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OCR for page 83
4
The Schooling Process:
Instructional Time and Course
Enrollment
A number of different approaches have been taken to
identify the process variables that affect student
learning. One approach has focused on effective teaching
practices (Rosenshine, 1976), including the capacity of a
teacher to plan and make decisions, use appropriate
instructional strategies, and manage the classroom. There
is some evidence that careful planning, decisiveness, and
consistency on the part of a teacher has positive effects
on student learning (Emmer et al., 1980; Brophy, 1983),
but most of this research has dealt with elementary
school, and further documentation is needed. A second
approach has been to identify differences in teacher/
student interaction and establish the effects, if any, on
student learning. The teacher behaviors that are thought
to make a difference include frequency of interaction
with students, frequency of feedback, smallgroup versus
largegroup instruction, and providing for independent
work suited to individual student learning style and
progress. Here again, research is not sufficiently far
advanced to provide unequivocal conclusions (Berliner,
1980; Gage, 1978).
The one process variable that, again and again, has
shown to be correlated with student learning is the time
devoted to an area of the curriculum, usually expressed
in minutes per day at the elementary level and in course
enrollment at the secondary level. Borg (1980) summarized
the considerable research in this area. While he suggests
that further studies are needed to determine how large an
effect quantity of schooling has on achievement, he con
cludes (Borg, 1980:47): "There can hardly be any doubt,
however, that a significant effect is present." An
important caveat, however, is to distinguishespecially
in elementary schoolamong time allocated for instruc
83
OCR for page 83
84
tion, time actually given to instruction, and time that
students are engaged in learning tasks. A mechanical
lengthening of allocated time may have little effect on
student learning (Levin, 1984) or may even have negative
consequences (Rosenshine, 1980).
INSTRUCTIONAL TIME AND STUDENT LEARNING
The effect of time spent on a subject is particularly
evident in mathematics instruction. Even such gross
measures as years of instruction and hours of homework
are correlated with student achievement: Table 12 dis
plays the results of a general mathematics test given to
some 28,000 1980 seniors participating in High School and
Beyond. Most of the 33 items in this test were on arith
metic, and all but 3 items dealt with mathematics gener
ally taught before 10th grade. Evidence of even more
marked effects on achievement of taking advanced mathe
matics courses comes from the level1 mathematics test
given to 1982 seniors in the High School and Beyond
followup. This test largely covered arithmetic and
9thgrade algebra; all but two of the 28 items on the
test were based on mathematics taught before 10th grade.
The effects on achievement persisted even when adjusted
for race, sex, socioeconomic status (SES), and 10thgrade
scores on the same mathematics test given to the same
students when they were sophomores in 1980: Table 13
shows that the average score for students who took the
full sequence of high school mathematics courses is
nearly a standard deviation higher than that for students
who took no mathematics at the level of Algebra 1 or
above, even after adjustment for other factors affecting
test scores.
Evidence also comes from data summarized in Table 14,
derived from a special 19751976 NAEP study on mathematics
achievement of the nation's 17yearolds. A mathematics
test was constructed from exercises selected from the
first NAEP mathematics assessment in 19721973 to assess
basic skills in computation, elementary algebra and
geometry, and logic and measurement. The analyst
comments (Jones, 1984:1211):
The average score for students who reported not
having taken Algebra 1, Algebra 2, or geometry is
seen to be 47%, whereas the average for students
who had taken all three courses is 82% correct for
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OCR for page 83
87
TABLE 14 Average Mathematics Score (Percent Correct)
by Number of Years of Algebra 1, Geometry, and Algebra
2 for 17YearOlds, 19751976
Number of
Years of Average
Courses Score
Percent of Students
with 0, 1, 2, or 3 Years
Black White All
0 47 29 18 20
1 59 37 24 26
2 70 21 26 25
3 82 13 32 29
SOURCE: Adapted from Jones (1984:1211).
the same mathematics exercises. This is a differ
ence of nearly two standard deviations. The
relation of mathematics achievement to courses
taken is strong and clear. . . . The data . .
show a disproportionate representation of black
students and white students for differing numbers
of years of high school algebra and geometry.
