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3
Research on Instruction
Whatever is known about the acquisition of reasoning
skills in mathematics and science, such knowledge needs
to be translated into classroom instruction. Teachers
and curriculum are key to the amount and quality of time
spent on instruction; testing assesses the outcomes of
instruction. This chapter discusses research on each of
these three elements.
RESEARCH ON TEAC B RS
To use time given to ~ nstruction effectively, teachers
must be competent and willing to exert sufficient effort.
(See Levin, 1980, for a cogent discussion of teacher
inputs to educational productivity.) Teacher competence
involves adequate cognitive mastery of the subject matter
to be taught and, in the case of science especially,
proficiency in handling experimental materials that can
lead students to form new concepts from observation and
evidence. For example, Arons (1981) argues that even the
best curricula will be ineffective unless teachers are
trained to deal with various modes of abstract logical
reasoning, for example, the logic of arithmetic involved
in ratios and division, the logic of control of variables,
dealing with propositional statements, recognizing gaps
in available information, making inferences and pre-
dictions from mental models, doing hypothetico-deductive
reasoning, and the like. In fact, the processes and
problems involved in educating teachers to acquire these
capacities are not very different from those involved for
any other learners. But, Arons (1983) also argues,
subject-matter courses taken by prospective teachers--
usually the standard courses offered by science
15
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16
departments--often cover too much content at too rapid a
pace and seldom pay explicit heed to developing reasoning
capacities. Hence, prospective and practicing teachers
often lack a genuine understanding of concepts and lines
of reasoning that characterize the subject(s) they are
teaching and, having missed effective training themselves,
are unable to cultivate and enhance the basic abstract
reasoning capacity of their students.
The shortcomings in his or her college courses may be
one of the reasons a teacher's background in science (as
well as preparation in professional education) shows
relatively low correlations with student outcomes (Drava
and Anderson, 1983). However, there may be other pos-
sible explanations for these low correlations, including
lack of significant variations in teacher training, low
correspondence between subject matter taught and the
content of tests (Freeman et al., 1~83), and such other
factors as teacher motivation and energy level.
Whatever its effect, little is known about the subject
matter preparation of the 2.37 million teachers in the
current pool (Raizen and Jones, 1985), much less about
their competence for teaching science and mathematics.
Two ongoing surveys, one by the National Center for
Education Statistics and one by Research Triangle
Institute, will provide some relevant information, but it
will be limited in scope. Much general information on
teachers is also being collected in connection with the
National Assessment of Educational Progress; assessments
in mathematics and science and concomitant teacher surveys
are scheduled for 1986. Meanwhile, in the absence of
sufficient knowledge about the nature of teacher prepara-
tion programs, assessment of teacher quality has been
based on reviewing SAT scores of college freshmen
planning to be teachers (Weaver, 1979; Schlechty and
Vance, 1983) and increasingly on the scores of newly
entering teachers on the National Teacher Examination or
on state-constructed teacher tests.
Over the last five years, states have made various
policy changes intended to increase the quality of
teachers: 32 states have changed teacher certification
requirements; 28 states have changed teacher education
curricula, and 20 states have raised entrance require-
ments for teacher education programs (Goertz et al.,
1984). Other policies that have been proposed include
salary increases and structural changes in compensation
for teachers, requiring liberal arts majors for all
teachers and possibly a five-year rather than a four-year
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degree program (Scannell and Guenther, 1981; Boyer, 1983;
National Commission for Excellence in Teacher Education,
1984), and ensuring teacher competence through a nation-
ally recognized licensing examination (Albert Shanker, as
reported in the Chronicle of Higher Education, 1985a).
With respect to increasing the quality of science and
mathematics teaching specifically, monies have been
appropriated by Congress and by a number of states to
provide loans and scholarships for students preparing to
enter these fields (U.S. Department of Education, 1984),
and a program for developing models for teacher education
has been established by the National Science Foundation.
Few of these policy changes are based on research
evidence that relates the proposed interventions to
observed responses on the part of individuals who might
enter teaching (Murnane, 1985) or to the acquisition of
knowledge and skills deemed necessary for science and
mathematics teaching. Indeed, there are indications the t
some of the new policies may prove ineffective or have
some undesirable consequences. For example, Summers and
Wolfe (1977) found a statistically significant negative
correlation between teachers' scores on the National
Teachers Exam and their students' test score gains.
