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1 Introduction and Summary INTRODUCTION Background In the last 2 years, concern over the state of science and mathematics education in the schools of the United States has become a prominent topic on the public agenda. Special commissions and task forces have emphasized the importance to the nation of adequate student preparation in science and mathematics. For example, the National Science Board Commission on Precollege Education in Mathematics, Science and Technology (National Science Foundation, 1983:1) states that "improved preparation of all students in the fields of mathematics, science and technology is essential to the maintenance and develop- ment of our Nation's economic strength, to its military security, to its commitment to the democratic ideal of an informed and participating citizenry and to fulfilling personal lives for its people." The Task Force on Education for Economic Growth (1983) in the report Action for Excellence views the declining exposure of students to technical subjects as a serious problem that threatens to become more so as American workers face increasing technological demands. The Report of the Twentieth Century Fund Task Force on Federal Elementary and Secondary Education Policy (1983) presents the view that training in mathematics and science is critical to both the nation's economy and polity--to the economy by ensuring that there are ample personnel who are capable of filling the increasing number of jobs demanding these skills, and to the polity by providing citizens with the education in science that is essential if they are to participate intelligently in political decisions about 1
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2 such controversial issues as radiation, pollution, and nuclear energy. The National Commission on Excellence in Education (1983) recommends that schooling now include "five new basics": in addition to 4 years of English and 3 years of social studies, all high school students should study no less than 3 years of mathematics, 3 years of science, and 1/2 year of computer science. These national bodies, convened with private or gov- ernmental sponsorship, agree that there are serious problems in precollege mathematics and science education and that those problems may constitute a threat to the economic future and to the security of our nation. Other groups, sponsored by a number of states, have reached similar conclusions. The reports suggest that many U.S. students are leaving high school without adequate preparation in science and mathematics, whether for the job market or for continuing their education. The reports also identify specific school deficiencies: teacher shortages, inadequate curricula, low standards of student performance. According to some critics (see, for example, Peterson, 1983; Stedman and Smith, 1983), however, not all of the conclusions of the national commissions are adequately documented. Yet the expressed concerns about deficiencies already have led to initiatives by government and by the private sector at the national, state, and local levels. Legislation passed by Congress in 1983 made available funds to the National Science Foundation to be invested specifically in training mathematics and science teachers and in providing improved instruction in these fields, and there were further congressional appropriations in 1984. More than 40 states either have increased high school graduation requirements in mathematics and science or are considering an increase in requirements (Education Commission of the States, 1983). University systems in several states have announced higher admission require- ments. State and local initiatives provide in-service education in mathematics or science for teachers already practicing and encourage college students to embark on careers in mathematics or science teaching. Private corporations are donating equipment, providing training and research experiences for teachers and students, and lending staff members to the schools for special programs. The renewed interest and investment in precollege mathematics and science education make it especially important to understand the current condition of these fields and to be able to track future changes. Two major
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3 reports on education released recently have urged that educational progress be systematically monitored. The National Science Board Commission (National Science Foundation, 1983:12) recommends: The Federal government should finance and maintain a national mechanism to measure student achievement and participation in a manner that allows national, state and local evaluation and comparison of educa- tional progress . . . [an] assessment mechanism is needed to enable local communities, States and the Nation to monitor their progress toward improving mathematics, science and technology skills among elementary and secondary students and to incorporate such information into their program development activities. . . . The Commission firmly believes that achieving its educational objectives requires regular monitoring of educational progress, and that such monitoring will itself increase the speed of change. The report of the Carnegie Foundation for the Advance- ment of Teaching (Boyer, 1983) recommends that new student achievement tests be developed. They would be linked to the content of the high school curriculum and would be given to all students toward the end of high school to evaluate what students have learned. Even before the issuance of these reports, the National Academy of Sciences and the National Academy of Engineer- ing (1982) had expressed concern about the status of pre- college science and mathematics education and also about the facilities available for monitoring the nation's educational progress. A national convocation on pre- college science and mathematics education held by the Academies drew attention not only to the problems but also to the lack of adequate information regarding teachers, enrollments, and other important issues. To lay the foundation for the development of a monitoring system for use at the national, state, and local levels, the Committee on Indicators of Precollege Science and Mathematics Education was created in 1983. The committee is charged with proposing a framework for an efficient set of education indicators, filling in the framework to the extent possible with existing data, and suggesting data and data analyses that will be needed in the future for a continuing portrayal of the condition of precollege science and mathematics education. This report covers the first phase of the committee's work.
