Indicators of Precollege Education in Science and Mathematics A Preliminary Review (1985) / Chapter Skim
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2. The Selection and Interpretation of Indicators
2. The Selection and Interpretation of Indicators
Pages 25-43
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From page 25... ...
. The Center publishes two major compilations annually: The Digest of Education Statistics, issued since 1962, which provides an abstract of statistical information on United States education from prekindergarten through graduate school, and The Condition of Education, issued since 1975, which presents the statistics in charts accompanied by discussion.
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From page 26... ...
The NSF has special responsibility in the area of science and mathematics education, but most of its data collection activities focus on higher education and scientific and engineering personnel rather than on precollege education. However, NSF does support some of TEA ~ ~ work and has sponsored special studies on science and mathematics in the SChOOlS, most recently a national science assessment using the NAEP framework (Hueftle et al., 1983)
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From page 27... ...
THE CONCEPT OF INDICATORS The existence of potentially relevant information does not necessarily make it possible to formulate conclusions about the state of mathematics education or science education -- or any other field. For one thing, the data often are not comparable; see, for example, the critique by Gray (1984)
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From page 28... ...
There are advantages, then, in adopting a small number of indicators, carefully selected to highlight major aspects of education in the areas of interest, so as to encourage continuing data collection. There are four stages in the development of indicators: identifying the central concepts relevant to the system in question; deciding what measurable variables best represent those concepts; analyzing and combining the data collected on the variables into informative indicators; and presenting the results in succinct and clear form.
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From page 29... ...
Outcomes (Outputs) Student Student Student characteristics behaviors achievement Teacher Teacher Student characteristics behaviors attitudes Curriculum Classroom Career choices materials environment Teacher changes Public attitudes External Institutional Goals influences effects Advances in science .
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From page 30... ...
Hence, student achievement must be considered as the primary indicator of the condition of science and mathematics education. A second outcome often stated as a goal of science and mathematics education is the development of favorable attitudes of students toward these fields.
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From page 31... ...
The committee believes that the question of developing and using an indicator representing student attitudes towards science and mathematics deserves reconsideration in any further work on indicators. Other outcomes of education generally considered to be important include college attendance, choice of college majors, choice of careers, and later career paths, including life income and job satisfaction.
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From page 32... ...
Pending research findings that more clearly link schooling variables to career achievement and other life outcomes, the committee has not chosen to include in this preliminary review indicators representing such outcomes. Schooling Inputs and Processes The selection of student achievement as the outcome variable of greatest interest determines to a considerable extent what schooling input and process variables need to be selected, namely, those that seem to have some causal relationship to student achievement.
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From page 33... ...
Based on educational practice and experience and the available research evidence, the committee believes that time given to a subject in elementary school and course enrollment in secondary school ought to be considered key process variables in developing indicators of mathematics and science education. This is not to say that instructional time is the only factor affecting learning or that
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From page 34... ...
The correlation of student achievement with number of mathematics courses taken becomes even stronger when the content of the mathematics courses is taken into account: with the variables controlled for one another, Horn and Walberg (1984) found that an index of the number of advanced mathematics courses taken correlated somewhat more highly with mathematics achievement than did just the number of all mathematics courses taken.
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From page 35... ...
Although the teacher share of the school dollar has dropped in the last decade -- in part because teacher salaries have not kept pace with inflation -- those salaries still represented 38 to 44 percent of total direct operating costs for public schools during 1982-1983, even without counting pension payments or fringe benefits (Feistritzer, 1983; Educational Research Service, 1984, personal communication)
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From page 36... ...
n Little is known, however, about the ways in which teacher and student behaviors are related to alternative investments, say, in teacher salaries, materials and equipment, school plant, specialist teachers, and the like. A major cost factor is class size, yet the evidence indicates that marginal (if costly)
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From page 37... ...
But while the programs supporting science and mathematics education within the National Science Foundation and the Department of Education are generally identifiable, some others of considerable magnitude -- for example, those sponsored by the Department of Defense and by the National Aeronautics and Space Administration -- are not. In the absence of relevant budgetary information and without further evidence on the relationship between educational spending and student performance, the committee, in this preliminary review, decided not to recommend use of expenditure data as an indicator.
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From page 38... ...
For example, counting the number of certified mathematics teachers actively teaching in a particular school year provides a datum that could be displayed against other pieces of information: total secondary school enrollment, enrollment in mathematics courses, total number of secondary school teachers, expected demand for mathematics teachers, numbers of mathematics teachers in some previous year, or -- if there are separate counts for different geographic entities-comparisons of the density of mathematics teachers related to student population. Education System INPUTS PROCESS OUTCOME Teachers quantity qual ity ~ Curricul urn content Instructional ti me/cou rse ~ ach tenement en rol I me nt Student FIGURE 1 Areas of science and mathematics education to be monitored.
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From page 39... ...
; some, such as several of the NCES data collections, are repeated annually; others -- IEA, for example -- are repeated at irregular intervals; still others are designed as longitudinal studies that follow a cohort population over a number of years. Methods for collecting information pertinent to the selected variables depend on the nature of a particular variable and on the types of analyses appropriate for portraying values associated with it.
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From page 40... ...
DISAGGREGATING DATA Collecting Data at the State and Local Levels Much of the data used to document the several recent reports on education that have given impetus to various reform efforts come from national surveys or nationally administered tests. Such information may be useful for developing federal education policy and for following general national trends.
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From page 41... ...
Disaggregating Data by Demographic Descriptors To serve the national goal of equal educational opportunity, it is important to collect certain data by gender and minority status. The reason for this type of disaggregation is to obtain information on critical distributional issues; for example, different enrollment rates by members of different minority groups in advanced mathematics and science courses may provide at least a partial explanation for different achievement levels.
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From page 42... ...
A third basis for comparison is to establish an ideal value for an indicator and record the difference between it and the observed value; for instance, the number of qualified mathematics teachers available might be compared with the supply needed. The problem with this method is that determining the ideal value is usually difficult.
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From page 43... ...
Hence, international comparisons of the performance scores on these tests are relatively free of the kinds of cultural bias that would vitiate comparability in other studies less carefully designed and controlled, and the wealth of accompanying information has served to explain some of the differences in results All three methods of interpreting indicator values-comparisons over time, comparison among groups or geographic entities, and comparison to an ideal value -- are used in this report. These interpretations are accompanied by commentary on their appropriateness and associated difficulties in given instances.
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