Increases in credentialing requirements may rob local
districts of the flexibility to hire individuals who
exhibit the capacities for teaching mathematics and
science but lack the credentials; abolishing traditional
credentials, as New Jersey has done and other states are
considering, may have the perverse effect of setting
lower rather than higher standards (Chronicle of Hither
Education, 1985b). Moreover, simply raising requirements
to enter teacher education programs is likely to reduce
the socioeconomic and racial and ethnic diversity of the
nation's teaching force at a time when schools will be
educating a larger nether of minority students (Goertz et
al., 1984). Systems of compensation such as merit pay
that require evaluating teacher performance are hampered
by the difficulties of developing and implementing such
evaluations (Wise et al., 1984) and, perhaps for that
reason, historically have had a short life span
(Educational Research Service, 1979).
The current experimentation with incentives, teacher
education programs, and credentialing sharpens the need
to understand better (a) who gets access to teacher
preparation programs under various conditions, (b) the
content of these programs, and (c) the regulation of
access to teaching positions. These factors are poorly
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18
understood even for the current pool of teachers. The
unplanned variations resulting from current policy changes
provide a rich opportunity for assessing the effects of
various alternatives.
Therefore, the committee recommends the development of
a national data base on teacher preparation and qualifica-
tions sufficiently detailed and appropriately stratified
to reflect conditions in different types of school dis-
tri~cts and for varying student populations. We recommend
a research program to develop improved understanding of:
(1) the response to various monetary incentives designed
to attract able individuals to mathematics and science
teaching and keep them in these fields; (2) how to improve
the subject-matter education of both pre- and inservice
teachers, including optimal volume and pace of subject-
matter coverage in different sciences and experiences
that develop and enhance abstract reasoning capacity; and
(3) the effects of alternative requirements for entering
and being certified in the profession, particularly with
respect to developing an adequate pool of teachers
competent to teach mathematics and science.
Effective use of instructional time involves not only
the teacher's capacity, but also the teacher's effort
(Levin, 1980). Direct measures of the quantity of
teacher effort in the classroom (e.g., the amount of time
spent by the teacher on direct instruction or active
teaching) and indirect measures (e.g., the amount of time
students are on-task n or engaged in learning) show
positive correlations with student performance (Brophy
and Ever tson, 1976; Good and Grouws, 1977; Fisher et al.,
1980). Particular aspects of active teaching have also
been investigated as to their effectiveness--for example.
strategies for giving information (Rosenshine, 1968;
Armento, 1977; Smith and Sanders, 1981) and reacting to
their responses (Clark et al., 1979; Evertson et al.,
1980) and for assigning and checking homework (Good and
Gronws, 1977; Walberg and Rasher, 1985). Bowever,
attempts to assess teacher behavior have been limited to
specif ic instructional settings (Gage, 1978), and no
consistent pattern of success across subject areas or
specific groups of students has emerged (Brophy and
Evertson, 1976; Medley, 1979). m e exception is work on
the assignment of and feedback on homework--apparently an
effective way of extending learning time through teacher
effort.
Teacher effort is not solely a consequence of indi-
vidual attributes; it is also influenced by the organ)
-
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19
Rational characteristics of schools: the degree of
autonomy allowed teachers in their own classrooms and
their contribution to school practices and policies
(Levin, 1980; Lightfoot, 1983), opportunities for
professional interaction and encouragement of innovation
(Grant, 1981; Little, 1981; LipSitz, no date), explicit
and tacit reward structures and sanctions (Lortie, 1975;
Sykes, 1983), and the general values and attitudes of
teachers, for example, consensus on academic goals and
norms for behavior (Brookover et al., 1979; Rutter, 1979)
Unfortunately, assessing the effects of such factors on
teacher effort is even more difficult than measuring
teacher capacity or teacher behavior in the classroom.
Nevertheless, it is important to conduct research on how
societal pressures, school organization, and educational
policies affect the effort teachers are able and willing
to invest in instructing their students.