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4 Scope of Report In the work discussed in this report, the committee selected a preliminary set of indicators, based on the kind of information that is generally requested by people making decisions about education and on which some data have been collected. The committee also reviewed the information currently available on selected indicators and has provided some findings on temporal trends and comparisons with other countries. Lastly, the committee has judged the extent to which the available information can serve to construct indicators and has made recommenda- tions for improvement. This report is a preliminary statement rather than a definitive document on indicators. It represents a first attempt to select indicators of precollege mathematics and science education that might be constructed over the short range and presents the committee's recommendations for improving the information pertinent to the selected indicators. The report is addressed primarily to the agencies that are most likely to develop and publish education indicators for science and mathematics, the National Science Foundation, the National Center for Education Statistics, the National Institute of Educa- tion, the International Association for the Evaluation of Educational Achievement, as well as to state and local offices of education. It is also addressed to a wider audience of educators, educational researchers, scientists and mathematicians, with the intent of stimulating critical comment that may help to advise those agencies. This report has several limitations. The committee was asked to prepare a preliminary report promptly. Both the shortness of time and budgetary restrictions placed constraints on its work. As a consequence, the committee chose to restrict its scope to indicators that can be constructed from information already being collected at the national, state, or local levels or that could be collected by a modest extension of present data collection activities. In this report the committee summarizes conclusions and makes recommendations regarding the quality of avail- able information and its suitability for the selected indicators. The committee also derives from the data some findings about the current condition of science and mathematics education. In its interpretation of cited studies, the committee routinely has focused only on
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5 statistically significant results as indicated by the standard errors reported in the original sources. The committee does not provide value judgments about the findings derived from the studies and data cited. It is the committee's view that such judgments should be made by educators, scientists, legislators, school boards, parents--all those concerned with the quality of education in this country--based on a clear understanding of current conditions and trends. The report tries to further this understanding; it is not intended to be a certificate of health or a report card on the nation's mathematics and science education. The committee makes no attempt in this report to inves- tigate underlying causes of the observer cona~ons. Effective education policy requires, first, an understand- ing of current conditions, second, a definition of preferred conditions, and, third, an appreciation of means for changing current to preferred conditions, which in turn requires an understanding of their causes. This preliminary report deals only with a portrayal of current conditions; it does not define preferred conditions, nor does it discuss how changes leading to the preferred conditions might be brought about. When projections about conditions over the next several years are given, as in the section on teachers, they are based on extrapolations of current modes of school operation and on predictable changes such as demographic trends. Possible structural reforms of the present system, for example, that might accompany the application of information technology to education, or major alterations in the school curriculum with respect to the content and sequencing of mathematics, science, and perhaps newly added technology instruction, would alter the projections. Logical next steps in the development of an adequate monitoring system would entail considering more imagina- tive and less conventional indicators that might serve to guide policy for mathematics and science education, con- sidering indicators that might be useful in the context of possible changes of structure or function in the education delivery system, and, of course, designing better data gathering methods and analyses for all indicators. In the next phase of the work, these objectives will be addressed.
