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Group Reword Structures
in the Classroom
JOHN S. WODARSKI
By developing an understanding of such concepts as individual,
cooperative, and competitive learning structures,
school practitioners can develop a better understanding of
the social and academic problems faced by
pupils. The author surveys the theoretical base and
classroom application of these concepts .
• The application of behavioral
analysis to the field of education in the last decade has
provided many beneficial findings and is one of the most
significant developments in the educational system. 1 Recently, articles have begun to appear in the literature of
education and psychology concerning team learning techniques that are based on behavioral analysis and that seem
to have great promise in changing the basic structure of the
classroom to achieve positive effects on many dimensions at
the same time. These techniques are known by various
names, but they can be referred to as group reward
structures, since they all involve students working in
cooperative teams on academic material. 2
Such techniques are unique in that social and psychological principles of reward interdependence that have been
developed in laboratory work and short-term experimentation are applied to the development of practical classroom
procedures. Group reward structures set up a situation in
which the academic behavior of each student furthers the
goals of the group. This in turn has been shown to increase
students' support for academic performance, to increase academic performance itself under a variety of circumstances,
0162-7%1/81/0303/0045 $0.50
© 1981, National Association of Social Workers
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Social Work in Education
and to increase the frequency with which desirable social
behavior occurs.
School social workers may be called upon frequently to
help analyze difficulties in the classroom. However, the literature of school social work contains few guidelines on the
elements that are considered crucial in building a classroom
situation conducive to learning. This article focuses on the
following components, which are considered critical in the
conceptualization of the classroom gestalt and the guiding of
effective intervention: (1) theoretical background, (2) the
traditional classroom, (3) alternative classroom modes, (4)
merits of different reward structures, (5) applications to
problems, and (6) components of an effective group reward
structure.
Virtually no detailed explanations of group reward
structures appear in the school social work literature, and
thus their adoption by the school social worker is considerably hindered. This report will make substantial references
to the literature on such structures and will elaborate applications of the various structures as well as the effects they have
on several academic and social variables. The article is based
on the author's experiences in the application of team
methods to a variety of content areas and school populations. Thus, the report should provide school social workers
with conceptual tools that they can use to help teachers
attain academic and social goals for students.
Theoretical Background
A classroom may be seen as being composed of two essential
elements that can be modified with ease: a task structure and
a reward structure. 3 The task structure of a classroom refers
to the activities that students engage in when learning, that
is, what they are to do and how. In most classrooms at the
elementary and secondary levels, a variety of task structures
may be used by the same teacher. Most tasks involve students working alone (for example, completing work sheets
or reading silently) or listening to or interacting with the
teacher. Many fewer tasks involve students working or interacting with one another.
Group Rewards
47
The reward structure of the classroom refers to the
means, or incentives, that teachers use to motivate students
to perform school tasks; that is, it specifies the types of
rewards that are used to produce and maintain certain behavior and the frequency with which they are used. Thus, a
reward structure is simply the rules under which rewards are
dispensed. Every school has an explicit and implicit reward
structure that has a major impact on the academic performance, peer norms, and social behavior and attitudes of
students.
In most classrooms, the major rewards used by teachers
are verbal and nonverbal praise and grades. Teachers usually
administer these rewards on the basis of multiple criteria.
For example, most grades are given (consciously or unconsciously) on the basis of the comparison of a student's academic performance with the teacher's idea of what the student should have accomplished (that is, the pupil's "effort").
In addition, there is consideration of such factors as attitude,
neatness, and classroom behavior. Teachers administer informal praise according to the same general criteria.
One important element these criteria have in common is
that they are all examples of competitive or individual reward structures. That is, the criteria are determined either
comparatively (with students being essentially in competition for a limited amount of praise or a limited number of
satisfactory grades), or they are determined on some scale
that is absolute or is relative to the student's own performance. However, because few teachers would be willing to
give acceptable grades to all of their students regardless of
how well the students did, the reward structure of the great
majority of classrooms is primarily a competitive one in
which pupils seek rewards among a necessarily limited
number of acceptable grades.