RESEARCE ON CURRICULA AND CURRICULAR MATERIALS
Advanced scholarship in a subject is based on theories
and concepts that serve to make a domain accessible to
subject-matter experts. However, a theory for the expert
may not be good pedagogical theory for the novice. As
already noted, recent work in cognitive psychology has
described how acquired knowledge is organized and repre-
sented, and how cognitive models can facilitate reasoning
and thinking as students use and test these models to
solve problems and revise what they already know (Estes
et al., 1982; Rumelhart and Norman, 1981). Such research
has had little influence, however, on the rigidly hier-
archical conception of science and mathematics that under-
girds most classroom instruction. Nevertheless, effec-
tive teachers use their experience of how students learn
to shape the subject matter they present. This craft
knowledge provides a second source for developing peda-
gogical theory for teaching science and mathematics to
students at different levels of competence and education.
Still a third source is the current experimentation with
computer systems for intelligent tutoring, based on
models of how successful students perform various
cognitive tasks tSleeman and Brown, 1982; Anderson et
al., 1985).
Based on work from these sources, the committee
recommends research directed toward effective instruc-
tional strategies based on explorations of: (1) the
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design of pedagogical theories that students can test,
evaluate, and modify; (2) the techniques of ingenious
teachers who are able to devise such temporary models or
pedagogical theories; and (3) the design of intelligent
computer-assisted instruction that incorporates interroga-
tion and exploration.
In addition to these general research issues on cur-
riculum, there are specific questions surrounding the
subject matter of technology. Unlike the more traditional
domains of science and mathematics, technology and com-
puter science do not have well-established curricula.
Many schools are now introducing "computer literacy.
courses. Often, such courses focus on teaching program-
ming in a particular computer language. In other
instances,-computer literacy courses deal with the
capabilities and functioning of computers, either with or
without hands-on experience, and may include topics on
the effects of computers on the workplace and society.
At more advanced levels, science and mathematics courses
may devote some class time to illustrating changes in
these fields that have come about because of the avail-
ability of poweful computational tools. -
In the committee's view, there is insufficient
knowledge about the age and grade levels at which the
computer and programming should be introduced and about
the effects of alternative curricula in computer literacy.
Systematic attention must also be given to how the
knowledge structures and the processes of the sciences
and mathematics have changed as a result of readily
available computation and what these changes imply about
the school curriculum. For example, the advent of
calculators made traditional drill in using logarithm
tables superfluous. Similar issues need to be explored
regarding the advent of more powerful computers for all
the science and mathematics courses taught in school.
The committee recommends research targeted at
providing characterizations of the cognitive skills and
knowledge needed for understanding of and successful
performance in technological systems; based on such
characterizations, development of usable school curricula
in computer literacy; and investigating the effects of
computers on the knowledge structure of mathematics and
various sciences and the changes implied for the school
curriculum.
Recent research with preschool children suggests that
changing the context of the learning task, or ~recon-
textualiz ins, n can help students acquire some basic
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cognitive skills (holding information in memory, building
structural representations for later use, comparing
perspectives) essential to achievement in science.
Istomina (1975) compared the performance of Preschool
children on a test-like version of a free recall task and
the same task embedded in a role-playing game of being
Activa-
tion of the four- to five-year-olds' still-crude memoriz-
ing operations was greatly facilitated by the play
situation.
_
sent to a make-believe store for a list of items.
Similarly, Margaret Donaldson (1978) and her students
addressed the presumed inability of children younger than
10 to 11 years of age to take account of another person's
visual point of view (Piaget and Inhelder, 1975). They
demonstrated that perspective-taking ability is present
in very young children in the right circumstances.
Donaldson arranged for the problem to involve toy
children hiding from a toy policeman. Only by taking the
policeman's point of view could the child subjects know
where the toy children should hide.
Four- to f ive-year-
olds succeeded at this problem even when they had to
coordinate the points of view of two policemen, whose
view of the scene was different from their own.
As a final example, decades of research on delayed
responses," in which an object is hidden in one of
several boxes and children are required to search for it
several seconds or a few minutes later, has shown
children to be deficient in their ability to keep the
location of objects in mind. DeLoache and Brown (1979)
repeated this experiment with two- to three-year-olds
their homes. Instead of hiding a piece of candy,
children favorite toys were hidden under a piece of
furniture. Under these conditions, children would
remember the location of the hidden object for 24 hours,
the longest intervals tested.