About two thirds of black students but only 42% of
white students report having taken 0 or 1 year of
high school algebra and geometry. This difference
between black and white students in algebra and
geometry enrollments might be responsible for a
large part of the whiteblack average difference in
mathematics achievement scores.
Jones's conjecture appears to be borne out by the
previously cited results of the mathematics test (level
1) taken by the 1982 high school seniors in the High
School and Beyond followup. The mean test score was
51.6, with a standard deviation of 10 (see Table 13).
When scores were adjusted for courses taken, the differ
ence in unadjusted scores between males and females
(adjusted for race) was reduced from 1.52 to 1.08; the
difference between blacks and Asians (adjusted for sex)
dropped from 12.58 to 5.25; and the difference between
Asians and whites (adjusted for sex) changed from 4.07 in
favor of Asians to 1.26 in favor of whites.
The strong relationship between enrollment in high
school mathematics courses and test scores is likely, in
part, to result from the choices of high achievers to
OCR for page 83
88
enroll in more mathematics courses and the choices of low
achievers to enroll in fewer courses. In the data from
High School and Beyond, however, senior mathematics
scores are related to mathematics courses taken, even
after adjusting not only for race, sex, and SES, but also
for earlier (sophomore) scores on the mathematics test
(see final column, Table 13); this strongly suggests that
course taking per se influences test performance.
Although testing for science achievement is less common
than for mathematics achievement, both Welch (1983) and
Wolf (1977) found positive correlations between science
test scores and semesters of
The correlations are somewhat lower than in mathematics,
possibly because of the less sequential character of the
science curriculum.
Given the robust findings regarding this variable and
the need to limit the number of indicators, the committee
selected instructional time given to a subject to stand
as a proxy for schooling processes in general. Even so,
The complica
~ science or course exposure.
measurement of this variable is not simple.
tions include: __
discrepancies between time schedules For
a subject in school and time actually devoted to instruc
Lion; time used for homework; and the different organiza
tion of elementary and secondary education, requiring
different approaches to measuring time spent on a subject.
These issues are discussed below.
Allocated Versus Actual Instructional Time
A recent research review (Karweit, 1983) on the time
used for instruction concludes that, at most, instruction
in elementary school may occupy 60 percent of the 6hour
school day; this is reduced further by student absences
and student inattention. This loss of time from instruc
tion is not a new phenomenon; some 20 years ago, PA
W. Jackson (1965) published a landmark description of
life in the classroom that vividly drove home this point.
Classroom observation has continued to document the
extent to which students are actually engaged in learning
during instruction. An example of such observation done
on 21 Sthgrade classrooms in California is given In
Table 15, which shows that students are inattentive for
as much as a onethird of instructional time.
With respect to absences, the same study found that,
of the 180 days in a school year, 30 days are usually
lost to classroom instruction due to field trips, student
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89
TABLE 15 Allocated and Pupil Engaged Time in Mathematics
for Four 5thGrade Classes
Classes
B C D
Time
Number of days data collected
Average minutes allocated daily
Percent of time students engaged
Engaged minutes per day
73
23
74
17
89
28
91
61
80 80
22 49
93
57
66
38
SOURCE: Berliner (1978:21) as cited in Romberg and
Carpenter (1985).
illness, a Christmas play, and the like (Berliner et al.,
1978), although field trips and some extracurricular
activities may enhance learning. At the same time, poor
use of instructional time inhibits the effectiveness of
teachers. Karweit (1983) points out that, even under the
most favorable assumptions of minimal school absence and
loss of instructional time, students are occupied with
actual learning only a little more than onehalf their
scheduled time in school; for some students, it may be
less than onethird of the time.
While there have been fewer systematic studies of time
use in secondary school, anecdotal information gives
little reason to think that the situation is much dif
ferent (see, e.g., Boyer, 1983).
