Between 1954 and 1974 NSF spent over $500 million on teacher training institutes that at their peak involved 40,000 teachers (OTA, 1988:119-120~. The Teacher Enhancement Program has been revived somewhat since 1982, when it was virtually nonexistent. According to Charles Hudnall of the NSF staff, from 1983, when $11 million were appropriated, it has grown steadily to $43 million in 1989. There is little national information available on the extent to which inservice programs other important professional resources are used. Most of the existing data on this topic were collected from teachers, through self-reporting, in 1985-86 and reported in Weiss (1987~. The SASS local education agency questionnaire asks whether the district reimburses teachers' tuition and course fees. It also asks whether free retraining is available for teachers for shortage areas, and what those shortage areas are. The school questionnaire for the 1990 follow-up of NELS:88 asks principals (primarily of middle or junior-high schools) whether teachers are rewarded with time off for professional workshops, extra materials, choice of classes, etc. Teachers in NELS:88 are asked about the number of hours spent on noncollege inservice education. The NEA Survey of the American Public School Teacher (described in Appendix B) includes three fairly detailed items concerning inservice of various types over the past three years, including how much of the teacher's own money was spent on college credit programs. More data on policies related to inservice and other professional programs are needed from school districts. Among useful measures to obtain on inservice program use would be the number of hours of inse~vice training in mathematics, science, and related pedagogy accumulated in the last 12 months. Graduate courses should be distinguished from refresher workshops. Substantial inservice work in the form of graduate courses in one's primary field may indicate a high level of quality and professionalism or the intent to move from middle school to high school. The SASS teacher

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146 PRECOLLEGE SCIENCE AND MATHEMATICS TEACHERS teacher quality or student outcome. Thus, it is important that the National Science Foundation fund a program of controlled experiments on factors that do measure teacher or teaching quality. Such research would include identifying the relationship between measurable teacher qualifications and student outcomes. If the Carnegie or Holmes recommendations for higher professional standards are adopted, the consequent changes in the teaching force should be monitored, together with any changes in supply as a result of the more rigorous requirements. Other factors beyond teacher quality-such as textbook use, time commitments, the structure of science and mathematics curricula, and home environment were noted as influences on teaching quality and student outcomes. These factors complicate any attempts to link outcomes with particular teacher qualifications. In conclusion, to understand the crucial role of quality in bringing supply and demand for precollege science and mathematics teachers into equilibrium in the short term, we have acknowledged some rather daunting data needs and research issues. We realize that these needs might not be able to be met completely enough to introduce teacher quality measures into teacher supply models in the near future. But successful collection of more precise data, particularly through SASS and existing state information files, can be expected to contribute to an understanding of teacher quality, and additional research may help identify the characteristics of teachers and teaching that are determinants of student outcomes.

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STATISTICS RELATED TO QUALITY APPENDIX TABLE 5.2 Guidelines for Mathematics and Science Teacher Qualifications Specified by the National Council of Teachers of Mathematics (NCTM) and the National Science Teachers Association (NSTA) 151 NCTM Guidelines Early elementary school The following 3, each of which presumes a prerequisite of 2 years of high school algebra and 1 year of geometry: 1. number systems 2. informal geometry 3. mathematics teaching methods Upper elementary and middle school The following 4 courses, each of which presumes a prerequisite of 2 years of high school algebra and 1 year of geometry: 1. number systems informal geometry 3. topics in mathematics (including real number systems, probability and statistics, coordinate geometry, and number theory) 4. mathematics methods Junior high school The following 7 courses, each with a prerequisite of 3 to 4 years of high school mathematics, beginning with algebra and including trigonometry: 1. calculus 2. geometry 3. computer science 4. abstract algebra 5. mathematics applications 6. probability and statistics 7. mathematics methods NSTA Standards Elementary level 1. Minimum 12 semester hours in laboratory- or field-oriented science including courses in biological, physical, and earth sciences. These courses should provide science content that is applicable to elementary classrooms. 2. Minimum of 1 course in elementary science methods (approximately 3 semester hours) to be taken after completion of content courses. 3. Field experience in teaching science to elementary students. Middle/junior high school level 1. Minimum 36 semester hours of science instruction with at least 9 hours in each of biological or earth science, physical science, and earth/space science. Remaining 9 hours should be science electives. 2. Minimum of 9 semester hours in support areas of mathematics and computer science. 3. A science methods course designed for the middle school level. 4. Observation and field experience with early adolescent science classes. Secondary level General standards for all science specialization areas: 1. Minimum 50 semester hours of course work in 1 or more sciences, plus study in related fields of mathematics, statistics, and computer applications. 2. Three- to 5-semester-hour course in science methods and curriculum. 3. Field experiences in secondary science classrooms at more than 1 grade level or more than 1 science area.

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152 PRECOLLEGE SCIENCE AND MATHEMATICS TEACHERS (Appendix Table 5.2, continued) NCTM Guidelines NSTA Standards Senior high school The following 13 courses, which constitute an under- graduate major in mathematics, each presume a prerequisite of 3 to 4 years of high school mathematics, beginning with algebra and including trigomometry: 1-3. 3 semesters of calculus 4. computer science 5-6. linear and abstract algebra 7. geometry 8. probability and statistics 9-12. 1 course each in: mathematics methods, mathematics applications, selected topics, and the history of mathematics 13. at least 1 additional mathematics elective course Specialized standards Specialized standards 1. Biology: minimum 32 semester hours of biology plus 16 semester hours in other sciences. 2. Chemistry: minimum 32 semester hours of chemistry plus 16 semester hours in other sciences. Earth/space science: minimum 32 semester hours of earth/space science, specializing in one area (astronomy, geology, meteorology, or oceanography), plus 16 semester hours in other sciences. 4. General science: 8 semester hours each in biology, chemistry, physics, earth/ space science, and applications of science in society. Twelve hours in any 1 area, plus mathematics to at least the precalculus level. Physical science: 24 semester hours in chemistry, physics, and applications to society, plus 24 semester hours in earth/space science; also an introductory biology course. Physics: 32 semester hours in physics, plus 16 in other sciences. 5. 6. Source: Office of Technology Assessment (1988:64) .

