ABSTRACT INDUCING STAGE III SERIATION CAPABILITIES IN KINDERGARTEN CHILDREN THROUGH CUE FADING AND REINFORCEMENT By Larry Eugene Schafer The purpose of this study was to investigate the effectiveness (acquisition, retention, and transfer) of using cue fading and reinforcement to instruct children who were in Piaget's seriation stage II (the child orders with some difficulty but fails to insert a disarranged set of objects into an ordered set) for performance at Piaget's seriation stage III (the child both orders with ease and inserts objects into an ordered set). Of the 95 kindergarten children who were given a seriation pretest, 34 were found to be in seriation stage II. The group of 34, stage II children was divided into a control group, which received no training,_and an experimental group, which received training for seriation stage III. Each experimental subject was individually given approximately 30 minutes of training on each of three consecutive days. The primary objective of the training was to induce the ability to insert objects into an ordered set of objects. The same basic procedure was used during each 30 minute training session. Materials were set up at a number of training stations (45 training stations for session 1, 30 for session 2, and 24 for session 3), and each experimental subject was individually guided from one station to the next. The number of objects in the individ— ual tasks was increased in stages throughout each session. At the beginning and whenever the number of task objects increased during a session either the ease of object dis- crimination was high and then gradually decreased in levels, or cues were introduced and then gradually faded in levels. Three slightly different practice tasks were used for each cue or discrimination level. The subjects were required to meet a performance criterion for each cue or discrimina- tion level before they were allowed to progress to the next level. Posttests were given approximately one, eight, and 132 days after training. Each posttest consisted of both near and far transfer measures. The materials used in the near transfer measure were similar to those materials used in the training, whereas the materials used in the far transfer measure were unlike those materials used in the training. The results of repeated measures, and multivariate analyses revealed that the experimental subjects acquired and retained the specific target capabilities of the train- ing (near transfer data) but failed, in general, to transfer those capabilities to tasks involving new materials (far transfer data). Although no massive, overall transfer effect was observed, the experimental group did outperform the control group on the far transfer measure of the second posttest. Two explanations (test-retest and novelty) for the experimental group's unexpected far transfer means were contrived. The training method used in this study was found to be reasonably successful. However, because such large amounts of time, space, and material would be required, the unaltered use of the training method in the classroom would be prohibitive. Although this study does not seem to prescribe any specific seriation training techniques for immediate, direct use in the classroom, it does offer a tested method of cueing and cue fading that might be sub- sequently used to improve the seriation lessons found in the modern elementary science and mathematics programs. INDUCING STAGE III SERIATION CAPABILITIES IN KINDERGARTEN CHILDREN THROUGH CUE FADING AND REINFORCEMENT By Larry Eugene Schafer A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY College of Education 1971 To Penny ii ACKNOWLEDGMENT S The author extends a genuine expression of gratitude to Professors Joe Byers, Glenn Berkheimer, Julian Brandon, and Gordon Wood for the valuable guidance and instruction which they gave not only during the preparation of this thesis but during the other phases of doctoral study as well. To Professor Byers, the author's thesis advisor,~ goes a special note of thanks; for it was through interac- tion with Dr. Byers that the author gained a much deeper sense of what it means to be a scholar and a scientist. The dedication of this thesis to Penny, the author's wife, only begins to express the appreciation which she deserves. Her sacrifices and patient, loving support made this thesis possible. iii CHAPTER I. II. III. TABLE OF CONTENTS THE PROBLEM. . . . . . . . . . . . . . . . . The Objective of the Study . . . . . . . . Rationale for the Study. . . . . . . . . . Overview of Procedure and General Research Hypothesis . . . . . . . . . . . REVIEW OF LITERATURE . . . . . . . . . . . . Seriation Studies. . . . . . . . . . . . . Training Methodology: Support for the Research Hypotheses . . . . . . . . . . . Review of Piagetian Training Studies . Unsuccessful Attempts to Induce Length and Number Conservation. . Successful Attempts to Induce Length and Number Conservation. . Discussion . . . . . . . . . . Review of Instructional Psychology . . Conditions for the Acquisition of Capabilities . . . . . . . . . Conditions for the Promotion of Retention . . . . . . . . . . . Conditions to Enhance the Transfer of Learning . . . . . . . . . . . Research Hypothesis. . . . . . . . . . Hypotheses for the Experimental versus Control Group Analysis . . Page 0 ONNH 13 l4 14 27 27 33 4O 50 55 56 66 70 77 78 Hypotheses for the Experimental versus Control versus Special Control Group AnalysiS. O O O O O O O O O O O 0 THE RESEARCH PROCEDURE . . . . . . . . . . . Pretest Materials and Tasks. . . . . . . . The Sample . . . . . . . . . . . . . Training and Posttest Materials and Tasks. Training Materials and Tasks - First Training Session. . . . . . . . . . . Training Materials and Tasks - Second Training Session. . . . . . . . . . . Training Materials and Tasks - Third Training Session. . . . . . . . . . Posttest Materials and Tasks Post- tests One and Two . . . . . . . . . . iv 81 84 84 85 86 86 88 91 93 Posttest Materials and Tasks - Post- test Three. . . . . . . . . . . . . . Verbal Instructions Given During the POStteStS . . . . . . . . . . . . . . . . Training Procedures. . . . . . . . . . . . Reinforcements and the Orientation Sessions Offered During Training. . . The Performance Criteria for Progression Through the Training TrialS. . . . . . . . . . . . . . . . Sequence of Events and Design. . . . . . . Rationale for the Use of Two Groups (Groups I and II) . . . . . . . . . . Rationale for the Sequence of Treatment . . . . . . . . . . . . . . Sequence of Events . . . . . . . . . . Covariance and Dependent Measures. . . . . Covariance Measures. . . . . . . . . . Dependent Measures . . . . . . Design and Methods of Statistical Analysis IV. ANALYSIS OF DATA . . . . . . . . . . . . . . Experimental versus Control Group Analysis Experimental versus Control versus Special Control Group Analysis. . . . . . . . . . Correlational Data . . . . . . . . . . . . Summary. . . . . . . . . . . . . . . . . . V. DISCUSSION AND SUMMARY . . . . . . . . . . . BIBLIOGRAPHY o o o o o o o o o o o o o o o o o o o o APPENDICES A. Description of Pretest Materials . . . . . . B. Verbal Instructions for Seriation Pretest. . C. Description of Materials Used During the First Training Session. . . . . . . . . . . D. Description of Materials Used During the Second Training Session . . . . . . . . . . E. Description of Materials Used During the Third Training Session. . . . . . . . . . . F. Description of Materials Used in Posttests l and 2 . . . . . . . . . . . . . . . . . . G. Description of Materials Used in Posttest 3. H. Verbalization Used During Posttests 1 and 2. I. Verbalization Used During Posttest 3 . . . . J. Individual Difference Measures-—Three Parts of the Cincinnati Autonomy Test Battery . . K. Descriptions of the Two Lenient Methods of Scoring (L1 and L2) . . 97 100 101 101 104 106 106 108 110 114 114 115 117 125 125 143 147 150 156 173 180 181 183 185 187 191 194 199 207 211 215 Compilation of Data Used in the Analysis of Results . . . . . . . . . . . . . . . . . . . 220 Repeated Measures, Multivariate Analysis Information for the Experimental versus Control Group Analysis (E vs. C). . . . . . . 225 Multivariate Analysis Information for the Experimental versus Control versus Special Control Group Analysis (E x C x SC) . 235 vi TABLE 1. F1. F2. LIST OF TABLES Near Transfer Means and Standard Deviations (PercentageS) . . . . . . . . . . . . . . . . Far Transfer Means and Standard Deviations (PercentageS) o o o o o o o o o o o o o o o o Multivariate Test for the Treatment x Posttest x Test Type Interaction. . . . . . . Repeated Measures Analysis: Near Transfer (Percentages) . . . . . . . . . . . . . . . . Repeated Measures Analysis: Far Transfer (Percentages) . . . . . . . . . . . . . . . . Multivariate Analysis: Experimental (E) versus Special Control (SC) on the Three' Measures of Posttest 3. . . . . . . . . . . . Multivariate Analysis: Special Control (SC) versus Control (C) on the Three Measures of POStteSt 3. O O O O O O O O O O O O O O O O 0 Correlations Between Covariables and Between Covariables and Dependent Variables for the Experimental Group. . . . . . . . . . . . . . Correlations Between Covariables and Between Covariables and Dependent Variables for the Control Group . . . . . . . . . . . . . . . . Pretest Materials . . . . . . . . . . . . . . Materials Used During the First Training Session . . . . . . . . . . . . . . . . . . . Materials Used During the Second Training SeSSion O O O O O O O O C C O O O O O O O O 0 Materials Used During the Third Training seSSion O O O O O O O O O O O O O C O O O O O Sticks Used in Posttests l and 2. . . . . . . Lined Cards Used in Posttests 1 and 2 . . . . vi ‘3 Page 126 126 132 140 142 145 146 148 149 180 183 186 190 191 192 F3. F4. G1. G2. G3. G4. M1. M2. M3. M4. M5. M6. M7. M8. M9. 5110. M11. b112. Cars Used in Posttests l and 2. . . . . . . Colored Blocks Used in Posttests l and 2. . Sticks Used in Posttest 3 . . . . . . . . . Cars Used in Posttest 3'. . . . . . . . . . "Happies" Used in Posttest 3. . . . . . . . Story Cards Used in Posttest 3. . . . . . . Individual Subject Scores on the Dependent and ID Measures 0 O O O O O O I O O O O O 0 Transformation Matrix - New x Old Variables (E vs. C) . . . . . . . . . . . . Experimental and Control Group Means Calculated from the New Variables . . . . . sample Correlation Matrix (Within Cell) for the New Variables (E vs. C) . . . . . . . . Variances for the New Variables (E vs. C) . Symbolic Basis Vectors (E vs. C). . . . . . Mean Squares Between, Step-Down F's, and Probability Statements Associated with the Variables Under Hypothesis 1 (CO) (E vs. C) Hypothesis Mean Products Matrix Associated with Hypothesis 1 (CO) (E vs. C). . . . . . Mean Squares Between, Step-Down F's, and Probability Statements Associated with the Variables Under Hypothesis 2 (Cl) (E vs. C) Hypothesis Mean Products Matrix Associated with Hypothesis 2 (Cl) (E vs. C). . . . . . Mean Squares Between, Step-Down F's, and Probability Statements Associated with the Variables Under Hypothesis 3 (CO) (E vs. C) Hypothesis Mean Products Matrix Associated with Hypothesis 3 (CO) (E vs. C). . . . . . Mean Squares Between, Step-Down F's, and Probability Statements Associated with the Variables Under Hypothesis 4 (Cl) (E vs. C) viii 192 193 195 195 196 198 222 226 226 227 227 228 229 229 230 230 231 232 233 M13. N1. N2. N3. N4. N5. N6. N7. N8. Hypothesis Mean Products Matrix Associated with Hypothesis 4 (Cl) Experimental, Control, and Special Control Group Means . . . . (E vs. C). Sample Correlation Matrix (Within Cells) (ExCxSC).... Variances (E x C x SC). Symbolic Basis Vectors (E x C x SC) Mean Squares Between, Step-Down F's, and Probability Statements Associated with the Variables Under Part 1 (E vs. Hypothesis Mean Products Matrix Associated with Part 1 (E vs. Mean Squares Between, Step-Down F's, Probability Statements Associated with the Variables Under Part 2 (SC vs. Hypothesis Mean Products Matrix Associated with Part 2 (SC vs. SC). C). ix sc) C) and 234 235 236 236 236 237 237 238 238 FIGURE 1. LIST OF FIGURES Gelman's (1969) illustration of between trial variation within a training problem . . An illustration of the arrangement of sticks at each station during the first day Of training 0 O O O O O O O O I O O O O 0 An illustration of an ordered set of sticks displaying two cues. . . . . . . . . . An illustration of cue reduction during the second day of training. . . . . . . . . . Matrix showing independent and dependent variables and the respective levels for each. Matrix for the Experimental versus Control Group Analysis. . . . . . . . . . . . . . . . Matrix for the Experimental versus Control versus Special Control Group Analysis . . . . Graphs of the experimental and control groups' near and far transfer means . . . . . An illustration of the basic experimental design for testing the "novelty" and test-retest learning hypotheses . . . . . . . An example of a lined card (drawn to actual size). . . . . . . . . . . . . . . . . An illustration of the stick-man positions shown on the storycards used in posttest 3. (Drawn to actual size.) . . . . . . . . . Different arrangements used to illustrate the need for different scoring systems. . . . Page 48 87 9O 91 120 124 124 128 165 187 197 215 CHAPTER I THE PROBLEM During the past fifteen years American develop- mental psychologists have increasingly turned their attention toward the study of cognitive development in children (Sigel & Hooper, 1968, p. 2). Undoubtedly the work of Swiss psychologist, Jean Piaget, has played a major role in causing that change of attention to occur. In response to Piaget's prolific output of research and theory, American psychologists have followed at least two avenues of research. One avenue reflects efforts to replicate or validate Piaget's findings, while the other reflects attempts to modify cognitive growth through training (Sigel & Hooper, 1968, p. 4). In both validation and training research, Piaget's conservation capabilities (area, number, substance, weight, and length) have been prime targets of study. Although the conservation capabilities are central to Piaget's theOry of intellectual development and there- fore, justifiably draw upon the efforts of researchers, parallel lines of investigation must be launched into other important Piagetian capabilities. The research reported here was an attempt to extend a line of investi- gation into another of Piaget's capabilities, namely, the capability of serial ordering. Elkind (1964) has already taken the validation avenue to the study of serial ordering. The research reported here, on the other hand, was along the training avenue and thus, was a study of the effect of training on the development of serial order- ing. The purpose of Chapter I is to provide a basic introduction to the research reported. The objectives of the research will be discussed, and a rationale for the study will be described. Chapter I will be concluded with an overview of the experimental procedure and a statement of the general research hypothesis. The Objective of the Study In a concrete form, serial ordering consists of arranging material objects in order according to a par- ticular attribute. For example, wooden sticks could be serial ordered according to length from the shortest to the longest to form a stairsteps-like figure. Children usually acquire the ability to serial order material objects before the age of seven years (Piaget, 1965, p. 133; Elkind, 1964). Piaget (1965, pp. 122-134) has identified three 'seriation stages. In the first stage, children approxi- mately four years of age have the ability to make pairwise discriminations but are unable to use that ability to serial order four or more objects. Given a set of four sticks which are easily distinguishable according to length, the child in stage I is able to correctly identify the shortest and longest sticks of any pair presented to him; however, he is unable to serial order the sticks according to length. By the time children reach approximately five years of age,_their entrance into stage II is indexed by an ability to serial order by trial and error. Children in seriation stage II rarely serial order a set of sticks by successively choosing the shortest stick from the sticks yet to be ordered. In addition to lacking spon- taneity in serial ordering, the seriation stage II child fails to correctly insert a disarranged set of objects into an already serial ordered set. Children six or seven years of age generally exhibit characteristics of the third and final seriation stage. Children in seriation stage III serial order with few errors and are able to correctly insert a disarranged set of objects into a serial ordered set of objects. Piaget observed the seriation stages as they occurred in absence of any known systematic instruction in serial ordering. The question arises: Can specific instruction alter the rate at which young children progress through the seriation stages? This study, at least in part, was an initial attempt to answer that question. Specifically, this study was designed to investigate the effectiveness of using cue fading and reinforcement to train kindergarten children at seriation stage II (order with difficulty) for performance at seriation stage III (order objects with ease and insert a disarranged set into an ordered set). The effectiveness of the training was determined by repeatedly measuring the retention and trans- fer of the induced capabilities. In addition to the retention and transfer measures there were the four individual difference (I.D.) measures of chronological age, reflectivity, impulse control and field independence. These I.D. measures were included for the following reasons: 1) to increase the precision of the comparisons among the dependent measures by covary- ing on the I.D. measures and 2) to provide the opportunity for uncovering potential relationships between I.D. measures and training effects. The two reasons for including the I.D. measures imply suspected relationships between the various I.D. measures and the seriation abilities indexed by the depen- dent measures. Both Piaget (1965, p. 124) and Elkind (1964) have found that as children_grow older they become better able to perform seriation tasks. Consequently, chronological age and performance of the posttests are expected to be positively correlated. Kagan and Moss (1963) have found that reflective children demonstrate higher standards of mastery on intellectual tasks, greater persistence with such tasks, choose more difficult tasks, and work longer on the items than do impulsive children. In addition, they have found that analytic response styles are used more by reflective subjects than impulsive sub- jects. Consequently, it is suggested that the child who is more reflective will learn more from the seriation training and will do better on the seriation posttests. Banta (1968) has defined impulse control as the ability to control motor response. It is suggested, therefore,, that children who can control their impulse to respond will likely have at least the time to evaluate an anticipated reSponse and thus will make fewer errors in performing the seriation postests. According to Witkin (1950), a field- independent person tends to experience his surroundings analytically with object experiences being discrete from their backgrounds and tend to impose structure on a field which lacks it. Therefore,_since the seriation posttest tasks require analysis and the ability to impose structure on a field,_it is suggested that there will be a positive correlation between field independence scores and seria- tion posttest scores. Rationale for the Study The development of the periodic chart of chemical elements is evidence of the effective use of serial order- ing in scientific inquiry. Mendeleef observed that when the then known 65 elements were serial ordered according to the atomic weights, similar physical and chemical properties periodically occurred. From this observation evolved the periodic Chart of elements and the subsequent prediction of the chemical and physical properties of elements yet to be discovered. The use of seriation is by no means reserved for the mature,_competent scientists. Serial ordering can be used by the young elementary school child to investigate his environment. By ordering material objects according to one property, the child may more easily discover other properties related to the property used in ordering. In a similar fashion, the young child may use seriation to study the relationship between experimental variables.' Suppose, for example,_that a child performed an experiment deSigned to study the relationship between the amount of incandescent lighting and the growth of a particular kind of plant. To study the results of the experiment, the child could serial order his plants accord- ing to the amount of incandescent light they received and then observe the height of plants as a function of the amount of lighting. Once the plants had been ordered with respect to the amount of light received, other plant char— acteristics, such as the shade of green, the stem thickness, and the size of leaves, may be discovered to be related to the amount of incandescent lighting. Examples have been given to show how the elementary school child could use the serial ordering capability to facilitate his study of science. The authors of two major, contemporary elementary science programs, Science - A Process Approach and the Science Curriculum Improvement Study, apparently believe that seriation can facilitate the learn- ing of science since they have included serial ordering lessons in their programs. Assuming that seriation is an important aspect of elementary science education, the research reported here is relevant to the improvement of science education because it is an investigation of techniques used in helping children acquire seriation capabilities. Not only is serial ordering an important aspect of elementary science education, but it is also relevant to the child's development of the number concept. The impor- tance of the relationship between seriation and the number concept has been emphasized by Piaget (1965): Number is at the same time a class and an asymmetrical relation, the units of which it is composed being simultaneously added because they are equivalent, and seriated because they are different one from another [p. 184]. To find the cardinal value of a class of objects (a ball, block, and stick) all objects must be considered alike to the degree that they each contribute one unit to that cardinal value. While all objects are considered the same in one respect, they are simultaneously considered different. Each object must be counted once and only once and therefore must be distinguished from the other objects. In order to avoid counting an object more than once, the objects are enumerated in a particular order which can be purely arbitrary. The objects arranged in the order in ‘which.they were counted form a series. The series is formed not on the basis of some physical attribute but on the basis of ordinal position (the first object counted, the second object counted, etc.). In addition, as the objects of a group are enumerated,_the number of objects 'which have already been counted gradually increase (1 object counted, 2 objects counted, 3 objects counted,, etc.) just as the lengths of sticks gradually increase in a serial ordered set of sticks. Piaget does not suggest that the concept of number is merely reducible to the concepts of classification and seriation. He does argue, however, that without the concept of seriation, the concept of number cannot exist. Our teChnical society is requiring an increasing emphasis on the use of numbers and numerical relationships. There- fore,_more attention needs to be given to the factors influencing the development and use of the number concept. This research provided some of that attention by focusing on one method of influencing the deVelOpment of the seriation concept, a concept most important in acquiring the idea of number. Thus far, argument has been presented to support the contention that serial ordering is relevant to elementary science education and to the development of the number concept. This research was designed to study an attempt at training kindergarten children for the final stage of seriation. Children generally reach the final stage of seriation by the age of six or seven years. What rationale, then, is there for training children to do that which they ‘will eventually be able to do withOut specific training? Benjamin S. Bloom (1964) has found support for the ;proposition that ". . . a characteristic can be more drastically affected by the environment in its most rapid period of growth than in its least rapid period of growth 10 [p. 210]." Therefore, the extent to which the concept of seriation is relevant to processing information and devel- oping number concepts may very well depend upon the kinds and amount of stimulation that occurred during the develop- ment of seriation. This research did not attempt to relatetraining during development with performance after deVelopment. This research did,_however, provide the first step since it focused on ways to induce change during development. In his book, Intelligence and Experience, J. McV. Hunt (1961) reviews experimental work and theories related to intellectual development. The evidence, he maintains,. suggests that intelligence is a hierarchically arranged set of central processes, which develops as a result of child-environment interaction. With this view of intelligence,_Hunt (1961) writes: . . . it is no longer unreasonable oto.consider that it might be feasi- ble to discover ways to govern the encounters that children have with their environments, especially dur- ing the early years of their develop- ment, to achieVe a substantially faster rate of intellectual develop- ment and a substantially higher adult level of intellectual capacity. . . . The fact that it is reasonable to hope to find ways of raising the level of intellectual capacity in a majority of the population makes it a challenge to do the necessary research [p. 363]. 11 This thesis, therefore, was partially justified because it was a study of the effectiveness of training procedures used in an attempt to accelerate children through one phase of cognitive development. According to Kohlberg (1968), Piaget's interactional view of cognitive development suggests that massive gen- eral types of experience play a vital role in cognitive development and that ingeneral these broad types of experiences cannot be replaced by limited specific train- ing. Similarly, Sigel and Hooper (1968, p. 259) point out that while Piaget does not deny that learning processes are involved in cognitive deVelOpment, he does not believe that American learning theory can adequately explain the development of logical reasoning. This thesis was contrary to the Piagetian viewpoint in at least two respects. First, the training was spe- cific,_and second, techniques borrowed from behavior theory were used in an attempt to accelerate a child through one of Piaget's stages. Therefore, in addition to being relevant to elementary science education and to Hunt's quest for the means of raising intellectual capacity, this thesis has implications for testing the effectiveness of specific behavioral techniques, as well as Piaget's conten- tions about the necessary role that massive generalized experience plays in cognitive development. 