Traditional Classroom
The traditional classroom procedure may thus be characterized as consisting of an independent or individualistic
task structure and a competitive reward structure. This procedure has many virtues: it tends to be easily administered; it
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Social Work in Education
is "fair" in that an individual's rewards depend almost entirely on his or her own performance, however defined; and
it is easily understood by children, parents, and school personnel. However, this traditional approach has been under
assault for many years because of several supposed
shortcomings. These include the following:
• Traditional reward structures do not motivate all students well. Because of the competitive nature of these
structures, many students who perform poorly have no
chance of making acceptable grades regardless of the degree
of effort they expend. On the other hand, many students
who perform well can hardly avoid making acceptable
grades regardless of effort.
• Traditional reward structures set students against one
another and in turn set many students against academic
performance. Because the academic success of one student
decreases the chances that another student will be able to
make an acceptable grade and because only a limited number
of rewards are available for the top scores, one student's
success requires another's failure. Moreover, a competitive
reward structure tends to disrupt interpersonal bonds
among students. Students attempt to combat this tendency
by discouraging academic performance on the part of their
peers. This sets up a situation in which many students who
could achieve at high academic levels turn their attention to
activities such as sports, which have more support among
their peers. 4 In many elementary and secondary schools,
these antiacademic norms may be quite strong, creating for
some students a reward structure in which academic
achievement is more effectively punished by peers than it is
rewarded by teachers and parents.
• Traditional task structures provide few opportunities
for active learning. For example, in a class discussion involving thirty students, each student gets an average of only
about one-thirtieth of the time set aside for responses by
students. Of course, in practice this time is unevenly distributed, with most of it usually going to students who need the
least help.5 Most students spend most of their time in class
either listening passively or doing individual desk work for
which feedback may be received long after performance.
Group Rewards
49
• Moreover, research indicates that traditional reward
structures lessen students' achievements in such categories
as social connectedness; self-esteem; social competence;
norm commitment; interpersonal integration; belongingness
and comfort; liking for school, family, self, and other social
institutions; positive self-image; ability to relate to others;
ability to like and accept people whose racial background is
different from their own; and interpersonal attraction. 6
Alternative Classroom Modes
An alternative to the individual task is the group task,
whereas the alternatives to competitive reward structures are
individual noncompetitive reward structures and cooperative reward structures. A group task is one in which students
are permitted or encouraged to help one another learn. Peer
tutoring is one widely used example of a group task, as are
various group projects such as joint reports and discussion
groups. Note that a group task need not involve a group (or
cooperative) reward structure. That is, students may work
together but receive rewards (grades or praise) on an individual or competitive basis.
There are three categories of classroom reward
structures: competitive, individual noncompetitive, and
cooperative. Interpersonal reward structures involve the dependence (or lack of dependence) of one student on another
for rewards in the classroom or other setting. For instance, if
one student's receipt of rewards diminishes the probability
that another will also be rewarded, the students are operating under a competitive reward structure. In a chess game,
for example, for one player to win another must lose. Grading lion the curve" is also a competitive reward structure. If
one student works especially hard to make an A, and the
number of A's is fixed, then that student's performance
reduces the probability that other students will also receive
A's. If the granting of a reward to one student is unrelated to
the probability that any other student will receive a reward,
the students are in an individual noncompetitive reward
structure. This would be true in cases of individualized instruction or in any setting in which there were fixed criteria
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Social Work in Education
for performance, as would be found in a piecework schedule
in industry.
The final category refers to a situation in which an increase in the performance level of any student increases the
probability that another will receive rewards. This is known
as a cooperative reward structure. Most team sports involve
this sort of structure. On a football team, for example, extra
practice by a guard improves the chances that the quarterback or any other player will be rewarded (by winning), and
vice versa. Cooperative reward structures may be further
broken down into the categories of (1) group competition, in
which one team's performance is evaluated in relation to the
performance of another team or teams, and (2) group contingencies, in which the group is evaluated against a fixed
standard.
Group contingencies refer to reinforcements, or rewards, that are presented to all or most members of a class
following the display of certain behavior by the group or
selected members. This might consist of the group's accomplishment of certain tasks, such as increasing its general level
of reading comprehension, or it might refer to the accomplishments of specific members of the class. In either case, a
significant portion of the class's membership receives reinforcement following manifestation of the desired behavior.
Group contingencies modify behavior most readily
when all members of the class have to exhibit a given type of
behavior at a certain criterion rate or when one or two members are required to exhibit a certain rate of prosocial behavior. The situation and the behavior to be modified determine
which of these contingencies the teacher should structure.