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6 SUMMARY The first section of this summary presents a short discussion, given in greater detail in Chapter 2, of the reasons for choosing particular schooling variables as the basis for constructing indicators. Subsequent sections of the summary provide the committee's findings, conclu- sions, and recommendations on the selected indicators related to teachers, curriculum content, instructional time and course enrollment, and student achievement in science and mathematics. Selecting Indicators A large amount of statistical data and research in- formation on education in general is available. At the national level, the National Center for Education Statistics (NCES), a component of the Department of Education, publishes two major compilations annually. The NCES and other components of the Department also sponsor periodic surveys--for example, the National Longitudinal Study of 1972 (NLS 1972) high school gradu- ates and High School and Beyond Study (HSB), a survey of 1980 sophomores and seniors and 1982 seniors--that provide information on student enrollment and achievement, although information specific to mathematics and science education is limited. The Department, through the National Institute of Education, also supports the National Assessment of Educational Progress (NAEP), which has gathered information nationwide on scholastic achieve- ment (including mathematics and science achievement) and student attitudes since 1969. The National Science Foundation (NSF) has special responsibility in the area of science and mathematics education: it has sponsored studies on science and mathematics in the schools and published information from them and other sources. Both NCES and NSF have provided support for U.S. participation in the studies conducted by the International Association for Evaluation of Educational Achievement (TEA). Every state also has its own data collection system, much of it devoted to fiscal, demographic, and managerial information, but also including data on enrollments, personnel, and student assessment, although there is considerable variation in the types of data collected by states and in the manner of collection. (Examples of the types of data collected by states are given in the
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7 Appendix.) The larger local education districts similarly collect information they find necessary for their internal operation as well as data requested by the state agencies. Information systems of local education districts exhibit an even greater diversity than those of the state systems Thus, considerable data are available on precollege science and mathematics education, but they are derived from diverse sources, address similar questions differ- ently, and leave some pertinent issues unaddressed. To begin the development of an orderly monitoring system, the committee's first task was to select a limited set of variables and measures deemed essential to portraying the . state of science and mathematics education. The committee chose to concentrate on variables generally identified as critical to the condition of education and on which there were some data and information available. The outcomes of science and mathematics education were considered first, followed by the schooling processes and inputs that can be associated with the selected outcomes. Outcome Variables The primary goal of instruction in science and mathematics is student learning. The most explicit student outcome, and one that can be tied directly to schooling variables, is the knowledge and skills gained by students, that is, student achievement in science and mathematics. Hence, the first, most obvious outcome variable the committee selected is student achievement. A second outcome often desired from instruction in these fields is the development of more favorable student attitudes toward science and mathematics. the committee is not giving emphasis to indicators on attitudinal variables because their relationship to the primary goal of student achievement (or to later-life outcomes) is not clear. Other outcomes considered by the committee included choice of college majors, choice of careers, and later career paths. Each of these is impor- tant to individual and societal goals and is relevant to the distribution of human resources. However, the more distant an outcome from the immediate purpose of instruc- tion, the more tenuous the link and the more likely that nonschool variables affect the outcome. Pending research findings that more clearly link school experiences to life outcomes, the committee did not chose indicators representing such outcomes. At this time
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8 As to measures of achievement, the only ones available at the national level that are applicable to the whole student population are test results from NAEP, NLS, and HSB. The committee does not believe that the scores obtained on the Scholastic Aptitude Tests (SATs) developed by Educational Testing Service (ETS) are appropriate mea- sures of school outcomes for all students in science and mathematics, because the population taking these tests is self-selected and not representative of the whole student population. However, for college-bound students who take them, trends in scores on the achievement tests in specific subjects also developed by ETS for the College Board's Admission Testing Program and the tests of the American College Testing Program give an indication of changing levels of achievement over time in academic subjects offered in high school. time to time studies of school achievement in From var iOUS sive of countries are carried out. The most comprehen- these have been the studies conducted under the auspices of the TEA. However, the most widely published results for mathematics date back to 1964 and for science to 1970. New TEA studies are currently under way in both fields, and some preliminary results from