Homework
Homework is an inexpensive way of extending instruc
tional time. In addition to the data from High School
and Beyond, evidence on its relationship to student
performance also comes from the first TEA mathematics
assessment. Husen (1967) reports a strong positive
correlation between mean mathematics scores for all
countries and mean hours spent on all homework as well as
on mathematics homework specifically. According to the
IEA findings, a bit more than onethird of all homework
time, on average, is spent on mathematics in all coun
tries. These findings, based on student selfreports
from the 1964 mathematics assessment, indicate that 8th
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go
TABLE 16 Hours per Week Scheduled for Mathematics: 8th
Graders and Mathematics Students in Senior Year(1964 Data)
Mathematics Instruction Mathematics Homework
8 th G r ade Sen i or s 8 th G r a de Sen for s
Country Mean SD Mean SD Mean SD Mean SD
Australia 5.2 .6 6.9 1.6 2.5 1.6 6.1 3.3
Belgium 4.7 1.0 7.4 1.1 3.7 2.5 8.7 4.6
England 4.0 .8 4.4 1.3 1.8 .9 4.1 1.9
Finland 3.0 .2 4.0 0 2.9 2.2 6.6 3.5
France 4.4 .8 8.9 .5 3.4 1.9 9.6 3.5
Germany 3.9 .6 4.2 .5 3.4 1.9 5.1 2.a
Netherlands 4.6 1.5 5.1 .3 2.6 1.9 5.7 3.4
Israel 4.1 .5 5.0 .3 4.4 2.6 7.5 3.7
Japan 4.5 .5 5.4 1.1 3.0 1.8 5.2 4.3
Scotland 4.6 1.0 6.2 1.5 2.2 1.6 4.1 2.3
Sweden 3.8 .9 4.6 1.6 1.9 1.3 4.9 2.9
United States 4.6 1.3 5.0 .9 3.1 2.3 4.1 2.4
NOTE: Hours of instruction may refer to periods somewhat shorter than
60 minutes.
SOURCE: Husen (1967, Vol. I:278).
graders in the United States spent about 3.1 hours per
week on mathematics homework, slightly above the average
for all countries (see Table 16). For mathematics
students in the last year of secondary school, however,
the required hours of homework in most countries doubled
between 8th grade and 12th grade, while in the United
States the increase was only from 3 to 4 hours per week.
This difference may have contributed to the poorer per
formance of older U.S. students on the IEA tests. Data
on homework were again collected by TEA from students and
teachers in 19811982 during the Second International
Mathematics Study; the teacher responses have been
analyzed. For U.S. 8th graders, teachers estimated that
the time typically spent on assigned homework was 2.3
hours per week; 75 percent of the students were estimated
to spend 3 hours or less. For 12th graders, teachers
reported that they expected an average 4 hours of
homework per week from students in precalculus classes
and 5 hours from students in calculus classes (Travers,
1984).
Most other information available on the amount of
homework done by students is not specific as to subject
matter. Studies done on high school seniors in 1972 and
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91
1980 show that time spent on all homework dropped during
this period: the number of seniors who reported that
they spent at least 5 hours per week on homework
decreased from 35.2 to 24.5 percent, with decreases
greatest in the south (36 to 21 percent) (National Center
for Education Statistics, 1984c). The average amount of
homework time reported was 3.9 hours per week, down from
4.3 hours in 1972, although the amount of homework effort
reported by students in academic programs remained
virtually constant at 5.1 hours (National Center for
Education Statistics, 1984c). In contrast, according to
a recent study (Fetters et al., 1983), six times as many
seniors in Japan spend more than 10 hours per week on
homework as in America (36 compared with 6 percent) and
twothirds of the Japanese students spend at least 5
hours on homework compared with onefourth in America.
Research evidence indicates that the way homework
assignments are treated affects the contribution of
homework to student achievement (Walberg, 1985). Checks
on completion, discussion in class, and correction by the
teacher greatly increase the value of homework. Hence,
attempts to track hours of homework should not only record
the subject in which the homework is assigned, but also
the way homework is used to support classroom instruction.
MEASURING INSTRUCT IONAL T IME
The organization of high school according to curriculum
area permits tracking instructional time through course
enrollment, at least as a first approximation. For ele
mentary school, studies have been made of the time spent
on specific subjects, documented by classroom observation
to determine actual versus allocated instructional time.