The effectiveness with which group contingencies modify
behavior decreases as the proportion of class members who
receive reinforcement decreases. 7
The typical classroom has many types of reward
structures operating simultaneously, such as an individual
reward structure for behavior, a group reward structure for
achievement in mathematics, and a combination of both at
times for social behavior and academic achievement. Separation of individual and group structures is necessary for the
purpose of conceptualization and as a means of providing
Group Rewards
51
the school social worker with a guide for structuring appropriate intervention.
Individual Reward Structures
Individual reward structures may be competitive or noncompetitive. Noncompetitive reward structures with individual criteria have the advantage over traditional competitive structures in that all students may, if they work hard
enough, achieve a level of performance that entitles them to
rewards. However, if all students are given the same criterion, the standard will be much easier for some students to
meet than for others. In fact, some students may have less
chance of earning an acceptable reward (by meeting a high
criterion) in an individual noncompetitive reward structure
than in a competitive one.
Furthermore, although the effectiveness of a competitive reward structure does not depend on the difficulty of the
material (students can be ranked regardless of their absolute
level of performance), difficulty is a major factor in an individual noncompetitive reward structure in which a criterion
may be too easy or too hard for many students.
With the establishment of appropriate levels of criteria,
individual noncompetitive reward structures are completely
fair, since rewards are entirely dependent on the individual's
behavior. However, in competitive structures, rewards depend upon the skill or motivation of competitors. Individual
noncompetitive reward structures in which a set criterion
must be reached also have built-in quality control. If certain
criteria can be specified as essential for a given student, it
should not matter how much that student knows compared
to other students as long as he or she can meet the requisite
criteria. Comparative grades and praise, however, are easily
understood by parents, teachers, and students, whereas individual, noncomparative evaluation may have little meaning without substantial explanation, and thus might have
little motivational value.
Individual competitive reward structures, which research indicates are most widely used in teaching, frequently
lead to dysfunctional or unanticipated outcomes. 8 For in-
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Social Work in Education
stance, a structure of competitive activities may result in
failure and rejection for some members, exclusion of others
from positions of power in the group, decreased attainment
of goals for the group as a whole, and, perhaps, increased
antisocial behavior by certain members. Likewise, by reinforcing the behavior of only selected members in the presence of others through the use of individual competitive
contingencies, the teacher may in effect withdraw available
reinforcements from those who are not rewarded. The latter
members may perceive such relative deprivation as a form of
punishment, which could lead to academic and behavioral
dysfunctions.
Hence, the utilization of individual competitive reinforcement contingencies within classrooms may produce
undesired results. It not only may entail adverse consequences for the reinforced students, but may (1) decrease the
members' attraction to one another, (2) militate against
group sharing and the attainment of goals, and (3) diminish
the class's overall effectiveness as a prosocial influence.
Moreover, the children who do not receive reinforcements
may come to believe that further interpersonal exchanges
with the "successful" members will result in their own continued failure to receive desired reinforcements. Consequently, as the number of nonreinforcing exchanges increases, the tendency for children to interact with their peers
or to remain in school may decrease.
Cooperative Reward Structures
Cooperative reward structures, regardless of whether they
involve systems of group competition, have several advantages over individual reward structures. First, they motivate
all students equally well. An extra point contributed to a
team score is just as useful if it comes from a low-achieving
student as it is if it comes from a high achiever. Second,
cooperative systems completely reverse the process inherent
in competitive reward structures in which students are set
against one another and come to oppose academic or prosocial efforts made by their peers.
In a cooperative reward structure, the effective perfor-
Group Rewards
53
"In addition to having effects on academic achievement, cooperative reward structures have . . . consistently been shown to increase students' attraction, respect, and concern for one another. These characteristics of group reward structures have also been used
in desegregated settings to facilitate interracial
friendship, cooperation, and respect."
mance of a student always improves the chances that others
will be rewarded. As a result, academically effective students
gain sociometric status in a cooperative reward structure but
lose it in either a competitive reward structure or an individual noncompetitive structure. 9 Furthermore, cooperative
reward structures motivate students to help one another
with their academic work and to tutor one another. 10
In addition to having effects on academic achievement,
cooperative reward structures have had strong and consistent positive influences on social and attitudinal variables.