these studies are available. Most states have assessment programs as well, although they vary from state to state; they generally involve selective achievement testing at several grade levels, sometimes using commercial tests, sometimes state- constructed instruments. State tests are used for a variety of purposes: for assessing absolute achievement, for determining competency, for comparison with national results, for comparison of schools and school districts, for checking on the adequacy of curricula and instruction. Some of these purposes require periodic adjustment of the tests, which makes comparisons over time hazardous. Using test scores as measures of student achievement assumes at least moderate test validity for the assess- ment of student learning. Unfortunately, it has proved difficult with current testing methodology to construct tests for widespread use that adequately asses the range of complex skills and in-depth understanding needed for proficiency in mathematical or scientific concepts and processes. The committee, in its recommendations, dis- cusses the importance of improving tests, especially for testing the knowledge and skills acquired by individuals. Nevertheless, the committee has concluded that existing tests of mathematics and science of the kinds used by
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9 NAEP, HSB, and TEA are sufficiently valid for the purpose of indicating student achievement at the group level. Process Variables The selection of student achievement as the outcome variable of greatest interest determines to a consider- able extent what schooling input and process variables need to be selected, namely, those that have some causal relationship to student achievement. One process variable in particular is assumed in educational practice to be closely linked to student achievement: enrollment in or instructional time spent on the requisite subject. And recent work on the achievement of high school students in mathematics and in science documents the positive effects of time spent on relevant instruction or courses, especi- ally if instructional time is managed efficiently; in fact, it appears to be one of the most robust findings coming from major longitudinal studies and assessment efforts. Consequently, based on research evidence as well as on educational practice and experience, the committee decided that course enrollment and instruc- tional time spent on subject matter should be considered key process variables in indicators of mathematics and science education. A related exposure component is time spent on homework, which appears to be associated with student achievement, and it is included as part of these process variables. Selection of course enrollment and instructional time in no way is intended to minimize the importance of such other process variables as teacher behaviors, student behaviors, and classroom environment, but because of the present state of knowledge about the relationships between these variables and student achievement and about how to assess them, the committee decided it would be premature to use them at this time as indicators of mathematics and science education. Input Variables In addition to outcome and process variables, a third set of variables in measuring science and mathematics education are schooling inputs. The most obvious inputs are numbers (and quality) of teachers responsible for those areas of instruction and the content of the curriculum.
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10 Looking first at the numbers of mathematics and science teachers, reasonably consistent statistics are available from NCES and the National Science Teachers Association. However, the significant indicator is not the supply of teachers, but the supply compared with the numbers needed; this comparison~must be based not only on the size of the existing pool, but also on the teacher turnover rate, total high school enrollments, and the effects of increased high school graduation requirements that are being mandated by a number of states. But even good estimates of the numbers of teachers do not take into account quality, the competence of either those teachers now assigned to mathematics and science classes or of those entering the fields. There is no nationally accepted standard for a "quali- fied" science or mathematics teacher. While certification can be used as a first approximation of quality, certifi- cation requirements vary considerably from state to state. Hence, estimates of the numbers of qualified people teach- ing mathematics or science are open to question. In spite of these difficulties in measuring the supply and quality of teachers, however, the committee decided that their importance warranted selecting them as variables. The argument for selecting content of curriculum as a variable is analogous to that for selecting instructional time/course enrollment: the subject matter actually taught is important to student achievement. Recent syntheses of the sizable research literature on the efficacy of alternative science curricula and data from NAEP and HSB support this assumption. It should be noted that, of the variables the committee considered it impor- tant to assess, this one has received the least attention, probably because it is the most difficult to track. Two other indicators of input were considered by the committee: public attitudes toward science and mathe- matics education and funding for education. Examining the results of 15 years of polling by the Gallup Organiza- tion on the public's attitudes toward education yields consistent results: mathematics ranks high in importance as a school subject and science generally ranks in the middle. Since these public attitudes appear to have changed little over the last 15 years, and since the relationship between public attitudes and schooling outcomes is tenuous, at best, the committee decided not to recommend the development of further indicators for this variable.