12 Cue fading was chosen as the substantive element of the seriation training primarily because it has been found to be a particularly successful technique for train- ing young children to perform rather difficult tasks. Of those studies showing successful uses of cue fading in the training of young children (Hively, 1962, 1965; Moore and Goldiamond, 1964; Sidman and Stoddard, 1967; and Bijou, 1965), Bijou's study provides the most impressive example. By using a cue fading procedure, Bijou was able to success- fully train young, normal and retarded children to identify object images which showed particular angular rotations with respect to sample stimulus images. For the most part, the target capabilities of the cue fading studies have been complex discriminations. The target behavior of this thesis required that the sub- jects make discriminations. For example, to correctly insert objects into an ordered set, the subject had to discriminate between the correct and incorrect positions in the seriated set. Since the evidence shows that cue fading can be used as an effective means of producing discriminatiOn learning, and since the acquisition of the target behavior in this thesis involved discrimination learning, the cue fading method, .as used in this thesis, was expected to contribute to the successful induction of the insertion capability in kindergarten children. 13 Overview of Procedure and General Research Hypothesis A seriation test wasgiven to those children attending kindergarten at Scott Elementary School, DeWitt, Michigan.' The results of the test were used to identify those students in each of Piaget's three stages of seria- tion development. All stage II subjects were given the covariable measures to determine impulse control, reflec- tiveness, and field independence. Stage II subjects were then randomly divided into experimental and control groups. The experimental subjects received approximately 30 min- utes of individual training during each of three conseCu- tive days. The control subjects received no training. Three posttests weregiven to both control and experi- mental subjects after training was completed. The first posttest was given one day after training. The second and third posttests were given approximately one week and nineteen weeks after the training. All tests contained retention and transfer items. The results of the post- tests were analyzed by a repeated measures form of multivariate analysis. The general research hypothesis was that the experi— mental subjeCts will perform significantly better than the control subjects on the posttests. The basis for this hypothesis will be presented in Chapter II. CHAPTER II REVIEW OF LITERATURE Seriation studies and studies related to training methodology will be reviewed in this chapter. Seriation studies will be reviewed in order to relate that which is known about seriation to this thesis and to show how the techniques and findings of those seriation studies have been used in the thesis research. To provide support for the research hypotheses, Piagetian training studies and studies from instructional psychology will be re- viewed and related to those methods used in seriation training. Seriation Studies Although acquiring the ability to serial order is an important aspeCt in the cognitive development of children, the amount of research directly related to serial ordering along one dimension is surprisingly small. Much of the seriation research has seemingly been stimu- lated by the work of Piaget. To study the seriation capabilities of young children Piaget (1965, p. 123) used the following technique. 14 15 Ten sticks, differing in length by 0.8 cm. were presented to a child who was instructed to form a series from the shortest (A=9 cm.) to the longest (J=16.2 cm.). Once the sticks (A-J) had been ordered, the child was given nine more sticks (a-i), one at a time and in any order,_and was asked to insert these sticks in the right places. If the child had ordered and inserted the sticks correCtly, the final series would have been A a B b .... I i J. By using the technique described above, Piaget (1965, p. 124) has identified three distinct stages in the seriation of the sticks. The first stage is characterized by the child's inability to make a complete series with sticks A through J. The child in this first stage may make several short series which are placed side by side,_ or he may construct a staircase by considering only the tops Of the sticks while disregarding the bottoms. In stage two, the child is able to order by trial and error, but fails.to insert the additional sticks (a .... i). Children in the third stage of seriation are able to order without heSitation and are able to correctly insert the additional set of sticks into the ordered set. Piaget (1965, p. 124) did not report the mean ages of his subjects in the three.seriation stages. He‘did,, however, present sample protocols typical of those from subjects of the three different stages. These protocols 16 showed the ages of subjects in seriation stages one, two, and three to be about four, five, and six years, respec- tively. Elkind (1964) replicated Piaget's experiments on discrimination,_seriation,_and numeration and then, unlike Piaget, applied a statistical analysis. In addition to seeing whether or not Piaget's results were verifiable, Elkind attempted to test Piaget's intimation that the perceptibility of size differences might influence the age at which the stages appear, but not the order of their appearance. Assuming that the dimensionality of materials effects the perceptibility of size difference, Elkind used sets of one, two, and three dimensional items to test Piaget's intimation. The sets of one, two, and three dimensional items were respectively,_sticks (one-fourth inch diameter dowels of various lengths), slats (one and one-half inch by one-fourth inch rectangular pieces of wood of various lengths),_and blocks (three-fourths inch square pieces of wood of various lengths). Both ordering and inserting tests were administered with each of the three different sets of materials. For the seriation test, Elkind found that the ease of task performance increased as the dimensionality of the materials increased. That is, the subjeCts found seriating 17 sticks (one dimension) the most difficult, seriating slats (two dimensions) of intermediate difficulty, and seriating blocks (three dimensions) the least difficult. Elkind, therefore, claimed support for Piaget's contention that the perceptibility of size difference does influence task performance. Elkind's analysis further revealed that the insert- ing problem was more difficult than the ordering problem. Moreover, a significant Test X Material interaction dis- closed that difficulty was more pronounced when a rela- tively difficult task (insertion) was paired with a material of low dimensionality (sticks). The relationship between age and seriation capabil- ity revealed in Elkind's study was consistent with Piaget's findings. Children about four years of age could neither order nor insert, children about five years of age could order but not insert,_and children about six years of age could both order and insert. Shantz (1967) has studied the effects of additional relevant and irrelevant information on children's ability to perform double seriation tasks. Contrary to expecta- tion, she found that additional, relevant information did not significantly increase the number of correct responses. iHowever,_as was expected, the added irrelevant information did significantly reduce the number of correct responses. 18 In addition, no support was found for the hypotheses that the amount of added, relevant information required de- creases with age and that the amount of added, irrelevant information that can be tolerated without affecting the response increases with age. Elkind and Shantz's results will be compared with the understanding that the comparison may be jeopardized by the fact that Elkind and Shantz used different seria— tion tasks (single vs. double seriation) and different critical attributes (length vs. color brightness, amount of border,_etc.). Two different interpretations will be made with respect to Elkind's results, and each interpre- tation will be shown to be inconsistent with the results of Shantz. In Elkind's study, the slats (two dimensional materials) were constructed by adding the dimension of width to the sticks (one dimensional materials). Similarly, the blocks (three dimensional materials) were constructed by adding both dimensions of width and thickness to the sticks. On one hand, since neither width nor thickness varied within any set of Elkind's materials, these dimen- sions must be considered irrelevant to the task of seriat- ing with respect to length. On the other hand, these added irrelevant dimensions of width and thickness may have increased the dominance of surface area and volume, two 19 dimensions that are redundant to the relevant dimension of length. Thus, Elkind's increase in dimensionality may be interpreted as an increase in the number of irrelevant dimensions (width and thickness) or as an increase in the number of redundant, relevant dimensions (Surface area and volume). Elkind and Shantz's findings are inconsistent regardless of the way Elkind's increases in dimensionality are interpreted. If, on one hand, Elkind's increase in dimensionality is interpreted as an increase in the number of irreleVant dimensions, then Elkind found that increases in the number of irrelevant dimensions facilitated seria- tion performance. To the contrary, Shantz found that increases in the number of irreleVant dimensions retarded seriation performance. On the other hand, if Elkind's increase in dimensionality is interpreted as an increase in the number of redundant, relevant dimensions, then Elkind found that increases in the number of redundant, relevant dimensions facilitated seriation performance. Again the results were inconsistent, since, contrary to expeCtation, Shantz found that increases in redundant, relevant information did not facilitate seriation perfor- mance. From this comparison of two seriation studies, it is obvious that further research is needed to resolve the inconsistencies which exist between the findings of Elkind and Shantz. 20 Prentice (1963) administered various seriation tasks to 200 children in nursery school, kindergarten, and second grade. The tasks varied according to the num- ber of elements (five, ten, or fifteen),_the increment between elements (small or large), the materials (sticks of different lengths, pictures of objects that move at different speeds,_or pictures of sticks of different lengths), and the instructions (to seriate, to insert,‘ and to successively choose the smallest element of a group). From the data Prentice made the following observa- tions: 1. There was a significant tendency, especially strong for nursery school children, for series of five elements to be easier than series of ten or fifteen elements and for series of fifteen elements to be easier than series of ten elements. 2. Older children were found to per- form with significantly greater ease when the increment between elements was large rather than small. 3. Children who correctly serial or- dered by a logical analysis of the problem tended to correctly insert elements into partially ordered sets. 4. For kindergarten and nursery schOol children, but not for second graders,. it was significantly easier to make successive choices of the smallest element in a group than it was to form a series. 21 5. The children found the order of difficulty in using the materials to be, from easy to difficult,‘ // sticks, pictures of sticks, and pictures of moving objects. The seriation literature reviewed above will now be related to the training research reported here. Both Piaget (1965) and Elkind (1964) have found evidence for the existence of three qualitatively different stages in the development of the seriation capability. It should be made clear that these stages do not merely reflect a smooth, continuous growth in the development of a single seriation capability but instead reflect changes in the' kinds of seriation capabilities which can be performed. The concept of stage development and the existence of the particular capabilities at each stage of development have been accepted for use in the thesis research. This acceptance is reflected in the.stated purpose of this thesis: that stated purpose being to investigate a method of inducing seriation stage III capabilities in children possessing those capabilities characteristic of seriation stage II. Sticks were seriated and inserted according to length in the studies of Piaget (1965), Elkind (1964), and Prentice (1963). Likewise, sticks were used in this study in both testing and training. Piaget (1965) presented his subjects with 10 sticks to order and then another nine to be inserted 22 into the ordered set of 10. Elkind (1964) on the other hand, used a minimum of four and a maximum of nine sticks in ordering tasks. The insertion tagqsin.Elkind's study required that five sticks be inserted into an ordered series of nine. In this thesis the minimum and maximum number of sticks used in the insertion tasks consisted,, respectively, of two sticks inserted into an ordered set of four and six sticks inserted into an ordered set of twelve. Thus, in this study the numbers of sticks used in the tasks are more consistent with the numbers used by Elkind than with the numbers used by Piaget. Prentice's (1963) results have shown, as expected, that the increment between adjacent elements in an ordered set is a relevant factor in determining the ease of seriation. The increment used in the training study was relatively large. Piaget used an increment of 0.30 inch, Elkind used a 0.50 inch increment, and in this research a 0.75 inch increment was used. The purpose of using a comparatively large increment in this study was to reduce the discrimination problem and, hopefully, in doing so to release the subjects to concentrate on the seriation problem. In the seriation studies reviewed above, two differ- ent methods were used to present the insertion items to the subjects. Piaget presented the sticks to be inserted 23 one at a time, while Elkind, Shantz, and Prentice pre- sented the insertion sticks all at one time. To give the subjects more flexibility in responding, the method of presentation used by Elkind, Shantz, and Prentice Was also used in this training study. In the seriation studies discussed thus far, none of the researchers employed a partial credit method of ‘scoring performance on the individual task items. The subject received either a score of one if, at the end of the task, all elements were in serial order or a score of zero if the elements were not in serial order. This train- ing.study used three different methods of scoring. One method was exactly like the one used in the seriation studies reported above, and, therefore, no partial credit was given. The other two scoring methods used in this training study were two different ways of giving partial credit to task performance. One of Prentice's results was considered in designing the training procedure used in the research. Prentice found that the number of elements used in a task item was.‘ ‘1‘“ 1.. There- I inversely related to the ease of task performance?» fore, in the initial stages of training small numbers of elements were used to make the insertion tasks relatively easy. As the training progressed and the subjects bedame more capable of inserting, the numbers of elements in the 4‘ 24 training tasks were increased. Only certain aspects of the seriation studies reviewed above were relatable to the thesis reported here. This is somewhat understandable because the seriation studies and this thesis were not designed for the same or similar purposes. Seemingly, seriation training studies would be more relatable to this thesis. Unfortunately, only one such seriation study has been found, and it will be reviewed subsequently. Coxford (1964) studied the effects of instruction on the stage placement of children in some of Piaget's seriation experiments. Rather than attempt to induce serial ‘ordering and insertion capabilities, Coxford attempted to induce: l) the capability to construct serial correspon- dence between two sets of materials (stage II) and 2) the capability to conserve serial and ordinal correspondence between two sets of materials (stage III). Balloons and sticks were used by Coxford to deter- mine stage placement. To test for the ability to construct serial correspondence (stage II), the subjects were given disarranged sets of sticks and balloons and were asked to order the balloons and sticks in two separate, parallel arrangements so that the biggest stick went with the biggest balloon, etc. To test for the conservation of serial correspondence (stage III), the subjects were presented 25 with an ordered set of sticks and an ordered set of bal- loons. The two sets were parallel and ordered in the same direction but one set was spread out relative to the other set. The subject's task was to find the object in one set which corresponded to a specified object in the other set. In testing for the conservation of ordinal correspondence (Stage III), each subject was presented with one ordered set of materials and one disarranged set. The task was to find the object in the disarranged set which corresponded to a specified object in the ordered set. The results of Coxford's study reVealed that the training used to induce the conservation of serial and ordinal correspondence was successful but that the train- ing used to induce the ability to construct serial corres- pondence was unsuccessful. In other words, Coxford was able to induce stage III capabilities in stage II subjects but he was unable to induce stage II capabilities in stage I subjects. Coxford's study and this thesis research will be compared with respect to the purposes of training, the training materials and methods, and the testing procedures. Although both studies investigated the effectiveness of seriation training, little direct correspondence is found between them. The training procedures used in the two studies were 26 designed for different purposes. On one hand, Coxford's training was designed to help children acquire the ability to construct a serial correspondence between two sequences of objects, to conserve a serial correspondence when it is no longer perceptible, and to conserve an ordinal corres- pondence. On the other hand, the training used in the thesis was designed to help children acquire the ability to insert a disarranged set of objects into an ordered set of objects. With respect to training procedures, Coxford used four, ten to fifteen minute sessions,_spaced one week apart. Essentially, his training involved practice of the target behaviors. In the thesis reported here more of a massed training procedure was employed since three, thirty minute sessions were held over three consecutive days. Rather than have subjects practice the target behavior during the three sessions, cue fading was used to help the children gradually acquire the insertion capability with" little difficulty. Piaget (1964, pp. 17-18)has provided the following criteria for cognitive reorganization: a) stability over time,. b) broad transfer across tasks, and c) acquisition of new, more complex cognitive Operations. Coxford's study fails to account for these criteria in measuring the training effects since no retention or transfer measures 27 were used and since no attempt was made to see if new, more complex operations had been acquired subsequent to the induction of the target capability. In contrast to Coxford's study, retention and transfer measures were used in the thesis research. Thus,_the thesis research accounted for two of Piaget's three criteria, whereas Coxford's study accounted for none. The literature reviewed above revealed that very little systematic research has been performed to investigate the area of seriation. Most of the existing seriation studies, have been directed toward determining the effects of different materials on the child's performance of vari- ous seriation tasks. The area of research devoted to the study of seriation training was found to be nearly void. Only one seriation training study was found, and the rigor of that study was questioned. In general, this thesis study finds relevance and justification in attempting to partially fill that void which exists in seriation training research. Training Methodology: Support for the Research Hypotheses "Review of PiagetianTraining Studies Piaget has prOposed that limited, speCific training Will produce no significant changes in the cognitive" 28 develOpment of children (Kohlberg, 1968). Furthermore,. even though Piaget believes that learning processes are involved in cognitive development, he does not believe that American learning theory can adequately explain the development of cognitive capabilities (Sigel and Hooper, 1968, p. 259). Piaget's proposals and beliefs regarding the inef- fectiveness of limited, specific training and the inade- quacies of American learning theory have not gone unexamined. In most of the many attempts to induce Piagetian capabilities, specific,_short-term training methods have been used. These specific short-term train- ing methods tend to reflect two general positions regarding cognitive development. One position is consistent with Piaget‘s thinking, and the other is more representative of an American learning theory viewpoint. The Piagetian position is characterized by emphasis upon internal cognitive structures, logical operations, and equilibra- tion mechanisms. The learning theory approach as considered in this review is characterized by emphasis upon such factors as learning set, reinforcement,_corrective feedback, the influence of irrelevant cues, verbal rule learning, cue fading, and practice. The seriation research reported in this thesis was an attempt to investigate the effectiveness of using cue 29 fading and reinforcement to induce the Piagetian capability of seriation. Therefore, the nature of the seriation training obviously reflected the American learning theory position. Since this thesis followed a learning theory approach and since there exists a number of Piagetian training studies reflecting both Piagetian and learning theory approaches, an examination of the relative effec- tiveness of the two approaches might reveal some expecta- tions regarding the success or failure of the seriation training methods. In the Piagetian training studies, researchers have focused their attentions almost exclusively on the train- ing of conservation capabilities (Sigel and Hooper, 1968, pp. 258-434; Brainerd and Allen, 1971). Therefore, little will be lost by limiting the review to those training studies concerned with the induction of conservation. Since stick length and the number of lines per card were the critical attributes used in seriation training, the review will be further limited to those training studies concerned with the induction of length or number conserva- tion. Flavel (1963, p. 245) has defined conservation as "the.cognition that certain properties (quantity, number, length, etc.) remain invariant (are conserved) in the face of certain transformations (displacing objects or object 30 parts in space, sectioning an object into pieces, changing shape, etc.)." Hence, a child who conserves number will maintain, without counting,_that the number of objects before him remains the same regardless of any changes in their spatial orientation. Similarly, a child who con- serves length will insist that the lengths of two sticks remain the same regardless of their relative positions. Brainerd and Allen (1971) have reviewed training studies in the conservation of "first-order“ quantitative invariants (number, length, substance, weight, and area). They conclude from their review that the common element among the successful methods (defined by statistical significance) is training in reversibility. Reversibility refers to the idea that every direct operation (action or transformation) has an inverse which cancels or negates it. For example, the lengthening of a row of objects in number conservation tests can be cancelled or reversed by returning the row to its original length. According to Piaget (1964), "reversibility of thought" is a cognitive capability which must be present in the intellectual repertoire of the child in order for him to conserve. The child who is to conserve number, for example, must realize that since a rearranged set of objects can always be returned to the arrangement observed at the time of counting, the number of objects remains 31 the same. Since Piaget stresses the importance of revers— ibility and since Brainerd and Allen conclude from their review that reversibility training is commonly found in the successful training studies but not in the unsuccessful studies,_it would appear that the evidence supports the Piagetian position more than it supports the learning theory position. The apparent support for the Piagetian position rests on the validity of Brainerd and Allen's analysis of the lengthand number conservation studies. A careful reanalysis of the same studies, however,_brings that validity into question. Apparently, Brainerd and Allen attended primarily to the reversibility element and failed to regard other training conditions which may have accounted for the success or failure of training. Therefore, the conditions used to induce lengthand number conservation will be surveyed, the analysis will be broadened, and the various conclusions of Brainerd and Allen will be refuted or reaffirmed. Before beginning the analysis, perhaps typical tests for number and length conservation should be described. A test for number conservation usually begins with the examiner placing two numerically equivalent rows of objects parallel to each.other with the objects in eXact one-to-one correspondence. Either by having the 32 child count the objects or by having him observe the one- to-one correspondence, the numerical equivalence of the two rows is established. One row is then lengthened or shortened, and the child is asked if the numbers of objects in the rows are the same or different. Usually the child is requested to explain his answer. The child who fails to give a reasonable explanation is often judged to be a nonconserver, even though he maintains that the numbers are the same. A conserver might reasonably explain that the numbers of objects must still be equal since objects were neither added nor taken away. Testing for conserva- tion of length would proceed in a similar manner. Two sticks of equal length would be placed parallel with the ends aligned. Equivalence of length would be established, and then one stick would be moved so the ends of the sticks would no longer be in line. The question of equivalence would be asked and then followed by the request for an explanation. The training methods used to induce conservation capabilities tend to reflect two general positions regard— ing the development of conservation. One position is consistent with Piaget's thinking and the other is more representative of an American learning theory viewpoint. The Piagetian position is characterized by emphasis upon internal cognitive structures, logical operations, and 33 equilibration mechanisms. According to Piaget (1952),, before conservation can appear, the child must acquire the following operations: multiple classification, multiple relationality, atomism, reversibility, and seriation. The researchers favoring the Piagetian position construct their training procedures in accordance with Piaget's proposed prerequisite operations and his general mechanism for cognitive development (equilibration). The learning theory approach, on the other hand,_is characterized by an emphasis upon such factors as learning set, reinforcement, corrective feedback, the influence of irrelevant'cues,, verbal rule learning,cue fading, and practice. Some of the researchers (Gelman, 1969; and Kingsley and Hall, 1967) who favor this approach would contend that a young child may in some way be able to conserve but may fail to conserve because of inattention to the relevant quantita- tive attribute or because of the strong tendency to attend to changes in irrelevant attributes such as shape, position, or color. Unsuccessful Attempts to Induce Length and Number Conservation Relatively unsuccessful attempts to train for con- servation of length and number have been reported by Smedslund (1963), WOhlwill and Lowe (1962), and Mermelstein and Meyer (1969). 