Cooperative techniques, both in and out of the laboratory,
have consistently been shown to increase students' attraction, respect, and concern for one another. 11 These characteristics of group reward structures have also been used in
desegregated settings to facilitate interracial friendship,
cooperation, and respect. 12
On the other hand, cooperative reward structures must
be carefully designed if they are to have positive effects on
academic performance. First, they must have features to
prevent some individuals from letting the rest of the group
do the work. That is, each group member must be individually accountable to the group for his or her behavior. Second,
the group must have a task that requires the participation of
all members. A frequently used structure that may not meet
this criterion is the group report, in which several students
are expected to write one paper. Unless the work is carefully
divided, this type of task nearly always becomes an essentially individual activity.
A major difficulty with cooperative reward structures is
that they may be unfair in the sense that each student's
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Social Work in Education
reward depends on his or her luck at being put on a skilled or
motivated team. However, by introducing weighting procedures that equalize different academic abilities on teams,
program designers can alleviate this dysfunction and
provide all team members with the requisite incentives for
learning. 13 It must be kept in mind, also, that the larger the
team, the less the behavior of any individual determines the
outcome.
Substantial research is accumulating to show that individual reinforcement may not be the most productive means for
producing the achievement of either academic or social
goals. A series of studies supports the idea that children who
are from various socioeconomic classes, who range in age
from 3 to 11 years, and who are in classrooms ranging in size
from 4 to 17 members can work together effectively in instructional situations involving such curricula as mathematics, vocabulary development, reading, and nutrition, and
that they can serve as teachers for one another. Moreover,
the studies indicate that when appropriate reinforcement is
provided, cooperative behavior as weH as academic performance can be increased and disruptive behavior can be decreased. 14
An interesting by-product of using group contingencies
as opposed to individual reinforcement in academic environments is the finding that the liking of group members for
one another increases. Thus, one strategy for increasing the
liking among individuals of different races, academic
abilities, physical attributes, and so forth, is to place them in
contexts where each individual's rewards are dependent on
the performance of other group members. Likewise, the
sharing and enjoying of positive reinforcements increases
the frequency with which positive behavior is exchanged
among individuals. 15
Quasi-therapeutic Effects
In research on group contingencies in academic environments, the present author and a colleague found effects
they refer to as quasi-therapeutic. Children who were placed
on group contingencies in which the efforts of each member
Group Rewards
55
furthered the group's goals came to like, help, and respect
one another. This in turn has been found to increase group
members' self-esteem, trust in others, freedom from anxiety,
ability to relate to others, and feelings of being capable and
responsible and more a part of society.l6 Thus, group contingencies are particularly applicable in mainstreaming lowachieving and handicapped children. Group contingencies
create a learning situation in which handicapped children
and others are provided with tutoring in combination with
ample incentives to learn.
Building an Effective Structure
Given, then, that the reward structure of the classroom is
one of the most important manipulable features of the educational process, how should one construct an ideal system? In
applying the principles, it is assumed that curricula have
been chosen that are attractive and can secure the attention
of the students. The school social worker should analyze the
following in helping a teacher produce relevant academic
and social behavior.
1. The Need to Reinforce Appropriate Behavior. Studies
done in universities demonstrate that students study not for
the sake of learning alone but also because they are rewarded for studying. l7 Unless students are rewarded for
study, the frequency with which they engage in this behavior will be quite low. ls Thus, appropriate social behavior will
occur only when students gain sufficient reinforcement from
peers and the teacher. Disruptive behavior-a major problem in schools--will decrease when it is not reinforced, and
teachers therefore must issue rewards that are contingent
upon appropriate behavior. A program involving the issuance of tokens is one example of an approach in which it is
possible to reinforce highly specific behaviors.l9
2. The Importance of Availability. Reinforcers must be
available to all students, but should not be too easily available. As obvious as this sounds, it is the major failing of
traditional reward systems. For many students, the chances
of making an acceptable grade (A or B) are nil. Other students can achieve these rewards without much effort. In
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Social Work in Education
these circumstances, it is hardly surprising that a substantial
number of students do only what is required to be promoted,
which in most schools is not much. 20 Thus, reinforcement
systems must be structured in a manner that requires each
student to expend effort according to his or her specific
ability to attain the criterion. For heterogeneous groups with
unequal academic abilities, scoring systems can be used that
can increase the motivational value of a learning task by
grouping children in small homogeneous teams in which
pupils of equal ability earn rewards for the larger group.21
3. Timing and Frequency. For maximum effectiveness,
reinforcement, or feedback, should be delivered as soon as
possible after the occurrence of the behavior being reinforced. For younger students, less able students, and students who have not yet learned to delay gratification, a grade
delivered every six or nine weeks is not effective. Such
students may decide that grades are determined primarily by
such factors as fate or the eccentricities of teachers. Even
when students have a clear intellectual understanding of
where grades come from, it is terribly hard for them to turn
over a new leaf and maintain an improved level of performance for six, nine, or twelve weeks. Even when this is
possible, the reward system may not be sensitive enough to
recognize and reinforce improved performance in a student.