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STATISTICS RELATED TO QUAL17-Y 153 APPENDIX TABLE 5.3 States That Have Enacted Testing Programs for Initially Certifying Teachers: Fall 1987 State Enacted Effective Test Useda Alabama 1980 1981 State Arizona 1980 1980 State Arkansas 1979 1983 NTE California 1981 1982 CBEST Colorado 1981 1983 CAT Connecticut 1982 1985 State Delaware 1982 1983 PPST Florida 1978 1980 State Georgia 1975 1980 State Hawaii 1986 1986 NTE Idaho 1987 1988 NTE Illinois 1985 1988 State Indiana 1984 1985 NTE Kansas 1984 1986 NTE and PPST Kentucky 1984 1985 NTE Louisiana 1977 1978 NTE Maine 1984 1988 NTE Maryland 1986 1986 NTE Massachusetts 1985 b b Michigan 1986 1991 b Minnesota 1986 1988 PPST Mississippi 1975 1977 NTE Missouri 1985 1988 b Montana 1985 1986 NTE Nebraska 1984 1989 b Nevada 1984 1989 PPST and State New Hampshire 1984 1985 PPST and NTE New Jersey 1984 1985 NTE New Mexico 1981 1983 NTE New York 1980 1984 NTE North Carolina 1964 1964 NTE North Dakota 1986 b b Ohio 1986 1987 NTE Oklahoma 1980 1982 State Oregon 1984 1985 CBEST Pennsylvania 1985 1987 State Rhode Island 1985 1986 NTE South Carolina 1979 1982 NTE and State South Dakota 1985 1986 NTE Tennessee 1980 1981 NTE

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154 PRECOLLEGE SCIENCE AND MATHEMATICS TEACHERS APPENDIX TABLE 5.3 Continued State Enacted Effective Test Useda Texas 1981 1986 State Virginia 1979 1980 NTE Washington 1984 b West Virginia 1982 1985 State Wisconsin 1986 1990 b a Tests: CAT = California Achievement Test; CBEST = California Basic Skills Test; NTE = National Teacher Examination; PPST = Pre-Professional Skills Test; b State = State-developed test. -To be determined. Source: National Center for Education Statistics (1988f:249-250~.

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STATISTICS RELATED TO QUALITY APPENDIX TABLE 5.4 Comparison of Recommendations of Carnegie and Holmes Reports Pertaining to Preservice Education of Teachers Category of Recommenda- tion Fifth Year of Study Carnegie Report a Require bachelors degree in the arts and sciences as prerequisite of professional study of teaching. Require a master's degree for all teachers. Curriculum Develop new professional Revision curriculum in graduate schools of education leading to Master in Teaching degree based on systematic knowledge of teaching and including internships and residencies in schools. Coordination Connect institutions of higher education with schools through the development of professional development schools. Certification Create a national board for professional teaching standards to establish high standards for what teachers need to know and to be able to do, and to certify teachers who meet that standard. 155 Holmes Group b Make education of teachers more solid intellectually by pursuing an undergraduate major in an academic subject other than education, receive their professional training in a fifth year master's degree program, and complete a year-long supervised internship. Revise undergraduate curriculum in arts and sciences. Organize academic course requirements, including involvement of other departments in institutions of higher education. Need advanced studies inpedagogy (focus on human cognition, teaching and learning, and teaching), teachers' learning, assessment of professional performance, and evaluation of instruction. Need coherent program in schools and institutions of higher educa- tion that will support advanced study. Create professional development schools, similar to teaching hospitals, in which prospective teachers would receive their clinical training. Create 3-tier systems of teacher licensing: 0 Instructor--has BA degree, without year of supervised practice and study in pedagogy and human learning; has passed exams (see evaluation) Professional teacher--has MA in teaching; completed year of supervised practice; passed exams 0 Career professional--has completed all of the above plus further specialized study a

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156 APPENDIX TABLE 5.4, continued PRECOLLEGE SCIENCE AND MATHEMATICS TEACHERS Category of Recommenda- tion Carnegie Report a Holmes Group b Evaluation/ Assessment Differential Restructure teaching force Staffing and introduce new category of lead teachers with proven ability to provide active leadership in redesign of schools and in helping colleagues to uphold high standards of learning and teaching. Use multiple evaluations o Test basic mastery of writing and speaking o Demonstrate mastery of subject, skill in lesson planning, and instructional delivery prior to clinical internship 0 Evaluate variety of teaching styles during internship-- including own--and present analytic evidence as part of professional portfolio for advancement Recognize differences in teacher's knowledge, skill, and commitment in their education, certification, and work. a Carnegie Task Force on Teaching as a Profession (1986) A Nation Prepared: Teachers for the 21st Century,. Washington, D.C.: Carnegie Forum on Education and the Economy. Pp. 55-56. b The Holmes Group (1986) Tomorrow's Teachers: A Group. East Lansing: The Holmes Group, Inc. Pp. 65-66. Report of the Holmes Source: Regional Laboratory for Educational Improvement of the Northeast and Islands (1987:15-17~.