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DOCUMENT RESUME 



ED 248 641 

AUTHOR 
TITLE 



EC 170 419 

Zucker, Stanley H.; Prehm, Herbert J. 
Parameters of Cumulative Programming with 
Severely/Profoundly Handicapped Pupils. Final 
Report. 

Arizona State Univ., Tempe, Dept. of Special 
Education. 

Department of Education, Washington, DC. 
Jan 84 
G008001872 
51p. 

Reports - Research/Technical (143) 
MF01/PC03 Plus Postage. 

Elementary Secondary Education; Models; *Severe 
Disabilities; ^Teaching Methods 
^Cumulative Programing 



INSTITUTION 

SPONS AGENCY 
PUB DATE 
GRANT 
NOTE 

PUB TYPE 

EDRS PRICE 
DESCRIPTORS 

IDENTIFIERS 

ABSTRACT 

_ A project incorporating. .15 stjidies _o n 

cumulative programming instructional strategies in severely 
handicapped populations is presented. A model was developed to allow 
for controlled formal investigation of potentially relevant variables 
including those descriptive of the subject (such as handicapping 
condition, race, or age), the content (areas Of skill or knowledge), 
and the task (variables related to the actual instructional process). 
The model allows for design of new studies based on the results of 
previous ones. Fifteen studies on various aspects of subject, 
content, and task variables are then reviewed and data are presented 
in table form. (CL) 



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* Reproductions supplied by EDRS are the best that can be made * 

* from the original document. * 
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CO 

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FINAL REPORT 



PARAMETERS OF CUMULATIVE PROGRAMMING WITH 
SEVERELY/PROFOUNDLY HANDICAPPED PUPILS 



U.8. DEPARTMENT OF EDUCATION 

NATIONAL INSTITUTE OF EDUCATION 

EDUCATIONAL RESOURCES INFORMATION 
CENTER (ERIC) 
This document has been reproduced as 
received from the person or organization 
originating it 

Minor changes have been made to improve 
reproduction q jalily 

• Points of view or opinions stated in this docu 
mem do not necessarily represent official NIE 
position or policy. 



STANLEY H. ZUCKER 
HERBERT J.; PREHM 



DEPARTMENT OF SPECIAL EDUCATION 
ARIZONA STATE UNIVERSITY 

■ . " ■ '/ 



GRANT NUMBER - G008001872 
CFDA NUMBER - 13.443C 



JANUARY 1984 



er|c 



2 



2 



Table of Contents 

Page 



Objectives and Need for this Assistance 3 

Goal and Objective 12 

Results or Benefits Expected 16 • 

Approach . 17 

Plan of Action 17 

. Subjects 18 

Procedure 18 

Analysis 21 

Projection of Accomplishments 22 

Accomplishments * 26 

Study 1 *••*.* 26 

Study 2 26 

Study 3 29 

Study 4 29 

Study 5 ' 29 

Study 6 . . 31 

Study 7 . . ' 31 

Study 8 31 

Study 9 34 

Study 10 . 34 

Study 11 37 

Study 12 37 

Study 13 37 

Study 14 40 

Study 15 40 

Dissemination 43 

References 45 

Appendix A - Data Sheets 49 



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OBJECTIVES AND NEED FOR THIS ASSISTANCE 
Special education is currently facing a dilemma brought about, 
in part, by legislative mandates to provide services to the severely/ 
profoundly handicapped (SPH), while much of the information needed 
to provide these services is incomplete. Historically, very few 
public schools or institutions have providedmuch more than custodial 
care for the severely/profoundly retarded, multihandicapped population. 
In fact, the provision of publicly supported special education services ' 
to the mentally retarded has been marked by a concentration of effort 
in behalf of those most competent, while the severely and profoundly 
retarded have been systematically excluded and placed in institutions 
where little or no i programming was available. In the 1960 ' s less 

than 5% of the nation's retarded were in institutional settings 

i 

(Butterfield, 1969;; Dingman & Tarjan, I960), while about half the 
nation's profoundly retarded were institutionalized. 

i * 

Recent court decisions and the civil rights nature of the 
Education of All Handicapped Children Act of 1975 (Public Law 94-142) 
already have initiated and will continue the implementation of 
services f ^ all handicapped children in the least restrictive 
environment possible. The litigation and legislation is helping 
to remedy the situation described above by making services available 
to previously unserved populations and perhaps even more important, 
by making sure the services are appropriate. As Abeson and Zettel 
(1970) point out: 

"There simply will not be any grounds for depriving a 



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handicapped child, who because of that handicap, 
possesses unique learning needs requiring special 
education. No longer will it be permissible for 
a sch-ool person to exclude or postpone the education 
of such handicapped children on the grounds that they 
cannot learn, their handicap is too severe, programs 
do not exist, or for any other reason ... it means 
that no child is uneducable or stated in another way, 
all children can learn." (p. 122) 

We. not only have to take this statement seriously, we also 
must take it literallv. Responsibility for insuring success in 
these efforts fall in two major areas: (a) delivery agencies 
(e.g., public schools, institutions, etc.) and (b) training 
agencies (e.g., universities, colleges, etc.). Two problems emerge 
when educational efforts are directed at the severely handicapped. 
One problem is that of breaking new ground. The second problem 
involves systematically testing existing knowledge and techniques 
on this heretofore unserved population. Our previous educational 
efforts with the SPH were mostly based on intuition. That intui- 
tion, at best, was based on our previous experience. According to 
Haring and Pious (1977): 

"--it is our responsibility as educators to teach and 
to demonstrate unmistakably to the public that severely 
handicapped persons can learn. 

We are beginning to recognize some of the instruc- 
tional components necessary for the undertaking of educa- 
tional responsibilities mentioned earlier ... the 
procedures that educators have developed in their work 
with moderately handicapped children will have to take 
a quantum leap; what we now consider sophisticated skills 
m&y well seem primitive as we develop the instructional 
competencies necessary to teach our new educational 
clientele . . ." (p. 5-6) 

There is no question that special education is "tooling up" to 

meet the educational needs of the severely handicapped. The questio 



is in what areas or toward which objectives do we invest our resources? 
In the past few years there have been some programmatic efforts at 
identifying knowledge which would be of benefU to severely handi- 
capped populations. In general, these program can be classified 
into two broad categories: investigations of operant procedures with 
severely handicapped subjects and development of curricula for 
severely handicapped populations. 

* 

The first program was essentially designed to demonstrate the 
lav.' of effect across many different behaviors in severely handicapped 
populations. Different operant procedures that were investigated all 
depended on the law of effect for their theoretical base, thus their 
success or failure was not really a test of the law of effect but 
instead a gauge of the effectiveness of the reinforcer used. In essence 
then, most of these studies dealt with incentive motivation questions 
(Siegel, 1968). They answered questions involving the relative efficacy 
of various reinforcers and the relative preference of the subjects for 
them. Some recent examples of this include the preference of vibratory 
over visual stimulation by severely and profoundly retarded subjects 
(Ohwaki, Brahlek, and Stayton, 1973; Ohwaki & Stayton, 1976) and the 
use of contingent vibratory stimulation to train nonambulatory pro- 
foundly retarded students (Murphy & Doughty, 197/; Zucker, D'Alonzo, 
McMullen & Williams, in press). 

The second program was geared toward generating systematic and 
specific curricula to meet the needs of severely handicapped popu- 
lations. The focus of these programs was to use interdisciplinary 
and practitioner input for generation of competencies applicable to 



the severely handicapped. Evidently, this program has been quite 
successful as indicated by the dissemination of many books, reports 
and guides on curriculum for the severely handicapped (e.g., Donlon 
& Burton, 1976; Sontag, 1977). These documents address topics 
ranging .Vom general content areas such as c Mnunication and self- 
help to specific objectives for eye movements and tongue positions. 
The feature which is most noticable in the majority of these curriculum 
specification efforts is that they are not watered down versions of 
curriculums for moderately retarded children. Rather, these curricula 
are directed solely toward training areas which relate to SPH popu- 
lations. . ~ 

Notwithstanding the accomplishments of the above programs, 
there seems to be a major gap in our research efforts at elucidating 
information applicable to severely hand' capped populations. The 
focus of research must change from what to teach to how to teach. 
Answering the how to teach question by identifying additional 
reinforcers or novel ways in which they may be applied is circum- 
venting the question. Haywood (1977) stated: 

"We do not need any more studies of single subjects 
designed to demonstrate that the law of effect still 
works and can be applied to yet another aspect of 
behavior. The law of effect is as valid today as it 
was in 1927." (p. 315) 

Generating more curriculum, even appropriate curriculum, does 

not answer the process question of how to achieve the competencies. 

One example would be a recent special publication of the Division 

on Mental Retardation of the Council for Exceptional Children 

(Sontag, 1977). This volume entitled "Educational Programming 



v 



7 

for the Severely and Profoundly Handicapped" devotes very little 

actual space to the "how to" question. While many of the articles 

have provocative titles, close inspection reveals they are generally 

curricular descriptions. Implementation is generally assumed to 

be operant in nature. For example Bricker and Iacino (1977) 

relate this process: 

"The next stage is systematic implementation which may 
be largely dependent upon the personnel's knowledge 
of and skill in using teaching strategies based on 
behavioral principles." (p. 175) 

The important point to be gleaned here is that operant techniques 

cannot substitute for instructional strategies. These two dimensions 

are not interchangeable, they are complementary. Operant technique? 

are only as good as the instructional strategy which determines 

their use. The rewarding and often dramatic results that are 

accomplished using operants with severely handicapped populations 

should not limit our investigations and development of appropriate 

instructional strategies which would further enhance our success. 

It is only through research that we can systematically test 

existing strategies and based on the results develop new ones to 

be further tested. Haywood (1977) emphasizes that: 

"We need basic research on the fundamental mechanisms 
by which human beings learn. We need somewhat more 
complex research on the interactions among learning 
strategies, personal characteristics of individuals, 
types of material to be learned, settings for learn- 
ing, and incentive conditions." (p. 316) 

The identification and investigation of learning strategies 

would seem to be of paramount importance if we wish to meet the 

needs of low functioning children. In discussing the learning 



9 

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performance of mildly handicapped students, Prehm (1976) has indicated 
that handicapped children fail to use learning strategies spontaneously 
and that we should correct this by teaching the strategy along with 
the information to be learned. Learning strategies in this sense 
are techniques used to help people remember and use information. 
Providing learning strategies for severely handicapped populations 
which effectively enhanced learning would fill the gap mentioned 
earlier between operant procedures and curriculum implementation. 

One learning strategy approach which has been used with non- 
handicapped students is called cumulative programming. Becker, 
Engelmann and Thomas (1975) define cumulative programming as follows: 
". . . two concepts from a related set are brought to criterion. Then 
new concepts are added one at a time and brought to criterion." (p. 257) 
The use of this program as a method of instructio. as been explored 
by a few researchers. A brief review of these studies follows. 

Carnine (1976) demonstrated the effectiveness of introducing 
similar sounding stimuli cumulatively in a letter-sound correspondence 
task. The study was conducted with three groups of normal preschool 
children. In one group the stimuli were presented simultaneously, 
i.e., all the stimuli were on the same presentation sheet. For 
this group, the similar sounding letters, e and i, were introduced 
separately with four letters in between each presentation. The 
stimuli were presented to the other two groups cumulatively, i.e., 
a new letter was added to the set of previously learned letters 
only when the child had reached criteria on all the letters in 
the current set. For one of the cumulative introduction groups, 



9 

the similar sounding stimuli were presented together, i.e., i 
followed e. The similar sounding stimuli for the other cumulative 
introduction group were separated, i.e., e and i were presented 
with four other letters in between. The findings indicated that 
the cumulative introduction group in which the similar sounding 
stimuli were separated reached criterion more quickly than the 
other two groups. Also, posttest scores for both cumulative intro- 
duction groups were higher than the simultaneous group's posttest 
scores . 

Staats, Brewer & Gross (1970) studies alphabet reading in 
11 preschool children. The letters were presented sequentially in 
upper-case form. Pictures, used early in the program, were eliminated! 
when the child could identify several letters. When a new letter 
had been mastered, it was presented in sequence with several pre- 
viously learned letters, i.e., for P the sequence would be L M N 0 P. 
When the child learned the letter in sequence, it was randomly 
presented with all the earlier letters in the alphabet, thereby 
constantly reviewing those letters. The results demonstrated that 
the use of this type of cumulative programming strategy resulted 
in the children's acquisition of the letters at an increasingly 
faster rate, i.e., they required fewer trials to master the second 
half of the alphabet (N-Z) than were required to master the first 
half of the alphabet (A-M) . 

Ferster & Hammer (1966) used a cumulative programming strategy 
to teach chimpanzees binary arithmetic. They compared successive 
pairs and cumulative programming strategies on a number-symbol paired 



10 



10 



associate learning task. The experimenters found that discrimination 
of randomly presented numbers was accurate when cumulative programming 
was used but when successive pairs programming was used, the animals 
only responded at a chance level to randomly presented numbers. 

Gruenenfelder & Borkowski (1975) tested the spontaneous transfer 
of cumulative rehearsal during serial learning to a new list. They 
divided 60 normal first grade children into two groups: (a) no instruc- 
tion; and (b) cumulative rehearsal. From the data reported, the 
authors concluded that some of the children in the second group did 
not use the cumulative rehearsal strategy spontaneously after training. 
The serial lists (three 9-item and one. 4-item) were slides constructed 
using pictures from the Peabody Picture Vocabulary Test. The children 
who used cumulative rehearsal needed fewer trials to reach criterion 
than the other two groups (those with no instruction and those who » 
received cumulative rehearsal instruction but did not spontaneously 
transfer it after training). The cumulative rehearsal group took a 
significantly longer time to reach criterion. The time measure was 
contaminated because each subject in the study controlled the length 
of stimulus item exposure time. Subjects in the cumulative rehearsal 
group held items for significantly longer exposure periods. The 
children who were instructed with cumulative rehearsal were able 
to transfer their learning to a new serial list a week later where 
no instructions were given. 

Up to this point the studies cited have employed intellectually 
normal children. There have been two studies, however, which investi- 
gated cumulative programming strategies with moderately and severely 



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handicapped children. Fink and Brice-Gray (1979) conducted a pilot 
study investigating cumulative programming with 10 moderately and 
severely handicapped preschoolers. Half the subjects were assigned to 
a successive pairs programming group while the other half were assigned 
to a cumulative programming group. The results indicated that subjects 
who received the cumulative programming instructional treatment reached 
terminal criteria in significantly less trials than the subjects who 
received the successive pairs programming instructional treatment. Also, 
subjects in the cumulative programming instructional treatment made 
significantly more correct responses on an immediate recall measure 
than did the successive pairs programming instructional treatment group. 

P'/ehm, Zucker and Roth (1979) also tested the cumulative programming 
paradigm, this time with severely and moderately retarded school age 
children. They found subjects in a cumulative programming group required 
less trials to reach criteria than did a successive pairs group. Unlike 
Fink and Brice-Gray (1979), however, immediate recall did not differ be- 
tween groups. On seven day recall the cumulative group performed sig- 
nificantly better than the successive group. 

The studies reviewed above using intellectually normal and primate 
populations certainly reveal the potential utility of cumulative pro- 
gramming strategies for teaching. Especially promising are the salutory 
effects reported by Fink and Brice-Gray (1979) and Prehm, Zucker and Roth 
(1979) in handicapped populations. These positive results and the 
alarming dearth of other evicence in this area clearly call for more 
research, on a larger scale, which will systematically identify, investi- 
gate and validate cumulative programming strategies and the associated 
parameters which interact with cnem. 



Goal and Objective 

The major goal of this project is to investigate the parameters of 
cumulative programming instructional strategies in severely handicapped 
populations. Realization of this goal will result in pragmatic techniques 
which will have direct and immediate application to training in these 
populations. 

The major objectives which will accomplish this goal are: 

1) investigation of variables descriptive of the subject; 

2) investigation of variables descriptive of the content; 

3) investigation of variables descriptive of the task. 

In order to facilitate systematic exploration of these variables, 
the following Model has been developed (Figure 1 on page 17). This 
Model (adapted from Altman, 1973; Alt ' ' '-.Iking ton, 1971) will allow 
for controlled formal investigation v U'^e .tntially relevant vari- 
ables including: (a) those variable:, • of the. subject; (b) 
those variables descriptive of the conte, (c) those variables 
descriptive of the task. The list of variables comprising the dimensions 
of this Model is not meant to be exhaustive. The list will serve as the 
starting points for the beginning studies. Variables may be deleted or 
added to the Model as deemed necessary depending on the results of our 
explorations. 

The Subject Variables of this model will allow us to ask questions 
related to the effects of cumulative programming techniques on different 
handicapped populations. For example, there may be differences between 
severely and profoundly retarded, or between retarded and autistic, or 
between ambulatory and non-ambulatory, etc. Chronological age of the 
child may be a factor as could be sex or race. In addition, whether or 

13 



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Task Variables 



x 



Subject Variables 



Ability level 
Chronological Age 
Sex 
Race 



Institutionalization vs 
Non-ins ti tutionalization 




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Content Variables 



Figure 1 - Dimensions identifying cumulative programming parameters 




14 



14 

not the child resides at home or in an institution may be related to 
success at certain tasks. Subject variables then, are those character- 
istics of children which may effect the outcome of the instructional 
technique. 

Content variables refer to the different areas of skill or knowledge : 
we would be training, tfhile it is obvious that cumulative programming 

V' 

techniques may enjoy differential success across these areas it is also 
possible that dimensions within these may also effect outcomes. For 
example, in the pre-academic area do cumulative instructional strategies 
work equally well for recognition of shapes as opposed to beginning 
number concepts? For academics the same questions could be asked about 
reading and math skills. Socia] areas might involve differences between 
one-to-one skills as opposed to group skills. Psychomotor (locomotion 
vs. fine motor), language (receptive vs. expressive) and vocational 
(assembly vs. sorting) areas also lend themsel'.es to these kind of 
questions. 

Task variables reflect areas related to the actual instructional 
process. The interaction of this dimension with the other two may differ- 
entially effect cumulative programming outcomes. For example, consideration 
of the reinforcement variable would involve the efficacy of cumulative 
programming under reinforcement vs. no reinforcement. Also subsumed 
under this category would be the relative effectiveness of alternate 
reinforcers (e.g. social vs. edible). Under design features such questions 
such as group or individual instruction could be considered, Thecategory 
of antecedent variables would include items such as previous experience 
with the content and current skill level. Learning criteria refers to 



15 



a "barometer" of success which may differentially vary from a certain 
"number' of corfect-respoTises to generalization to other settings or 
different tasks. Finally, stimulus conditions refers to the number, rate 
of presentation, order of presentation, etc. of stimuli in the cumulative 
programming instructional sequence. > 
Thus the subject, content, and task variables outlining the dimensions/ 
of this Model comprise the possible parameters which interact with cumu- 
lative programming. At first inspection it. may appear that each cell 
of the Model represents a study in itself. Closer examination, however, 
reveals that each cell represents many separate studies within those 
relevant dimensions. We have the option of manipulating the variable 
dimensions while testing cumulative programming or holding the dimensions 
constant while comparing cumulative programming to another type of pro- 
gramming, or doing both simultaneously. Many times these decisions will 
be based on the number of subjects that are available from each category. 
One example of this would be the cell defined by the intersection of 
reinforcement under Task Variables, ability level under Subject Variables, 
and vocational under Content Variables. These dimensions suggest a variety 
of studies one of which might be the effectiveness of cumulative programming 
with three types of reinforcers (e.g., edible, social, and vibratory), on 
two types of vocational task (e.g., sorting and assembly) on the learning/ 
performance of severely handicapped children (e.g., profoundly retarded 
and autistic). Or, we could hold the dimensions constant and vary the 
type of instructional strategy (e.g., cumulative programming and succes- 
sive programming), or, we could simply add this fourth factor of instruc- 
tional programming to the previous three dimensions. What would determine 



the specific elements of a given study would be the number of subjects 
available and the specific questions under investigation. 

It is obvious that the model depicted could be used to generate 
a seemingly endless number of studies. In order to limit the scope of 
our studies we have a number of high priority variables which would 
receive. early attention. Specifically, along the content dimension we 
would highlight pre-academic and academic variables, along the subject 
dimension we would highlight ability level and chronological age variables 
and along the task dimension we would highlight stimulus conditions and 
learning criteria variables. These variables seem most relevant based 
on previous research and pragmatic value in the classroom. Thus, our 
initial series of studies will concentrate on these factors and the re- 
sults of these studies will aid in the choice of subsequent investigation 
variables from our model. 

RESULTS OR BENEFITS EXPECTED 

As indicated in the preceding section, there is very little available 
knowledge related to the effectiveness of various instructional strategies 
with SPH children. Educational efforts are dependent upon the teachers' 
knowledge of reinforcement techniques and rather standardized programming 
techniques. The effectiveness of alternative programming techniques, 
particularly as these techniques effect the learning of SPH children, 
is not known. If teachers are to make sound instructional judgments, 
evaluations of the parameters of potentially powerful educational pro- 
gramming techniques are needed. 

This three year project is iesigned to fill a void in our knowledge 
of effective instructional programming for SPH individuals. Completion 
of the project will provide teachers of the SPH and program planners 
with extensive information regarding the cumulative programming instructional 

17 



17 



strategy. The knowledge gained through the proposed project can be used 

i 

to plan curricula, to design specific instructional activities, and to 
implement actual instruction. Through this project more effective and 
efficient instruction for the SPH will be developed. The primary benefits 
of the proposed project will be the increased skill levels of (a) the 
pupils involved in the project and (b) the pupils taught by persons using 
the results of the project. Additional benefits will be increased ability 
of educators to design effective instructional programming strategies for 
SPH children. 
APPROACH 
Plan of Action 

The specific and general procedures to be detailed are to be con- 
sidered generic to all studies to be conducted in the research program. 
The model presented allows us to pick variables and construct investi- 
gations based on the actual results of our ongoing studies. This method 
is preferred to one which specifies in advance the exact dimensions of 
each individual study. It may be that certain dimensions of' the model 
will give us more useful information, thus, a flexible approach can capit- 
alize on this. The purpose of the following description is to outline 
the procedures which will be used independent of the variables under 
investigation. The variables used here are examples taken from the sub- 
ject, task, and content model. 

The pjrpose of chis sample study is to investigate the relative 
efficacy of two instructional strategies (e.g. cumulative and successive 
pairs programming) under two types of reinforcement (e.g. social and 
edible) on the learning of two-syllable functional sight words by severely 



18 



retarded and autistic children. Referring back to our model, this study 
would be varying two of the dimensions (task and subject) while holding 
the third constant (content) and adding and varying a fourth (instructional 
strategy). This demonstrates the flexibility available in structuring 
and investigating research questions. 
Subjects 

Severely retarded and autistic subjects will be randomly selected 
from their respective populations. Severely retarded subjects will be 
randomly assigned to one of four treatment conditions as will autistic 
subjects, thus, constituting eight total conditions. After assignment, 
subject characteristics such as age, sex etc. will be statistically 
compared to check on differences between conditions. It is anticipated 
that 10 subjects per condition will be required to satisfy general sub- 
ject/variable ratio requirements. Numbers of subjects may be a factor 
but, in general, the greater Phoenix area has many public and private 
facilities which serve severely handicapped children. Many of these 
have cooperated in tne past with either funded or individual projects 
and a sample of these have responded favorably to our current inquiries. 



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Procedure 

Each subject will be run individually in a predetermined random 
order each day. The experimental session will take place in an available 
room inthe student's school. Essentially, this room will be minimally 
distracting and contain a table and chairs for the experimenter and 
subject. The subject will sit across the table from the experimenter. 
The stimuli will be five two-syllable functional sighii words (e.g., 



19 



entrance, women, danger, exit, and poison) presented individually on 
13 x 20.5 em cards, randomly ordered from a through e. All stimuli 
used will be novel to the subjects. 

Instruction will begin with stimulus a. The experimenter will 
present stimuli a and b to the subject and touch stimulus a and 

say, "This is . Touch ." If the subject responds correctly, 

i.e., touches the correct stimulus, the experimenter will immediately 
reinforce the subject with praise or edibles, depending on which 
reinforcement treatment condition the subject is in. If the subject 
responds incorrectly, the experimenter will immediately say, "No, 

this is (and touch the correct stimulus). Touch . " The 

experimenter will then switch the left-right position of the stimuli and 
instruct the subject to touch the stimulus again. The order of the 
arrangement of the cards will be randomly determined prior to the 
beginning of the study. The subjects will be given twenty trials per 
day or the number required to reach criterion if less than twenty. 
Training will continue until the subject reaches a criterion of eight 
consecutive correct responses. When the subject reaches criterion 
on stimulus a, the experimenter will follow the same procedures to 
teach stimulus b. This would be step 2. 

In step 3, the subject will discriminate stimulus a from stimulus 
b. The experimenter will present both stimuli to the subject and 
instruct the subject to identify one stimulus at a time. For each 
trial, the experimenter will follow the order of switching stimuli 
referred to in step 1 and instruct the subject to choose stimuli in 
the order given on the data sheets in Appendix A. From this point on, 



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20 



the training will differ depending on instructional condition. 

For the next twelve steps the subjects in the successive pairs 
instructional programming group will be instructed as follows: the 
next single stimulus will be introduced with stimulus a and brought 
to criterion. Then, that stimulus will be discriminated from stimu- 
lus a. This procedure will continue until all single stimuli had 
been introduced and all possible pairwise discrimination are made 
by the subject. 

For the next six steps the subjects in the cumulative instruc- 
tional programming group will be instructed as follows: the next 
single stimulus will be introduced and brought to criterion with 
stimuli a and b, i.e., the subject will only have to identify the 
new stimulus. Then the subject will be required to identify the 
new stimulus as well as a and b. This procedure will continue until 
all single stimuli have been introduced and all possible stepwise 
discriminations have been made (see Appendix A). Subjects will be 
required to respond with at least 75 percent correct accuracy on 
previously learned stimuli after moving beyond stimulus c (step four) 
i.e., in step five, when the subject is required to identify stimuli 
a, b, and c, the subject could get 75 percent correct response or six- 
out-of-eight on a and b until the subject correctly identifies stimulus 
c eight consecutive times. 

When a subject has reached criterion on the last step of his 
respective program, a test will be administered. The experimenter will 
place all five stimuli on the table in front of the subject. Then, 
following the random order given on the data sheets in Appendix A, 



2i 



the experimenter will instruct the subject to touch each stimulus. 

/The subject's responses will be recorded. In addition to this data 
the experimenter will also record responses to each step of the instruc- 
tional program on the data sheets. This will allow tabulations of the 

• total number of trials each subject takes to reach criterion. 
Analysis 

The data will consist of scores on two dependent measures (trials 
to criterion and number correct on test) which reflect the dependent 
variables of rate and recall. The statistical technique that will be 
used to analyze the data and test appropriate null hypotheses will be a 
three-way (reinforcement x subject x strategy) multivariate analysis of 
variance (MANOVA) (Anderson, 1958; Morrison, 1967; Tatsuoka, 1971). 
Using the MANOVA reduces the possibility of a spurious rejection of null 
hypotheses, which increases when spearate analysis of variance (ANOVA) 
tests are performed for each of the dependent measures. The MANOVA can 
yield a number of criteria to test effects and interactions. These 
include Hotel ling-Lawley's Trace, Pillai's Trace, Wilks" Likelihood Ratio 
Criterion, and Roy's Maximum Root Criterion (Heck, 1969; Pillai, 1960; 
Schatzoff, 1966). The first two can yield approximations of the F 
distribution while the latter two are based on their own distributions. 
The evidence available at present does not indicate any superiority of 
one criterion over any other (excluding computational factors) for the 
purposes of this study (Ghosh, 1964; Kshirsager, 1972; Mikhail, 1965; 
Pearson, 1971, Pillai & Dotson, 1969; Pillai & Jayachandran, 1967; 1968). 

If the MANOVA indicates rejection of any of the null hypotheses, 

then separate univariate ANOVAs will be performed on each dependent 

/ 



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measure. In addition, where indicated, post-hoc Newman-Keuls comparisons 
will be used to indicate differences between means across conditions and 
simple or simple simple effects will be ascertained for significant 
interactions (Steel & Torrie, 1960). The probability level for rejection 
of all null hypotheses will be .05. 

It should be emphasized that following these procedures and based 
on the results, new studies will be designed and investigations of the 
parameters of cumulative programming will continue. It is anticipated 
that from three to five such studies can be conducted each year for the 
three year grant period. By utilizing the overall model and approach 
described above, the researchers can capitalize on the results of each 
of the experiments. 

Projection of Accomplishments 

It is anticipated that from 70 to 120 SPH persons (preschool, 
school age, and adolescents) will participate in project activities 
during' each of the three years of the research program. The Phoenix 
metropolitan area has sufficient numbers of SPH persons to support the 
research program proposed. Criteria consistent with the AAESPH defini- 
tion of SPH persons will be used as the basis for selecting the subjects 
to participate in the project. 

The proposed project is projected for a three year period. Pro- 
jected accomplishments of the project are listed below. 
Year 1 

July - September 1980 

Select parameters for study for first three experiments 
Develop materials 



ERIC 



23 



23 

Select subjects 

Hire Graduate Assistants 
October - December 1980 
Conduct Study 1 
Begin Study 2 

Submit proposals for dissemination at conferences and workshops 

Prepare continuation request 
January - March 1981 

Conduct Study 2 

Conduct Study 3 
April - June 1981 

Complete all Year 1 studies 

Write final report of Year 1 activity 

Design Year 2 Studies 

Make appropriate presentations 

Year 2 

July - September 1981 

Conduct Studies 4 and 5 

Submit proposals to appropriate professional organizations 
for conference presentations 
October - December 1981 

Conduct Studies 5 and 6 

Prepare continuation request 
January - March 1982 

Conduct Studies 6 and 7 

Conduct one local dissemination workshop 



ERIC 



2<1 



24 



April - June 1982 

Conduct Studies- 7^nd 8 
Make two national conference presentations 
Conduct one local dissemination workshop 
Complete all Year 2 activities 

Year 3 

July - September 1982 

Write report of Year 2 activity 
Design Year 3 Studies 

Submit professional meeting presentation proposals to 
relevant professional organizations 
October 1980 - March 1983 
Conduct Studies 9-12 

Conduct local dissemination workshops three, four and five 

Make appropriate conference presentations 
April - June 1983 

Conduct dissemination workshops six and seven 

Complete Year 3 activity 

Make appropriate conference presentations 

Write final report 
The benefits to be derived from this project are clear in terms 
of their impact on handicapped children. The results of clarification, 
validation, application and implementation of cumulative programming 
techniques tested in this research program and their related parameters 
can be immediately utilized in educational applications for the severely 
handicapped. There will be no research to practice lag in implementing 
these findings. The research program proposed here is entirely prag- 
matic in nature, it involves application of teaching strategies to various 

ERIC 2 0 



children across various tasks and areas. 

The dissemination plan involves much more than the typical re- 
search presentations at national conferences and publication in 
relevant journals. While these are important areas of dissemination, 
the time lag between exposure and implementation with children is too 
great. Therefore, in addition, project staff will conduct a series 
of dissemination workshops throughout the state for public and private 
agencies dealing with severely handicapped children. These workshops 
would enable immediate implementation of the findings by these respective 
agencies. In this way, over 1000 severely handicapped children would 
directly benefit from this project while many more would benefit 
indirectly. 

Also, this same type of approach (dissemination workshops) is 
planned for the national level. Organizations such as The American 
Association on Mental Deficiency and The American Association for the 
Education of the Severely and Profoundly Handicapped sponsor special 
courses and workshop sessions at their national meetings which are 
practitioner oriented. We would submit proposals to conduct these types 
of activities, thus enhancing the probability that our findings would 
be implemented at a national level. 



ERIC 



2d 



^1 



26 



ACCOMPLISHMENTS 

Using the timeline presented in the previous section as a reference, 
the following study descriptions will indicate that we have completed 
all project activities. All studies described below followed the gen- 
eral experimental procedures detailed earlier in this report. Data 
analysis was accomplished using a Mann-Whitney U test. The parametric 
analyses previously described were abondcned due to the small size of 
each study. It was decided that the non-parametric test would be much 
more robust in giving us accurate information regarding group differences. 

Study 1 

This study was conducted at Loloma School in Scottsdale. We 
compared cumulative and successive programming for teaching sight words-- 
to elementary severely regarded subjects, thus, it was a replication of 
Prehm, Zucker and Roth (1979). Data are presented below in Table 1. 
The data analysis indicated that cumulative programming was superior 
to successive programmong on the number of trials to criterion (p=,05), 
on the one-day post- test (p= .05 ) and on the seven-day post-test (p<.05). 



Study 2 

This study was conducted at the Arizona Preschool for Retarded 
Children in Phoenix. We compared cumulative and successive programming 
for teaching sight words to severely retarded preschool subjects, thus, 
it was areplication of <fink and Brice-Gray (1979). Data are presented 
below in Table 2. The data analysis indicated that cumulative pro- 
gramming was not superior to successive programming on the number of 
trials to criterion (p>.05) or on the one-day post-test (p?.05). However, 
on the seven-day post-test, cumulative was superior to successive (p=.05). 

erJc 2 "i 



TABLE 2 



Cumulative 

Subject Trials 3 Pl b " P2^ 

1 10 • 8 10 

2 16 8 9 

3 17 8 10 

4 17 9 10 

5 28 10 10 

6 34 10 10 



Successive 



X 20.33 x 8.33 X 9.83 



1 16 3 4 

2 16 4 v.5 

3 37 5 7 

4 49 9 9 

5 78 10 10 

X 39.20 X 6.20 I 7.00 



a = blocks of twenty 
b = one day posttest 
c = seven day posttest 



Study 3 

This study was a comparison of cumulative programming across age 
levels on an academic task. This was accomplished by comparing the 
cumulative group from Study 1 with the cumulative group from Study 2. 
In other words, we have two cumulative groups learning sight words 
witn the only difference between the groups being age of the subjects. 
The data are presented below in Table 3. 

The data analysis indicated that cumulative programming was dif- 
ferentially effective across age levels. While there were no signi- 
ficant differences between pre-school and elementary age students on 
one-day and seven-day post- tests, the preschool students took signi- 
ficantly more trials (p*.05) to reach criterion than the elementary 
age group. - 

Study 4 

This study was conducted at the Arizona Preschool. We used 
cumulative programming to teach the names of colors to a group of 
eleven preschool severely retarded subjects. The school year 
ended before we could complete data collection. 

Study 5 

This study was conducted at Loloma School. Seven severely 
retarded elementary subjects were instructed with cumulative pro- 
gramming to teach them manual signs for practical words. Data from 
this task will be compared to the cumulative data from Study 1 to 
ascertain differences between psychomotor and non-motor academic tasks. 

2B 




TABLE 3 



Cumulative Programming 
• Elementary - 



Subject Trials 3 Pl b 

' 1 29 10 

2 20 4 

3 20 10 

4 18 8 
•5 12 9 

6 11 7 

7 10 10 

8 10 10 

9 9 10 

10 9 10 . 

11 9 10 

51 14.27 X 8.91 

Pre-School 

1 10 8 

2 16 8 

3 17 8 

4 17 .9 

5 28 10 

6 34 10 

I 20.33 X 8.33 



a = blocks of twenty 
b = one day post-test 
c = seven day posttest 



30 



Additional data for this study were collected from subjects in Study 14. 
The data and results are presented under Study 14. 

Study 6 

This study was conducted at Loloma School. Ten elementary severely 
retarded subjects were instructed with cumulative programming to teach 
them sight words using 100% as the criterion for learning. Data from 
this task was compared to the cumulative data from Study 1 (where the 
learning criterion was 80%) to ascertain differences attributable to 
c anges in learning criteria. Data are presented below in Table 4. 
The data analysis indicated no significant differences between the two 
learning criteria groups (p>.05)o 

r 

Study 7 

This study was conducted at CIDS/ESP housed at Papago School in 
Phoenix. Sixteen elementary age profoundly retarded subjects with 
multiple handicaps were taught the names of common objects using the 
cumulative programming technique. The study was discontinued after 
80 days. No subjects were progressing toward criterion. 

Study 8 

This study was conducted at Loloma School. Six elementary 
severely retarded subjects were instructed with cumulative programming 
to teach them manual signs for practical words to 100% criteria. 
These data were compared to the data from Study five where the criterion 
was 80%. Data are presented below in Table 5. The data analysis 



31 



\ 



32 



■. TABLE 4 
Cumulative Programming 



80% 



Subject Trials 9 Pl b P2 C 

1 29 10 10 

2 20 4 6 

3 20 10 9 

4 . 18 8 10 

5 12 9 9 

6 11 • 7 8 

7 10 10 10 

8 10 10 7 

9 9 10 10 

10 9 10 10 

11 9 _10 JO 

X 14.27 X 8.91 X 9.00 



100% 



1 
2 
3 
4 
5 
6 
7 
8 
9 

10 



10 
10 
13 
10 
10 

9 

9 

10 
11 
18 

11.00 



10 
9 

10 
10 
10 
10 
8 

10 
10 
8 

X 9.50 



10 
10 

7 

8 

9 

10 

7 

10 
10 
_ 7 

X 8.80 



a = blocks of twenty 
b ■ one-day post-test 
c s seven-day post-test 



33 



TABLE 5 

Cumulative Programming 

100% 

Subject T rials 9 PI 6 ^ 

1 13 10 8 

2 10 . 10 10 

3 9 9 9 

4 9 10 9 
.5 9 10 9 

6 _ 9 io 10 

X 9.83 X 9.83 X 9.17 



80% 



1 31-9 10 

2 38 10 10 

3 33 9 9 

4 12 ,8 10 

5 17 9 10 

6 15 10 9 

7 15 8 8 

8 16 10 10 

9 11 9 9 

10 11 10 10 

11 20 10 10 

12 j 16 10 ' 10 

13 I 32 6 .6 

14 _ 11 8 8 

X 18.43 X 9.00 X 9.21 



a = blocks of twenty 
b = one-day post-test 
c = spven-day post-test 



9 

ERIC 



33 



34 

indicated it took significantly longer to learn the signs at 80% 
criterion (p<.05). There were no difference.-., however, between the 
groups on the post- tests (p>.05). 

Study 9 

This study wa? conducted at Loloma School . Ten elementary 
severely retarded subje^s were instructed with cumulative progamming 
to teach them the pairing of words and numbers from 1-5 to 80% cri- 
terion. Data from this study was compared to the cumulative data from 
Study 10 to ascertain differences between academic and motor (pre- 
vocational )task. Data are presented in Table 6. 

The data analysis indicated a significant difference in trials 
to criterion in favor of the academic task (p<.05). There were no 
differences between groups on the first and second post-test (p>.05). 

Study 10 

This study was conducted at Tonalea School. Elementary age 
severely retarded subjects were taught a pre-vocational sorting task 
using either cumulative or successive programming. The task involved 
size descrimination along one dimension and a motor response. Data 
are presented below in Table 7. 

The data analysis indicated no differences between groups on 
trials to criterion and seven-day post-test (p>.05). One-day post- 
test scores were significantly different in favor of the cumulative 
group (p<. 05) . 



34 



35 



TABLE 6 
Cumulative Programming 



Academic 



Subject 

1 
2 
3 
4 
5 
6 
7 
8 
9 

10 



Trial s d 

11 

9 
9 
9 
9 
9 
9 
9 
9 

_ 9 
X 9.20 



7 

10 
9 
8 
9 

10 
' 10 
10 
7 

10 
X 9.09 



P2 
6 

10 

9 
10 

7 

10 
10 
10 
6 

_10 

X 8.80 



Motor 



1 
2 
3 
4 
5 



65 
22 

9 

9 

11 

X 23.20 



9 
8 
9 
9 

10 
X 9.00 



4 
9 
8 
8 

JO 
X 7.80 



a = blocks of twenty 
b = one-day post-test 
c = seven-day post-test 



3o 



36 



TABLE 7 



Cumulative 
Subject 

1 

2 
3 
4 
5 



Trials 0 

65 
22 

9 

9 

_ 11 
X 23.20 



EI 

9 
8 
9 
9 

10 
X 9.00 



£2 

4 
9 
8 
8 
10 

f 7.80 



Successive 



1 

2 
3 
4 
5 
6 
7 
8 
9 



21 
21 
15 
28 
15 
15 
15 
15 
15 

17.78 



4 
5 
3 
4 
7 
6 
7 
5 

_ 8 
X 5.44 



2 
0 
5 

10 
9 
8 
8 
6 

_ 5 

X 5.89 



a = blocks of twenty 
b = one-day post-test 
c = seven-day post-test 



9 

ERIC 



Jo 



Study 11 

This study was conducted at Tonalea School. Adolescent age 
severely retarded subjects were taught a pre- vocational sorting task 
using either cumulative or successive programming. The task involved 
size discrimination along one dimension and a motor response. Data 
are presented below in Table 8. The data analysis indicated a sig- 
nificant difference in trials to criterion in favor of the cumulative 
group (p<.05). There were no significant differences between groups 
on the post-tests (p>.05). 

Study 12 

This study was a comparison of cumulative programming across age 
levels on a pre-vocational motor task. This was accomplished by com- 
paring the cumulative group from Study 10 with the cumulative group 
from Study 11. Data are presented below in Table 9. The data analysis 
indicated a significant difference between groups only on the one-day 
post-test (p<.05). There were no significant differences in trials to 
criterion and seven-day post-test (p?.05). 

Study 13 

This study was conducted at the CIDS/ESP housed at Papago School 
in Phoenix. Ten elementary profoundly retarded students were taught 
a pre-vocational assembly task requiring a motor response, using the 
cumulative programming technique. This study was discontinued after 
a year and a semester. Many of the subjects had over 1700 trials and 
were not progressing toward criterion. The data are presented below 
in Table 10. 



38 



TABLE 8 



Cumulative 



Subject 

1 
2 
3 
4 



Trials* 

10 
9 
9 

_ 9 
X 9.25 



PI 

8 
8 
8 
5 

X 7.25 



P2 

6 
9 
8 
5 

X 7.00 



Successive 

1 
2 
3 
4 
5 



15 
15 
15 
15 

_ 15 
X 15.00 



8 
8 
0 
9 
6 

X 6.20 



9 
7 
6 
8 

_ 1 

X 6.20 



TABLE 9 
Cumulative Programming 



Elementary 
Subject 

1 

2 
3 
4 
5 



Trials 9 

65 
22 

9 

9 

J 23.20 



Pl° 

9 
8 
9 
9 

10 
I 9.00 



P2 

4 
9 
8 
8 

JO 

X 7.80 



ERIC 



Adolescent 

1 
2 
3 
4 



a = blocks of twenty 
b = one-day post-test 
c - seven-day post-test 



10 
9 
9 

_ 9 
X 9.25 



33 



8 
8 
8 
5 

7.25 



6 
9 
8 

_ 5 

X 7.00 



TABLE 10 
Cumulative Programming 



Subject 


Trials 3 


1 


90 


2 


91 


3 


98 


4 


89 


5 


88 


6 


90 


7 


82 


8 


85 


9 


89 


10 


91 



a = blocks of twenty 
b = one-day post-test 
c = seven-day post-test 




Study 14 

This study was conducted at Tonalea School. Fourteen elementary 
severely retarded subjects were instructed with cumulative programming, 
to teacti tham manual signs for practical words. These data were com- 
pared to the cumulative data from Study 1 to ascertain differences 
between psychomotor and non-motor academic tasks. The data is pre- 
sented below in fable 11. The data analysis indicated no significant 
differences between groups (pr.05). 

Study 15 

This study was conducted at Tonalea School. Fourteen adolescent 
severely retarded subjects were instructed with cumulative programming 
to teach them manual signs for practical words. Half the subjects 
learned to QQ% criterion while the other half learned to 50% criterion. 
The data is presented below in Table 12. 

The data analysis indicated a significant difference in trials to 
criterion in favor of the 50% group (p<.05). There were no significant 
differences in post-test performance (p>.05). 

In summary, it can be seen that our studies were directly related 
to the stated project objective cf investigating variables related to 
the subject, the content, and the task. 



40 



41 



Sight Words 



Signs 



a = blocks of twenty 
b = one-day post-test 
c = seven-day post-test 



TABLE 11 
Cumulative Programming 



Subject 


Trials 3 


1 


29 


2 


20 


3 


20 


4 


18 


5 


12 


6 


11 


7 


10 


8 


10" 


9 


9 


10 


9 


11 


9 




X 14.27 


1 


31 


2 


18 


3 


33 


4 


12 


5 


17 


6 


15 


7 


15 


8 


16 


9 


11 


10 


11 


11 


20 


12 


16 


13 


32 


14 


11 




J 18.43 



o 

ERIC 



41 



Pl b ' * P2 C 

10 10 
4 6 
10 9 

8 10 

9 9 
7 8 

10 10 
10 7 

10 10 

10 10 

_10 JO 

X 8.91 X 9.00 



9 10 

10 10 

9 9 

8 10 

9 10 
10 9 

8 8 
10 10 

9 9 
10 10 
10 10 
10 10 

6 6 

_ 8 8 

X 9.00 X 9.21 



TABLE 12 
Cumulative Programming 



42 



80% 



Subject 

' 1 
2 
3 
4 
5 
b 



Trials 0 

15 

16 

11 

11 

20 

16 
_ 11 
X 14.29 



£1 

8 
10 
9 

10 
10 
10 
8 

X 9.29 



P2 L 

8 
10 
9 

10 
*10 

10 
_ 8 
X 9.29 



50% 



1 
2 
3 
4 
5 
6 
7 



9 
9 
9 

. 9 
9 
9 
9 

19.00 



10 
10 
10 
10 
10 
10 
10 

10.00 



10 
10 
10 
10 
10 
10 
10 

10.00 



a = blocks of twenty 
b = one-day post-test 
c = seven-day post-test 




4 



Dissemination 

The project dissemination activities served as the major forum 
for discussion of project study results and their utility for class- 
room/traing setting implementation and the direction of future research 
As indicated in the project timeline, dissemination took place over 
three-years and was quite extensive. A summary of dissemination 
activities is presented below: 

Local dissemination workshops/staff training were conducted 
at the following sites: 



Loloma School 


- Scottsdale 


Getz School 


- Tempe 


Arizona Preschool 


- Phoenix 


Montebello School 


- Phoenix 


Papago School 


- Phoenix 


Rich School 


- Phoenix 


Tonal ea School 


- Sco + tsdale 


Tolleson Elementary 


- Tolleson 



National dissemination presentations/workshops were as fol^ws: 



Presented: Zucker, S. H. & Prehm, H. J. Cumulative versus 
successive programming with severely retarded students. The 
Gatlinburg Conference on Research in Mental Retardation/ 
Developmental Disabilities, Gatlinburg, Tennessee, March, 1981. 

Presented: Zucker, S. H. & Prehm, H. J. Alternative teaching 
strategies for severely handicapped students. Annual Meeting of 
the American Association on Mental Deficiency, Detroit, May, 1981. 

Session Moderator: Instruction of the Severely/Profoundly Retarded. 
Annual Meeting of the American Association on Mental Deficiency, 1981. 



43 



44 



Panelist: National Workshop Conference on Vocational and Employment 
Opportunities for 'he Mentally Retarded. President's Committee on- 
Mental Retardation, Madison, Wisconson, March, 1982. 

Presented: Zucker, S. H. & Prehm, H. J. Research on ii tructional 
strategies for severely/profoundly retarded students. A,.inual 
Meeting of the Council for Exceptional Children, Houston, Texas, 
April, 1982. 

Chair: Session on Mental Retardation. Annual Meeting of the Council 
for Exceptional Children, Houston, Texas, April, 1982. 

Presented: Zucker, S. H. & Prehm, H. J. Durability of training 
among severely retarded children as a function of teaching 
'str'atdgy; " The '6ift1t1lb'uf^'X9hTSn9fRSe 'on Research in Mental 
Retardation/Developmental Disabilities, Gatlinburg, TN, April, 1982. 

Session Moderator: Research Symposium on Educational Programming 
for the Moderately and Severely Retarded. Annual Meeting of the 
American Association on Mental Deficiency, Boston, June, 1982. 

Presented: Zucker, S. H. & Prehm, H. J. Cumulative teaching 
strategies for increasing the retention of severely retarded 
handicapped students. Annual Meeting of the American Association 
on Mental Deficiency, Boston, June, 1982. 

Presented: Zucker, S. H. Stability of response choice of severely 
retarded children. The Gatlinburg Conference on Research in Mental 
Retardation/Devel jpmental Disabilities, Gatlinburg, TN, March, 1983. 

Chair: Session on Mental Retardation. Annual Meeting of the Council 
for Exceptional Children, Detroit, April, 1983. 

Presented: Zucker, S. H. & Prehm, H. J. Effects of two teaching 
strategies on acquisition and retention among severely retarded 
students. Annual Meeting of the Council for Exceptional Children, 
Detroit, April, 1983. . 

Presented: Zucker, S. H. & Prehm, H. J. Instructional research 
on retention of information among severely retarded students. 
Annual Meeting of the American Association on Mental Deficiency, 
Dallas, June, 1983. 

Presented: Zucker, S. H. Cumulative teaching strategies for 
severely retarded students. Southeast Regional Resource Center, 
Juneau, Alaska, September, 1983. 



44 



45 



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4o 



0 

ERIC 



46 



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o 

ERIC 



4d 



49 



APPENDIX A 



er|c 4i) 



DATA SHEET - SUCCESSIVE PAIRS PROGRAMMING 



Subject: a= d= 

Date:- b= e = 



Experimenter: c- 



Directions: circle each correct answer, cross-out each wrong answer. 



STEP 1 


STEP 2 


STEP 3 


STEP 4 


STEP 5 


STEP 6 


STEP 7 


a a 


b 


b 


ab 


ab 


c 


c 


ac 


ac 


d 


d 


ad ad 


a a 


b 


b 


ba 


ba 


c 


c 


ca 


ca 


d 


d 


da da 


a a 


b 


b 


ab 


ab 


c 


c 


ac 


ac 


d 


d 


ad ad 


a a 


b 


b 


ba 


ba 


c 


c 


ca 


ca 


d 


d 


da Ha 


a a 


b 


b 


ab 


ba 


c 


c 


ac 


ca 


d 


d 


ad da 


a a 


b 


b 


ab 


ab 


c 


c 


ac 


ac 


d 


d 


ad ad 


a a 


b 


b 


ba 


ab 


c 


c 


ca 


ac 


d 


d 


da ad 


a a 


b 


h 


ba 


ab 


c 


c 


ca 


ac 


d 


d 


da ad 


a a 


b 


b 


ab 


ba 


c 


c 


ac 


ca 


d 


d 


ad da 


a a 


b 


b 


ab 


ab 


c 


c 


ac 


ac 


d 


d 


ad ad 


STEP 8 


STEP 9 


STEP 10 


STEP 11 


STEP 12 


STEP 13 


STEP 14 


e e 


ae 


ae 


be 


be 


bd 


bd 


be 


be 


cd 


cd 


ce ce 


e e 


ea 


ea 


cb 


cb 


db 


db 


eb 


eb 


dc 


dc 


ec ec 


e e 


ae 


ae 


be 


be 


.bd 


bd 


be 


be 


cd 


cd 


ce ce 


e e 


ea 


ea 


be 


cb 


bd 


db 


be 


eb 


cd 


dc 


ce ec 


e e 


ae 


ea 


cb 


cb 


db 


db 


eb 


eb 


dc 


dc 


ec ec 


e e 


ae 


ae 


be 


be 


bd 


bd 


be 


be 


cd 


cd 


ce ce 


e e 


ea 


ae 


cb 


be 


db 


bd 


eb 


eb 


dc 


cd 


ec ce 


e e 


ea 


ae 


cb 


be 


db 


bd 


be 


be 


dc 


cd 


ec ce 


e e 


ae 


ea 


be 


cb 


bd 


db 


be 


eb 


cd 


dc 


ce ec 


e e 


ae 


ae 


be 


be 


bd 


bd 


eb 


be 


cd 


cd 


ce ce 



STEP 15 



de de 

ed ed 

de de 

de ed 

ed ed POSTTEST: a c d a b 

de de 

ed de e d b e c 

ed de 

de ed 

de de 



bo 



DATA SHEET - CUMULATIVE PROGRAMMING 
Subject: a= d= 



Date: b= e= 

Experimenter: c= 

Directions: circle each correct answer, cross-out each wrong answer. 

STEP 1 STEP 2 STEP 3 .STEP 4 STEP 5 STEP 6 STEP 7 



a a 

a a 

a a 

a a 

a a 

a a 

a a 

a a 

a a 

a a 

STEP 8 



b b 

b b 

b b 

b b 

b b 

b b 

b b 

b b 

b b 

b b 

STEP 9 



ab ab 

ba ba 

ab ab 

ba ba 

ab ba 

ab ab 

ba ab 

ba ab 

ab ba 

ab ab 



c c 

c c 

c c 

c c 

c c 

c c 

c c 

c c 

c c 

c c 



bca acb 
cab bca 
bac bac 
acb cab 
bca cba 
abc bca 
cba cab 
bca acb 
abc abc 
cab acb 



d d 

d d 

d d 

d d 

d d 

d d 

d d 

d d 

d d 

d d 



cadb cbda 
dcab bade 
bacd cdba 
dcab abed 
dbac abed 
dabc bdac 
cbda dcab 
abdc bade 
cdba dcab 
deba abed 



e e adbce debca 

e e dbcea daceb 

e e edeba dacbe 

e e adebe abdee 

e e bdeae daecb 

e e bcead cadeb 

e e adecb ceadb 

e e cbdea abced 

e e edeba baced 

e e adebe bedca 



POSTTEST: acdabedbec