Feedback on academic tasks should occur daily at first and
then be phased out as students acquire necessary social and
academic skills. Feedback can be given in the form of credits
on posters and charts, in daily newsletters, and so forth.
4. Consistent Application. Studies indicate students must
know what kind of behavior is going to be reinforced and
how often. Also, teachers must be consistent in the application of rewards. Data conclusively show that inconsistent
application of rewards leads to ineffective acquisition of relevant academic and social behavior and to an increase in the
probability of disruptive behavior. Thus, contingencies must
be specified in such a manner that students understand what
is involved in securing rewards. 22 Children should possess a
written description of the reward system that is in operation.
In many instances, this could be in contract form.
5. Effectiveness of Reinforcement. The type of reinforce-
Group Rewards
57
"Traditional reward structures set students against one
another and in turn set many students against academic
performance. Because the academic success of one student decreases the chances that another student will be
able to make an acceptable grade and because only a
limited number of rewards are available ... one student's success requires another's failure."
ment chosen for a group of students may not be appropriate
for the individual. That is, the group reinforcer may be weak
compared to other reinforcers that are currently maintaining
the behavior of some individuals. Three critical questions
relate to the appropriateness of the incentives: (1) How much
of such reinforcement has the student had in the past? (2)
How much does the student currently receive? and (3) How
much do the student's peers receive? The power of the
reinforcer is inversely related to the answer to these three
questions. The reinforcer may be appropriate, but the
amount may not be proportional to the effort involved in
changing the behavior. Likewise, the amount or size of the
reinforcer may be appropriate, but the reinforcer may not be
provided at a high enough frequency or the schedule of
reinforcement may be too erratic to override the difficulties
the student faces in changing the behavior. Teachers can
determine what types of reinforcement would be effective by
asking the children what they would like, observing them in
free-time periods, and administering a reinforcement survey.23 Such information assures the teacher that he or she
possesses the requisite information for structuring an effective reinforcement system.
6. Patterns of Reinforcement by Significant Others. The establishment of appropriate reinforcers and delivery conditions is important, but there must also be cooperation from
significant others in the student's environment-for such
others may be providing reinforcement that maintains the
undesirable behavior and may in fact be punishing behavior
that is being reinforced in the classroom. The significant
others chosen to participate in the modification plan may,
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Social Work In Education
however, be inconsistent in applying the agreed-upon plan
of behavioral change or may not be influential enough to
facilitate the behavioral changes. Teachers, with the help of
the school social worker, should isolate existing patterns of
peer-group reinforcement and structure reinforcement systems to encourage peer support for appropriate academic
and social behavior. 24
Summary
How important is the reward structure of the classroom?
One can argue that it is the most important manipulable
feature of the educational setting. Studies on what is taught,
styles of teaching, methods of delivery, and the like have
been notoriously ineffective in demonstrating that important
changes can be produced in the behavior of students as a
result of variations in these dimensions. 25 On the other
hand, the making of major changes in reward structures has
been associated with changes in the behavior of students. By
having teachers administer simple, highly contingent praise
in classrooms, researchers in the behavior modification tradition have been consistently successful in increasing students'
ability to perform tasks, to answer quizzes, and to adhere to
classroom rules. 26 Such approaches have also been effective
in teaching children who have failed in school because of
deficiencies in such areas as reading and arithmetic. 27
Accumulated research on cooperative reward structures
indicates that they have a consistent positive effect on academic performance, the amount of time spent on tasks,
attitudes toward academic activities, and other variables. 28
Whereas research on highly competitive reward structures
indicates they produce behavior that is clearly undesirable
(such as cheating, lack of tutoring, and concern only for
one's own academic achievements) and that they produce
peer norms that oppose exhibition of the academic behavior
that the institution seeks to increase, such as studying and
participating in class. In elementary and secondary schools,
these antiacademic norms may be quite strong, creating for
some students a reward structure in which academic
achievement is more effectively punished by peers than it is
Group Rewards
59
rewarded by teachers and parents. Group reward structures
provide school social workers effective procedures for altering such destructive processes.