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11 With regard to funding, it is widely assumed that the quality of schooling is a direct function of the amount per pupil of financial support provided to a school; however, research studies do not consistently yield that conclusion. Major cost factors are teacher salaries, class size, and expenditures for physical plant and facilities; none of these has been demonstrated to relate consistently to student learning. - Of course, one might speculate that higher salaries would attract to the teaching profession many highly competent persons who in the past have chosen other, more lucrative, occupations. Even if research results more clearly supported the hypothesis that increased financing yields better learning in the schools, serious problems would remain in using an index of financial support as an indicator of mathematics and science education. For example, data would need to be collected for salaries of teachers in mathematics and science, rather than for salaries of all teachers. In addition, some adjustment of reported financial data would have to be made to compensate for widely differing costs of services in different regions of the country and even in different communities within a region. For these reasons, the committee decided not to use any financial data as indicators of science and mathematics education at this time. Given interest in the funding of education as well as the mixed research findings, however, financial data should be retained for future consideration as an indicator. In sum, the committee identified a minimal set of key variables that should be monitored, shown below, as a beginning set of indicators of the condition of precollege science and mathematics education. The rest of the chap- ter presents the committee's findings, conclusions, and recommendations about that condition using the four selected variables. They are presented in the logical order of inputs, process, and outcome. Although the committee selected for the development of indicators four aspects of precollege mathematics and science education generally recognized to be essential, due to limitations in the data base, only partial and limited indicators of these aspects can be constructed at this time. The committee has developed recommendations designed to improve the quality of available data and thus to enhance the value of these indicators. Even at their best, these indicators are not sufficient to provide an adequate portrayal of the state of science and mathematics education in the nation's schools. There
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14 Such choices will in part be influenced by state and federal support policies for teacher education and in part by local board policies and teacher contracts. To the degree that increased high school graduation requirements will entail having to offer more courses in mathematics and science, teacher shortages will be aggravated, but how much is unknown. (4) Demand forecasts are generally based on extrapolation of current conditions, taking account of likely changes in enrollment, class size, and curriculum. They do not take into account possible structural changes in the education system. Findings: Quality Lack of Information · Adequate information is lacking on the quali- fications of the teachers who are responsible for teaching mathematics and science in high school, middle/junior high school, or elementary school. · Information on certification, the only proxy available for qualification, is lacking for all but new entrants, although data on a national sample of the teaching force are now being collected. Requirements for Teaching Mathematics and Science · Even if available, information on certification is of questionable use as a measure of qualification because state certification requirements and preservice college curricula reflect a wide range of views on what constitutes a qualified or competent teacher in mathe- matics or science. Moreover, teachers currently cer- tified obtained their certification at different times that may have required different types of preparation; therefore, certification even within the same state does not connote equivalent preparation. · Although guidelines on teacher preparation developed by professional societies are generally available, they have not been uniformly adopted.
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15 Conclusions and Recommendations Supply and Demand · A suitable indicator to assess the sufficiency of secondary school science and mathematics teachers would be either the ratio of or the difference between projected demand and anticipated supply of qualified teachers. The ratio would indicate how close to balance demand and supply are; the difference would indicate the number of teachers that need to be added or that exceed the demand. The construction of such an indicator on teacher demand and supply is at present not feasible at the national level because of the lack of a meaningful common measure of qualification. · Individual states and localities might construct this type of indicator by using certification as an approximation for qualification or developing alternative criteria for teacher competence. In each case, an ade- quate determination would entail estimates of both demand and supply under alternative sets of assumptions about anticipated enrollments in mathematics and science classes and new entrants into the teaching of these fields. Aggregation of the state data might provide a useful national picture, especially if, in addition, information was reported concerning differences among states. Quality · The disparate views on teacher qualification and the variation in certification standards indicate the need to rethink the initial preparation and continuing training appropriate for teachers with instructional responsibilities in science and mathematics. Guidelines that have been prepared by professional societies need to be considered by the wider educational community, includ- ing bodies responsible for the certification of teachers and accreditation of teacher education programs. Require- ments should be detailed separately for teachers in ele- mentary school (grades 1 to 5 or 6), middle or junior high school (grades 6 or 7 to 8 or 9), and high school (grades 9 or 10 to 12), with particular attention to requirements that can be translated into effective college curricula and in-service education for teachers.