The method to be used for tracking time for grades 7 and
8 varies depending on their organization.
Elementary School
Recent national data on time scheduled for mathematics
in grades 16 come from three sources, one of whichthe
Weiss (1978) surveyalso collected information on science
instruction. Data reported by teachers, shown in Table
17, indicate that time spent in teaching mathematics and
science increases somewhat in the upper elementary grades;
average time increases from 41 minutes in grades K3 to
OCR for page 83
92
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93
51 minutes in grades 46 for mathematics and from 17 to
28 minutes for science. Collecting information on time
spent on science instruction in grades 16 is difficult
because there is no common understanding on what subjects
in elementary school are actually considered part of
science. With the coming of more work using computers,
mathematics will also become more difficult to define.
The second source of information is the Sustaining
Effects Study (Wang et al., 1978), which examined the
nature and effectiveness of Title I compensatory educa
tion programs. The data from this study show more time
spent on mathematics per day than do the Weiss data,
ranging from 47 to 68 minutes. One striking finding is a
lowered emphasis on reading in the upper grades (see
Figure 2). Information from the previously mentioned
California study (Berliner et al., 1978) shows the range
of time allocated to mathematics in 5th grade to be from
23 to 61 minutes per day (see Table 15, above); about the
same amount of variation was observed in 2nd grade.
According to these data, students in one classroom spent
nearly three times as much time on mathematics as did
students in another class of the same grade.
Similar variability has been observed in time alloca
tion studies over the past 60 years. Because several of
these studies recorded their methodology with great care,
it is possible to compare allocation of instructional
time over the last 100 years (Borg, 1980); see Figure 3.
It is interesting that the time allocated to mathematics
instruction has stayed relatively stable, considering the
general decrease in time devoted to all academic
instruction.
The amount of time scheduled for mathematics instruc
tion in 8th grade is approximately the same as that in
elementary school, according to the 1964 TEA data. Com
parison with 11 other industrialized countries shows that
the mean hours of mathematics instruction reported for
the United States were exceeded only in Australia and
Belgium; there was greater variation around the mean in
the United States than in most other countries (see Table
16, above). Similar information, including time spent on
specific topics, was collected in 19811982 during the
Second International Mathematics Study. Preliminary
results for the United States indicate that, while
mathematics is generally taught 5 periods per week in 8th
grade, class length can vary from 40 to 60 minutes.
Thus, while the median number of clock hours of mathe
matics instruction per year is 145, the range is from 115
to 180 hours (Travers, 1984).
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99
TYPE OF COURSE
Math
Science
Engl ish
Social
Studies
Foreign
Languages
.. : : ~~
1972
1 982
—; 
.......................................... .~ ~ ~ , ~
1 1 1 1 1 1
0 1 2 3 4 5 6
NUMBER OF SEMESTERS
FIGURE 4 Courses reported taken in grades 1012 by 1972,
1980, and 1982 high school seniors. Data from High
School and Beyond and the National Longitudinal Study of
1972 Seniors.
SOURCE: NCES (1984:26); Wisconsin Center for Education
Research (1984).
Education Research, 1984) are also given. Not much change
is apparent over the 2 years, although the enrollment gap
between males and females in calculus and total number
of years of mathematics taken seems to be narrowing
somewhat.
As Figure 4 shows, in 1980, students reported taking
an average of 31/2 semesters of science in grades 1012,
about the same as in 1972. The amount of mathematics
OCR for page 83
100
reported has increased by about half a semester to 4+
semesters in 1980. Since almost all students report that
they take mathematics in grade 9 as well, this means
that, on average, students report that they take more
than 3 years of mathematics in secondary school. Since
about threefourths of all students take a science course
in grade 9, high school graduates report that on average
they will have taken nearly 21/2 years of science. Some
of the increase in mathematics enrollment may be due to
the fact that, from 1972 to 1980, high school remedial
mathematics courses increased from 4 to 30 percent
(National Center for Education Statistics, 1984b),
however, data on collegebound students (see Figure 7,
below) indicate that enrollment increased in the
higherlevel courses as well. Preliminary data on course
enrollments reported by 1982 seniors (Wisconsin Center
for Education Research, 1984) show little change in
mathematics or science since 1980 (see Figure 4).