•
ABOUT THE AUTHOR
John S. Wodarski, Ph.D., is Director, Research Institute, School of
Social Work, University of Georgia, Athens. Preparation of this
manuscript was facilitated through funding from
Public
Health Service research grants MH18813 and MH2190S, awarded
by the National Institute of Mental Health, Center for Studies of
Crime and Delinquency; research grant NE-C-003-0114 awarded
by the National Institute of Education; and faculty research awards
presented by the University of Maryland and the University of
Georgia.
u.s.
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Social Work in Education
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Group Rewards
61
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Slavin, Teams.-Games- Tournament: A Final Report on Research, Center Report
No. 217 (Baltimore, Md.: Center for Social Organization of Schools, Johns
Hopkins University, 1976); Johnson and Johnson, op. cit.; Kazdin, The
Token Economy; and Thoresen, op. cit.
15. Elliot Aronson et aI., "Bus sing and Racial Tension: The Jigsaw
Route to Learning and Liking," Psychology Today, 8 (February 1975), pp.
43-44; DeVries and Slavin, "Effects of Team Competition on Race Relations in the Classroom: Further Supportive Evidence"; Feldman and
Wodarski, op. cit.; and William G. Lucker et aI., "Performance in the
Interdependent Classroom: A Field Study," American Educational Research
Journal, 13 (Spring 1977), pp. 115-123.
16. Robert E. Slavin and John S. Wodarski, "Decomposing a Student
Team Technique: Team Reward and Team Task." Unpublished paper
presented at the Annual Convention of the American Psychological Association, San Francisco, 1977.
17. John M. Johnson, ed., Behavior Modification and Technology in
Higher Education (Springfield, Ill.: Charles C Thomas, Publisher, 1975);
and Robert Travers, ed., Second Handbook of Research and Teaching (Chicago:
Rand McNally & Co., 1973).
18. Albert Bandura, Principles of Behavior Modification (New York:
Holt, Rinehart & Winston, 1969).
19. Alan E. Kazdin, "The Application of Operant Techniques in
Treatment Rehabilitation and Education," in Sol L. Garfield and Allen E.
Bergin, eds., Handbook of Psychotherapy and Behavior Change: An Empirical
Analysis (New York: John Wiley & Sons, 1978); and Wodarski and
Bagarozzi, op. cit., chap. 9.
20. Charles B. Schultz and Roger H. Sherman, "Social Class, Development, and Differences in Reinforcer Effectiveness," Review of Educational
Research, 46 (Winter 1976), pp. 25-59.
21. DeVries, Edwards, and Fennessey, op. cit.
22. William De Risi and George Butz, Writing Behavioral Contracts
(Champaign, Ill.: Research Press, 1975).
23. Joseph R. Cautela, "Reinforcement Survey Schedule: Evaluation
and Current Applications," Psychological Reports, 30 (February 1972), pp.
683-690; and Cautela and Robert Kastenbaum, "A Reinforcement Survey
Schedule for Use in Therapy, Training, and Research," Psychological Reports, 20 Gune 1967}, pp. 1115-1130.
24. John S. Wodarski, "Procedures for the Maintenance and Generalization of Achieved Behavioral Change." To be published in a forthcoming issue of Journal of Sociology and Social Welfare.
25. Hamblin et aI., op. cit.; and Travers, op. cit.
26. Alan E. Kazdin and Joan Klock, "The Effect of Nonverbal Teacher
Approval on Student Attentive Behavior," Journal of Applied Behavior
Analysis, 6 (Winter 1973), pp. 481-486; Johnson, op. cH.; and Teodoro
Ayllon and Michael D. Roberts, "Eliminating Discipline Problems by
Strengthening Academic Performance," Journal of Applied Behavior
Analysis, 7 (Spring 1974), pp. 71-76.
27. Hamblin, Hathaway, and Wodarski, op. cit.
28. DeVries and Slavin, Teams-Games-Tournament: A Final Report on
Research.