34 Smedslund (1963) hypothesized that training methods would be successful if they were consistent with Piaget's concept of equilibration. Piaget (1950) asserts that the logical structures of the child develop as a function of the internal process called equilibration. Through inter— action with his environment the child has experiences which are sometimes inconsistent with his way of thinking. This inconsistency puts the child in a state of disequilib- rium. To make experience and thinking match and to return to a state of equilibrium, the child goes through a process of reorganizing his thoughts. This process of reorganiza- tion is called equilibration. According to Smedslund, conservation can be induced by stimulating the equilibra- tion process through the presentation of conflict situations. Smedslund studied the relative effectiveness that five different conflict producing procedures had upon the induction of length conservation in young children. In <‘) were used to create a perceptual changeof length. Although Smedslund did not report a statistical analysis of his data, such an analysis has been performed and reported by Brainerd and Allen. The results show that only one of Smedslund's five experimental treatments (the anticipation condition) produced significant increments in length conservation with respeCt to the control condition. 35 Although the anticipation method of training was found to be better than no training (control),_it was not found to be superior to the other four training methOds. In the anticipation method, subjects were asked to anticipate and judge the relative lengths of two equally _1ong sticks before and after movements back and forth between an optimal comparison position (sticks side-by-side without Muller-Lyer arrowheads) and a perceptually dis- torting position (sticks spread apart with Muller-Lyer arrowheads). The procedure for one unit of the anticipa- tion method of training is more explicitly explained as follows: \/ l. Sticks with the angles (/N\<;) were presented to subjects. Subjects were then asked, "If the sticks are moved tOgether from under the angles, will this one be longer,_will they be equally long, or will this one be longer?" Following subject's response, the sticks were placed together and shown to be equal. 2. The subject was then asked to anticipate the rela- tive lengths of the sticks if they were moved out to the angles again. 3. The sticks were moved out under the angles, and the subject was asked again about the relative lengths of the sticks. 36 4. In the final step of the instructional unit, the subject was requested to anticipate the relative lengths of the sticks if they were moved in from under the angles. Each subject in the anticipation group received four instructional units similar to the one just described. The only difference between the units was the color of the sticks used. It should be pointed out that the experi- menter extended neither reinforcements nor corrective feedback to the subjects during any of the training. Brainerd and Allen suggest that Smedslund's antici- pation method of training was successful because the subjects were given reversibility training. A careful examination of the instructional steps, however, reveals that the last step in the usual method of reversibility training was omitted. Usually, an equality - apparent inequality - equality sequence is used in reversibility training. In Smedslund's anticipation method, the final state of equality was not demonstrated. The subject was merely asked to anticipate the relative stick lengths if the transformation was reversed (i.e., if the sticks were moved from under the arrowheads back to the side-by-side position). The reverse transformation was not actually carried out. Thus, the success of the anticipation method cannot be attributed to reversibility training. 37 The failure of the other four training methods used by Smedslund is not surprising. The maximum number of times a subjeCt responded under any of the unsuccessful 'training conditions was 16. Furthermore, no feedback was- {given to the subject even when he did respond. Wohlwill and Lowe (1962) studied the effects that four different methods had on the induction of number conservation in young children. The four training condi- tions were: Reinforced Practice, Addition and Subtraction, Dissociation, and Control. The training series for each condition consisted of nine trials administered on each of two successive days. Wohlwill and Lowe's results revealed that all three experimental conditions as well as the Control condition produced significant effects on a nonverbal measure of conservation, but virtually no demonstrable effeCts on a verbal test of conservation. Moreover,_the experimenters found no reliable differences in effectiveness among the four training conditions. In View of what they consider to be a predominantly negative experimental outcome, Wohlwill and Lowe offer a Vgeneral conclusion. Since the children in their experi- ment rather consistently responded on the basis of length differences in making numerical comparisons between two collections, the experimenters maintain that there exists 38 support for interpreting the lack of conservation as a failure to differentiate number from irreleVant perceptual cues. Admittedly, Wohlwill and Lowe's conclusion is based on somewhat scanty evidence. NevertheleSs, their conclu- sion has been supported by the well designed and rigorous research of Gelman (1969), which will be reported subse- quently. Merelstein and Meyer (1969) studied the effects that five treatment conditions (four experimental and one con- trol) had on the induction of the number conservation in young children., The subjects were tested three weeks, two and oneéhalf months, and five months after the last train- ing session, and the results indicated conservation was not induced by any of the training.techniques. The four experimental training conditions were similar to Smedslund's.Cognitive Conflict technique, Beilin's Verbal Rule Instruction, Bruner's Language Activa- tion technique, and Sigel's Multiple Classification train- ing. Eight training trials were given under each experimental condition. The amount of traininggiven under each experimental condition was indeed minimal (eight trials). Of the eight cognitive conflict trials, only the last three were designed to actually produce a conflict situation. Thus, subjects in the Cognitive Conflict group, essentially received only 39 three trials of training. Under the Multiple Classifica- tion condition an attempt was made to give subjects train- ing in multiple labeling (a poker chip can be called a checker or a toy coin), multiple classification (a poker chip can be classified according to color, shape, texture), multiple relations (a poker chip can have color and shape), and reversibility. Since eight trials were used to train the subjects for all five of the target capabilities, the Multiple Classification subjects probably never acquired any of the capabilities to a respectable degree. Some questions can be raised as to whether or not certain training situations were properly designed. For eXample, in the reversibility training,_transformations were never reversed, and in Language Activation training the question was phrased in such a way that it would tend to minimize rather than maximize language activation. Considering the inadequacies of the training and testing techniques, Mermelstein and Meyer's study could hardly be considered a fair test of the relative effective- ness of the four training conditions studied. In the face of such inadequacies, it becomes difficult to accept Mermelstein and Meyer's general conclusion that specific training, regardless of procedure, is ineffective in inducing conservation concepts. Brainerd and Allen have observed that unsuccessful 40 attempts to induce number and length conservation are characterized by the absence of adequate reversibility training. They use this observation to support the con- tention that the presence or absence of reversibility training determines the success or failure of training attempts. Although Brainerd and Allen's observation is cor- rect, the use of that observation in support of their con- tention is questionable since the failures can be explained by other inadequacies. In all the unsuccessful attempts, the number of training trials was very small,_none of the subjects were trained to criterion performance level, and feedback given to the subjects was almost nonexistent. Therefore, it is quite possible that failures could be attributable to insufficient amounts of training rather than to the method of training, as suggested by Brainerd and Allen. ' Successful Attempts to Induce Length and Number Conservation Relatively successful attempts to induce number and/or length conservation have been reported by Goldschmid (1968), Wallach and Sprott (1964), Wallach, Wa11,and (Anderson (1967), Gelman (1969), and Kingsley and Hall (1967). Goldschmid (1968) used six experimental groups and one control group to study the relative effectiveness 41 of using three different training procedures to induce' various conservation capabilities. Each subjeCt in half the experimental groups was trained to conserve discontinu- ous quantity (amount of beads poured into containers of different shapes), two-dimensional space,_and substance (amount of clay). Each subjeCt in the other half of the experimental groups was trained to conserve continuous quantity (amount of liquid poured into containers of differ- ent shapes), number, and weight. One of three different training procedures was used with each of the three groups receiving training on the' same concepts. The different procedures consisted of reVersibility training, compensation training, and a com- bination of reversibility and compensation training. The reversibility procedure involved repeated demonstrations showing that any transformation can be reversed. The child was to infer from reversibility training that since an action can be reversed,_the original quantity remains unchanged regardless of the transformation. ‘Compensation training involved step-by-step transformations of one of two quantitatively equal objects (or sets of objects). This training procedure was used to show the child that change in one dimension (tall to short) was compensated for by change in another dimension (skinny to fat). The combination of reversibility and Compensation training 42 involved aspects of both procedures described above. One of the three training procedures was used with each subject during three one-half hour sessions. Each session was devoted to training on one conservation capability. Train- ing characteristics such as the number of training trials, the use of a training criterion, and the use of feedback were not reported by Goldschmid. Posttests were administered three and six weeks after training. During the two posttests every subject was teSted on six conservation tasks, the three he received training on (acquisition), and the three he received no training on (specific transfer). Only during the second posttest were the subjects teSted on conservation of length, and area (nonspecific transfer). The results from the posttests revealed that all experimental groups performed significantly better than the control group on all test items of both posttests, and that reversibility training was more effective than either compensation or combination training. Goldschmid concluded from the data analysis that the training procedures were effective means of inducing conservation concepts, that the acquired conservation capabilities were transferable, and that the effects were durable over a six week time period. In addition, Goldschmid claimed support for the idea proposed by Piaget that reversibility and compensation 43 are thought processes underlying conservation. Wallach and Sprott (1964) successfully induced num- ber conservation in children by using a combination of reversibility and addition/subtraction training. The training materials consisted of six dolls and six beds. At the beginning of each trial the beds with the dolls in them were placed side-by-side in a row before the subject. The dolls were then taken out and placed closer together or farther apart in a row in front of the beds, so that there was a bed without a doll or a doll without a bed. In half the trials either a doll or bed was added or re- moved so that the two rows became the same length. After the transformations, the subject was asked the following series of questions: _"Do you think we can put a doll in every bed now? Will there be any beds left over? Any dolls left over?" After answering the question the subject was asked to put a doll in each bed. The subjects were presented the training situations in the following order: ,1) dolls together; 2) dolls together, bed removed; 3) dolls apart; 4) dolls apart, bed added; 5) dolls together; 6) dolls together, doll added; 7) dolls apart; 8) dolls apart, doll removed. Each situation was repeated until the subject made the correct prediction and then confirmed it. All experi- mental subjects were trained to a criterion of a correct 44 prediction on the first trial of four situations in succession. Two posttests were given, one immediately after training and the other between 14 and 23 days after train— ing. Dolls and beds as well as checkers and cards were used in the first posttest. In the second posttest bowls and spoons, checkers and cards, and dolls and beds were used. The questions asked during the posttests were not the same as those used in training. Training questions asked nothing about the number of objects,_whereas testing questions asked if there were the same number of objeCts. The analysis of the posttest results indicates that the experimental group performed significantly better than the control group on both posttests. The c0nclusion was made that the treatment was an effective means of inducing sustained number conservation. These results seemingly provide more support for the Piagetian contention that reversibility is a fundamental prerequisite for conservation. In spite of the results,~ Wallach and Sprott were not willing to claim unquestionable support for the Piagetian contention. They observed that over half the experimental subjects reSponded correCtly in all training trials to the question, "Do you think we can put a doll in every bed now?" :From this observation, they concluded that many subjeCts already knew that transfonmations 45 were reversible prior to both the training and the acquisi- tion of number conservation. Thus, Wallach and Sprott reasoned that the training did more than simply supply the subjects with the knowledge of reversibility. Wallach and Sprott (1964) gave reversibility train- ing the credit for successful induction of number conserva- tion. However, since the training procedure was actually a combination of reversibility and addition/subtraction training, no reasonable conclusion can be made about the individual effectiveness of the two kinds of training. Wallach, Wall,_and Anderson (1967) followed up the Wallach and Sprott study with an attempt to investigate the separate effects that reversibility and addition/subtraction 'training had upon the acquisition of number conservation. All experimental subjects were trained to a performance criterion of four successful trials in succession. The results of the study showed that reversibility training was a successful means of inducing sustained num— ber conservation,_but that the addition/subtraction train- ing was not. Furthermore, the results indicated that number conservation induced by reversibility training did not transfer to the conservation of liquid amount. The expected conclusion made from the results would seemingly be that children acquire number conservation once they become able to recognize reversibility. Wallach, 46 Wall, and Anderson, however, did not make such a conclusion. Instead, they maintained that reversibility was successful, not because it led the subjects to reCognize reversibility, but because it led them to stop relying on misleading cues. The evidence for the experimenters' conclusion came from subjects' explanations of the conserving responses. Rarely did the conserving subject use the idea of reversibil- ity to explain that number was conserved. Most often the conserving subject gave an explanation which referred to the spacing of the objects (closer together or farther apart) rather than to the overall length of the row. The implica- tion was that a shorter row did not necessarily mean that there were fewer objects but that the objects were just closer together. Wallach, Wall, and Anderson interpreted this most frequent explanation as evidence for suggesting that the subjects had learned to ignore the misleading cue of row length. The study by Wallach, Wall, and Anderson generates the queStion:~ Can number conservation be induced by a method which trains the subjeCts to disregard the misleading cues while at the same time minimizes any suggestion of revers— ibility? Gelman (1969) used such a method and found the answer to be affirmative. Gelman (1969) hypothesized that a young child may in some Way be able to conserve but may fail to conserve beCause 47 of inattention to the relevant quantitative attribute or because of the strong tendency to attend to changes in irrelevant attributes such as shape, position, or color. She investigated the supportability of her hypothesis by using discrimination learning set training on length and number tasks. In learning set training procedures, the sub- jects receive training with a large number of problems containing many different stimuli; although the stimuli differ, across problems there is one common relationship, and the attentional reSponses to this common cue are rein- forced. Gelman trained her subjects to attend to the rele— vant quantitative attributes of length and number while dis- regarding irrelevant attributes of color, shape, and spatial arrangement. The training consisted of 32 six-trial prob- lems. In half the problems the relevant attribute was length, and in the other half the relevant attribute was number. The number problems were alternated with.the length problems. Three stimulus objects (Sticks or rows Of chips) were used in each problem. Two of the objects (sticks or rows of chips) were identical while the third was different. For example, two rows of five chips were used with.one row of three chips and two 6-inch sticks were used with one 'lO-inch stick. In the training problems, the subject's task was to point to two sticks that had the same (Or dif- ferent) length or to point to the two rows that had the 48 same (or different) number of items in them. After a sub- ject made a correct response he was told that his response was correct and he was given a prize (trinket). When an incorrect choice was made, the subject was told that his response was wrong. Contrary to Brainerd and Allen's report, a noncorrection procedure was followed. For the six trials of each problem the stimulus objects remained the same. The variation between trials within a problem took the form of changes in spatial orien- tation. Gelman used Figure l to illustrate the between trial variation within a problem. PROBLEM TYPE TRIAL NUMBER LENGTH 1 :33}: :7 2 313:: E 3 :13 33 .5: 4 .333. E 5 23.3.5 L: 6 0.0.0........ —_——"_ Fig. l. Gelman's (1969) illustration of between trial variation within a training problem. 49 There is no indication in this figure that reversibility training did take place, as suggested by Brainerd and Allen. Between problem variations consisted of changes along the following irrelevant attributes: 1) color of chips and sticks,. 2) size and shape of chips and sticks, 3) starting arrangements (horizontal, vertical, etc.), and 4) quality combination (i.e., whether the odd stick or set of chips was small or large compared to the other two sticks or sets). Gelman employed two control groups. One control group received oddity training with toys. The other group received the same training as the experimental group except that no feedback was given. Conservation posttests were given to all groups the day after training and then 2-3 weeks later. The posttests contained items designed to test conservation of length and number (specific transfer) and conservation of mass and liquid (nonspecific transfer). The results showed near perfect specific (lengthand number), and approximate- ly 60% nonspecific (mass and liquid amount) transfer of training. Over the 2-3 week retention interval these effects were found to be durable. Gelman concluded that support was found for the hypothesis that young children fail to conserve because of inattention to relevant 50 quantitative relationships and attention to irrelevant features in classical conservation tests. Gelman's study does not stand alone. Kingsley and Hall (1967) also successfully trained subjects to conserve length and weight with learning set procedures. Rather than speCifically train_the subjects to ignore irrelevant and attend to relevant aspects of the conservation problem, Kingsley and Hall used Gagné's learning set analysis and trained the subjeCts on a graded series of subtasks related to conservation (e.g., the appropriate use of scales and measuring instruments, the effects of addition and subtraction, the relation between spatial orientation and length). The subject's experiences during the sub- training most likely led them to ignore the irrelevant cues. Thus Kingsley and Hall's subtask training indireCtly served the same purpose as the learning set training used by Gelman. Contrary to Brainerd and Allen's reView,. KingsleY-and Hall reported no use of reversibility training. Discussion The unsuccessful studies were characterized by very few training trials (maximum number of trials was 18), no training performance criteria,_and almost no means of ‘providing subjects with feedback. In comparison, the successful studies used more training (Goldschmid, 1.5 51 hours; and Gelman, 192 trials), trained to criteria (Wallach and Sprott; Wallach, Wall, and Anderson; and Kingsley and Hall), and often provided the subjects with feedback. This comparison suggests that future training studies use adequate amounts of training and provide the subjects with feedback, and that possibly those method- ological comparisons made in the unsuccessful studies should be repeated with more emphasis given to the exten- siveness of the training and to the use of feedback. Contrary to Brainerd and Allen's conclusion, the successful and unsuccessful studies are not necessarily distinguished on the basis of whether or not reversibility training was given. It is true that the unsuccessful studies did not employ reversibility training. It is not true,_however, that all successful studies employed reversibility training. In fact, the most successful .attempt (Gelman) did not include reversibility training. Gelman's study and the study by Kingsley and Hall lend strong support to the contention that children fail to conserve not because they lack certain cognitive capabilities (reversibility) but because they are unable to distinguish the relevant from the irrelevant cues. The successful studies which employed reversibility train- ing do not challenge this contention, but instead support it, since reversibility training has the potential for 52 leading subjects to disregard irrelevant cues and attend to relevant cues. In fact,_reversibility training might be considered one kind of learning set training. With respect to the theoretical position,_the work reviewed here seemingly provides more support for the learning theory position than for the Piagetian position. First,_SomeWhat contrary to Piaget's notion, young children can acquire at least speCific conservation concepts through speCific experience. second, the learning theory position with emphasis on attention, stimulus factors, and learning set can explain the succeSs of both the studies using learning set procedures (Gelman, and Kingsley and Hall) and the studies using reversibility training (Goldschmid; Wallach and Sprott; and Wallach, Wall, and Anderson). The Piagetian position with emphasis on requisite cognitive structures and reversibility training,_however, fails to explain the SUCCESS'Of the learning set procedures. AS’a final note of clarification, it should be stated that this review has cited no evidence which suggests that conservers need not recognize reVersibility. In fact, it seems reasonable to propose that all "real“ con- servers should be able to reCognize reversibility. The evidence merely suggests that either children already recognize reversibility before they are taught to attend to the relevant cues, or that they acquire the ability to 53 recognize reversibility as a consequence of learning to attend to the relevant cues. Although the conclusions resulting from this review of Piagetian training studies cannot be directly used in formulating hypotheses for the theSis study, the conclusions do reveal some hint of eXpectations regarding the success of the seriation training methods. In general, the eVi- dence shows that not all Piagetian capabilities are reSis— tant to training and furthermore, that the learning theory position can be used as an adequate bases for training. Therefore,_since learning theory is the basis for the seriation training, and since the seriation capability is seemingly not as complex as the conservation capability, the seriation training methods are expected to be success- ful. In general, the Piagetian training studies pre- viously reviewed were attempts to answer academic or theoretical questions rather than educational questions. Like many "academic" studies, the training studies were characterized by relatively shOrt training periods, reten- tion intervals which were of little more than minimal length, and meaSurements of transfer which,_for the most part, were limited to the use of tasks very similar to those used in training. According to Piaget,_thedesign characteristics of 54 the training studies did not permit adequate tests of his theoretical proposition concerning cognitive reorganiza— tion. In addition to maintaining that cognitive change cannot be induced by limited, short-term training, Piaget (1964, pp. 17-18) contends that broad transfer, stability over time, and the acquisition of new, more complex capabilities are the three criteria necessary for inferring cognitive reorganization. If these criteria are inter- preted in a broad sense, then the review of conservation training studies has shown that those studies rarely even approached a consideration of Piaget's three criteria. If Piaget is correct in his selection of criteria, then certainly more massive, long-term studies are needed. It would seem that these studies while answering theoreti- cal questions could at the same time answer educational questions. In fact, studying the effeCts of induced intellectual capabilities on school learning might be interpreted as an attempt to account for Piaget's criteria of broad transfer and acquisition of new, more complex capabilities. Although the training studies have not produced convincing answers to the theoretical questions and have certainly been of little immediate educational worth, they have indeed established the basis necessary for the development of those massive, long-term studies which have 55 both theoretical and educational relevance. For example, without the conservation training studies, no methods would have been developed for inducing conservation capabilities. As a result, no rationale would exist for attempting the large scale investigations in the schools to see if extended training in conservation would have a significant impact on: 1) the nature (quality, rate, and sequence) of intel- leCtual development observed over a considerable time period, and 2) the nature of school learning observed,_ as well, over a considerable time period. The more thorough conservation training studies have produced a foundation upon which the more masSive, the- oretically and educationally releVant studies can be built. A similar foundation for the seriation capabilities has not yet been constructed. The seriation training study reported in this thesis is, therefore, particularly rele- vant since it contributes to the sound foundation from which will eventually spring those longitudinal studies in which intellectual development and school learning will be observed as a function of induced seriation. Review of Instructional~Psychologyy Studies in instructional psychology will be reviewed to provide support for the general research hypothesis. That hypothesis states that the instruction given to the 56 experimental subjects will be successful in helping them acquire the ability to correctly insert objects into a seriated set of objects. The organization of the review will be structured according to Gagné‘s set of instructional conditions. According to Gagné (1965, pp. 205-236),_the manager of instruction may manipulate the following set of conditions: a) Conditions for the Acquisition of Capabilities - l. the techniques to gain and maintain the attention of the learner,, 2. the establishment of certain preconditions for learning,, 3. the presentation of the stimuli directly involved in learning, 4. the use of prompting and guiding to facilitate the learning process,. 