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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, small-group versus large-group 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 distinguish--especially in elementary school--among time allocated for instruc- 83

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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 level-1 mathematics test given to 1982 seniors in the High School and Beyond follow-up. This test largely covered arithmetic and 9th-grade 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 10th-grade 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 1975-1976 NAEP study on mathematics achievement of the nation's 17-year-olds. A mathematics test was constructed from exercises selected from the first NAEP mathematics assessment in 1972-1973 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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86 o o s u U] s ~ - - :n a) .,, s 11 en a) EN H U] U In ~ ~ S S ~ ~: o V ~n ~; ,' ~ 4 O a ~5 4 U) r~' ~: U] o ,. 0 a) ~, ~ ~. .,, a U. cn c X s a U] ~ X 0 ~ ~ CO ~ ~ ~ `: U] :~ a ~: u O ~ U] 0 U] U) ~ 0 ~ .- a, a' ~ ~ U] ~ c: u a O O s ~ c) s V] -, 0,, Y 0 E~ ~ 11 ~q O O O 0 a) ~ u' U) ~ ~ C) a' 0 V ~ O ~ ~ 5 m ~ S 0 ~0 u) ~ ~ o ~ ~ ~ ~ ~ 0 ~ ~ a~ r~ ~ e S O O 1 1 1 1 ~ U] o ., 4 0 r~ e CD 1 1 ~D CO 1 1 S ~ n k (J O Z C~ O ~ C~ O 1 a~ ~ O 1 h 4J o C~ C~ CD ~ CO CD CO ~ ~4 a) k o _t k ~ O O a' a C~ s" aJ ~ <: ~: . n a' ~: h Q} O ~ C) .,' U) 8 UB .,. 3 S C~ S ~ ._' k ~ k O . S k o 3 a) C' .,' a a) s a 0 ~ . a) 0 E~ U, :e U' .,, ~n ~ _~ C) - - 0 ~ U) U)

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87 TABLE 14 Average Mathematics Score (Percent Correct) by Number of Years of Algebra 1, Geometry, and Algebra 2 for 17-Year-Olds, 1975-1976 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 white-black 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 follow-up. 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

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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 6-hour 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 Sth-grade classrooms in California is given In Table 15, which shows that students are inattentive for as much as a one-third 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 5th-Grade 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 one-half their scheduled time in school; for some students, it may be less than one-third 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 one-third of all homework time, on average, is spent on mathematics in all coun- tries. These findings, based on student self-reports 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 1981-1982 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 two-thirds of the Japanese students spend at least 5 hours on homework compared with one-fourth 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 1-6 come from three sources, one of which--the Weiss (1978) survey--also 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 K-3 to

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93 51 minutes in grades 4-6 for mathematics and from 17 to 28 minutes for science. Collecting information on time spent on science instruction in grades 1-6 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 1981-1982 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 10-12 by 1972, 1980, and 1982 high school seniors. Data from High School and Beyond and the National Longitudinal Study of 1972 Seniors. SOURCE: NCES (1984:2-6); 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 3-1/2 semesters of science in grades 10-12, about the same as in 1972. The amount of mathematics

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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 three-fourths of all students take a science course in grade 9, high school graduates report that on average they will have taken nearly 2-1/2 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 college-bound students (see Figure 7, below) indicate that enrollment increased in the higher-level 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 9-12, 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 one-half 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.

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101 TABLE 20 Average Number of Years of Science and Mathematics in Grades 9-12 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 self-reports in 1980. . SOURCE: National Center for Education Statistics (1984b) . Enrollment results derived from the 1982 High School and Beyond follow-up data are quite similar to the NAEP data. A recent study (Welch et al., 1983) of enrollment in science courses in grades 7-12, including private schools, found that 56 percent of students in grades 10-12 were

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102 TABLE 21 Percentages of 17-Year-Olds Who Have Completed at Least One-Half Year of Specific Courses Course 1978 1982 General or business mathematics Pre-algebra Algebra Geometry Algebra 2 Trigonometry Pre-calculus/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 1981-1982, up 4 percent from 1976-1977; the percentage of students taking science in grades 7-9 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 physics--in grades 9-12 between 1949 and 1982 as a percentage of all students enrolled is shown in Figure 5; these courses make up about three-fourths 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 college-bound 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 (1973-1984)--about one-third 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 1948-1949 1960-1961 1972-1973 1981-1982 \ - - - - 1 1 1 1 YEARS 1 976-1 977 FIGURE 5 Percentage of total enrollment in eight science courses (general science, biology, botany, zoology, physiology, earth science, chemistry, and physics)-- grades 9-12, 1948-1949 to 1981-1982. SOURCE: Welch et al. (1983). high school seniors--show considerably more mathematics and science for these students than for all students: the mean number of years of mathematics studied in grades 9-12 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 college-bound 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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105 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 (1973-1984).

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106 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 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 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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107 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 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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108 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 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

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109 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 these policy changes on student enrollment in high school mathematics and science courses and on the content of these courses should be monitored.