This research suggests that a fundamental way of
changing how much time is needed for a particular task is
to change the context of the task as Presented to and
understood by the learner.
In
The cognitive task was more
successfully completed when it was embedded in some
larger activity involving familiar scripts and human
intentions.
These examples from research on young children are not
intended to suggest that recontextualization for older
learners must always strive for simplification or that it
should only involve making materials more familiar and
obviously utilitarian. Knowledge is unavailable on how
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the insights gained from the work with young children can
be applied at higher levels of the curriculum in the
areas of science, mathematics, and technology. However,
there is evidence that science curricula combining
activity-based instruction with appropriate text materials
are more effective than traditional curricula in teaching
higher-order skills (Shymansky et al., 1983; Boldzkom and
Lutz, 19841.
On the basis of such research, it has been argued that
programs and school curricula In science and mathematics
should stress utility and practical applications rather
than heavy reliance on theory (Harms and Yager, 1981).
Hands-on, laboratory, and activity-oriented are accurate
descriptions of most programs identified in recent surveys
as exemplary, especially at the elementary level (Penick,
1983). Bowever, activity-based teaching is notoriously
difficult to carry out and appears at times to be in
conflict with the high level of control of the teacher
over classroom activities advocated by some proponents of
research results on effective teaching (Starlings, 1975;
Hunter, 1984; Brophy and Good, 1985). Moreover, a broad
conclusion rejecting more abstract curricular forms is
clearly premature. For example, a trademark of the SEED
program (Johntz, no date) is demonstrating the success of
minority students in performing highly theoretical mathe-
matical manipulations with little focus on applications
or ties to anything concrete. At least in the hands of
an extremely competent and knowledgeable instructor--
usually a scientist or mathematician in the case of the
SEED model theoretical training works.
Because of the great importance of curricular orienta-
tion and context to learning, particularly to the learning
of mathematics, science, and technology, the committee
urges special emphasis on this research area. Priorities
include research on how important tasks can be embedded
in contexts that reduce the time needed for learning;
under what circumstances and in what ways activity systems
using physical objects and "real. events [whether hands-
on experience, models based on systematic laws, or story
lines that mirror common experiences) can be used to
enhance learning; and what makes theory-oriented instruc-
tion work, especially with individuals from some minority
groups and women generally said to require a more prag-
matic, utilitarian approach.
Curricula depend on and are built around educational
materials. Textbooks and, to an increasing degree,
educational computer software are central factors in
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determining what is learned on what time schedule (Stake
and Easley, 1978). The content of textbooks is influenced
by the authors' sense of appropriate learning goals, the
publishers' perception of the demands of the education
market, and state and local district priorities and pro-
cedures for textbook approval and selection. There is
some information on choice of textbooks, but it dates
back to a 1977 survey (Weiss, 1978). This survey will be
repeated in 1985, but even though it may yield informa-
tion on what texts are used, there is no systematic
effort under way to analyze the content of these texts.
During the development of reform curricula in the
1960s, much attention was paid to the balance between
emphasis on facts and emphasis on concepts and learning
how to learn. Students using the reform curricula did
appear to make greater gains than their counterparts on
reasoning and problem-solving skills as well as on
general achievement measures (Shymansky et al., 1983).
There is no equivalent current information on textbook
content (Walker, 1981), although analysis of the struc-
ture and language of science textbooks has documented
that the learning of special or technical vocabulary.
i.e., rote memorization, is a central feature of these
texts (Yager, 1983).
The increasing use of standardized tests to assess
student achievement assumes that a curriculum covers the
material on the test. Based on a detailed analysis of
fourth-grade mathematics texts and tests, Freeman et al.