5. the specification of.the conditions of responding,‘ 6. the employment of feedback methods; b) Conditions for the Promotion of Retention; c) Conditions to Enhance the Transfer of Learn- ing. The manipulation of Gagné's conditions in the thesis research will be discussed and literature relevant to the employed conditions will be reviewed. Conditions for the Acquisition of Capabilities The‘techniques to gain and maintain the attention of the learner. In summarizing a review of recent research on.methods of gaining and maintaining attention, Gagné and Rohwer (1969) concluded that the application of techniques 57 using reinforcement contingencies seemingly holds much promise for maintaining attentional sets. In support of their conclusion Gagné and Rohwer cited a study by Parker and Nunnally (1966), who found that penny rewards increased children's "time of looking" at nonsense syl- lables presented in a spin-wheelgame. In a similar manner,_Staats and associates (1962, 1964a, 1964b) found that token reinforcers served well as effective reinforcers in teaching beginning reading skills to four-year-olds. The token reinforcers were accumulated by the children and eventually exchanged for small trinkets and toys. Staats and associates concluded that the reinforcement system solved the major problem in teachingyoung children, namely, to keep them at the task over long periods of time. Since the effectiveness of token reinforcement systems,_ as shown by Staats and associates, has been replicated a number of times (Howard and Tracy Kendler and associates,_ 1959,_1960; and Whitlock and Bushell, 1967), the token system, therefore, seems to be a reliable technique which can be used to teach young children various skills. The material reinforcers used in this thesis con- sisted of marbles which the subjects stacked in "marble banks." .Unfortunately, at the request of the subjeCt's teachers, no "back-up" reinforcers (candy or trinkets) could be exchanged for the marbles. Although the desired 58 token reinforcement system was not employed in the thesis research, it was assumed that acquiring and stacking marbles in columns would provide the subjects with a significant increment of reinforcement to keep them at the tasks. Non-material, social reinforcement in the form of verbal praises (Gerwirtz and Baer, 1958a, 1958b) and teacher attention (Harris,_Wolf, and Baer, 1964; and Harris, Johnston, Kelley and Wolf, 1964) has been found to facili- tate the training of young children. Zigler and Kanzer (1962) found that "praise" (Vgood," “fine") reinforcers were more effective with lower socioeconomic class children than with middle-class children and that "correct" ("right," "correct“) reinforcers were more effective with middle-class than with lower-class children. Since there existed the possibility of having both lower and middle-class children in the seriation study, both kinds of social reinforcers described by Sigler and Kanzer were used. Whenever a sub- ject responded correctly to a seriation training task, he was told that his response was correct ("Right!,V "Correct!"), and he was given praise ("Good job!,W "Very nice!"). With the research on social reinforcement showing that social stimuli can be used as reinforcers in training young children, the social stimuli used in seriation training ‘were assumed to provide a measure of reinforcement sufficient 59 enough to keep the subjects interested in acquiring the target seriation capabilities. The establishment of certain preconditions for learning. According to the Gagne model, another instruc- tional event which should be considered by the instructor is the establishment of preconditions for learning. To facilitate learning, students may be given verbal direc- tions and pretraining and may be asked to recall past learning which is relevant to the subsequent instruction. In the thesis study, an orientation session was given before each of the three training sessions to prepare the subjects for the instruction which followed. The orientation sessions were used to introduce the tasks and materials, point out the cues, illustrate correct and incorrect responses, show how reinforcement would be admin- istered, and allow the subjeCts to demonstrate their under- standing of the instructions.‘ It was assumed that these sessions would prepare the subjects for instruction and thus facilitate their acquisition of the target capabili- ties. The presentation of the stimuli directly involved in the learning. Instructional designers often have the option of presenting materials in the form of objects, pictures, or words. Gagne and Rohwer (1969) have suggested 60 that when such an option exists in preparing materials for young learners, the stimulus type chosen should be either objects or pictures rather than words. With.respect to the use of various stimulus types in seriation research, Prentice (1963) has found that children seriate sticks more easily than they seriate pictures of sticks. Further- more, Elkind's (1964) seriation study revealed that the ease of performing seriation tasks increased as the dimen— sionality of the objects increased. The findings of Elkind and Prentice and the sugges- tion of Gagné and Rohwer seemingly imply that, for young learners, task difficulty increases as the abstractness of the stimulus material increases. This implication was used in this thesis to determine the order of presenting two different training materials. To help the children acquire the ability to insert, the material which made the insertion task the easiest for the children was used first. This material, according to the above implication, would have a concrete nature. Thus, sticks, rather than lined 'cards, were used in the initial stages of the training sequence since stick length was assumed to be a more con- crete quality than line density. The use of prompting and guiding to facilitate the learning process. The degree of guidancegiven to the learner during the learning process must be considered in 61 any thorough design of an instructional procedure. In some procedures very little guidance is given,_and as a consequence the frequency of error responses is relatively high at the start of the training and gradually decreases as learning takes place. In other procedures much guidance is given, and the subjects acquire the target behavior having emitted very few, if any, error responses. B. F. Skinner (1961, pp. 59-66) has argued that errors are not essential to the successful acquisition of target behaviors. He maintains that a cue fading proceSs can be used to minimize error and thus accelerate learning. In the cue fading process cueing or prompting stimuli are used to supplement the stimuli to which the learner is to eVentually respond without aid. The cueing stimuli are chosen to increase the probability of correct responding. As the learning process proceeds, the supplementary cueing stimuli are gradually withdrawn or faded at a rate which maintains a minimum frequency of error responses. Eventu- ally no cues are needed and the terminal behavior is acquired. » Seemingly, Terrace's pioneering work (1963a, 1963b) in errorless discrimination stimulated the production of relevant research on fading. Terrace (1963a) found that if cue fading techniques were used, pigeons could learn a red-green discrimination withOut producing error reSponses. 62 In a seCond study, Terrace (1963b) extended the use of fading and obtained errorless transfer of training from the red-green discrimination to horizontal-vertical dis- crimination. Studies.by Hively (1962, 1965), Moore and Goldiamond (1964), Sidman and Stoddard (1967), and Bijou (1965) have shown that cue fading can be efficiently and effectively used in training young children to make relatively complex discriminations. For example, Bijou (1965) revealed an impreSsive demonstration of the successful use of errorless training teChniques and fading when he induced right-left form concepts in young normal and retarded children. On a terminal task item, the subject was presented with five stimuli and was directed to choose the one stimulus which was the same as a given sample stimulus except for an angular rotation. Bijou cued for the correct response by deforming the correct stimulus choice. Then as training progressed, the deformed Choice was gradually altered so that it showed progressively greater resemblance to a rotation of the sample stimulus. The target behavior of this thesis required kinder- garten subjects to make discriminations., Given an object to be inserted into a seriated set of objects,_the subjeCts had to discriminate between the correCt position in the’ seriated set and the incorrect positions. To induce this 63 discrimination capability, cues were introduced and then .gradually faded. Since the evidence shows that cue fading can be an effective means of producing discrimination learning, and since the acquisition of the target behavior in the thesis study involves discrimination learning, it is hypothesized that the cue fading method, as used in the thesis study, will contribute to the successful induction of the inser- tion capability in kindergarten children. The-specification'of‘the'condition5‘of‘responding. Anderson (1967) claims that enough is known to make a reasonably safe conclusion about the relative learning effects of overt and covert responding. ‘Anderson concludes that learning is facilitated when subjects are required to make Overt, constructed responses. In the thesis study, the subjects who reCeived the training were required to make overt, constructed responses. For each training trial, the experimental subjeCts reSponded by attempting to insert a disarranged set of objeCts into a serial ordered set of objects.' According to Anderson's conclusion the response mode used in the training should facilitate’learning. The employment of feedback methods. Stimuli pre- sented to,a subjectfollowing his emitted response can 64 serve informative as well as reinforcing functions. The completeness of the information provided by the feedback may vary considerably. For example, the subjeCt may be merely told whether his response was correct or incorrect, or he may be shown the correct response and then given a full explanation of why the response was correct or in- correct- Bourne and Pendleton (1968) compared two conditions of feedback completeness in concept identification prob- lems. In one condition the subject was told whether hiS' response was correct or incorrect. In the other condition, the subject was, in addition, shown the correct response whenever a.mistake was made. The results indicated that the latter, more complete, feedback condition was superior to the former, less complete, feedback condition. In a similar study, Travers, Van Wagen, Haggood,_and McCormick (1964) studied the relative effectiveness of four differ- ent feedback systems used to teach elementary school children the English equivalents of German words. They found that the two conditions in which the subjects' :incorrect responses were correCted were significantly more effective than the two conditions in which no correction procedures were used. In this thesis study,_informative feedback was given to the subjects during seriation training. Whenever a 65 subject responded incorrectly, he was told why his response was incorrect,_and he was shown the correct response. Thus, at the end of every training trial, the subject was given the opportunity to see the correct behavioral product (a seriated set of objects) regardless of whether he or the experimenter was responsible for its construction. Since the kind of informative feedback used in this thesis has been found to facilitate learning (Bourne and Pendle- ton, 1968; Travers at 21., 1964), it was assumed that such feedback would facilitate the acquisition of seriation capabilities. The studies reviewed from instructional psychOlogy have provided support for the methods used in the seriation training. The conservation.studies have suggeSted that Piagetian capabilities can be induced and that learning theory can provide a sound basis for constructing the training methOds used in successfully inducing Piagetian capabilities. Furthermore, Coxford's results have.sug- vogested that some seriation capabilities can be induced. Therefore,_as a consequence of this accumulated support,. .it is hypothesized.that the experimental subjects in this thesis will acquire the insertion capability characteris- tic of seriation stage III. 66 Conditions for the‘Promotion'of~Retentionv There is reason to believe that retention of knowl- edge is more a function of the degree of original learning than a function of other variables which may, for instance, influence the efficiency of learning. For example, it has been known that when the degree of original learning is held constant, learning speed (Underwood, 1954), intralist similarity (Underwood and Richardson,_l958),meaningfulness (Underwood and Richardson, 1956), and associative strength (Underwood and Keppel, 1963) are of no significant conseé quence for retention. This phenomenon has reCeived additional support from a recent study by Olton (1969). 'Olton examined the effects of grammatical context on the retention of paired associ- ates. He found that when original learning was equated, the amount retained by the group which learned paired associates in a grammatical conteXt was no different than the amount retained by the group which learned paired associates in abSence of grammatical aid. As expected,. howeVer, learning was more rapid when the pairs were embed- ded within the grammatical conteXt. The review of literature up to retention has been focused on methOds which increase the degree of acquisition. The review led to hypotheSizing that the methods used in seriation training would produce significant increments in 67 seriation ability. Therefore, if retention is positively related to original learning, and if this relationship can be extrapolated from adult verbal retention to the retention of induced nonverbal capabilities in young children, then the subjects given what has been hypothesized to be successful seriation training will be expected to show a significant amount of retention. The pattern of reinforcement used in conditioning a response determines to a large degree the extent to which the reSponse is resistant to eXtinction. DeeSe and Hulse (1967, p- 152) report that there exists literally hundreds of eXperiments shOwing that partial patterns of reinforce— ment produce greater reSistance to extinction than a con- tinuous pattern of reinforcement. For example, Jenkins, MCFann, and Clayton (1950) found that a variable ratio schedule, in which different numbers of responses were' required for succeSsive reinforcements, produced five times as many responses during extinction as did a continuous reinforcement schedule, in which reinforcement wasgiven after every reSponse. The pattern of reinforcement used in the seriation ‘training was continuous in nature. 'Therefore, the pattern used in seriation training is not expected to.contribute much to the long term retention of the acquired seriation capabilities. 68 Distribution of practice is another factor which influences retention. Although spaced practice, in certain situations, impedes learning, it may, in those situations, facilitate retention (Underwood, 1964). For example,. Underwood (1964) reported that spaced practice in which interference is present (learning to make different responses to the same stimuli) seriously impedes learning in the initial stages but greatly facilitates retention after eight days. In a study having nearly direct applicability to instruction, Rothkopf and Coke (1966) found that distributed practice was superior to massed practice in promoting reten- tion of prose material. Each of eight sentences were rephrased and repeated once, either in immediate succession or after other intervening material. Retention was facili- tated when repetition of the sentences was delayed. In the seriation training, "practice" was massed for the same material and task,_but distributed between differ- ent materials and tasks. Approximately 30 minutes of training were given to eVery experimental subject on each of three successive days. The materials used in the first and second training sessions were the same, but the tasks were slightly different. During the second and third train- ing sessions the tasks were the same but the materials were different. 69 The 24 hour spacing between the three training sessions was expected to contribute to the retention Of the acquired seriation capability. However,_since only three sessions were used as compared to Underwood's eight,. and since the condition in which spaced practice best facilitates retention (namely, a condition where responses interfere) was not present, the extent to which the spacing of practice in seriation training facilitates retention is expected to be somewhat limited. In addition to the degree of original learning, the pattern of reinforcement, and the distribution of practice, delay of feedback has been found to influence retention. Lintz and Brackbill (1966) found that bigrams learned by a paired—associate method were recalled better after one week when feedback was delayed. Similar effects were found by Sassenrath and Yonge (1968). During the last two sessions of seriation training, feedback was delayed for most of the responses. The train- ing trials required the subjects to insert a number of Objects into a serial ordered set. The feedback for each object was delayed until all Objects used in a trial had been inserted. According to the research on delayed feed- back, the feedback delay used in seriation training would be expected to promote retention. The amount Of original learning, pattern Of 70 reinforcement, distribution of practice, and delay of feed- back have been found to be factors which influence reten— tion. Research relevant to these factors has been reviewed and the findings have been related to the methods used in seriation training. In general, the research suggested that certain characteristics Of the seriation training (degree of original learning, delay of feedback, and, possibly, distribution of practice) should promote the retention of the acquired seriation capabilities. There- fore, it is hypothesized that the experimental subjects will retain the capabilities acquired in the training. Conditions to Enhance the Transfer of Learning Transfer of training may be deScribed as the influ- ence of prior learning or experience ,in one task on performance in another. Depending on the transfer tasks and the characteristics of the original learning, the carry-over effects may be positive (facilitating), negative (inhibiting) or negligible. Gagné (l965,_p. 231) has distinguished between lateral and vertical transfer. Vertical transfer refers to the degree to which learning in one task influences learning in a different task. Lateral transfer refers to the degree to which the learning of a task influences the performance of the same general class of task in a different 71 stimulus setting. In this thesis, lateral transfer of the acquired seriation capabilities was the main concern. MOre specifically, the transfer tasks used in this thesis study were designed for the purpose Of identifying whether or not the subjects could transfer the acquired insertion capabilities to different stimulus objects. Transfer has been studied as a function Of the degree of similarity between the stimuli in two tasks and as a function of the degree of similarity between the responses in the two tasks. Some time ago Osgood (1949) presented a transfer surface which illustrated the direction (posi- tive or negative) and magnitude Of transfer as a function Of the stimulus and response similarities existing between the learning task and the transfer task. In part,_the surface showed that positive transfer increased as stimulus similarity increased, provided that the responses were the same or similar. In several studies (Bugelski and Cadwallader, 1956; Dallett, 1962; and Wimer, 1964) most of the possible relations have been examined. All three studies cited above revealed that for the same or very similar responses, positive transfer increases as the stimulus similarity between the learning and transfer tasks increases. Therefore, if this finding is generalizeable, a consideration of the stimulus similarity between the training and transfer tasks used in this thesis should 72 give an indication of the degree of transfer to be ex- pected, since the reSponses required in both training and transfer tasks were nearly the same. Three seriation posttests were administered. The first two posttests consisted Of two different measures and the third posttest consisted of three different measures. The two measures of the first two posttests and the first two measures of the third posttest were called near and far transfer measures. The third measure Of the third posttest was called a far-far transfer measure. The stimulus materials used in the training tasks consisted Of sticks and lined cards. The sticks were placed side-by-side to form what looked like stairsteps. The lined cards were ordered side-by-side from the card with the fewest black lines to the card with the most black lines. Sticks and lined cards were the materials used in the near transfer tasks of the first two posttests. Only sticks were used in the near transfer tasks Of the third posttest. Since the materials used in the near transfer tasks were the same as those materials used in training, it may be more appropriate to call the near transfer measures retention measures. However, since the number Of Objects used in the training and testing tasks were not the same, the testing tasks will be called near transfer items. 73 The far transfer trials of the first and second posttest were the same. The materials used in these far transfer trials consisted of "cars" and colored blocks. The "cars" (sticks with wooden wheels attached) were ordered end-to-end according to length along a track to form a train. The colored blocks were painted various shades Of blue and were ordered from light blue to dark blue. Only "cars" were used in the far transfer measures of the third posttest. The far-far transfer trials of the third posttest consisted of “happies" and story cards. The "happies" were rectangular pieces of cardboard with smiling faces drawn on them. The faces were used so that the girth or "fatness" Of a "happy" could be distinguished from its height. The girth of the "happies" was the relevant order- ing dimension used in the testing trials. The irrelevant dimension of height was not correlated with width. The storycards were rectangular pictures showing a stickeman, a diving board, and water. When the cards were sequenced properly, they showed the story of the man climb- ing up the diving board and diving into the water. The materials used in training and testing have been briefly described. An examination of the stimulus simi- larities between the training and testing materials will now be made to predict whether or not transfer will be eXpected. 