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16 · The development of guidelines for the preparation and continuing education of teachers would be advanced if the attributes of successful teaching in science or mathematics were better understood. Further research is necessary on the relationships between teacher training and student outcomes; for example, the effects on student achievement of different types of preservice and in- service training and of teaching experience. Current initiatives to augment the pool of science and mathe- matics teachers should be monitored to assess their effectiveness. Curriculum Content Findings Opportunity to Learn · Exposure to specific content as conveyed by curriculum materials and explicit teaching is a critical factor in student achievement. · Although commonly used textbooks and tests introduce a modicum of similarity in the range of topics generally treated within a year's course of instruction, emphasis varies from text to text, class to class, and test to test. Hence, for the nationally normed achieve- ment tests often used at the elementary and middle school levels, there may be a discrepancy between a student's opportunity to learn and the subject matter covered on the test, while at the same time the student may have learned considerably more than the test indicates. Textbooks and Courses · To a large extent, the content of instruction is based on the textbook used in a class, yet there is no continuing mechanism to encourage periodic and systematic analysis of the use and content of science and mathe- matics texts. The Commission on Excellence in Education has called for more widespread consumer information services for purchasers of texts. · At the secondary school level, and particularly in mathematics, course titles are a questionable indicator of content studied. The current practice of accepting similar course titles as representing exposure to similar
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17 material is likely to produce data of questionable quality. Conclusions and Recommendations Curriculum Content · There are no established standards for content derived either from past practice, practice elsewhere, anticipated need, or from theoretical constructs developed, say, from the nature of the discipline being taught or from learning theory. Until some consensus can be reached on instructional content that represents desirable alternatives for given learning goals, it is premature to suggest a specific indicator for this area. . Although the identification of an indicator for the content of mathematics and science instruction is not feasible at present, this does not alter the importance of this schooling input. Finding out what content students are exposed to is a necessary first step. · When information on what is currently taught has been collected and analyzed, reviews of the curriculum should be done by scientists, mathematicians, and other experts in the disciplines as well as teachers and educators. The reviews should evaluate material covered at each grade level or by courses, such as first-year algebra or introductory biology; consider relationships among grade levels or courses; and identify the knowledge and skills expected of students at the completion of each grade or course. Such reviews are needed in conjunction with addressing the critical matter of what content should be taught in mathematics and science. Textbooks and Courses . At a minimum, periodic surveys should be conducted to determine the relative frequency of use of various mathematics and science textbooks at each grade level in elementary school and for science and mathematics courses in secondary school. Timing of surveys should take into account the common cycles of textbook revision. · Surveys of textbook use should be followed by content analyses of the more commonly used texts. Analyses should proceed along several different lines: balance between the learning of recorded knowledge
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18 (concepts, facts) and its application (process), emphasis given to specific topics, adherence to the logic of a discipline, opportunity and guidance for student discovery of knowledge, and incorporation of learning theory. . Intensive studies should collect information from teachers and students on topics actually studied within a given grade or course. Observation of samples of indi- vidual classrooms can help to document the content of instruction. Such studies could help to inform curriculum decisions by local districts, even though the results may not lend themselves to generalization over a state, let alone over the United States as a whole. · Improved definitions of secondary school courses, based on their content, should be developed. As a first step, use of a standardized course title list, such as A Classification of Secondary School Courses (Evaluation Technologies, Inc., 1982), should be considered. Tests · Critical analysis of standardized tests should continue so as to establish their degree of correspondence to the instructional content of the class subjects for which they are used. Consideration should be given to inviting the judgment of teachers (and older students) concerning the students' opportunity to learn the material that is covered on each test. Instructional Time and Course Enrollment Findings Instructional Time and Student Learning · The amount of time given to the study of a subject is consistently correlated with student per- formance as measured by achievement tests, at the elementary school as well as at the secondary school level. Time spent on homework is also correlated with student achievement. The attention paid to homework by the teacher affects its contribution to student performance. .