A recent study by the National Center for Education
Statistics (1984b) examined enrollment data from a sample
of over 12,000 transcripts of the 1982 HSB high school
seniors (see Table 20). As noted above, the transcripts
tended to reflect somewhat less course work taken than
the seniors had reported. The transcripts of the 1982
seniors showed, on average, 2.2 years of science and 2.7
years of mathematics taken during grades 912, rather
than the 2.5 years of science and 3+ years of mathematics
reported by the students themselves. Differences by
selected student characteristics are also shown in Table
20.
Data from National Assessment of Educational Progress
(1983), shown in Table 21, appear to confirm that
increases in mathematics enrollment may have come about
in part through increased enrollment in general and
remedial mathematics, but there has also been a sizable
increase of enrollment in computer courses. It should be
noted that differences in mathematics enrollment between
whites and blacks and males and females persist, although
they have narrowed somewhat (National Assessment of
Educational Progress, 1983): in 1982, the percentage of
students taking at least onehalf year of trigonometry
was 14.9 for whites and 8.2 for blacks, 15.0 for males
and 12.7 for females; for precalculus/calculus, it was
4.4 for whites and 2.8 for blacks, 4.7 for males and 3.6
for females; for computer courses, it was 9.6 for whites
and 11.3 for blacks, 11.1 for males and 8.6 for females.
OCR for page 83
101
TABLE 20 Average Number of Years of Science and
Mathematics in Grades 912 by 1982 Seniors, by Selected
Characteristics of Students
Sample
Subgroup Science Mathematics Size
All students 2.2 2.7 12,116
Sex
Male 2.4 2.7 5,914
Female 2.1 2.6 6,202
Race/ethnicity
Hispanic 1.9 2.4 2,420
Black 2.1 2.6 1,599
American Indian 2.0 2.3 173
Asian American 2.7 3.2 327
White 2.3 2.7 7,497
High school programa
Academic 2.9 3.3 5,356
General 2.1 2.5 3,710
Vocational 1.7 2.2 2,744
Region
New England 2.6 3.0 623
Middle Atlantic 2.6 2.9  2,154
South Atlantic 2.3 2.7 1,673
East south central 2.2 2.5 562
West south central 2.3 2.8 1,334
East north central 2.0 2.5 2,S71
West north central 2.3 2.7 901
Mountain 2.1 2.4 543
Pacific 1.8 2.6 1,755
NOTE: Transcript data from High School and Beyond
Abased on student selfreports in 1980.
.
SOURCE: National Center for Education Statistics (1984b)
.
Enrollment results derived from the 1982 High School and
Beyond followup data are quite similar to the NAEP data.
A recent study (Welch et al., 1983) of enrollment in
science courses in grades 712, including private schools,
found that 56 percent of students in grades 1012 were
OCR for page 83
102
TABLE 21 Percentages of 17YearOlds Who Have Completed
at Least OneHalf Year of Specific Courses
Course
1978 1982
General or business mathematics
Prealgebra
Algebra
Geometry
Algebra 2
Trigonometry
Precalculus/calculus
Computer science
45.6
45.8
72.1
51.3
36.9
12.9
3.9
5.0
50.0
44.3
70.9
51.8
38.4
13.8
4.2
9.7
SOURCE: National Assessment of Educational Progress
(1983:3)
enrolled in science in 19811982, up 4 percent from
19761977; the percentage of students taking science in
grades 79 has remained relatively stable at 86 percent
of the total population. While recent trends may be
encouraging, science enrollments are still much lower
than they were in the early 1960s, when science and
mathematics was emphasized in the schools in response to
the launching of Sputnik by the Union of Soviet Socialist
Republics. Total enrollment in eight science courses
general science, biology, botany, zoology, physiology,
earth science, chemistry, and physicsin grades 912
between 1949 and 1982 as a percentage of all students
enrolled is shown in Figure 5; these courses make up
about threefourths of the total science enrollments in
these grades. There are sizable regional variations in
the percentage of students taking science, with enroll
ments consistently higher in the northeast than elsewhere
(see Figure 6). For all regions except the northeast,
10th grade is the last year that the preponderance of
students take a science course.