74 Since the "cars" were simply sticks with wooden wheels,_and since length was the relevant ordering attribute for both "cars" and sticks, the stimulus characteristics for the two materials are considered to be similar. There- fore, the training with sticks is expected to transfer to performance with "cars." Because of the stimulus similarity between the lined cards used in training and the colored blocks used in test- ing, more transfer is expected. When the lined cards were ordered according to increasing line density,_the amount of light reflected from each card in sequence gradually decreased. The cards then appeared to be ordered from light to dark; thus, training with lined cards is expected to transfer to performance With colored blocks. The materials used in training were shown to be similar to the materials used in the far transfer trials of the three posttests. The far-far transfer materials Of the third posttest, as the adjective "far-far" implies, were less similar to the training materials than the far transfer materials. For example, there existed little similarity between the stimulus characteristics of the story cards (far-far transfer) and sticks (training). Therefore, stimulus similarity cannot be used as a basis for predicting transfer of training from sticks and lined cards to "happies" and story cards. 75 Stimulus-response similarity is not the only basis for expeCting transfer. In addition to stimulus-response similarity, certain training conditions determine the extent Of transfer. Two such conditions have been found to be the degree of original learning and the variety Of training tasks. Grant and co-workers (Grant and Berg, 1948; Grant and Cost, 1954) reported two investigations in which trans- fer was studied as a function of the degree of original learning. The results of both studies revealed that trans- fer tO new problems increased as the amount of learning 1 on previous problems increased. A series Of studies (Adams, 1954; Callatine and Warren,_l955; and Morrisett and Hovland, 1959) has been performed to determine whether the extent (depth) of learn- ing or the variety (breadth) of learning is the dominating factor affecting the transfer of learning. The results of thOse.studies led to the final conclusion that transfer improves with the number Of different training problems provided that a high degree of learning occurs with each problem. Research concerning the relationship between trans- fer and the nature Of training (variety and extensiveness) has been reviewed. The conclusions from that review will be used in conjunction with an examination Of the seriation 76 training to determine whether or not transfer from that training can be expected. Seriation training was divided into three sessions. Since a different combination of task and material was used during each session, the three sessions may be con- sidered as training on three different problems. The sub- jects receiving seriation training were exposed, on the average, to a minimum of 43 trials for each Of the three different problems.' Morrisett and Hovland (1959) exposed their subjects to 64 trials on each Of three different problems and found maximum transfer. Although the number of trials per seriation problem was somewhat less than the number used by Morrisett and Hovland, the level of learning was maintained by requiring the subjects.to meet criterion performance levels on the average of 11 times per seriation problem. The seriation training conditions were similar to those conditions which Morrisett and Hovland found to promote transfer. Furthermore, high levels of learning were maintained on a variety Of seriation training prob- lems. Thus, in accordance with the conclusions Of the transfer studies, the variety and extensiveness of the seriation training is expected to promote transfer of training. Stimulus similarity has already been proposed as a 77 basis for expecting the experimental subjects to transfer their acquired capabilities to the tasks of the far trans- fer measures. In addition, the extensiveness and variety of seriation training are expected to further increase‘ transfer to those tasks. Stimulus similarity does.not serve as an adequate basis for predicting transfer to the "happies" and story— cards used in the far-far transfer measures Of the third posttest. The basis for predicting such a transfer lies, instead, in the extensiveness and variety of the seriation training. In summary, the capabilities acquired during seria- tion training are eXpected to transfer to the far and far- far transfer measures. The basis for the expected transfer was found in the variety and extensiveneSs of the seriation training and in the stimulus and response similarities existing between the training tasks and the far and far—far transfer tasks. ' Research-Hypothesis Since not all levels of the reSearch design were completely crossed with all other levels, the analysis of the data was necessarily performed in two parts. One part, the Experimental versus Control Group Analysis, was an analysis Of the experimental and control groups' means from 78 the near and far transfer measures of the three posttests. The other part, the Experimental versus Control versus Special Control Group Analysis, was an analysis Of the experimental, control, and special control groups means from the near,_far,_and far-far transfer measures Of the third posttest. In the following sections the research hypotheSes for each Of the two parts will be constructed from the bases established in the review of literature. Hypotheses for the Experimental versus COntrOl Group Analysis As a result of the training, the experimental subjects will acquire the insertion capability. Furthermore, since the experimental subjects received what is expected to be successful training, and the control subjects reCeived no training at all, the experimental group should outperform the control group at least on some Of the posttest measures. The expected result stated as a research hypothesis is: H1: There will be a Treatment main effect with the direction Of the effect favoring the experimental group. When sticks were used in ordering tasks, the cor- :rect arrangement Of sticks usually looks like stairsteps. flflie stairsteps configuration can be used by the subject 79 to monitor his performance. When the configuration looks like stairsteps, performance is correct, but when the configuration does not look like stairsteps errors have been made and need correcting. Sticks were used in the near transfer tasks. Con- sequently, the configuration was available and could be used to monitor performance. oNone'of the far transfer tasks offered any configural aid. Therefore, the near transfer tasks are expected to be leSs difficult than the far transfer tasks. Since the control subjects had already shown some ability to seriate with sticks on the seriation pretest and since configural aids were present in near transfer tasks and not in far transfer tasks, the control subjects are expeCted to show better performance with the near transfer tasks than with the far transfer tasks. Likewise, the experimental subjects should shOw better performance on the near than on the far transfer tasks since the experimental subjects were trained with the near transfer materials but not with the far transfer materials. With both experimental and control subjects expected to show better performances on the near than on the far transfer tasks, the following hypothesis regarding test type effects (near versus far transfer) can be made: 80 H2: There will be a Test Type main effect with that effeCt favoring the near transfer test type. The materials and tasks used in the training were nearly the same as those used in the near transfer measures. Therefore, the experimental group's performances Of the near transfer measures shOuld provide information concern— ing the degree to which the induced capabilities were retained. Since the experimental subjects are expected to retain those capabilities acquired in training, and since the control subjects received no training at all, the research hypothesis associated with the comparison of the experimental and control groups' near transfer per- formances becomes: The experimental group's mean 0) u for the near transfer measureS' will be greater than the control .group's mean for the near trans- fer measures. The far transfer teSts basically provided measures (of transfer since the materials used in thOse teSts were 'unlike the materials used in the training. According to 'the literaturereview,_the experimental subjects are (expected to transfer the capabilities acquired in training. 81 This expected result should be confirmed by the experi- mental group'sacquisition of an overall far transfer mean that is greater than the controlgroup's overall far trans- fer mean. Stated in the form of a research hypothesis, the expected result regarding transfer effects becomes: H4: The experimental group's overall far transfer mean will be greater than the control group's overall far transfer mean. Hypotheses for the Experimental versus Control versus Special Control Group Analysis, For this second part Of the overall analysis, three groups (experimental, control,_and special control) will be compared on three different measures (near,_far, and far-far transfer measures) of the third posttest. The experimental and control groups were the same as those used in the first part Of the analysis. The subjects Of both‘ the eXperimental and control groups were in stage II at the beginning of the study, whereas the subjects Of the special control group were in stage III. The purpose of the training was to induce stage III capabilities in the experimental group. In other words, the training was designed to provide the experimental group with those capabilities already possessed by the 82 special control group. In accordance with the review Of literature, the experimental group is expected to acquire, retain, and transfer those stage III capabilities possessed by the special control group. Therefore, the experimental and special control groups should perform equally well on the posttest measures. Since the control group entered the.study with stage III capabilities and was given no training, the special control group with its stage III capabilities should perform better than the control group on the posttest measures. Put in the form Of research hypotheses the propositions contrived above become: There will be no difference between the experimental and special control group means for each of the following transfer measures of the third post- test: H5: near transfer H6: far transfer H7: far-far transfer The special control group's mean will be greater than the control group's mean for each of the following measures of the third posttest: 83 H8: near transfer H9: far transfer H10. far-far transfer The research hypotheses Of major interest have been presented. These hypotheses, in general predicted that the experimental group will outperform the control group on the posttest measures, that the near transfer measures will be easier for all subjects than the far transfer measures,_and that the special control group's performance being no different from the experimental group's performance’ will be superior to the performance shown by the control ~group. CHAPTER III THE RESEARCH PROCEDURE Pretest Materials and Tasks Orange painted sticks were the Objects used in the seriation pretest. The sticks were three-quarters inch thick,_three-quarters inch wide, and varied in length from one and one-half to nine inches. Two kinds of tasks were presented. One task required the child to serial order a set of disarranged Sticks from the shortest to the talleSt to make stair- steps. The other task required correct insertion Of a set of three disarranged sticks into a serial ordered set Of sticks. There were three ordering tasks and each was followed by a corresponding insertion task. This order of task presentation was chosen so that the ordered set <3btained from an ordering task could be used in the inser- ‘tion task which followed. The number of Objects in the <3rdering tasks was gradually increased as the test con- tinued, but the number of sticks to be inserted was always three. The pretest tasks were presented as follows: 4 sticks were ordered and 3 were inserted, 6 were ordered and 3 inserted, and 8 were ordered and 3 inserted. Appendix 84 85 A provides a detailed description Of the materials used in each pretest task. TO help each child understand what was to be expected Of him on the test, the experimenter provided examples of how to perform the ordering and inserting tasks. The experimenter's monologue used during the illus- tration and the verbal instructions given to the subject during the testing are found in Appendix B. The subjects were assigned to stages according to the following criteria. TO be considered in stage III, the subject had to correctly perform all three of the ordering tasks and at least two Of the insertion tasks. For the stage II subjects two or three ordering tasks had to be performed correctly and two or three insertion tasks had to be performed incorrectly. All subjects not fitting stage II or stage III criterion were considered to be in stage I. The Sample The subjects for this study were selected from the 'three kindergarten classrooms of Scott Elementary School,‘ IDewitt, Michigan. TO identify stage II children for inclusion in this study, the seriation pretest was individ- 'ually administered to each available kindergarten child. (3f the 95 children pretested, 32 were found to be in 86 stage II as defined by the pretest. The mean age of these stage II children at the time Of pretesting was approxi— mately 5.44 years. Training and Posttest Materials and Tasks The following six different kinds of materials were used in the study: sticks of various lengths were ordered side-by-side according to length, cards with various num- bers of parallel black lines were ordered according to line density, wooden "cars" Of various lengths were ordered end-to-end according to.length, blocks painted various shades of blue were ordered according to the shade of blue, rectangular pieces Of poster board (happies) which varied in width and height were ordered according to width,, and story cards which showed frames of a stickman diving into water were ordered according to the sequence Of events. Below is a more detailed description of the specific 'tasks and materials used in the different portions of the study. Pretest materials and tasks have already been pompoooot tom Homogeneous mafisosm xfiuumz .nomm MOM mHm>mH O>Huomommu .m .mam AcOflpmamuuoov mmmoom pamwcma u NA Amocoooomv mmuoom panacea n Hg mmHOOm ucmmsfluam u m Hommsmnp HMNIHMM u 9mm summons» How u an Hmmmomup How: u 82 mosOHmQSm Houusoo n U mononmoom HmucmEflHmmxm u m "panama Honucoo mama Oz amaommm 0 HH macho m U H moouw m mg as No as m mg Ho mu HA m mu an m mu an w mg an ass (em. 92 .em 92 em Hz m.ummuumomp ~.ummuumom H ammuumom 121 univariate analysis would have been necessary for each different dependent variable. With the multivariate model, on the other hand, the dependent variables can be considered simultaneously and a single probability state- ment can be applied to all dependent measures taken together. In addition to being more suitable for analyz- ing multiple dimensional designs, the multivariate model,_ unlike the univariate model, avoids the precarious assump- tion that the Off diagonal elements of variance-covariance matrix are equal.1 The computer program used in the data analysis was a modified version Of the program developed by Jeremy D. Finn (1968). Neither this program nor the model which' it serves could be used to analyze the entire set Of data as illustrated in the data matrix of Figure 5. Figure 5 shows that the far-far transfer measure and the control group factor were not completely crossed with the other levels of the design. The far-far transfer measure was administered only during the third posttest, and the special group was teSted only during the third posttest. As a consequence of the incompleteness of the 1Information concerning the appropriateness of multivariate analysis for the design Of this study was acquired through personal communication with Dr. William Schmidt, Educational PsychOlogy, Michigan State Univer- sity,_l970. 122 design, the data was initially analyzed in two parts. One part, the Experimental versus Control Group Analysis, consisted of a repeated measures, multivariate analysis of variance Of the following factors and their respective levels: Groups (groups I and II), Treatment (experimental and control), Posttest(posttests l, 2,_and 3),_Test Type (near and far transfer), and Scoring Methods (S, L1, L2). The other part, the Experimental versus Control versus Special Control Group Analysis, was a multivariate analysis of the performance Of all subjects, including subjects of the special control group, on all measures Of posttest 3, including the far-far transfer measure. Preliminary analyses considerably simplified the analyses reported in Chapter IV. To determine whether or not the three different methods Of scoring (S, L1, and L2) were providing unique bits of information a regression analysis was performed. The results Of that analysis revealed that knowledge Of one score allows near perfect prediction of the.other two (x2 = 454.55,_df = 98, p < .00001). Since the stringent method Of scoring was the method used in other seriation studies and since the stringent score (percent of tasks performed without error) was considerably more meaningful than the two lenient scores,_stringent (S) scores were used in the final analysis. 123 Two further simplifications were made as a result of preliminary analysis. First, another regreSSion analysis revealed that the four covariates (age,_field independence. reflectivity, and impulse control) were not significantly associated with the dependent variables (chi square for the test of the hypothesis of no associa- tion between dependent variables and covariables = 30.4855, df = 28,_p < 0.3404). Therefore, in the final analysis the covariates were eliminated. Second, the Experimental versus Control Group Analysis, was carried out with the two groups (groups I and II) separated. No main effect,. nor any interaction effects associated with.the Group variable were found. As a consequence, the Group variable, being Of no particular interest, was eliminated in the final analysis, and the results were reported in terms of only Experimental versus Control. Since the Groups factor and two of the three differ- ent scoring methods could be eliminated, the matrices for the two parts of the analysis reported in Chapter IV became as shown in Figures 6 and 7. The data from the matrix in Figure 6 was analyzed with a repeated measures, multivariate analysis Of variance. The data from the matrix in Figure 7 was analyzed with a multivariate' analysis of variance. The reSults Of both analysis are described in the next chapter. 124 Posttest.l. Posttest,2, Posttest 3 NT FT TNT FT NT FT Experimental (N=15) (pooled from groups I and II) Control (N=l7) (pooled from groups I and II) Fig. 6. Matrix for the Experimental versus Control Group Analysis. The stringent scores (S) were the numbers in the cells. Note, there was an attrition Of two experimental subjects because of illness. Posttest 3 NT FT FFT Experimental (N = .15) Control (N = 17) Special Control (N. = 13) Fig. 7. Matrix for the Experimental versus Control versus Special Control Group Analysis. Only stringent scores (S) were used. FFT refers to the far-far transfer measure. CHAPTER IV ANALYSIS OF DATA Because not all levels Of the design were completely crossed with all other levels and because the special con- trol group was administered only the third and final post- test, the analysis of the data, was necessarily performed in two parts. The matrices corresponding to those two parts have already been shown in Chapter III (Figures 6 and 7). In this chapter, the analysis Of the data within each of those matrices will be described and discussed. See Appendix L for the compilation of all the data used in this study. Experimental versus Control Group Analysis The data considered in this part of the analysis consisted Of the experimental and control subjeCts' near and far transfer scores from each of the three posttests. Each score was the per cent of seriation tasks performed without error. The group means (mean per cents correct) and standard deviations calculated from the near and far transfer scores appear in Tables 1 (near transfer and 2 (far transfer). 125 126 Table 1 Near Transfer Means and Standard Deviations (Percentages) Experimenta1~ 'Control ' Overall Mean SD Mean SD Mean SD Posttest 1 83.9% 18.7% 38.7% 24.4% 59.9% 31.9% Posttest 2 Posttest 3 80.0 22.6 52.4 21.4 65.3 26.4 76.7 40.3 52.9 43.6 64.1 44.4 Overall 80.2 28.9 '48.0 32.1 Table 2 Far Transfer Means and Standard Deviations (Percentages) Experimental Control' Overall Mean SD Mean SD Mean SD Posttest l Posttest 2 Posttest 3 Overall 41.7% 19.7% 35.3% 22.8% 38.3% 21.9% 68.3 33.5 39.7 24.3 53.1 32.8 46.7 42.7 41.2 30.8 43.8 37.6 52.2 35.3 38.7 26.3 127 The means from Tables 1 and 2 are shown in Figure 8 in the form of two graphs, one (A) showing a comparison of the experimental and control groups' near transfer means from the three posttests and the other (B) showing a similar comparison with the far transfer means. The graph of near transfer means reveals that the experimental group's near transfer capabilities remained relatively unchanged across the posttests and were, at the same time, seemingly superior to the control group's corresponding capabilities. The graph of far transfer means, on the other hand, does not allow a set of conclusions which are parallel to those derived from the near transfer graph. Contrary to what might be initially expected, the experi- mental group's superior far transfer capability was seem- ingly shOwn on the second posttest rather than on the first. In any respect, there clearly was no massive,. substantial far transfer superiority revealed by the experimental group. Since there were repeated measures (posttests l, 2, and 3) on multiple variables (near and far transfer measures), a repeated measures, multivariate analysis of variance (Bock, 1963) was used to statistically analyze the data described above. For this particular kind Of analysis the scores were assumed to be distributed in a multivariate normal form. See Appendix M for a thorough 128 Fig. 8. Graphs of the experimental and control groups' near and far transfer means. TO give at least some indication of the time span between posttests, the dis- tances from the absissa to the posttest numbers were scaled according to the function N'=.5JN} where N' was the number scaled and N was the number of days between the end of training and the particular posttest. Posttests were given approximately 1, 8, and 132 days after training. Note, the depen- dent measure used tO calculate the means was the per cent of seriation tasks performed without error. MEAN PERCENT CORRECT MEAN PERCENT CORRECT I00 80 60’ 4o- 20 IOO (D C) O) (D .b C) no (3 129 NEAR TRANSFER MEANS EXPERIMENTAL °——-' ”CONTROL.- ----- - -.\“3— ’ W'llllllll I A III I b [I.- ————————————————————— -. 0”, L l 1 I l 2 3 POSTTESTS FAR TRANSFER MEANS ' « I I I l_l..'.B_l_|_i-i._|._l_|__l_l_iJ_'_J4.1.1 ,___.. . ,4 1 I I 2 3 POSTTESTS 130 display of information (sample correlation matrices, variances,_hypothesis mean products) relevant to the multivariate analysis reported here. The repeated measures, multivariate analysis tested null hypotheses for the following sources Of variation: 1) Treatment main effect,, 2) Posttest main effect, 3) TeSt Type main effect, 4) Treatment x Posttest interac- tion,_ 5) Treatment x Test Type interaction,. 6) Posttest x Test Type interaction, and 7) Treatment x Posttest x Test Type interaction. Of those sources Of variation, the Treatment main effect and the Test Type main effect were of prime interest since they were the sources associ- ated with the following two research hypotheses developed in Chapter II: H1: There will be a Treatment main effect with the direction of the effect favoring the experimental group. H2: There will be a Test Type main effect with the direction Of the effect favoring the near transfer teSt type. Rather than begin the discussion Of results with the simple main effects, the complex Treatment x Posttest 131 x Test Type interaction will be treated first. The reason for considering this interaction first stems from the need to discuss all the other significant results in light of this significant three—way interaction. For each test to be described in this analysis, the probability Of falsely rejecting a true null hypothesis will be 0.05 (i.e., a = 0.05). Because of the particular nature of the analysis, there existed no single test for the Treatment x Posttest x Test Type interaction. Instead, the test was performed in two parts. If significance was found in the test of either part, then a significant Treatment x Posttest x Test Type interaction was considered preSent.2 Table 3 shows the multivariate F ratio for part 1 Of the three-way interaction to be significant (p<0.0235). Hence, the null hypotheSis associated with the Treatment x Posttest x Test Type interaction was rejected. Since the three-way interaction is not easy to interpret in any simple numeric way, the graphs shown in Figure 8 will be used to facilitate an interpretation. Whereas a two-way interaction is determined by the degree to which the shapes of tWO'lings-correspond,_a three-way interaction is determined by the degree to which the shapes of two surfaces correspond. The two surfaces 2Dr. William Schmidt, Educational Psychology, Michigan State University, personal communication, February, 1971. 132 Table 3' Multivariate Test for the Treatment x Posttest x Test Type Interaction ’MfiItiVariate Source' df F Ratio p less than Treatment x Post- test x Test Type - part 1 1,30 5.7668 0.0235 Treatment x Post- test x Test Type - part 2 1,30 3.2314 0.0839 referred to in consideration of the Treatment x Posttest x Test Type interaction are surfaces A and B in Figure 8. Since the surfaces, A and B, are not geometrically simi- lar,_a three—way interaction is implied. The bottom sides Of the two surfaces (i.e., the performances of the control group) seem to be "parallel." Hence, the difference in the shapes Of the top sides (i.e., the performances of the experimentalgroup) appears to hold within it the locus Of the three-way interaction. Since the ability to perform a task Often tends to gradu- ally decline in time from the end of instruction, the Slight gradual decrease in the experimental group's per- formance of the near transfer tests (top line, surface A, 133 Figure 8) was not unexpected. In a reasonable manner,. the experimental group's performance of the far transfer tests (top line, surface B, Figure 8) might be expected to follow a similar decline, thus showing a decrease from maximum transfer on the first posttest to minimum trans- fer on the third posttest. However,_contrary to expecta- tion, maximum transfer was found on the second posttest rather than on the first. A t test (Winer, 1962, pp. 36- 38) revealed that the experimental group outperformed the control group on the second far transfer measure (t=2.736, df=25, p<0.01). Although there is no simple analytic way to unequivocally identify the locus Of the three-way interaction, it would appear that the locus stems from the eXperimental group's.unexpected low performance on the first far transfer test (posttest l) coupled with its relatively high performance on the second far transfer test (posttest 2). There was a significant Treatment main effect (Multivariate F= 8.1623, df= l/3,.p<0.0077). Since the graphs in Figure 8 indicate the performance superiority Of the experimental group and since the experimental _group's overall mean per cent correct (66.2%) was greater than the control group's overall mean per cent correct (43.4%), the significant Treatment main effect favored the experimental group. Consequently, the null hypothesis 134 associated with the Treatment main effect must be rejected in favor of the research hypothesis, H1, which predicted a Treatment main effeCt showing higher performance for the experimental group. Differences between the experimental and control groups with respect to seriation ability undoubtedly con- tributed to the Treatment main effeCt. However, since a three-way interaction (Treatment x Posttest x Test Type) was Observed, the difference in.seriation ability was not the only factor which was involved in producing the Treatment main effect; the Posttest and Test Type factors must have been involved as well. Seemingly, the locus of interaction which contributed to the Treatment main effect was the experimental group's secOnd fair transfer mean. That mean was by far numerically greater than any other far transfer mean and set a pattern among the far transfer means which was uneXpected and inconsistent with the pat- tern Of near transfer means. Apparently, then, the experimental group's capabilities (Treatment factor) at the time Of the second posttest (Posttest factor) inter- acted with the materials and tasks of the far transfer test (Test Type factor) to produce an elevated mean which contributed to the eXperimental group's superior overall performance as indicated ”by the Treatment “main effect. The repeated measures, multivariate analysis 135 revealed a significant Test Type main effect (Multivari- ate F = 16.1776, df = 1/30, p <0.0004). Since for both groups (experimental and control) the near transfer score was numerically greater than the far transfer score on each posttest and since the overall mean for the near transfer measures (63.1%) was numerically greater than the overall mean for the far transfer measures (45.1%),_the direction of the Observed Test Type main effect favored the near transfer test type. Thus, support was found for the research hypothesis H2, which predicted a Test Type main effect favoring the near transfer test type. Since there existed a three—way interaction, the data must be examined to determine Whether or not that interaction contributed to the observed TeSt Type main effect. The experimental group's elevated second far transfer mean has been suggested as the locus of the three- ‘way interaction. Since this elevated mean would contribute to a smaller rather than to a larger, difference between Test Type means, the three-way interaction likely played no part in producing the Test Type main effect. Tests of those hypothesis which were of prime interest and which were the most soundly based have been (described. The multivariate analysis tested the null hypotheses associated with four other sources of variation. Because these four remaining hypothesis tests are somewhat 136 peripheral to the central focus Of this study, the results Of those tests will be described and discussed in brief form. The multivariate test for a Posttest main effect was necessarily performed in two parts. The first part compared the mean associated with postteSts 1 (49.1%) and 2 (59.2%) and revealed that the mean per cent correct on posttest 2 was significantly greater than the mean per cent correct on posttest l (Multivariate F=4.4951,.df=1/30, p-<0.0424). The second part of the Posttest main effect test compared means for posttests 2 (59.2%) and 3 (53.9%) and revealed that the mean per cent correct on posttest 2 was significantly greater than the mean per cent on post- test 3 (Multivariate F=14.0421, df=l/30, p< 0.0008). The Observed superiority Of the overall mean associated with posttest 2 most likely was enhanced by the experi— mental group's elevated second far transfer mean, which has been suggested as the locus Of the significant three- way interaction. The Posttest x Test Type interaction was tested in two parts and neither test revealed significance (Multi— variate F=0.3834, df=l/30, pf<0.5410; and Multivariate F=0.0964,_df=l/30, p <0.7588). Failure to index a signifi- cant PostteSt x Test Type interaction implied that the difference between near and far transfer means (calculated 137 across treatment groups) did not change significantly across the three posttests. The multivariate test Of the null hypothesis associated with the Treatment x Posttest interaction was performed in two parts. "Since the analysis revealed no significance for either part (Multivariate F=0.3963, df= 1/30, p Control). Therefore,, since the experimental group's overall near transfer mean was greater than the control group's overall near transfer mean, support was found for the research hypothesis H3. There was neither a PostteSt main effect nor a Treatment x Posttest interaction. The failure to index a Treatment x Posttest interaction was interpreted to mean that the experimentalgroup's performance‘ superiority on near transfer tasks remained relatively unchanged across posttests. Repeated measures -— far transfer data. NO Treatment main effect was Observed for the far transfer data. Consequently, no support was found for the research hypothesis H4. The absence of a Treatment main effect was interpreted to mean that the procedures used to train the experimental subjects lacked the necessary as- pects to insure transfer of training to unfamil- iar materials. The repeated measures analysis Of far transfer data further revealed a Posttest 154 main effect but no Treatment x Posttest interaction. For the Experimental versus Control versus Special Control Group Analysis, a multivariate analysis Of variance was used to compare the performances of the experimental, control,_and special control groups on the near, far, and far-far transfer measures Of posttest 3. From that analysis the following observations were made: 1) Since for each measure of posttest 3 there was no difference between the performances of the experimental and special control groups,sup- port was found for research hypotheSes H (H 5! and H7. Thus, approximately 132 days after 6 training, the experimental group subjects, who began the study with.seriation stage II capabilities, performed seriation tasks just as well as the special control group subjects,. who began the study with seriation stage III capabilities. 2) A comparison of the special control and control Vgroups' performances Of posttest 3 measures showed that the special control group outper- formed the control group on the near and far- far transfer measures of postteSt 3 but not on 155 the far transfer measures Of posttest 3. Thus, support was found for research hypothe— ses H8 and H10 but not for research hypothesis H9. A cursory survey of some correlational data revealed that, for the experimental group, age was negatively cor— related with both seriation performance and with the other individual difference factors. These negative correlations gave rise to the idea that the experimental group contained Older subjects which were less bright (with respect to the measures taken) than the younger subjects. TO summarize,_the experimental subjects, for the most part, acquired and retained the specific target capabilities of the training. They, however, did not acquire the ability tO.transfer those acquired capabilities to seriation tasks requiring the use of unfamiliar materials. CHAPTER V DISCUSSION AND SUMMARY This chapter includes: 1) a brief summary Of the _study, 2) a discussion of the transfer data and the two hypotheses generated to explain that data,, 3) a discussion of the relationship between the results Of this seriation study and the results of other Piagetian training studies (conservation and seriation), and 4) a concluding state— ment. Implications for future research are described as they arise out of the discussions. Fifteen kindergarten children, who began the study with stage II seriation capabilities (i.e., could serial order sticks but could not insert a number Of sticks into an already ordered set), were individually given 30 minutes of seriation training on three conseCutive days. Cue' fading and reinforcement were used in the training to help the children meet the successive.performance criteria leading to the acquisition Of stage III capabilities (i.e., both order Objects and insert Objects into an already ordered set). Posttests, each consisting of a retention and transfer measure, were given approximately one, eight, and 132 days after training. In general, the results revealed that the subjects acquired and retained the 156 157 specific target capabilities of the training, but failed to substantially transfer those acquired capabilities to the performance Of seriation tasks involving unfamiliar materials. Although the analysis of far transfer data did not reveal the expected substantial transfer effects, there are some interesting transfer data which should be discussed. Since the ability to perform a task Often tends to gradually decline in time from the end Of instruc- tion, the slight gradual decrease in the experimental group's performance Of near transfer tests was not unex- pected. In a similar manner, the experimental group's performance Ofthe far transfer tests might be expected to follow a similar decline, thus showing a decrease from maximum transfer on the first postteSt to minimum transfer on the third posttest. However, contrary to expectation the experimental group showed a relatively low performance (mean = 41.7%) on the first far transfer test and a relatively high performance (mean = 68.3%) on the second far transfer test. The low third far transfer mean (46.7%) for the experimental group, although not desired, was probably not an unreasonable outcOme. Why didthe experimental group's unexpected first and second far transfer performances occur? Before considering some experimentally based reasons for the 158 unexpected transfer performances, possible extra-experi- mental influences will be discussed. As previously mentioned, in carrying out the experiment there Were two groups, groups I and II, each with an experimental and control subgroup. The experimental subjects of group I acquired far transfer mean percentages Of 35.7% and 60.7% for the first and second posttests, respectively. The experimental subjects of group II acquired the correspond- ing far transfer mean percentages of 46.9% and 75.0%. Hence, bothgroups of experimental subjects showed low performance on the first far transfer test and high per- formance on the second far transfer test. Since these teSts were administered to the two experimental_groups at different times, the unexpected far transfer means were not likely to have been associated with any specific facilitative or inhibitive extra-experimental events which might have occurred on the days of testing. Further- more, if extra-experimental events were the basis for the unexpected far transfer means, those events would likely be reflected in the corresponding near transfer means. However, since, for each group,_the near and far transfer means followed different patterns, extra-experimental events were probably not the cause for the unexpected nature Of the experimental groups' far transfer effects. Eleven Of the 15 experimental subjects performed 159 better on the second far transfer test than they did on the first. The performances Of the remaining four sub- jects were the same on both tests. Thus, the experimental group's unexpected performance on the first two far trans- fer tests does not appear to be attributable to the spurious performances Of a few individuals. Since the data does not seem to support extra- experimental events and spurious performances as causitive factors underlying the experimental group's unexpected far transfer means, there is more reason to believe that the nature of those means might be explained in terms Of task related, experimental phenomena. For example, it could be speculated that the experimental subjects' low performances on the first far transfer test reflected, in part, a spread of attention to the "novel" irrelevant stimuli rather than a focusing Of attention on the rele- vant stimuli. With the "novelty" of the far transfer materials having worn Off from the first posttest, the experimental subjects could have then attended more to the task relevant stimuli and used the capabilities acquired in training to foster the production Of the ele- vated second far transfer mean. This "novelty" hypothesis is not totally unfounded since Gelman (1969) has provided evidence indicating that children sometimes attend to task irrelevant stimuli and 160 as a consequence perform the tasks poorly even though they are capable Of performing the tasks. The "novelty" hypothesis, however, should still be considered with caution since inherent within it is the precarious assumption that the experimental group actually possessed the ability to perform the far transfer tasks of posttest 1. Why would the "novelty" effect foster the production of such a sizable difference between the experimental group's near (83.9%) and far (41.7%) transfer means Of posttest l and fail to foster such a difference for the control group (near=38.7%, far=35.3%)? It could be argued that "novelty" played no part in producing the control group's difference since the control subjects, for the most part, had been exposed to neither set of materials and consequently had no opportunity for developing differ- ential perceptions of novelty with respect to those materials. The experimental group, on the other hand, had been exposed to the near transfer materials during training but had not been exposed to the far transfer materials. Therefore, by comparison to the near transfer materials the far transfer materials most likely seemed "novel" to the experimental subjects, thus distracting them from the tasks they were capable of performing. Since the same tasks and materials were used on the first and second far transfer teSts, teSt-retest learning, 161 in addition to the attentional factors, could have con- tributed to the experimental group's relatively high second far transfer mean. From their experience with the first set Of far transfer tasks, the experimental subjects, aided by the capabilities acquired in training, could have learned: 1) to more clearly distinguish the relevant from the irrelevant stimuli, 2) to compare the Objects so that meaningful decisions about the order Of Objects could be made, 3) to identify and correct errors, and, in general,. 4) to apply the newly acquired seriation capabilities to the unfamiliar set Of far transfer materials. If indeed this learning did occur, it could very well be the basis for the improved performance of the second far transfer test. It should be stressed that the test-retest learning effect was probably not as pronounced for the control subjects since they lacked the underlying seriation capabilities acquired by the experimental subjects in training and therefore could not learn as well from the testing experiences. unlike the "novelty" hypothesis, the test-retest hypothesis does not rest upon the assumption that the experimental subjects possessed transfer capabili- ties at the time Of the first posttest. The "novelty" and the test-retest hypotheses have both implied that the transfer effects were genuine. TO 162 the contrary, it might be suggested that even the Observed treatment group difference on the second far transfer test was artificial and, hence,_indicated no genuine under- lying transfer capability. At this time, however, no substantial reasons can be contrived for explaining why the effect occurred withOut at least some transfer capabil- ity being present. Both the “novelty" and the test-retest hypotheses suggest interesting ideas concerning transfer. The experi- mental group did outperform the control group On the second far transfer test. The "novelty" hypothesis sug- _gests that the experimental group had the transfer capability on the first far transfer teSt but failed to reveal the capability. Hence, the suggestion of the "novelty" hypothesis and the observation of the second far transfer performances together imply that the experi- mental subjects did possess the ability to transfer at least up to the time Of the second posttest. If indeed the experimental subjects did possess the transfer capabilities up to the time of the second posttest but not up to the time of the third posttest, then the results of the seriation study would suggest that the training successfully induced the transfer capabilities but did not insure the long-term retention of thOse capabilities. From the suggestions initiated by the "novelty" hypotheSis, it 163 would seem that future research might very well be directed toward improving the seriation training techniques in such a way that children learn to cope with "novel" stimuli and at the same time retain the transfer capabilities for longer periods Of time. According to the test-retest hypothesis, the experi- mental subjects, although unable to perform the far transfer tasks of posttest l, learned (as a consequence of the training) from their experience with posttest 1 tasks and thus produced an elevated far transfer performance on post— test 2. Since transfer, in part, refers to the ability to use acquired capabilities to learn from new experiences, the test-retest hypothesis suggests that transfer was taking place during the performance of the first posttest. It is important to note that the test-retest hypothesis not only suggests that the acquisition of far transfer capabilities took place but also that the experimental subjects retained the acquired transfer capabilities over the seven day interval between posttests l and 2. If,» indeed,_the test-retest hypothesis has a reasonable founda- tion, then the results of this seriation study might suggest that once a specific seriation capability has been induced through somewhat intense training, the difficulty Of learning to perform seriation tasks with different materials will likely be reduced considerably. Should 164 the test—retest hypothesis find support in the future,, this suggestion arising from the seriation study might lead to a worthwhile training strategy. That training strategy would probably consist of two phases. In the first (or induction) phase, specific seriation capabili- ties would be induced through the use Of a carefully designed, somewhat intense,_short-term training sequence, much like the sequence used in this study. In the second (or generalization) phase, Opportunity for using the induced capabilities with many different kinds of materials would be periodically given. It should be made clear that the "novelty" and the test-retest hypotheses and the implications drawn from them are speculations. To test the hypotheses and bring the implications out Of speculation this seriation experiment might reasonably be replicated with the inclu- sion of two additional groups Of trained subjects. All three groups would receive the same seriation training and all three groups would be given the same far transfer test eight days after training. The groups would differ in the following ways (See Figure 9): 1) Group 1 would receive a far transfer test one day after training. This test would be identical to the one given eight days after training,, 2) One day after training, group 2 would perform tasks with the materials used in the far transfer test. 165 The tasks, however, would not be seriation tasks,‘ 3) Group 3 would be given only the far transfer test eight days after training. TRAINED GROUPS INTERIM TRAINING FAR TRANSFER TEST(’0) (All groups receive‘ (Given one day (Given 8 days after the same training) after training) training) Trained Group 1 0 (far transfer 0 test) Trained Group 2 Nonseriation tasks 0 performed with far transfer materials Trained Group 3 NO treatment '0 Fig. S). An illustration Of the basic experimental design for testing the "novelty" and test-retest learn- ing hypotheses. The groups' performances of the far transfer test given eight days after training should yield information concerning the "novelty“ and the test-retest learning hypotheses. For example, if group 1 does better than group 2, there is evidence for the test-retest.1earning hypothe- sis since a differential novelty effect is eliminated by having both groups interact with the materials. If groups 1 and 2 do better than group 3 and groups 1 and 2 perform no differently, thereis evidence for the "novelty" hypothesis since involvement with materials (bOth groups 1 166 and 2) facilitated subsequent performance but prior per- formance Of the actual tasks (group 1) produced no advantage indicative of learning. Of course, if groups 1 and 2 perform no differently than group 3, neither Of the two hypotheses is supported. Both the "novelty" hypothesis and the test-retest hypothesis suggest that transfer did occur. Neither hypothesis suggests, however, that transfer effects were substantial. According to the "novelty" hypothesis, the transfer capability was present at the time Of the first posttest but apparently was not strong enough to overcome the distraction of the "novel" task irreleVant stimuli. According to the test-retest hypothesis, at the time Of the first posttest there was only the ability to learn from the transfer tasks, no ability to perform them. Therefore, regardless of which hypothesis finds support (possibly neither will),_the results of this seriation study imply that future research needs to be directed toward finding ways of improving the acquisition and reten- tion of seriation stage III transfer capabilities. One possible approach to improvement is the previously described two phase strategy in which an intense training session (induction phase) with only a few kinds of mater- ials is followed by a number of occasional, leSS'intense,, training sessions (generalization phase) in which many 167 different materials are used. Another approach, of course, would be to include many different kinds Of materials and tasks in the intensive training session and possibly minimize or eliminate the occasional, less intense follow- up sessions. Research might very well be direCted toward investigating the relative effectiveness Of these two approaches for improving transfer. In reviewing the conservation training studies the criterion for success was statistical significance in which the trained group showed performance superiority over the untrained or control group. If that same criterion is used with the seriation training study reported here, then the seriation training would be judged a success. The question then becomes: How do the results of the thesis compare with the reSults of the successful conserva— tion studies (length and number)? All of the successful conservation studies reviewed in Chapter II included retention and transfer measures. Retention of the specific induced capabilities was found in all of those studies. The maximum retention interval used in the conservation studies ranged from approximately three weeks (Gelman, 1969; Wallach and Sprott, 1964; and Wallach, Wall, and Anderson, 1967) to 16 weeks (Kingsley and Hall, 1967). The maximum retention interval used in this seriation study was approximately 19 weeks. Since 168 retention of induced capabilities was found in the seria- tion study, the conservation studies and the seriation study seemingly correspond with respect to retention. All but one Of the successful conservation studies (Wallach, Wall, and Anderson, 1967) revealed transfer of training. In the seriation study, howeVer, there was only a hint Of transfer on the second posttest and absolutely no transfer on the first and third posttests. Thus,_with respect to transfer, conservation training was superior to the seriation training. The difference between the success Of the seriation training and the success Of the conservation training should be put in proper perspective. The success of the conservation studies undoubtedly rests, in part, upon the groundwork laid down by the many unsuccessful attempts to induce sustained conservation capabilities. The seriation study,_on the other hand, withOut the aid of previous seriation training research, laid down some groundwork for future seriation training and at the same time was, in part,.successfu1. Coxford's (1964) study,_which was the only seriation training study reported in the literature review, revealed that it was possible to induce conservation of serial and ordinal correspondence in children who, before training,_ could construct serial correspondence. Similarly, the 169 results of this thesis revealed that it was possible to induce specific seriation stage III capabilities (order and insert) in children who, before training, exhibited seriation stage II-capabilities (order but not insert). The two seriation training studies taken together agree in support of the hypothesis that the ability to perform seriation tasks can be changed, at least to some extent, by relatively short periods Of specific training. Al- though the evidence from the seriation training studies hardly refutes Piaget's notion that cognitive capabilities cannot be substantially induced by specific training, the evidence does cast some doubt on that notion and hence, suggests that it might be worthwhile to look further for methods that produce substantial changes in cognitive capabilities associated with seriation. This thesis went beyond Coxford's study by showing that the specific target capabilities, in addition to being induceable,_were durable but not, in general,_ transferable. Whereas the results of the thesis point to the specific need for improving instruction relative to transfer,_the results of Coxford's study give no specific directions for improving instruction. The results Of this study revealed that the train- ing.sequence, which involved.cue fading and reinforcement, produced the induction Of specific stage III seriation 170 capabilities in kindergarten children who, prior to train- ing, possessed stage II capabilities. The results further revealed that the acquired capabilities were rather durable, but not substantially transferable to new materials. It should be pointed out, however, that althOugh the transfer effects were not substantial,_the trained subjectS‘ (experimental) performed the far and far-far transfer tests of posttest 3 no differently than those subjectS' (Special control) who had acquired stage III capabilities "naturally" or without specific instruction. Since a reasonable degree of SUCCGSS'haS been found, there may be the tendency to draw implications from the study which concern seriation training in the classroom. Without alterations, however, the training sequence used in this study would require such large amounts of time, space, and material that its use in the classroom would be pro- hibitive. In addition, any attempt to merely shorten the training sequence for classroom use would likely lead to leSs success than that found in this study. AlthOugh this study does not seem to prescribe any specific, reliable,, seriation training techniques for immediate use in the classroom, it does Offer a method Of cueing and cue fading which might be subsequently used in developing the more practical, classroom-like, training techniques. In fact cueing and cue fading methods might be reasonably used in 171 attempts to improve the seriation training Offered in some of the elementary science and mathematics programs. Since in this study, less than outstanding training effects were produced with a somewhat extensive and care- fully designed training sequence, those elementary science and mathematics lessons which give children only brief Opportunities for practicing seriation are not likely producing significant changes in seriation capabilities and hence should probably be revised. Hunt (1961) has contended that it is now reasonable to believe that early childhood experiences can be governed to produce increased rates of intellectual development as well as expanded adult levels Of intellectual capacity. Bloom (1964) has suggested that adult intellectual characteristics might be most easily influenced during childhood when those characteristics are developing most rapidly. Seriation capabilities likely play important' roles in school learning and intellectual functioning. For example, concepts of seriation are necessarily involved in the concept of number. In addition, serial ordering is used in science to organize information and hence‘ facilitate discovery. Undoubtedly, seriation is inherent in logical processes (if...then) and is an important element in the information processing system of the mind. From the propositions of Hunt and Bloom and frOm the 172 contention that seriation plays vital roles in intellectual functioning and school learning, it seems reasonable to undertake a thorough,_systematic search for thOse seriation training methOds which produce significant changes in intellectual development and school learning. The seria- tion training study reported in this thesis was an attempt to initiate that search. BIBLIOGRAPHY4 BIBLIOGRAPHY Adams, J. A. Multiple versus single problem training in human problem solving. Journal Of Experimental Anderson, R. C. Educational psychology. Annual Review of Psychology, 1967, 18, 129-164. Banta, T. J. Tests for the evaluation Of early childhood education: The Cincinnati autonomy test battery. Cognitive Studies, Vol. 1, 1968. Bijou, S. W. Systematic instruction in the attainment of right—left form concepts in young retarded children. In J. G. Holland and B. F. 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Osgood's transfer surface: Extension and test. ‘Journal Of Verbal Learning and Verbal Behavior, Winer, B. J. Statistical principles-in eXperimental design. New York: McGraw-Hill, 1962. Witkin, H. A. Individual differences in ease of perception Of embedded figures. Journal Of Personality, 1950,_ “19, 1-15. Wohlwill, J. F., & Lowe, R. C. An eXperimental analysis of the development Of the conservation of number. Child Development, 1962, 55,.153-167. APPENDICES APPENDIX4A Description of Pretest Materials Only sticks were used in the pretest. had a 0.75 x 0.75 inch, square cross-section. Each stick The sticks used in each task are identified in Table A by the lengths in inches. TABLE A Pretest Materials Kind of Task Objects to be (Inserted .Objects to be Ordered‘QE' Ordered set of Insertion Task Ordering 4 Objects Inserting 3 into 4 Ordering 6 Inserting 3 into 6 Ordering 8 Inserting 3 into 8 3.5,_4.5, 5.5 1.5, 3.5, 6.5 2.5,,5.5,_8.5 3: 5, .5: 5. 6: .6, 6: 180 APPENDIX B Verbal Instructions for Seriation Pretest Illustrations of Ordering and Inserting for Pretest "Here are some sticks that have different lengths. We want to put these sticks side by side on this line so they go from the shortest all the way to the tallest to make stairs. Watch - (EXperimenter orders sticks by successively choosing the shortest stick from those sticks to be considered.) See how the sticks go from the shOrtest one here all the way to the tallest here. Here is a stick that was forgotten. We want to put this stick with the others so all Of the sticks make stairs. The forgotten stick would go between these two sticks. (Experimenter places the forgotten stick into the ordered set.) See how all of the sticks O from the shorteSt to the talleSt to make stairs." (Experimenter removes sticks used in example.)' Instructions Given During Pretest The instructions were the same for each pair of ordering and inserting tasks. "Here are some other sticks. (Sticks are disarranged before the subject.) Place these sticks on the line from the shOrtest to the tallest to make stairs. (The subject makes an attempt and the 181 182 instructions are continued.) Look at your sticks to see if you have made any mistakes. You may make changes if you wish. (After the child indicates he is satisfied with the sticks as they are, or after he makes changes, the performance is judged correct or incorreCt. If the set of sticks are not properly ordered,_the experimenter arranges them in the proper order for the insertion task which' follows. The sticks to be inserted are brought out, and the instructions are continued.) Here are some sticks that have been forgotten. You put these sticks along with the others so all of the sticks go from the shortest to the tallest to make stairs. (The subject makes an attempt and when he is finished the instructions continue.) Look at the sticks to see if any mistakes have been made. You can make changes if you find mistakes." (After any correc- tions have been made, the result is judged correCt or incorrect, the sticks are removed, and a new Set of sticks is preSented for the next ordering task.) APPENDIX C Description Of Materials Used During the First Training Session Sticks Of various lengths were used during the first training session. Each stick had a 0.75 x 0.75 inch,, square cross-section. The sticks used at each training station are identified in Table C by the lengths in terms of 0.75 inch units. The discrimination levels are indi- cated by the difference between the lengths of the two ordered sticks (1 unit = 0.75 inch). TABLE C Materials Used During the First Training Session Discrim- . ination Training Sticks in the Sticks in the Level .Station, Ordered Set ' Disarranged Set Sticks to be Other Inserted Sticks 1 1.5, 4.5 3.0 6.0 3 2 6.0, 9.0 7.5 4.5 3 10.5, 13.5 12.0 9.0 4 4.00, 6.50 5.25 7.75 2.5 5 «7.75,,10.25' 9.00 6.50 6 11.50, 14.00 12.75 15.25 7 1.5, 3.5 2.5 4.5 2.0 8 6.5, 8.5 7.5 5.5 9 9.5, 11.5 10.5 8.5 183 184 Discrim- ination Training Sticks in the Sticks in the Level Station Ordered Set Disarranged Set Sticks to be Other Inserted StiCkS' 10 3.00, 4.50 3.75 2.25 1.5 11 5.25, 6.75 6.00 7.50 12 9.00, 10.5 9.75 11.25 13' 1.5, 4.5 3.0 6.0, 9.0 3 14 4.5, 7.5 6.0 3.0, 9.0 15 7.5, 10.5 9.0 12.0, 15.0 16 2.75, 5.25 4.00 1.50, 6.50 2.5 17 7.75, 10.25 9.00 4.00,_6.50 18 9.00, 11.50 10.25 12.75, 15.25 19 4.5, 6.5 5.5 1.5, 3.5 2.0 20 6.5, 8.5 7.5 5.5, 9.5 21 10.5, 12.5 11.5 9.5, 13.5 22 3.75, 5.25 4.50 1.5, 3.00 1.5 23 6.00, 7.50 6.75 8.25, 9.75 24 12.00, 13.50 12.75 9.75, 11.25 25 1.5, 2.5 2.0 3.0, 4.0 1.0 26 5.0,_6.0 5.5 3.5, 4.5 27 11.0, 12.0 11.5 9.5, 10.5 28 3.0, 6.0 4.5 ‘l.5, 7.5, 10.5 3 29 4.5, 7.5 6.0 9.0, 12.0, 15.0 30 10.5, 13.5 12.0 9.0, 6.0,_15.5 31 7.75, 10.25 9.00 6.50, 4.0, 1.5 2.5 32 1.50, 4.00 2.75 5.25, 7.75, 10.25 33 9.00, 11.50 10.25 5.25, 8.00, 12.75 34 2.5, 4.5 3.5 1.5, 5.5, 7.5 2.0 35 7.5, 9.5 8.5 2.5, 4.5, 6.5 36 8.5, 10.5 9.5 7.5, 11.5, 13.5 37 6.00, 7.50 6.75 5.25, 3.75, 2.25 1.5 38 6.75, 8.25 7.50 6.0, 4.5, 9.0 39 1.5, 3.0 2.25 3.75, 5.25, 6.75 40 4.5, 5.5 5.0 4.0, 3.0, 2.0 1.0 41 8.0, 9.0 8.5 9.5, 10.5, 11.5 42 12.0, 13.0 12.5 9.5, 10.5, 11.5 APPENDIX D Description of Materials Used During the Second Training Session Sticks Of various lengths were used, and each stick had a 0.75 x 0.75 inch,_square cross-section. The sticks used at each training station are identified in Table D by the lengths in terms Of 0.75 inch units. In many Of the tasks locations between adjacent sticks were cued. Where no cues appeared in an ordered set the sticks increased in length by regular 0.75 inch increments; however,_wherever a location between two sticks was cued, the difference in length ("cued" incre- ment) between those two sticks was greater than the regular increment of 0.75 inch. Cue levels are indicated in Table D by the lengths Of the "cued increments (1 unit 0.75 inch). 185 TABLE D 186 Materials Used During the Second Training Session Cue Training Sticks to be Level Station Inserted Sticks in the Ordered Set 1 3, 7 1.5, 4.5, 5.5, 8.5 3 2 3, 6 1.5, 4.5, 7.5, 8.5 3 4, 7 1.5, 2.5, 5.5, 8.5 4 2.75, 6.25 1.5, 4, 5, 7.5 2.5 5 2.75,_5.25 1.5, 4,_6.5, 7.5 6 3.75, 6.25 1.5, 2.5, 5, 7.5 7 2.5, 5.5 1.5, 3.5, 4.5, 6.5 2.0 8 2.5,_4.5 1.5, 3.5, 5.5, 6.5 9 3.5, 5.5 1.5, 2.5, 4.5, 6.5 10 2.25, 4.75 1.5, 3, 4, 5.5 1.5 11 2.25, 3.75 1.5, 3, 4.5, 5.5 12 3.5, 4.75 1.5, 2.5, 4.0, 5.5 13 2, 4 1.5, 2.5, 3.5, 4.5 1.0 14 3, 4 1.5, 2.5, 3.5, 4.5 15 2, 3 1.5, 2.5, 3.5,_4.5 l6 3, 7, 11 1.5, 4.5, 5.5, 8.5, 9.5,12.5 3 l7 4, 7, 11 1.5, 2.5, 5.5, 8.5, 9.5,12.5 18 3, 6,_9 1.5, 4.5, 7.5,10.5,1l.5,12.5 l9 2.75,5.25,9.75 1.5, 4.0, 6.5, 7.5, 8.5, 11 2.5 20 2.75,6.25,8.75 1.5, 4.0, 5.0,_7.5,10.0,ll.0 21 4.75,7.25,9.75 1.5, 2.5,_3.5, 6, 8.5, 11 22 2.5, 6.5, 8.5 1.5, 3.5, 4.5, 5.5, 7.5, 9.5 2.0 23 3.5, 6.5, 8.5 1.5, 2.5, 4.5, 5.5, 7.5,_9.5 24 2.5, 4.5, 6.5 1.5, 3.5, 5.5, 7.5, 8.5, 9.5 25 2.25,3.75,7.25 1.5, 3, 4.5, 5.5,_6.5, 8.0 1.5 26 2.25,3.75,6.25 1.5, 3, 4.5, 5.5, 7.0, 8.0 27 3.25,4-75,6.25 l.5,_2.5, 4.0,_5.5, 7.0, 7.0 28 2, 4,,6 1.5, 2.5, 3.5, 4.5, 5.5, 6.5 1.0 29 2, 3, 5 1.5, 2.5, 3.5, 4.5, 5.5, 6.5 30 3, 4,.5 1.5, 2.5, 3.5, 4.5, 5.5, 6.5 APPENDIX E Description Of Materials Used During the Third Training Session Lined cards with evenly spaced, parallel black lines were used during the third training sesSion. Each Of the lined cards was constructed by cementing a photograph Of parallel, evenly spaced black lines to a rectangular piece of posterboard (4.5 x 11.5 cm.). The black lines were' parallel to the short side of the card as shown in Figure E. Fig. E. An example Ofma lined card (drawn to actual size). Thirty-seven different line widths were required in the construction Of the lined cards. Since it was almost impossible to manually draw and accurately repro- duce 37 different line widths, large scale productions,, in which line width could be easily controlled, were con- structed and then photographically reduced in size to make the lined cards. The dimensions of the large scale 187 188 productions were 47 x 122 cm., and the dimensions of the lined cards were approximately one-tenth (.094) the dimen- sions of the large scale productions. More Specifically, this means that the lines on the cards were approximately one-tenth as wide as the lines of the large scale produc- tions. The cues for the lined cards took the form Of redundant relevant information. The redundant relevant dimension was line width. Line width did not vary on the individual cards but did vary from card to card. In cued sets Of cards, line width increased as the number Of lines increased. The subjects could use both line width and the number Of lines (or line density) in determining serial position. Since line Width was more readily dis- criminable When the variability of line width.was greater, it was assumed that greater line width variability would produce greater degrees of cueing. To Obtain the four different cue levels four sets Of 12 cards each were.constructed. The sets were identi- cal with respect tO the number of lines on the cards; that is, the cards in each set had the following number Of lines: 3, 4, 5, 7, 9, 11, 14, 17, 20, 24, 28, 32. The four sets.differed with respect to the variability of line lflidth. In the fully cued set, line widths varied from 0.2mm. to 2.4 mm. The variation of line width in the 189 second set of cards was two-thirds the variation Of the fully cued set. In this second set line width varied from 0.41 mm. to 2.19 mm. Variation of line width in the third set was one-third the variation of the fully cued set. The line widths in this third set varied from 0.71 mm. to 1.89 mm. The fourth set Of cards, the uncued set, showed no variation in line width. All lines on each card of the uncued set were 1.3 mm. in width. The cards used in training and testing were chosen from these four sets Of cards. Table B shows the cards used at each training sta- tion. Two numbers are required to describe a card. The first number,_the one to the left Of the hyphen,_refers to the number of lines of the card, and the second number, the one to the right of the hyphen, refers to the millimeter width Of the lines. 190 TABLE E Materials Used During the Third Training Session Cue Training Cards to be Level. Station Inserted Cards in the_Ordered Set 1 7-.8 4-.4;.14-1.4 F111]. 2 5-06 9.100, 24.200 3 20-1.8 11-1.2, 28-2.2 4 28-2.03 9-10.6, 20-l.71 2/3 5 20-1.7l 5-.73.'14-l.38 6 ll-l.22 l7-1.54, 32-2.19 7 5-.92 4-.82, 9-1.14 1/3 8 3-.7l' 5-.92, 11-1.25 9 32-l.89 l4—1.35, 24-1.67 10 24-1.3 20-1.3, 28-1.3 None 11 5-1.3 4-1.3, 7-1.3 12 20-l.3 ll-l.3. 17-1.3’ 13 5-.6 3-.2, ll-l.2, l7-1.6,_24—2.0 Full 14 14-1.4 3*.2,f5-.6,g9-1.0, 24-2.0' 15 5-.6, 20-1.8 3-.2,‘9-1.0, l4-1.4, 28-2.2 16 ll-l.22 4-.57, 7-.9, 17-l.54, 24-l.87 2/3 17 4-.57, 32-2.l9 7-.9, 11-1.22,_17-1.54, 24-l.87 18 4-.57, l7-1.54 7-.90, 11-1.22, 24-1.87, 32-2.19 19 5-.92, 20-l.57 4-.82, 9-1.14, 14-1.35, 24-1.67 1/3 20 11-l.25,32-1.89 5-.92,_9-1.14, 17-1.46,_24-l.67 21 3-.71,_20-1.57 5-.92,_9-1.l4, 14-1.35, 24-1.67 22 4-1.3; 17-1.3 3¥l.3, 5-1.3, 9-1.3; 14-1.3 None 23 5-1.3, 14-1.3 7-1.3; 11-1.3, 17-1.3; 24-1.3 24 20-1.3, 28-1.3 11-1.3, 17-1.3..24-1.3. 32-l.3 APPENDIX F Description of Materials Used in Posttests l and 2 Sticks, lined cards,_cars, and colored blocks were the four different kinds of materials used in posttests l and 2. The general characteristics of the sticks and lined cards have been described in Appendices D and E. Cars of various lengths were esSentially sticks with 0.75 inch dowels glued to one side to give the appearance of wheels. Colored blocks were blocks of wood painted vari— ous shades of blue. Tasks performed with sticks and lined cards were considered near transfer tasks. Tasks performed with cars and colored blocks were considered far transfer tasks. The tasks were performed in the order described below. Sticks The numbers in Table Fl refer to the lengths of the sticks in 0.75 inch units (1 unit = 0.75 inch). Table Fl Sticks Used in Posttests l and 2 Kind of Objects to ,Objectsmto be Ordered(Ordering Task' be Inserted Task) or Objects in Ordered Set (Insertion’Task) 4 1.5,,2.5,_3.5,,4.5g "4,.6 1.5, 2-5, 3.5, 4.5,_5.5, 6.5 “41'5" 7 W105’m205’ '3'05'1 4.5’5‘05'p'6jo'5’7'05’8.5 . 191 Inserting .2 Inserting 3, Inserting~ 2 192 Lined Cards The numbers in Table F2 refer to the number of lines on a card. The line widths were the same on all cards (1.3 mm.). TABLE F2 Lined Cards Used in Posttests l and 2 Kind of Objects to Objects to be Ordered(Ordering Task) Task , be Inserted, or Objects. in Ordered Set(InsertimTask) Ordering - 4, 7, 11, 17 Inserting 9, 28 4, 7, ll, 17 Ordering - 3, 5, 9, 14, 20, 28 Inserting 4, ll, 24 3,_5, 9, 14, 20, 28 Cars The numbers in Table F3 refer to the lengths of the cars in terms of 0.75 inch units (1 unit = 0.75 inch). TABLE F3 Cars Used in Posttests l and 2 Objects to be Ordered (Order- Kind of Objects to ing Task) or Objects in Ordered Task Abe_Inserted, Set.(Insertion Task) Ordering - 2, 3, 4, 5, 6,,7 Inserting 2.5, 5.5, 7.5 2, 3, 4, 5, 6:.7 193 Colored Blocks The blocks used in the testing tasks were chosen from a set of 12 blocks. Each block (representing a particular shade of blue) was given the number correspond- ing to its ordinal position in the set of 12 blocks ordered from the lightest (l) to the darkest (12) blue. The numbers in Table F4 refer to the various blocks used in the testing tasks. TABLE F4 Colored Blocks Used in Posttests 1 and 2 Kind of Objects to ( Ogjegts t0 fie Ordgged t Or ering Tas or jec 5 Task be Inserted in Ordered Set (Insertion Task) Inserting l, 5, ll 2, 4, 6, 7, 8, 9, 10, 12 APPENDIX G Description of Materials Used in Posttest 3 Sticks, cars, "happies,' and story cards were the fcnir different kinds of materials used in posttest 3. Sticks and cars have been described in Appendices D and F, respectively. "Happies" were rectangular pieces of posterboard which varied in height and width. Smiling faces were drawn on the posterboard pieces to suggest the proper orientation. Width of the card was the relevant ordering dimension used with.the "happies." Story> cards were rectangular pieces of posterboard, each show- ing a picture of a stick man, the ground, a diving board, and water. The cards showed the man at different stages in the process of climbing up the diving board and diving into the water. The cards were to be ordered according to the time sequence. Tasks performed with sticks were considered near transfer tasks, tasks performed with cars were considered far transfer tasks, and tasks performed with "happies“ and story cards were considered far-far transfer tasks. Tasks were performed in the order described below. Sticks The numbers in Table G1 refer to stick lengths in terms of 0.75 inch units (1 unit = 0.75 inch). 194 195 TABLE G1 Sticks Used in Posttest 3 Kind of Objects to Task ‘ be Inserted ObjeCts in Ordered Set Inserting 1.5, 4.5, 6.5, 2, 3,_4,_5, 6, 7, 8, 9,_ 7.5, 10.5 10, ll Inserting 5.5, 8.5, 10.5,, 4, 5, 6, 7, 8, 9, 10, 11, 11.5, 13.5, 15.5 12, l3,_l4, 15 Cars The numbers in Table G2 refer to car lengths in 0.75 inch units (1 unit = 0.75 inch). TABLE G2 Cars Used in Posttest 3 Kind of Objects to Task. be Inserted Objectsin Ordered Set Inserting 2.5, 4.5, 8.5 2, 3, 4, 5, 6, 7 Inserting 3.5, 5.5, 6.5, 8.5 2,_3, 4, 5, 6, 7, 8, 9 "Happies" A pair of numbers is required to describe each "happie." In Table G3 the number to the left of the hyphen refers to the width (the relevant dimension) and 196 the number to the right of the hyphen refers to the height (irrelevant dimension) (1 unit = 0.75 inch). TABLE G3 "Happies" Used in Posttest 3 Kind Objects Objects to be Ordered (Ordering of to be Task) or Objects in Ordered Task Inserted Set (Insertion Task) Ordering - 1.5-7.0, 2.7-5.5, 4.3-2.5, 7.3-5.0, 8.3-3.0, 12.5-4.5 Inserting 2.1—3.5,» 1.5-7.0, 2.7-5.5, 4.3-2.5, 7.3-5.0, 9.7-1.5 8.3-3.0, 12.5-4.5 Story Cards Figure (3 shows the stick man in the 12 positions shown on the individual cards. The numbers in Figure G refer to one particular card in which the stick man is in the particular position shown by the number in Figure G. The numbers are used in Table G4 to indicate the particular cards used in the various testing tasks. Fig. G. An illustration of the stick man positions shown on the story cards used in posttest 3. (Drawn to actual size.) 197 198 TABLE G4 Story Cards Used in Posttest 3 Kind Objects Objects to be Ordered (Ordering of to be Task) or Objects in Ordered Task Inserted ,Set (Insertion Task) Ordering - 1, 3, 5, 6, 7, 8, 9, 11, 12 Inserting 2, 4, 10 1, 3, 5, 6, 7,_8, 9, 11, 12 APPENDIX H Verbalization Used During Posttests 1 and 2 Prior to testing with a particular kind of material an orientation session was given to acquaint the subjects with the materials and with the tasks to be performed with the materials. General Introduction to Posttests 1 and 2 "Today we are going to play many different games. It is important that we do our best. We shOuld check our work to make sure we do not make mistakes." Orientation with Sticks "These sticks go from the shortest stick here (E points) all the way to the talleSt stick here (E points). The sticks make stairsteps. These sticks (E points) have' been forgotten. We want to put theSe sticks along with these sticks to make more stairsteps. (E inserts the’ sticks and says...) See h0w all the sticks make stairsteps. See how we have the shOrteSt one here, then the next tall- eSt,_then the neXt tallest (etc.)... all the Way to the tallest. (E takes out the inserted sticks, scrambles them, and says...) Now you try to put these sticks with these to make stairsteps. (If S is correct, E says...) 199 200 Very good! The sticks go from the shortest to the tallest to make stairsteps. (E takes S to testing with sticks) (If S performed the orientation task incorrectly, E says...) These sticks do not make stairs. This one is not right. This one is not right(etc.). Let's see what we can do to make it right. (As E makes corrections he says...) See how this one fits here to make stairsteps (etc.). (When E has made all the corrections, he says...) Now all the sticks go from the shortest to the tallest to make stairs. Try putting these sticks with these to make stairs. (E helps S make the correct responses and then says...) Very _good! The sticks gofrom the shOrtest to the talleSt to make stairs. (E takes S'to testing with sticks.) Testing with Sticks Here are some sticks that go from the shortest one here to the next tallest, to the next tallest, all the way to the tallest. TheSe sticks have been forgotten. You put these sticks along with these sticks to make stairs. (When S stops, E says...) Let's check our work to see if we have made any mistakes. You may make any changes you want. You may not have made any mistakes. (After S checks and makes changes, E says...) Now let's go to the neXt game. (The same verbalization was used with all the' testing tasks in which sticks were used.) 201 Orientation with Lined Cards. These cards have many black lines on them. .This card has the most lines and this one has the feWest. (While ordering the cards,_E says...) We want to put these cards side-by-side so we have the one with the fewest lines here, the one with the next most lines here(etc.),_and finally the one with the most lines here. See how we have the fewest black lines here, the next most lines here, all the way to the most lines here. (E scrambles the' cards and says...) Now you try it. Put the one with the fewest lines here,_then the one with the next most lines here and so on. (If S is correct in performing the orien— tation task, E says...) Very good! You have the one with the fewest lines here, then the one with the next most lines (etc.), and finally the one with the most lines. (E takes S‘to testing with lined cards. (If S performed the orientation task incorrectly, E says...) This is not right, but let's see what we can do to make it right. This one does not belong here because .... It should go here (etc.). (When E has finished with the corrections,_ he says...) See how we have the one with the feweSt black lines here,_then the one With.the next most lines (etc.) and finally the one with the most black lines. (E scrambles the cards and says...) Try putting the cards side-by-side so we have the one with the feweSt lines here, then the' 202 one with the next most lines (etc.). (E helps S whenever necessary and then says...) Very good! You have the one with the fewest lines here, then the one with the next most lines here, all the way to the one with the most lines. (E takes S to testing with lined cards.) Testing with Lined Cards Verbalization for Ordering Tasks- Here are some cards with black lines. You put the card with the fewest lines here, then the one with the next most lines,_and so on all the way to the one with the most lines. (When E stops,_E says...) Let's check our work to see if any mis— takes have been made. If you find any mistakes, please make changes to correct them. You may not have made any mistakes. (If S makes any mistakes, E makes the corrections and then says...) Verbalization for Insertion Tasks- Here are some lined cards that were forgotten. You put them along with these cards so that we have the one with the fewest black lines here,_then the one with.the next most lines, and so on all the way to the one with the most black lines. (After 8 stOps, E says...) Let's check our work to see if any mistakes have been made. You make any changes you wish. You may not have made any mistakes. 203 Orientation with Cars We are going to pretend that these are cars of a train and that this line is a railroad track. (While ordering the cars on the track, E says...) We want to put the cars on the track so we have the shortest car first, then the next longest, then the next longest (etc.), until we get to the longest. (When the cars are ordered,_E says...) See h0w we have the shortest car, then the next longest, all the way to the longest. (E brings out a car and says...) Here is a car that was forgotten. Watch how I put it with the others so all the cars go from the shortest to the longest. (When E has finished putting the car into the ordered set, he says...) See how all the cars go from the shortest to the longest. (E scrambles the cars and then says...) You put the cars on the track so the shortest car is first, then the next longest car is second, and so on all the way to the longest car. (If S performs the orientation task correctly, E says...) Very good! You have the shortest car here, then the next longest, then the neXt longest (etc.), all the way to the longest. (E then takes 8 to testing with lined cards.) (If S performs the orientation task incorrectly, E says...) Some mistakes have been made. Let's make the corrections. This one is not right. It should go here.