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19 Measuring Instructional Time: Elementary School · For elementary schools, not enough data are available to discern clear trends over the last 20 years with respect to amount of instructional time spent on mathematics and science. On average, about 45 minutes a day are spent on mathematics and 20 minutes on science. Existing information, however, points to great variability from class to class in the amount of time given to in- struction in general and to each academic area specifically. Measuring Instructional Time: High School · The average high school senior graduating in the early 1980s has taken about 2-3/4 years of mathematics and 2-1/4 years of science during grades 9-12. · Compared with 20 years ago, average enrollments of high school students in science have declined. While this trend now appears to be reversing, enrollments have not returned to the level of the early 1960s. . High school enrollments in mathematics have increased over the last decade by about a semester. · College-bound students are taking more mathe- matics and physical science courses in secondary school than they did 10 years ago, and the increases were con- tinuous throughout that period. The gap in enrollment between males and females in advanced mathematics courses is narrowing. · A number of problems attend enrollment data currently available: uncertainties generated by using self-reports, differences in questions and method from survey to survey, and ambiguities created by similar course titles in mathematics that refer to different content or different levels of instruction. Conclusions and Recommendations: Elementary School Measures of Instructional Time . The average amount of time per week spent on mathematics instruction and on science instruction should be measured periodically for samples of elementary schools. This measure would serve as an indicator of length of exposure to pertinent subject matter; values
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20 can be compared for different years. Care must be taken, however, to ensure common understandings in collecting measures of time as to what constitutes science or mathe- matics instruction. Time given to mathematics or science, expressed as a percent of all instructional time, would indicate the priority given to these fields. · Efficiency of instruction should be assessed by comparing allocated time with instructional time and with time that is actually spent on learning tasks that appear to engage students, as established by observation. · Time spent on science and mathematics instruction in elementary school should be tracked on a sample basis at the national, state, and local levels. Logs kept by teachers could be used for this purpose, with selective classroom observation employed to check their accuracy. Improving Methods for Collecting Information · Time allocated by the teacher to instruction is not equivalent to time actually spent by the student. Classroom observation is needed to differentiate between the two. Time spent on such different components of instruction as laboratory work, lecturing, and review of text or homework may also affect student outcomes. Case studies that document use of instructional time are expensive, but this variable has proven to be a suffici- ently potent mediator of learning that the investment appears warranted. · Experimentation and research should be carried out to develop a proxy measure for time spent on instruction that would permit collecting the pertinent information at reasonable costs. Further documentation is needed to establish the variability of time spent on instruction over calendar time. The results of such should serve to establish the extent and periodicity of data collection needed for this indicator. . over classes and documentation Conclusions and Recommendations: Secondary School Measures of Course Enrollment · For grades 7 to 12, enrollments in mathematics and science courses at each grade level and cumulatively for the 6 years of secondary school or for the 3 or 4
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21 years of senior high school should be systematically collected and recorded. (See the pertinent recommenda- tion in the above section on curriculum content.) Alternatively, the mean number of years of mathematics or science taken or percentages of students taking 1, 2, or 3 or more years of such courses can be used as a measure. science enroll- . The disparities in mathematics and ment among various population groups warrant continued monitoring, so that distributional inequities can be addressed. National data on student enrollments collected in connection with the periodic surveys recommended above may be insufficient for this purpose. States should consider biennial or biannual collection of enrollment data by gender, by ethnicity, and by density of the school population. Improving Measures of Course Enrollment · Comparisons of enrollment over time are likely to be of great interest, but high-quality data are needed. Obtaining such data requires consistency in the design of surveys, data collection, and analysis. It also requires reduction of current ambiguities, for example, using a standardized