The preparation of collegebound students is of
interest because it is related to their future education
and choice of majors, and thus to the potential future
supply of scientists and engineers. Enrollment data for
students participating in the Admissions Testing Program
of the College Board (19731984)about onethird of all
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103
70
o
CC
Z 60
En
By
LLJ
CD
J
a:
LL
o
A
UJ
I:
UJ
50
40 _
30
19481949 19601961 19721973 19811982
\




1 1 1 1
YEARS
1 9761 977
FIGURE 5 Percentage of total enrollment in eight science
courses (general science, biology, botany, zoology,
physiology, earth science, chemistry, and physics)
grades 912, 19481949 to 19811982.
SOURCE: Welch et al. (1983).
high school seniorsshow considerably more mathematics
and science for these students than for all students:
the mean number of years of mathematics studied in grades
912 is 3.62, and mean number of years of science studied
is 3.25. The number of years of mathematics and of
physical science being studied by these students has
increased steadily between 1973 and 1983 (see Figure 7).
Males still enroll in more mathematics courses than do
females, although the gap, at least for collegebound
students, has been narrowing: in 1973, 60 percent of
males and 37 percent of females taking the Scholastic
Aptitude Tests (SATs) reported expecting to complete 4 or
more years of mathematics in high school; in 1983, the
percentages were 71 for males and 57 for females.
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104
100
80
60
20
o
100
80
60
L1J
cat
40
20
o
Northeast 1 00
80
60
UJ
cat
40
20
o
Southeast
r I I I I I
7 8 9 10 11 12 7 8 9 10 11 12
G RAD E G R AD E
Central 1 00
80
60
LL
cat
`< ~ 40
20
I _
 \/\
West
1 1 1 1 1 1 o 1 1 1 1 1
7 8 9 10 11 12 7 8 9 10 11 12
G RADE G RAD E
FIGURE 6 Percentage of grade enrolled in science
courses, by region; special survey of 16,000 students in
600 secondary schools.
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3.70
3.60
3.50
3.40
3.20
en
cr
a:
us 3 10
r
LL
O ~
111 ~
m
2.00
1.90
1 .80
1.70
1.60
1 .50
1.40
1.30
Mathem:





Biological Sciences



1 1 1 1 1 1 1 1 1 1 1
1974 1976 1978 1980 1982 1 984
YEAR
FIGURE 7 Number of years of selected subjects studied by
college students taking scholastic aptitude tests.
SOURCE: Admissions Testing Program of the College Board
(19731984).
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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.
.
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 variabil
ity from class to class in the amount of time given to
instruction in general and to each academic area
specifically.
High School
· The average high school senior graduating in the
early 1980s has taken about 23/4 years of mathematics
and 21/4 years of science during grades 912.
· 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.
· Collegebound students are taking more mathematics
and physical science courses in secondary school than
they did 10 years ago, and the increases were continuous
throughout that period. The gap in enrollment between
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males and females in advanced mathematics courses is
narrowing.
· A number of problems attend enrollment data
currently available: uncertainties generated by using
selfreports, 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
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
mathematics 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 expen
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sive, but this variable has proven to be a sufficiently
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 classes and
over calendar time. The results of such documentation
should serve to establish the extent and periodicity of
data collection needed for this indicator.
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
years of senior high school should be systematically
collected and recorded. (See the pertinent recommendation
in the section on content in Chapter 2.) 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.
· The disparities in mathematics and science enroll
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 tr iannual 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 highquality 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
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student selfreports, 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 inclass
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
these policy changes on student enrollment in high school
mathematics and science courses and on the content of
these courses should be monitored.