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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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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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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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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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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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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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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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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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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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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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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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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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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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· 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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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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(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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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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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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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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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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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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· 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:
mathematics education