(1983) found (p. 511) "the proportion of topics covered
on a standardized test that received more than cursory
treatment in a textbook was never more than 50%.~ Limited
as it is, such evidence indicates possible inaccuracies
in general assumptions about the curricular content of
educational materials in current use. Further evidence
on disparities between the assumed (.intended~) and
actual (nimplemented.) curriculum comes from several
large-scale studies on student achievement. For example,
the studies conducted by the International Association
for the Evaluation of Educational Achievement (IEA) have
attempted to relate the items on student achievement
tests to the opportunity students had to learn the
material through asking their teachers whether pertinent
instruction had been provided. The opportunity to learn
the material turned out to be highly correlated with
student test scores (Husen, 1967; wolf, 1977; Crosswhite
et al., 1985). The National Assessment of Educational
Progress (1985) also includes measures of the implemented
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curriculum, such as asking teachers of students taking
the mathematics tests what topics are included in
mathematics instruction in grades 6-8.
Differences in implemented curricula presented to
different sorts of students affect their opportunity to
learn (Alexander and McDill, 1976; Entwisle and Hayduk,
1982; Barr and Dreeben, 19831. Thus, the effects of
ability grouping and tracking on learning are realized
not only through differences in instructional strategies
and peer influences but also through differences in the
curriculum to which different groups of students are
exposed (Rosenbaum, 1976; Cicourel and Kitsuse, 1983;
Hallinan and Sorensen, 19841.
The committee recommends a concerted research effort
on how educational curricula and materials are created,
their content, and how they are used, specifically, on
(1) whether and how the treatment of substantive content
in current textbooks and software supports the learning
of reasoning, thinking, and problem-solving skills as
well as lower-order recall and memorization tasks; (2)
the exploration of new content areas within various
fields and at various grade levels that might be pro-
ductive additions to promoting higher-order skills; (3)
the abilities, skills, and perspectives of those who
write textbooks and software (for example, to what extent
do they understand the importance of curricular context,
as discussed above) and the means for attracting better
prepared individuals to those fields; (4) the development
of consensus on appropriate subgoals, content, and
sequencing by grade level to facilitate greater emphasis
on higher-order skills; (5) the effects of state approval
processes on content issues; and (6) further studies on
the relation between what is tested and what is included
in textbooks and software and between the intended and
the implemented curriculum.
RESEARCE ON TESTING
The testing of cognitive achievement and aptitude
plays a powerful role in American schools. Tests are
used to group and track pupils, resulting in the differ-
entiation of pupil experiences. Tests are used to
diagnose current knowledge and skill prior to instruc-
tion. Tests are used to assess mastery of instructional
objectives. Tests are used to evaluate teaching and
instruction. There is a widespread consensus among
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cognitive scientists that many of these procedures are
inadequate, particularly in the assessment of higher-
order thinking skills (Frederiksen, 1984).
Assessing reasoning ability is not easy. Tradi-
tionally, it has best been done by open-ended tests
requiring problem solving and free-form answers (e.g.,
essay and problem tests). Such tests are difficult to
administer and to grade, particularly for large numbers
of individuals. There is a long and productive line of
research within the field of psychometrics on the prac-
tical measurement of a variety of intellectual skills.
There is a new and promising line of research that links
traditional psychometrics to the growing understanding of
reasoning skills described above (Hunt et al., 1973;
Glaser, 1981 ; Sternberg , 1977, 1984 ) . Inexpensive,
powerful computers provide a new possibility for more
effective interactive testing. Using current microcom-
puters to test students could be more accurate and less
time-consuming for those taking tests as well as less
labor-intensive for those administering tests (Weiss,
1983), but further research is required to substantiate
that possibility.
Tests also play a role in the learning process
itself. They tell students what in the curriculum is
impor tent and shape the teaching and learning process
(Frederiksen, 1984). If, for example, testing is confined
to memorizable end results, students will concentrate on
these end results, ignoring the more sophisticated levels
of understanding and reasoning to which teachers and text
materials may be rendering lip service. Teachers and
school administrators also use tests as a guide to cur-
riculum emphasis, especially when student performance on
given tests is used as a measure of teacher and school
performance.
The committee recommends a program of research on
testing, including: (1) the development of practical
tests that reliably assess reasoning ability, perhaps
using interactive testing made possible by microcompu-
ters; (2) improving the testing of mathematics and
science achievement to reflect important instructional
goals and objectives; and (3) techniques for educating
teachers to become better writers of test questions,
particularly of questions that test for the higher-order
intellectual skills and levels of learning.
Representative terms from entire chapter:
policy changes