system for describing courses, relying on transcripts or school enrollment logs rather than on student self-reports, and sampling a comparable universe from study to study. · The periodic studies of high school students have provided useful information, but greater effort should be directed toward reducing methodological dissimilarities. Also, the time between studies sometimes has been too long. Surveys of the type represented by High School and Beyond and NAEP should be repeated no less than every 4 years. · Time spent on homework in mathematics and science should be documented at all levels of education. Studies need to record how homework is used to support in-class instruction in order to prompt the use of better measures of total learning time in each grade. Assessing the Effects of Policy Changes · Many states are increasing requirements for high school graduation; some state university systems are increasing requirements for admission. The effects of
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22 these policy changes on student enrollment in high school mathematics and science courses and on the content of these courses should be monitored. Student Outcomes Findings Tests · It has proved difficult with current test methodology to construct tests that can be used for large numbers of students and yet are adequate for assessing an individual's cognitive processes, for example, the ability to generalize knowledge and apply it to a variety of unfamiliar problems. However, existing tests of mathe- matics and science of the kind employed by NAEP, HSB, and TEA are sufficiently valid for the purpose of indicating group achievement levels. Achievement: All Students · Evidence suggests an erosion over the last 20 years in average achievement test scores for the nation's students in both mathematics and science. Results of the most recent assessments indicate a halt to this decline and, at some grade levels, even a slight increase in scores in mathematics. Much of this generally observed but small increase is due to increasing achievement scores for black students, especially for mathematics in the lower and middle grades. · Analysis of the most recent NAEP mathematics assessment yields evidence that gains have been made on computational skills but that there is either no improve- ment or a slight decrease in scores on test items that call for a deeper level of understanding or more complex problem-solving behavior. . Available information on how well U.S. students perform compared with students in other countries shows U.S. students generally ranking average or lower, with students in most of the industrialized countries perform- ing increasingly better than U.S. students as they move through school. Taking account of different student retention rates in different countries changes this finding somewhat in favor of the United States, but the
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23 most recently available data, especially data comparing the United States to Japan, are unfavorable for the United States. Achievement: College-Bound Students · There is evidence that college-bound students perform about as well on tests of mathematics and science achievement as they did a decade or two ago. Conclusions and Recommendations Assessments of Achievement · Systematic cross-sectional assessments of general student achievement in science and mathematics, such as the ones carried out through NAEP, should be carried out no less than every 4 years to allow comparisons over relatively short periods of time. The samples on these assessments should continue to be sufficiently large to allow comparisons by ethnic group, gender, region of the country, and type of community (urban, suburban, rural, central city). . Longitudinal studies such as High School and Beyond are important for following the progress of students through school and later and should be maintained. . International assessments in mathematics and science education such as those sponsored by TEA need to be carried out at least every 10 years. Tests · Developmental work on tests is needed to ensure that they assess student learning considered useful and important. Instruments used for achievement testing should be reviewed from time to time by scientific and professional groups to ensure that they reflect contempo- rary knowledge deemed to be important for students to learn. Such reviews may lead to periodic changes in test content--an objective that must be reconciled with the goal of being able to compare student achievement over time.
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24 · Work is needed on curriculum-referenced tests that can be used on a wider than local basis, especially for upper-level courses. This work will require careful research on the content of instruction, tests constructed with a common core of items, and alternative sections of tests to match curricular alternatives. · Assessments should include an evaluation of the depth of a student's understanding of concepts, the ability to address nonroutine problems, and skills in the process of doing mathematics and science. Especially for science, it is desirable that a test involve some hands-on tasks.
Representative terms from entire chapter: