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OCR for page 44
Schooling Inputs to Science and
Mathematics Education:
Teachers and Curriculum Content
Ideally--for clarity and efficiency--each indicator
would be represented by a single measure that could be
applied to elementary and secondary schools and at each
jurisdictional level, the local district, the state, and
the national level. The organization of American schools
precludes this ideal. For example, differences in
specialization of teachers at different grade levels
argues for at least two measures regarding teachers, on
for elementary schools and one for secondary schools.
Because of the reality of the U.S. school system, the
committee has not combined various measures into a single
indicator for each area to be monitored. When possible,
a single best indicator is suggested for each appropriate
level of disaggregation. The accompanying discussion
deals with the problems attached to the measures asso-
ciated with each indicator and gives suggestions for
future improvements. In addition, the best current
values, based on available data, are given for each
measure so as to portray the present situation.
e
TEACHERS
Much of the concern regarding the condition of
mathematics and science education has been about the
supply of teachers who are qualified to teach mathematics
and science courses in grades 9 through 12. A number of
surveys have been conducted to assess the extent of the
shortage; all of them have been based on the opinions of
various education authorities, extrapolating from their
perception of current conditions. In 1980, 1981, and
1982, Howe and Gerlovich (1982) surveyed state science
supervisors and teacher certification directors on their
44
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45
opinion as to supply and demand for secondary school
science and mathematics teachers. Their survey covered
53 jurisdictions: the 50 states, the District of
Columbia, Puerto Rico,
and American Samoa. They used a
5-point rating scale: 1, surplus; 2, slight surplus; 3,
adequacy; 4, shortage; 5, critical shortage. In 1982, 44
of the 47 state authorities responding reported that they
saw shortages or critical shortages of mathematics
teachers, 45 of 50 saw shortages in physics, and 44 of 50
saw shortages in chemistry.
officers - ~
decline between 1971 and 1980 of 79 percent of persons
A survey of teacher placement
(shymans~y and Aldridge, 1982) indicated a
who were pursuing teaching degrees in mathematics and a
decline of 64 percent of those pursuing teaching degrees
in science. (Smaller decreases of 64 percent and 33
percent, respectively, were found by NCES (1983) in an
analysis of bachelor's degrees; see Table 3.) A third
kind of survey (Shymansky and Aldridge, 1982), of secon-
dary school administrators, revealed that half the
science and mathematics teachers newly employed for the
1981-1982 school year were hired on an "emergency" basis,
that is, without state certification.
The results of these surveys have been instrumental in
drawing public attention to the issue of adequate supply
and preparation of teachers in science and mathematics.
Numerous initiatives at the national, state, and local
levels have been directed toward providing both greater
numbers and also better trained teachers for high schools.
By fall 1983, 17 states had enacted undergraduate scholar-
ship or loan programs, many of them targeted toward
training teachers of science and mathematics (Flakus-
Mosqueda, 1983). A number of states are focusing on the
retraining of college graduates not now teaching or
teaching other subjects.
= ~ ~ ~ ~ ~ . ~ _ _ ~ _
A third approach has been to
make teaching more attractive through incentive pay ana
career ladders. Indeed, according to the Gallup Poll
(Gallup, 1983), 50 percent of the people favor differ-
entially higher pay for mathematics and science teachers
(35 percent were opposed).
How good are the data being used to formulate such
policies? A more recent survey conducted by the Education
Commission of the States (Flakus-Mosqueda, 1983) shows 38
rather than 44 states reporting teacher shortages in
either mathematics or the physical sciences (physics,
chemistry, or earth sciences), with some of the most
populous states in the east and midwest not reporting
shortages. Has there been an increase in the supply of
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46
teachers or a decrease in demand (e.g., fewer students)
in the intervening year? Has the definition of shortage
changed? Are different criteria being used to determine
shortage in different responses, or are there errors in
the data? What conclusions can be drawn from existing
information? What additional information is needed to
formulate effective policy regarding teachers at the
national, state, and local levels?
Two sets of questions are paramount. First: Is the
number of teachers adequate for the number of mathematics
and science courses now being taught in secondary school?
Will there be an adequate supply for the number to be
taught at some point, say, 5 years, in the future? This
set of questions requires a definition of who is to be
counted in the available pool, which leads to a second
set of questions: Are the teachers at all levels quali-
fied to teach their current assignments in mathematics
and science? Are they qualified for the responsibilities
they will have in the future? Any response to this set
of questions requires defining the term "qualified at
the different grade levels.
These are questions that entail both the setting of
norms and the collection of descriptive data before they
can be answered: What is the number of teachers avail-
able? What is the anticipated demand? How are teachers
prepared? How does this preparation compare with existing
standards? Are existing standards--for example, state
certification--acceptable definitions of "qualified"?
The importance of these questions varies according to
different dimensions at different grade levels.
At the elementary school level, the question of
numbers is not pertinent, since nationwide there appears
to be an ample supply of elementary school teachers, at
least until the mid-1980s when enrollments are expected
to rise again (National Center for Education Statistics,
1982f, 1984a). However, there is concern about the
preparation of teachers who are expected to teach mathe-
matics and science in the self-contained classrooms of
grades 1 to 6 and sometimes in the block programs of the
middle school. For middle and junior high schools, the
nature of the questions on numbers and qualification
varies according to whether mathematics and various
sciences are taught as separate subjects, as in high
school, or as part of a core curriculum by a nonspecial-
ist teacher. At the high school level, information is
needed both as to the number of teachers and as to their
qualifications. But the numbers are dependent on who is
~ _, ~
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47
to be counted as a science or mathematics teacher and
thus become confounded with questions on preparation and
qualification. In the following section on number of
teachers, the status of individuals being counted is
defined in each case--for example, "assigned to mathe-
matics or science classes," "degrees earned," "certi-
fied"--without judgment as to their qualifications. The
problems of defining "qualified" are discussed in the
next section.
Number of Teachers
Supply of Teachers
At the elementary school level, only a small number of
teachers specialize in mathematics and science, either as
specialist teachers or in grades 7
are part of the elementary system.
and 8 when these grades
In a survey of teacher
demand and supply conducted in 1979-1980, the National
Center for Education Statistics (1982e) estimated that
1.4 percent of all elementary school teachers (16,400--
15,400 full time) were assigned to teach mathematics
specifically and 0.7 percent of all elementary school
teachers (8,600--nearly all full time) were assigned to
teach science. A large proportion of these teachers are
probably in the upper grades.
At the secondary school level, there are available two
data bases that have been analyzed regarding the number
of mathematics and science teachers. The first is the
survey of teacher demand and supply conducted in 1979-1980
by the National Center for Education Statistics (1982e),
which yielded responses from administrators of 1,273 of a
sample of 1,448 school systems (an 88 percent response
rate). Based on this sample, NCES estimated that, during
1979-1980 in public secondary schools, 115,000 persons
were assigned to teach mathematics either full or part
time, and 104,700 persons were assigned to teach science
courses either full or part time (see Table 2). This
represented 11.4 percent and 10.4 percent of all secondary
school teachers, respectively. ~
At this time, there is no
readily available information on the preparation or
certification of these teachers. To fill this gap, at
least partly, NCES plans a 1985 survey of a national
sample of teachers in ten broadly defined fields on their
training and background; there will also be questions on
how teachers spend their time, assignment of homework,
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48
TABLE 2 Secondary School Teachers Assigned to Mathematics
and Science Classes in Public Schools in 1979-1980
Field of
Assignment Totala Full Time
Mathematics 115,000 112,900
Science 104,700 101,000
Biology 25,000 24,300
Chemistry 11,400 10,500
Physics 6,700 5,700
General science 59,600 58,600
Other sciences 2,000 1,900
Reachers assigned to more than one field were counted
in the field in which they spent most of their time.
SOURCE: National Center for Education Statistics (1982e).
and availability of resources including teacher aids.
Between 8,000 and 10,000 teachers in more than 2,000
public schools are expected to participate; both teachers
and principals in the schools will be asked to respond.
Information on the preparation of teachers in private
schools, derived from a special NCES study of private
education, will become available early in 1985.
The second data base regarding the number of science
and mathematics teachers is derived from a survey by the
National Science Teachers Association (NSTA) conducted in
the fall of 1982. Using a sample of 2,236 schools that
offered high school curricula, NSTA asked principals how
many classes in mathematics or science were being taught
and how many teachers were teaching these classes. On
the basis of the first 846 responses (a 38 percent
response rate), the numbers of such teachers were esti-
mated. Despite the low response rate and methodological
differences in the way the estimates were made, the NSTA
estimate of the number of persons teaching mathematics in
secondary school is reasonably close to that derived from
the NCES survey: 106,190 (Pelavin and Reisner, 1984),
compared with the NCES estimate of 115,000. Part of the
difference might be explained by falling high school
enrollments in the 3 years between the two surveys.
Estimates for specific science fields are more difficult
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49
to reconcile. For example, NCES estimates 10,500 full-
time teachers in chemistry and 5,700 in physics;
estimates for full-time equivalent teachers derived from
the NSTA data are 13,620 and 6,900, respectively.
A third data base currently being analyzed is the NSTA
list of science, mathematics, and social science teachers
for grades 7 to 12, maintained by grade level, by state,
and by subject taught. The list was updated in November
1983, with principals of more than 23,000 schools respond-
ing (a response rate of better than 80 percent). Prelimi-
nary analyses indicate that there are some 75,600 people
teaching biology, chemistry, physics, or a combination of
these subjects in grades 7 to 12. Over 50 percent teach
biology only, 15 percent teach chemistry only, 11 percent
teach physics only, and the rest teach some combination
of these subjects. It should be pointed out that the
numbers include all people listed by their principals as
teaching in the designated fields, rather than only those
teaching the subject(s) full time (or full-time
equivalents).
The discrepancies in definitions and resulting numbers
exhibited in these three surveys illustrate some of the
problems with the current data. And lack of information
on how many of the persons counted in any of the com-
pilations are actually certified or otherwise qualified
to teach science and mathematics raises additional
uncertainties about the estimated numbers.
Whatever the uncertainties, the current number of
teachers, while an important statistic, becomes meaning-
ful as an indicator only when compared with the number
needed. But if estimates of numbers now teaching are
attended by some ambiguity, estimates of future supply
and demand are even more so. Estimates of future supply
must take into account, in addition to the existing pool,
the number of teachers leaving and entering the field.
Estimates of demand must take into account current
vacancies, the desirability of replacing those teachers
who lack minimum qualifications for their teaching
assignments, changes in total student enrollment, and
changes in percentage of the total number of enrolled
students who take specific science or mathematics courses.
The teacher turnover rate (i.e., teachers leaving the
profession) has been estimated at 6 percent for the last
decade (Froomkin, 1974; National Center for Education
Statistics, 1978, 1982b). In an unpublished analysis of
the survey of principals and a separate teacher survey,
NSTA estimates the rate to be 5 percent for science and
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50
mathematics teachers in 1981-1982. Pelavin and Reisner
(1984), in an analysis of the availability of teachers,
use a 6 percent turnover rate and an estimate of 110,000
mathematics teachers and 103,500 science teachers for
1982-1983, reconciling the NCES and NSTA estimates.
Thus, they project a loss of 6,600 mathematics teachers
and 6,200 science teachers (son in chemistry . 500 in
physics, and 4,900 in other science areas) in 1983-1984.
(A 5 percent turnover rate would mean a loss of 5,500
mathematics teachers and 5,100 science teachers.) There
is evidence that the teacher pool is aging (National
Center for Education Statistics 1983; Feistritzer, 1983),
which may mean a higher turnover rate a decade from now
due to retirements--at a time when high school enrollment
will be increasing and the cohort of young adults that
might furnish new teachers will be decreasing.
The supply of teachers can be increased either by
persons newly entering the field or by persons returning
to mathematics or science teaching. No national data are
available on this second component, although one state
reports that 65 percent of vacancies in all fields in
1982-1983 were filled by returning teachers (Flakus-
Mosqueda, 1983). The potential pool is considerable.
According to Graybeal (1983), as of fall 1981, about 6.1
million people (aged 21 to 65) had been certified as
public school teachers: of this total, only about 2.2
million were teaching in 1980-1981; 1.9 million had left
teaching; 1.9 million had not entered the profession; and
140,000 were newly qualified.
With respect to new entrants, the number prepared to
teach mathematics or any of the sciences, particularly
the physical sciences, has been decreasing over the past
decade. Data from NCES show that the decline in the
number of college students majoring in science or mathe-
matics education has taken place in the context of a
general decline of teaching degrees conferred over the
last decade (with the exception of degrees in special
education); see Table 3. (The discrepancy between NCES
data and the data from the NSTA survey of teacher
placement officers cited above may be due to problems
with the response rate on the NSTA survey and to somewhat
differently worded questions on this survey and the NCES
survey.) It should be noted, however, that neither the
NSTA data nor Table 3 include newly certified entrants
who obtained bachelor's degrees in fields other than
mathematics education or science education, including
degrees in mathematics or a science. For example, as
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shown in Table 4, there were 3,150 newly certified
entrants in mathematics and about 3,600 in the sciences
who graduated in 1980. These entrants could replace half
or more of the teachers lost through teacher turnover,
although in the sciences the distribution of incoming
teachers is likely to be skewed, with proportionally more
being added in the biological than in the physical
sciences.
Table 4 indicates the modest proportion of new teachers
in science and mathematics who are reported to be certi-
fied or eligible to be certified in the field in which
they are teaching, 45 percent and 42 percent, respec-
tively. These data suggest that many newly graduated
high school teachers who are not prepared in science or
mathematics nevertheless may be assigned to teach these
subjects. Current initiatives to encourage entry into
the field may increase the proportion of adequately
prepared entering teachers and reverse earlier forecasts
of continuing declines of individuals available to teach
mathematics or science.
Demand for Teachers
On the demand side, the National Center for Education
Statistics (1982e) survey on teachers also included data
on vacancies as of fall 1979: there were estimated to be
900 unfilled teaching positions in mathematics and 900 in
science, including 400 in chemistry and 200 in physics.
The vacancies for mathematics and science as a whole
represented less than 1 percent of the total number of
persons now teaching in those fields. However, that
percentage does not take into account the number of
teachers already in the system who were assigned to
classes they were not qualified to teach. Particularly
in times of shrinking enrollments, it is not unusual to
fill a vacancy in a shortage area with a tenured teacher
from an area with a teacher surplus. Fourteen states
have no rules prohibiting out-of-field teaching.
Total high school enrollment (grades 9-12) is a major
determinant of teacher demand. The National Center for
Education Statistics (1984a) projects enrollment at 13.7
million in 1985, down from 14.7 million in 1980, and at
12.1 million in 1990--a decrease of more than 17 percent
over 10 years. The National Center for Education Statis-
tics (1984a) also estimates a somewhat smaller decline in
the total number of teachers in public secondary schools,
OCR for page 53
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54
about 10 percent over the same decade. A relatively
larger decrease already took place between 1980 and 1982,
when the number of secondary school teachers declined
from 1,074,000 to 1,039,000. If that rate were to
continue until 1990, the 10-year loss would be more than
15 percent. On the assumption that NCES's estimate of a
10 percent decrease over 10 years is more nearly correct,
a decrease of some 72,000 teachers for 1982-1990 can be
expected, for a total 1980-1990 decrease of 107,000.
After 1990, however, there is expected to be an increase
of teachers, as high school enrollments begin to increase
again starting in 1991. If mathematics and science
teachers were to continue to represent, respectively, 11
percent and 10 percent of the high school teaching force,
the total number of teachers needed for mathematics would
decrease by 7,700 by 1990 in comparison with the number
needed in 1982, and the total number of teachers needed
for science would decrease by 7,000.
A countervailing factor to decreasing enrollments is
the increase in high school graduation requirements
already mandated by some states and being considered by
others (see Table 5). It should be noted that these
increased requirements would not affect all students: in
1982, about 46 percent of high school graduates had taken
3 years or more of mathematics in grades 9-12; 30 percent
had taken 3 years or more of science (National Center for
Education Statistics 1984b). However, where recent state
or local mandates would require more courses than were
actually taken before the new requirements, additional
mathematics and science teachers would be needed.
A number of state university systems also have recently
increased entrance requirements, often beyond those
required for high school graduation (U.S. Department of
Education, 1984). The National Commission on Excellence
in Education (1983) recommended that all students be
required to take 3 years of mathematics, 3 years of
science, and 1/2 year of computer science for high school
graduation. If these recommendations were to be imple-
mented, it would certainly require a large increase in
the number of mathematics and science teachers. In the
committee's estimates of annual demand for the next few
years (see below), it is assumed that decreased demand
due to lower high school enrollments will be balanced by
increased demand due to higher graduation requirements.
However, Pelavin and Reisner (1984) estimate the increased
demand to be 8,600 mathematics teachers and 6,500 science
teachers.
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72
teachers should be monitored to assess their effective-
ness.
CURRICULUM CONTENT
Opportunity to Learn
Giving students the opportunity to learn subject
matter not part of their home or social environment is a
primary reason for formal schooling. The opportunity to
learn mathematics and science is dependent, in part, on
the content of the curriculum. It is also dependent, in
part, on the time devoted to each curriculum area--a
process variable discussed in the next chapter. These
two aspects of instruction are considered separately for
analytic purposes, although they are obviously closely
related.
The relationship between the emphasis given a topic in
the curriculum and student achievement was demonstrated
by information collected by the International Project for
the Evaluation of Educational Achievement (IEA) in 1970.
In conjunction with science achievement tests administered
in some 16 countries, TEA asked teachers to rate each
item in the test according to the following scale:
1--None of the students has studied the relevant topic;
2--Fewer than 25 percent of the students have studied
the relevant topic;
3--Between 25 percent and 75 percent of the students
have studied the relevant topic;
4--More than 75 percent of the students have studied
the relevant topic;
5--All of the students have studied the relevant topic.
From the rating data, a national opportunity-to-learn
score was obtained for each school; the scores were then
aggregated to determine an overall rating for each country
at each population level. The results show (Wolf, 1977)
rank-order correlations between opportunity to learn
science and achievement, across countries, of .51, .75,
and .36, respectively, for the three populations tested:
10-year-olds (I), 14-year-olds (II), and all students in
the terminal year of secondary school (IV). Table 9
exhibits this relationship for the United States. It
should be noted that the U.S. ranking for category IV is
affected by the fact that, in some European countries,
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73
TABLE 9 United States Rank Order in Opportunity to Learn
and Science Achievement for Populations I, II, and IV, 1970
Countr ies Testing
Rank Order of United Statesa and Rating
In Opportunity In Science Opportunity to
Population to Learn Ach ievement Learn (Number )
I ( 10-yr-olds ) 1 4 14
I I ( 14-yr-olds ) 6 7 16
IV (terminal year ) 13 14 16
-
al indicates the highest rating, i.e., greatest opportunity to learn or
h ighes t ach ievement .
SOURCE: Wolf (1977 :40) .
the terminal year of secondary school comes 2 to 3 age
years later than in the United States.
A shorter version of the rating scale used in the TEA
science assessment was also administered in conjunction
with TEA mathematics testing in 1964. Teachers used a
three-point rating scale for each topic in the test: 75
percent or more of the students had the opportunity to
learn the topic, 25-75 percent had the opportunity, or
fewer than 2S percent had the opportunity. Correlations
between ratings and scores by countries was .73 for 8th
graders; that is, students scored higher marks in coun-
tries where teachers rated the tests to be more closely
related to the curriculum. Husen (1967:168) concludes
that "a considerable amount of the variation between
countries in mathematics score can be attributed to the
differences between students' opportunities to learn the
material which was tested." The IEA'S second inter-
national mathematics study and the second science study
currently under way are collecting similar information on
opportunity to learn.
In the United States, local districts determine school
curricula, usually within guidelines set by the state.
The degree to which guidelines are mandatory varies from
state to state. Most states, although not all, specify a
minimum number of credit hours for high school graduation,
including requirements in such key fields as English,
mathematics, and science (see Table 5, above). For most
subjects, however, local authorities have considerable
discretion as to the content to be covered within the
required credit hours and state guidelines. Some populous
states, including California, Florida, and Texas, have
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74
state textbook adoption boards; however, the lists of
texts approved for school use by such bodies usually are
comprehensive enough to allow much room for local choice.
The state education authority in New York is unique in
its history of involvement with local districts. Examina-
tions (the "Regentsn) are constructed at the state level,
based on specified courses of study for each subject
matter field. Although the examinations are voluntary,
all high school curricula are required to be based on
them. Similar curriculum guidelines became mandatory for
grades 7 and 8 in 1984, and there are also some mandatory
curriculum requirements for elementary school.
For some disciplines, mathematics in particular,
professional societies have recently developed guidelines
for the content of the school curriculum (National Council
of Supervisors of Mathematics, 1977; National Council of
Teachers of Mathematics, 1980, 1981b; Conference Board of
the Mathematical Sciences, 1983). Although there may be
agreement on principles by professionals, just as in
teacher education, that agreement does not necessarily
extend to others concerned with education. As a result,
textbooks intended for the same grade or course emphasize
different topics; some topics may be included in one test
and excluded from another; and teachers may stress differ
ent subject matter. Such choices are not always based on
the recommendations of subject matter experts. The lack
of agreement on course content is especially true for the
science curriculum and for nontraditional mathematics
topics in elementary school, for the life sciences, and
for science and technology education for students not
taking the traditional precollege sequence. It will be
important to monitor the extent to which the recommenda-
tions being made by professional groups are translated
into texts or teaching methods that are likely to affect
student learning.
The Role of Textbooks
Textbooks appear to be central to instruction. While
other teaching and learning devices are in use, such as
computer-aided instruction, films, and laboratory experi-
ments, their role is decidedly subsidiary. Stake and
Easley (1978), in a set of case studies supported by NSF
on the state of precollege science education, found that
more than 90 percent of all science teachers use a text-
book 90-95 percent of the time. This finding has been
-
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75
replicated over and over by classroom observers. Hence,
one way of establishing the content of instruction would
be to document what textbooks are used, what scientific
concepts, factual knowledge, and processes inherent in
the discipline are covered in the most commonly used text-
books, how much textbooks intended for the same grade
level or course differ from each other, and the emphasis
given by the teacher to different topics within a given
text.
There have been occasional studies on various aspects
of textbook content and textbook use, but information has
not been collected systematically over time. There is
even less information available on other teaching and
learning tools, especially with respect to their role in
conveying content. The most comprehensive information on
the use of mathematics and science textbooks comes from
one of the NSF-supported studies, the 1977 National Survey
of Science, Mathematics, and Social Studies Education
(Weiss, 1978). According to teacher reports, one-half of
all science classes and about two-thirds of all mathe-
matics classes use a single published textbook or program,
and about one-third use multiple texts. Only in grades
K-3 science instruction was there any noticeable absence
of the use of a published textbook or program (37 percent
of the classes).
Over one-half of the elementary school
teachers surveyed used one or another of the most popular
five mathematics textbook series; somewhat more diverse
choices were reported in science.
The extent to which textbooks published for the same
grade and subject actually differ has been open to ques-
tion and has occasionally been the subject of empirical
study. During the era of curriculum reform in the 1960s,
texts in mathematics and the sciences were often classi-
fied as to whether they emphasized facts ("traditional"
texts) or concepts, processes, and learning how to learn
("new" texts) and whether they included such "new" topics
as set theory in mathematics or genetics and evolution in
The error`, ~1 the Hi ff~r~nc~s built into the
biology.
~ ,. ~ ~ ~ . ~ ~
reform curricula did indeed bring about differences in
It performance. Accordino to NLSMA findings, stu-
_
dents studying the new mathematics did better on tests of
comprehension, application, and analysis; students using
conventional texts performed better on computation, though
new math students tended to catch up in later grades
(Begle and Wilson, 1970). With respect to science, a
number of evaluation studies have recently been reviewed
to assess the overall effects of the reform curricula;
OCR for page 76
76
after examining 111 studies dealing with science cur-
ricula, Shymansky et al. (1983:392) conclude:
Especially interesting . .
general achievement. . .
.
.
. are the statistics for
Much criticism regarding
the new science curricula focused on the apparent
decline of general science knowledge among students
exposed to the new programs. At the height of the
new curricular movement (and even today) the pre-
vailing notion was that the process goals of the
new science curricula were being achieved at the
expense of the content goals--although no compre-
hensive database existed for either claim. The
data . . . show clearly that students exposed to
new science curricula achieved 0.43 standard
deviations above (exceeding 67% of the control
group), or nearly one-half of a grade level better
than, their traditional curriculum counterparts on
general achievement measures.
Students taking the new courses also gained on their
counterparts in analytic thinking, problem solving,
creativity, and other higher-order cognitive skills and
in process skills relevant to the doing of science.
More recently, analysis of science textbooks has been
concerned with the structure and language used to present
topics (Robinson, 1981:5-68). A question of particular
interest has been the degree to which science learning
involves the memorization of unfamiliar technical words.
Building on previous work that indicated that some texts
required learning thousands of new words, Yager (1983)
analyzed 25 frequently used science textbooks. These
included two science series for grades 1-6, six texts at
the middle/junior high school level, and alternative
texts for high school biology, chemistry, and physics.
At all levels, Yager found terminology to be a central
feature of science texts, with 2,700 to 3,500 special or
technical words included in books intended for grades 4-6
and as many as 9,300 in one of the physics texts. Even
if only a small percentage of these words are new or
entail new definitions, a lot of learning time is spent
on vocabulary. To a lesser but still considerable extent,
this is true even of the new texts. Concentration on
vocabulary may in part be responsible for a large propor
tion of students reporting that they are bored with
science classes--82 percent of 17-year-olds in one study
(Hueftle et al., 1983).
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77
While this sort of analysis points to possible
similarities among textbooks in learning difficulty, it
does not further establish concordance of subject matter
coverage. Despite the key role of the textbook in
instruction and student learning, there has been little
content analysis of texts since the mid-1970s (Walker,
1981). One might hypothesize that the widespread use of
standardized tests would lead teachers to emphasize cer-
tain common topics, even if texts included other mater-
ials. To investigate to what extent different textbooks
treat the same topics and the text materials match topics
covered on tests, Freeman et al. (1983a) examined four
popular 4th-grade mathematics textbooks and five stan-
dardized tests. A set of 22 core topics was identified
by analyzing all the texts and tests. Approximately
50-60 percent of the more than 4,000 problems in each
book focused on 19 of the 22 core topics, showing that
there is indeed some agreement among texts on a common
core. The match to tests was rather worse, however
"Freeman et al., 1983a:504): "Of these 22 topics, only
six were emphasized in all textbooks and tests analyzed.
Three topics were emphasized in all books but in no
tests. Three other topics were covered in all tests, but
they received limited attention in the books. The other
10 topics were emphasized in all four books, but they
appeared in only some of the tests. The match between
topics contained in the texts and in the tests analyzed
is shown in Table 10. The authors conclude that (p. 511)
"[t]he proportion of topics covered on a standardized
test that received more than cursory treatment in a
textbook was never more than 50%."
Variations in Topic Emphasis
Though teachers rely heavily on textbooks for instruc-
tion, they use them differently. Another investigation
by the same research team (Freeman et al., 1983b) showed
that student exposure to the content covered by several
of the tests included in the study varied to some degree
depending on styles of textbook use, even when the text-
book was the same. Berliner (1978), using logs of how 21
5th-grade teachers in California allocated their instruc-
tional time, found great differences in time spent on
common mathematics topics from class to class, as shown
in Table 11. While some of these differences may be
OCR for page 78
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OCR for page 79
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TABLE 11 Pupil Time (in minutes) in Content Areas of
Mathematics for Four 5th-Grade Classes
Content Area
Classroom
- A B C D
Computation
Addition 33 234 95 26
Subtraction 77 205 248 4
Multiplication: basic facts 40 79 89 142
Multiplication: speed tests 34 51 8 24
Multiplication: algorithm 341 910 720 343
Division 243 19 1,548 2,223
Fractions 54 370 495 2,016
Other 0 82 213 0
Concepts/application
Computational transfer 49 24 160 147
Numerals/place value (whole number) 0 53 29 0
Word problems 58 3 322 15
Geometry: perimeter 0 53 73 0
Geometry: area 0 103 49 0
Geometry: number pairs 90 40 0 0
Geometry: lines or figures 418 126 70 280
Other 174 128 1,411 68
NOTE: Time was logged over an average of 90 days of instruction observed
between October to May.
SOURCE: Berliner (1978:21) as cited in Romberg and Carpenter (1985).
related to differences in total time spent on mathematics
instruction (compare, for example, classrooms A and D),
variation in topic emphasis is evident apart from varia-
tions in total time. It may be conjectured that pupils
from classrooms C and D performed differently on division
problems on tests than did pupils from classrooms A and B.
There may be even greater variation at the secondary
level than at the elementary level in the content of
instruction as embodied within such common course titles
as general mathematics, introductory (first-year) algebra,
earth sciences, or introductory biology. Moreover,
curriculum supervisors at the state level report that
there has been a proliferation of course titles, with few
standards as to content. Presumably, logging which
textbook is being used would give some indication of the
content of a course, if the content of that textbook is
known. Since there is considerable variation in textbook
use, however, content analysis of commonly used texts
would have to be augmented by observation and analysis of
instruction within samples of classes; such observations
could provide more detailed information on what is
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80
actually taught to students enrolled in a given course.
If aggregation of course titles, let alone course content,
is difficult at the state level, it requires truly heroic
assumptions to infer what "years of enrollment" in mathe-
matics or science collected at the national level might
mean in terms of the content studied.
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 intro-
duce 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 mathematics
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
material is likely to produce data of questionable
quality.
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Conclusions and Recommendations
Curriculum Conten
.
There are no established standards for content
derived either from past practice, practice elsewhere,
anticipated need, or from theoretical constructs devel-
oped, 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
wih 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 (con-
cepts, 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, incorporation of learning theory.
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· 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
the 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 correspon-
dence 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.
Representative terms from entire chapter:
elementary school