(etc.). (When all corrections have been made, E says...) See how our cars go from the lllllr Fl , lt‘li 204 shortest to the longest. You try it again. (E scrambles the cars) Put the shortest car first, then the next longest, then the next longest, all the way to the longest. (E gives help where necessary and then says...) Very good! That's right. You have the shortest car first,then the next longest, and so on all the way to the longest. Testing with Cars Verbalization for Ordering Tasks. Put these cars on the track from the shortest to the longest. Start with the shortest one here, then the next longest, and so on. (When S finishes, E says...) Let's check our work to see if any mistakes have been made. If you find any mistakes please correct them. Maybe no mistakes have been made. (E correctly orders the cars if S has made any mistakes.) Verbalization for Inserting Tasks. These cars have been forgotten. Put them along with the others so we have the shortest car in front, then the next longest, all the way to the longest car. (When S is finished, E says...) Let's check our work to see if any mistakes have been made. You may make any changes you wish. Maybe no mistakes have been made. Orientation with Colored Blocks These cards are all painted blue. This card is the lightest blue, this card is the darkest blue. We want to 205 arrange these cards so we have the lightest blue first, then the next darkest blue (etc.), until we have the darkest blue. See how we have the lightest blue here, then the next darkest, then the next darkest, all the way to the darkest. (E scrambles the blocks and says...) You put the lightest blue here, then the next darkest, then the next darkest, all the way to the darkest. (If S is correct,_E says...) Very good! See how all the blocks go from lightest to the darkest. (E takes S to testing with colored blocks) (If S performed the orientation task incorrectly, E says...) We've made some mistakes. This one should go here (etc.). Now, see how the blocks go from the lightest to the darkest blue. (E scrambles the blocks and says...) You try it again. Put the lightest blue here, then the next darkest blue, and then the next darkest, all the way to the one with the darkest blue. (E gives help where necessary) Very good! See how the blocks go from the lightest blue to the darkest blue. (E takes S to testing with colored blocks.) Testing with Colored Blocks Verbalization for Ordering Tasks. Put these blocks side-by-side so we have the lightest blue first, then the next darkest, then the next darkest, and so on. (When S is finished, E says...) Let's check our work to see if any mistakes have been made. You may make any changes you wish. Maybe no mistakes have been made. (If S leaves 206 mistakes, E makes the corrections and then goes on to the insertion task.) Verbalization for Inserting Tasks. Here are some colored blocks we forgot. You put them along with these so all of the blocks go from the lightest to the darkest. (When S is finished, E says...) Let's check our work to see if any mistakes have been made. Make any changes you wish. Maybe no mistakes have been made. APPENDIX I Verbalization Used During Posttest 3 The verbalizations used with sticks and cars were the same as those used in posttests l and 2. Only the verbalizations used with Happies and story cards are presented here. Orientation with Happies We are going to call these Happies. See how the Happies are all smiling. Happies become sad when they are put on their sides. (E moves a Happie on its side.) Happies become sad when they are put on their heads too. (E puts a Happie on its head.) We want to make sure the Happies stay happy, so we always keep them up, like this. (E moves the Happie to the upright position.) Some Happies are wide. Some Happies are thin. Some are short, and some are tall. We only care about how wide they are. We do not care how tall they are. (The orientation session with Happies included some discrimination training designed to get the S's to distinguish the width of Happies from the height of Happies. Four cards, each showing a picture of two Happies, were used in the discrimination training. The cards were presented one at a time, and the S's task was to point to 207 208 the widest Happie. The S was cycled through the cards until he correctly performed four discrimination problems in a row. The verbalization used in the discrimination training was as follows.) Point to the widest Happie in the picture. (If S is correct, E says...) Very good! Yes that is the widest Happie. (If S is incorrect, E says...) You pointed to the thinnest Happie. This one is the widest Happie. See how it is wider than this one. Now point to the widest Happie. (E presents the next picture and goes through the same dialogue until criterion performance is reached. Once criterion is reached E goes on by saying...) We are’ going to play a game with Happies. (E orders the Happies while saying...) We want to put the Happies side-by-side so that we have the thinnest Happie first,_then the next widest Happie,_then the next widest, all the way to the widest. See how all the Happiesgo frOm the thinnest to the Widest. (E scrambles the Happies and says...) Now you try it. Put the thinneSt first, then the next widest, then the next widest, all the way to the wideSt Happie. (If S performs correctly, E says...) Very good! The Happies go from the thinnest tO.the widest. (E then takes the subject to testing with Happies.) (If S performs the orientation ordering task incorrectly, E says...) Some mistakes have been made. This one should go here (etc.). 209 (After E makes the necessary corrections he says...) See how the Happies go from the thinnest to the wideSt. Now you try it again. (E helps S where necessary and then says...) Good! See how all the Happies go from the thin- nest to the next widest, to the next widest, all the way to the widest. (E takes S to testing with Happies.) Testing with Happies Ordering with Happies. Here are some Happies. You put the thinnest on here, then the next widest,_then the next widest, and so on. (When S stops E says...) Let's check our work to see if any mistakes have been made. If you find mistakes, you may make any changes. Maybe no mistakes have been made. (E makes sure the Happies are in order for the insertion task and then says...) Inserting with Happies.. Here are some Happies that were forgotten. Put these Happies along with the other Happies, so that all of the Happies go from the thinnest to the next widest, to the next widest, all the way to the widest. (When S stops E says...) Let's check our work to see if any mistakes have been made. If you find mistakes, you may make any changes. Maybe no mistakes have been made. Testing with the Story Cards Ordering with Story Cards.- Here are some pictures shOwing a man climbing up a diving board. He dives off 210 the diving board into the water. This is the first pic- ture. Put the other pictures side-by-side so that they show the story of the man climbing up to the diving board and diving into the water. (When S stops E says...) Let's check our work to see if any mistakes have been made.. You may make any changes. You may not have to make any changes. Inserting with Story Cards. Here are some pictures that were forgotten. Put these pictures in with the others so that all of the pictures show the story of the man climbing up to the diving board and diving into the water. (When S is finished E says...) Check your work and see if you want to make any changes. APPENDIX J Individual Difference Measures--Three Parts of the Cincinnati Autonomy Test Battery All of the subjects, except the special control subjects, were individually given the following three parts of Banta's Cincinnati Autonomy Test Battery (CATB) (1968); The Early Childhood Embedded Figures Test (EC-EFT), The Draw-a-Line Slowly Test (EC-MFF), and The Early Child- hood Matching Familiar Rigures Test (EC-MFF). The CATB was designed for the use with children from three to six years of age. Reliability measures were given for each part. The three tests used in this study are discussed below in the order in which they were administered. The Early ChildhOod Embedded Figures Test (EC-EFT) The EC-EFT was designed to test field independence. Field independence is defined by the test designer as the tendency to separate an item from the field or context of which it is a part. In the EC-EFT,_fourteen test pictures embed a figure which looks like an ice cream cone. The subject is given a paper cut-out figure of an ice cream cone which is the same size and shape as the embedded cone. The subject is instructed to put the paper cone on top of the 211 212 picture of the cone in the various figures. Prior to the testing, the subjeCt is subjeCted to a training session in which three pictures are used to assess the subject's comprehension and readiness to perform the task. Banta (1968) has reported an average reliability coefficient (internal consistency) of .54 for the EC-EFT. The subjects used in obtaining the mean reliability coeffi- cient were lower class Negro children who were between the ages of three and six years. The Draw-a-Line Slowly Test This test was used to measure the ability of the child to restrain impulsive motor activity. It is assumed that the child who can draw a line slowly has the ability to restrain impulsive motor activity. The teSter begins the Draw-a-Line Slowly Test by drawing a fast and a slow line to_give meaning to the words "fast" and "slow." The child then draws three lines slowly. He draws the first two lines as slow as he.can, and then he is asked to draw the third line even slower than the previous two. Since the rate of drawing the lines is the dependent variable in this test, both the lengths of the lines and times taken in drawing the lines are reCorded. To calculate the average rate of line drawing, the total length of the three lines in inches is divided by the total time in 213 hundredths of a minute. Banta (1968) has reported correlations between the two members of each possible pair of line rates. The correlations between lines 1 and 2, lines 1 and 3, and lines 2 and 3 were respectively .55, .47, and .80 for a sample of 72 lower class Negro children. An inter-rater reliability coefficient of .96 was found using a sample of 33 children. In addition, a test—retest reliability coefficient of .43 was reported for 33 children who experi- enced a two month time interval between tests. The Early Childhood Matching Familiar FigureS'Test‘(EC-MFF) This matching familiar figures test is designed to measure the child's tendency to behave reflectivelywhen confronted with conditions of uncertainty. As the title of the test implies, the subject's task is to match a sample figure with the same figure which is among similar figures. The child is first presented with a sample figure. He is then presented with an array of similar figures, one of which is the same as the sample. He is instructed to find the sample figure in this array. It is assumed that the reflective child tends to make less mistakes. Banta styled the test after the original test which was devised by Kagan (1965) to study refleCtivity in first grade children. Kagan (1965) used time latencies and error scores and found that the probability of error increased 214 as the time latencies shortened. In other words, children who take time to reflect over their decisions tend to make fewer errors. Banta omitted the measurement of time‘ latencies and used only the number of correct responses as a measure of reflectivity. He maintains that nursery and kindergarten school children, for whom this test is designed, very often take long periods of time to respond because they are easily distracted, and tend to fantasize and talk with the tester. Therefore, these behaviors which take the young child away from the task render the time variable meaningleSs. The only score the child receives on the EC-MFF is the number of correCt responses. It is assumed that the reflective child will make more correct responses. Banta (1968) reports that data on the EC—MFF is sparse. From a sample of 62 subjects, a reliability coef- ficient of internal consistency (odd vs. even items) was found to be .37. APPENDIX K Descriptions of the Two Lenient MethOds of Scoring (L1 and L2) The need for two different methods of lenient scor- ing becomes apparent when a deCision has to be made as to which of the two incorrect arrangements shown in Figure K is more correct. 123456 246135 132546 Correct Incorrect A Incorrect B Fig. K. Different arrangements used to illus- trate the need for different scoring systems. The number associated with‘ each objeCt refers to the ordinal‘ position of that object in the properly ordered set. The incorrect arrangement labeled "A" shows two separate three member sequence'(2-4—6 and 1-3-5) which seemed to be 215 216 placed side-by-side. It should be noted that in the "A" arrangement, small objects do not necessarily appear to the left and neither do large objects necessarily appear to the right. The incorrect arrangement labeled "B,“ on the other hand, has three, two member sequences (1-3, 2-5, and 4-6) and in general tends to show small objeCts toward the left and larger objects toward the right. If having small objects toward the left and larger objects towards the right ("B" in Figure K) is judged to be more correct than having two or more correctly ordered sequences incorrectly placed side-by-side ("A" in Figure K), then performance resulting in arrangement "B" would demand a higher score. If, on the other hand, sequencing ("A") is judged to be more correct than having smaller objects to the left and larger objects to the right ("B"), then performance resulting in arrangement "A" would demand a higher score. Rather than arbitrarily choose one partial credit scoring method which would favor one kind of arrangement over the other, two scoring methods were used,, each.des1gned to primarily reflect one of the two kinds of arrangements. One partial credit or lenient scoring method,. labeled Ll, yielded a sequence score. The sequence score was tailored to give arrangements like "A" (Figure K) a higher score than arrangements like "B." To calculate 217 the sequence score for any arrangement the following formula was used: sequence score = where: 171-51' M = maximum number of possible sequences, which was equal to the total number of objects used in the seriation task since the maximum number of se- quences occurs when each object appears as a "sequence of one"; and A = actual number of sequences appearing in the par- ticular arrangement being scored. A sequence was defined in terms of the numbers used to record the positions of objects in an arrangement. Each object was given the number which corresponded to its ordinal position in the correctly ordered set of objects. These numbers were used to record the actual positions of the objects in the arrangements constructed by the subjects. For example, 1-3-2 referred to an incorrectly ordered arrangement which should have been ordered 1-2-3. In terms of the numbers used to describe an arrangement, a sequence was defined as: l) a series of numbers which increased in value from left to right but not necessarily at regular intervals (...-2:4:6...;'l:2:3...;), or 2) a number which was immediately preceded by a larger number and immediately followed by a smaller number (...-3-2fl...; ..-6-3él...), or 3) a number which came at the right end of the arrangement and which was preCeded by a larger number (..-5-§; 2-3-4-1), or 4) a number which was at the left end of an arrangement and which was larger than the 218 number immediately following it'(4f3-l..; 675-2..). For an example of calculating the L1 sequence scores, consider the arrangements labeled "Incorrect A" and "Incorrect B“ in Figure K. The sequences in "A" are 2-4-6 and 1-3-5. Therefore, A equals two, and since there are six Objects, M equals six. The sequence score for "A" then becomes g;% or 0.8. The sequences in "B" are l-3,_2-5 and 4-6 making A equal to 3. With M equal to 6, the sequence score for "B" becomes g;%or 0.6. Note that the fewer the sequences, the larger the sequences and hence the larger the sequence score. Note also, that when all objects are ordered correCtly, as in the "Correct" arrangement of Figure K, there is only one sequence and the sequence score becomes 3;; or 1.0. With the sequence formula and the definition of a sequence,_the maximum and minimum scores were respeCtively 1.0 and 0.0. The second method of lenient scoring, identified as L2, yielded scores which reflected the general tendency to have small objects toward the left and larger objects toward the right. This tendency was indexed by calculating a rank order correlation (Kendall Tau) between the order which appeared and the correct order. So the distribution of L2 scores could be assumed to be normal for analysis purposes, the correlation coefficients were transformed into Z values through the use of Fisher's r to Z .f" 9.),— u. 1“!“ . A.— 219 transformation. The Z value calculated for each particu- lar arrangement was used to derive the near, far, and far-far transfer scores for the data analysis. The Z values used in the study ranged from 0.00 which corresponded to a correlation of 0.00,to 5.00, which corresponded to a correlation of 1.00. The L2 scores for the incorrect arrangements "A" and "B" are respectively, 0.203 and 0.933. Note that the L2 scoring method reverses that order of "A" and "B" correctness established by scoring method Ll. Where the L1 or the sequence scoring method yielded a higher score for "A" than for "B,“ the L2 method of scoring yielded a higher score for "B" than for "A." Thus far two different methods for scoring any one arrangement have been described. Since a number of tasks were used to assess a particular kind of transfer ability,. a number of arrangements had to be considered in deriving near, far, and far-far transfer scores for an individual. A near, far,_or far-far transfer score for either lenient scoring method (L1 or L2) was found by first summing the attained lenient scores for the set of tasks and then calculating the per cent attained of the maximum attain- able sum. These percentages were the scores used in the data analysis. APPENDIX L Compilation of Data Used in the Analysis of Results Initially, there were two large groups (Groups I and II) of subjects,_each with an experimental (E) and a control (C) subgroup. Each subject, therefore is desig- nated by two numbers and one or two letters. The number to the left of the letter(s) designates the large group number (1 or 2), the letter designates the treatment group (E = experimental, C = control, SC = special control), and the number to the right of the letter designates the specific individual. For example, 1E7 would indicate subject number 7 from the experimental subgroup of large _group 1. The Special control subjects were not members of either large group; hence, no number precedes their letters SC. Seven dependent variable scores are given for each subject. NT refers to a near transfer measure, FT refers to a far transfer measure, and FFT refers to a far-far transfer. The number following the test type designation (NT, FT, or FFT) indicates the posttest number. For example, FT3 refers to the far transfer measure of posttest 3. Each dependent variable score is a per cent of tasks 220 221 performed without error. For example, a score of 50.0 under NTl would mean that 50% of the near transfer tasks of posttest l were performed without error. Individual difference measures of age, field inde- pendence (EFT), motor control (IC), and reflectivity (MFF) are given. Age is in terms of months determined at the time of the first posttest. The other three ID measures are from Banta's CATB (Appendix J). EFT refers to an embedded figures test, IC refers to an impulse control test, and MFF refers to a matching familiar figures test. 2 0 0H0. 0 00.00 0.0 0.0 0.00H 0.00 0.H0 0.00 0.H0 mmN Mu HH 00H. 0H 00.00 0.00 0.00H 0.00H 0.00H 0.00H 0.00 0.00H NmN 0 H00. 0 00.00 0.0 0.0 0.00 0.00 0.N0 0.00 H.00 HmN 0 000. 0 0H.00 0.0 0.0 0.0 0.0N 0.N0 0.0N 0.0N 00H 0 00H. 0 0H.00 0.00 0.00H 0.00 0.00 H.00 0.0N 0.N0 00H 0 H0N. NH 00.00 0.0 0.00 0.00H 0.0N H.00 0.0N 0.N0 00H 0 0NN. HH 00.00 0.0N 0.00 0.00H 0.00 0.N0 0.0N 0.0H 00H 0 000. NH 00.N0 0.00 0.00 0.00H 0.00 0.H0 0.0N 0.00 00H 0 00H. NH 00.00 0.0 0.00 0.00H 0.0N 0.N0 0.0N H.00 00H 0 00N. 0H 0H.H0 0.0N 0.00 0.00 0.0N 0.00 0.0N H.00 NoH 0 H0H. 0H 00.00 0.0N 0.0 0.0 0.0N 0.0N 0.00 0.0H HoH 0 00H. HH 00.00 0.0 0.0 0.0 0.0N 0.N0 0.0N 0.00H 00H 0 00H. HH 00.H0 0.00 0.00 0.00H 0.0N H.00 0.0N 0.N0 00H 0H 000. NH 00.N0 0.00 0.00H 0.00H 0.0N 0.00H 0.00 0.00H 00H 0 HNH. 0H 00.00 0.0 0.00H 0.00H 0.00H 0.H0 0.0N 0.00 00H 0H 000. 0H 00.00 0.0N 0.0 0.0 0.0 0.00H 0.0 0.00H 00H 0 00H. NH 00.00 0.0 0.00 0.00H 0.00H 0.00H 0.00 0.00H NmH 0 0NH. 0H 00.N0 0.00 0.00 0.00H 0.00H 0.00H 0.00 0.00 HmH mm: oH emm 600 0000 000 002. N00 N02 H00 H02 0060350 mousmmmz DH mmusmmmz ucmpcmmmo meSmmmE 0H paw pampcmmmo mgu no mmHoom pomnnsm HMD©H>HUGH A mqmdB 0.00 0.00H 0.00H 060 Mu 0.00 0.00 0.00H 0cm 2 0.00 0.00H 0.00H «om 0.0 0.0 0.00H mom 0.00H 0.00 0.00H Now 0.00 0.0 0.00 H00 0 00H. HH 00.H0 0.00 0.00 0.00H 0.00H 0.00H 0.00 0.00H 0oN 0 0N0. 0H 00.00 0.0N 0.0 0.00 0.00 H.00 0.00 0.0N moN 0 00H. 0H 00.00 0.0 0.00 0.0 0.00 0.0H 0.0N 0.0N NoN 0 000. HH 00.00 0.0 0.00H 0.00H 0.00 0.H0 0»00H 0.H0 0oN 0 00H. HH A00.00 0.0 0.00 0.00H 0.0N 0.0N 0.0N 0.0H moN 0 00H. NH N0.00 0.0 0.00 0.00 0.0N H.00 0.00 0.0H woN 0H 0HH. 0H 00.00 0.00 0.00 0.0 0.0N 0.N0 0.0N 0.0N moN 0 0H0. 0H 00.N0 0.0 0.0 0.0 0.0 0.0N 0.0 0.0N NoN 0 00H. NH N0.H0 0.0 0.0 0.0 0.0N 0.N0 0.0N 0.0H HoN 0H 0HN. HH 00.00 0.0N 0.0 0.00H 0.00 0.00H 0.0N 0.00H mmN 0 0NH. NH N0.00 0.00 ,0.00H 0.00H 0.00H 0.00H 0.00 0.00 NmN 0H 000. 0H NH.00 0.00 0.00 0.00H 0.00H 0.00 0.00 0.00H 0mN 0 H0N. 0 00.00 0.0 0.0 0.0 0.0N 0.N0 0.0N H.00 mmN 0H 000. 0H 00.00 0.00H 0.00H 0.00H 0.00 0.00 0.00 0.H0 0mN 4002 oH amm 600. memm. mam mez _mamn ~02 .H00 H02 0600000 ,mwlhfinmmmz D H mmnfimmmz vampcwmma H0.Hcoov H mHmNe 224 0.0N 0.0 0.00H 0Hom 0.00 0.00H 0.00H NHom 0000 0.00 0.00 HHom 0.00H 0.00 0.00H 0Hom 0.00H 0.00H 0.00H 000 0.0 0.0 0.00H 0cm 0.00 0.0 0.00 000 222 _oH . 02m 600 meme _mem .092 N02 ~02 Hem. H92 muomflQSm monumMmz_QH mwnfimMmz pampammma H0.ucoov H MHmNB APPENDIX M Repeated Measures, Multivariate Analysis Information for the Experimental versus Control Group Analysis (E vs. C) The input dependent variables were: near (NTl) and far (FTl) transfer measures from posttest 1, near (NT2) and far (FT2) transfer measures from posttest 2, and near (NT3) and far (FT3) transfer measures from posttest 3. These input dependent measures were determined from the stringent (S) methodof scoring (proportion of tasks per- formed without error). The input dependent variables were transformed to new variables by the transformation matrix shown in Table M1. The variable labeled "const" refers to a constant. The variable AlA2 is associated with the difference between posttests l and 2. The variable A2A3 is associated with’ the difference between posttests 2 and 3. The.variable BlB2 is associated with the difference between near and far transfer test types. The variables, interl and inter2 refer to interaction contrasts. 225 226 000000.0 00HH00.0- 0000HH.0 H00000.0- 0000HH.0- N0NN00.H Houpaoo 000H00.0- 0000NH.0 N00N00.0 0000NH.0 00H000y0u 000HN0.H HmucmaHummxm NmmezH .HmmazH NmHm. mNNN. NNH4_ amzoo mmHQMHHm> 302 may Eonm commasoamu mammz msouw Houucov paw Hmucmfiflummxm NE mamfla 000000.0 000000.0- 000000.0- 000000.0 000000.0- 000000.0- NmmezH 0 0N000N.0 00000N.0- 00000N.0 00000N.0- 0000N0.0- 000000.0 HmmazH 0 00N000.0- 00N000.0 00N000.0- 00N000.0 00N000.0- 00N000.0 NmHm 0 000000.0u 000000.0- 000000.0 000000.0 000000n0- 000000.0u mNNN m 00000N.0- 00000N.0- 00000N.0- 00000N.0- 000000.0 000000.0 NNHm N 00N000.0 00N000.0 00N000.0 00N000.0 00N000.0 00N000.0 00200 H mam mBZ Nam «82 Hem HBZ AU my mmHQMHHm> UHO x 3oz I xflnpmz GOHHMEHommGMHH HS mqmde 227 oooooo.H NmmEZH Nmoaov.o oooooo.H HmMBZH wmmmmo.o hwmmmo.o bmmmmo.o mmammo.o mmmmmo.o bmwmom.o moZflHm¢> NmMBZH HmMBZH NmHm mfimfi N4H¢ BmZOU Hmmwmxo mqmflHm¢> AU .m> my mmHQMHHm> 302 map How mmOCMHHm> mvamho.OI Nwamwa.ol oooooo.H NmHm Ho .m> my mmHanum> 362 man v2 mqméfi ommmho.o mmahva.o Hmoomo.o oooooo.H mdmfl m2 mqmfiB 00000N.0 00NNH0.0 000000.0 000000.0 000000.H N my Aouv H mammnpommm £003 cmumfioomm¢ xflupmz mpOSUOHm com: mammnuommm NE mamfifi cm H mommm mom Soammmm m0 mmmmwmn H. H mHmmmBOmMm mom ZOOmmmm m0 wmmmwma 0000.0 0000.0 0N00.0 NmmazH 0H00.0 0000.0 0000.0 HmmazH 0000.0 000H.0H 0N00.H NmHm 0000.0 HN00.0H 0000.0 00N0 0N00.0 H000.0 000N.0 N0H0 2000 000H 0 0 2200:0000 00 2002.2002000 0H00H00> Ho .0> 00 Hoov H 0Hmmnuommm H0022 mmHhmHum> man squ U00000000m mpGGEmgmum.muHHHanoum paw .m.m :3oolmmum .cmm3umm mmumsvm £002 02 mqmflB NmMBZH HmMBZH NmHm m¢m< Ndafl 230 Hypothesis 2 (C1) F-ratio for the multivariate test of equality of mean vectors = 4.1688, df = 5 and 26, p less than 0.0065. TABLE M8 Mean Squares Between, Step-Down F's,_and Probability Statements Associated with the Variables Under Hypothesis 2 (Cl) (E vs. C) VARIABLE BETWEEN MEAN SQ STEP-DOWN F P LESS THAN AlA2 0.0211 0.3963 0.5338 A2A3 0.1452 2.0586 0.1621 B132 0.4176 6.0730 0.0202 INTERl 0.2437 5.7668 0.0235 INTER2 0.0741 3.2314 0.0839 DEGREES OF FREEDOM FOR HYPOTHESIS = 1 DEGREES OF FREEDOM FOR ERROR = 30 TABLE M9 Hypothesis Mean Products Matrix Associated with Hypothesis 2 (Cl) (E vs. C) AlA2 A2A3 BlB2 INTERl INTER2 AlA2 0.021112 A2A3 0.055360 0.145167 3132 0.093893 0.246211' 0.417586 INTERl 0.071723. 0.188076 0.318987 0.243669 INTER2 -0.039540 -0.103685 -0.l75855 -0.134332 0.074056 l I I I'll I III. III lIIlJl l I I {I 231 Step-down F's for variables AlA2 and A2A3 (Hypothe- sis 2) indicated no Treatment x Posttest interaction. The step-down F for variable BlBZ indicated a significant Treatment x Test Type interaction. A significant Treat- ment x Test Type x Posttest was shown by the step-down F's for variables Interl and Inter2. Hypothesis 3 (CO) F-ratio for the multivariate test of equality of mean vectors = 42.1651, df = 6 and 25, p less than 0.0001. TABLE M10 Mean Squares Between, Step-Down F's, and Probability Statements Associated with the Variables Under Hypothesis 3 (CO) (E vs. C) VARIABLE BETWEEN MEAN SQ STEP-DOWN F P LESS THAN CONST 56.1407 183.6840 0.0001 AlA2 0.2395 7.8893 0.0089 A2A3 0.0909 2.4734 0.1271 B1B2 1.5628 2.0525 0.1635 INTERl 0.0303 0.0777 0.7827 INTER2 0.0524 1.1215 0.2998 DEGREES OF FREEDOM FOR HYPOTHESIS = 1 = 30 DEGREES OF FREEDOM FOR ERROR lull l l I I ,III.‘ 1 .' III .I II 1 .232 hmmmo.o NmmBZH Ho mmmmo.OI omomo.o HmmBZH N000N.0- 000HN»0 00N00»H NmHm 00000.0- 00HHH.0. H00H0.H- 00N00.0 0H000.0- 0N000.H 0000000 N0HH0.0- 00000.0 00000.0 0000Hu0- 0000N.N 0000Nu0 00000.00 0000H.00 00N0 N0H< 00200 .0> my AOUV m mfimmnuomwm £003 p000000004 Nahum: 00oscoum c002 mammnuommm HHS mqmfie NmmEZH HmmBZH NmHm m¢N¢ Nflad BmZOU 233 None of the tests associated with Hypothesis 3 were used in interpreting the results of this study. Hypothesis 4 (Cl) F-ratio for the multivariate test of equality of mean vectors = 5.1300, df = 6 and 25,_p less than 0.0015. TABLE M12 Mean Squares Between, Step-Down F's, and Probability Statements Associated with the Variables Under Hypothesis 4 (Cl) (E vs. C) VARIABLE BETWEEN MEAN SQ STEP-DOWN F P LESS THAN CONST 2.4947 8.1623 0.0077 A1A2 0.0211 6.6518 0.0153 A2A3 0.1452 1.6925 0.2039 BlB2 0.4176 3.3209 0.0795 INTERl 0.2437 3.8701 0.0600 INTER2 0.0741 1.0706 0.3108 DEGREES OF FREEDOM FOR HYPOTHESIS = 1 DEGREES OF FREEDOM FOR ERROR = 30 The significant step-down for the const variable (Hypothesis 4) was interpreted as evidence for a Treat- ment main effect. 234 mmo¢ho.o NmMBZH Nmm¢MH.OI mmmmvm.o HmMEZH AU .0> my AHUV 0 mflmmnpomwm £003 U00000000¢ xfluumz mgosooum c002 mammspommm 00000H.0- 0000H0.0 0000H0.0 NmHm 00000H.0- 00000H.0 HHN00N.0 00H00H»0 mfimfl MHZ mqmflfi 000000.0u 0N0HN0.0 000000.0 000000.0 NHHHN0.0 Nfidd 0N00N0.0- 000000.0 N000N00H 00NH00.0 0000NN.0 000000.N BmZOU NMMBZH HmmBZH NmHm m4m¢ N¢H¢ BmZOU APPENDIX N Multivariate Analysis Information for the Experimental versus Control versus Special Control Group Analysis (E x C x SC) There were two major parts to this analysis. One part (experimental versus special control) focused on the comparison of experimental and special control groups' performances of the near (NT3), far (FT3), and far—far (FFT3) transfer tests of posttest 3. The other part (special control versus control) focused on the compari- son of the control and special control groups' performances of the same three tests. The dependent measures were determined from the stringent (S) method of scoring (proportion of tasks performed without error). TABLE N1 Experimental, Control, and Special Control Group Means NT3 FT3 FFT3 Experimental 0.766667 0.466667 0.300000 Control 0.529412 0.411765 0.205882 Special Control 0.884615 0.461538 0.519231 235 236 TABLE N2 Sample Correlation Matrix (Within Cells) (E x C x SC) NT3 FT3 FFT3 NT3 1.000000 FT3 0.525585 1.000000 . FFT3 0.227875 0.497719 1.000000 TABLE N3 Variances (E x C x SC) VARIABLE VARIANCE NT3' 0.148704 FT3 0.156708 FFT3 0.088979 TABLE N4 Symbolic Basis VeCtors (E x C x SC) CO. GRAND MEAN U Basis Vector = 1.0000 1.0000 1.0000 Cl. EXPERIMENTAL VS. SPECIAL Basis Vector = 0.6667 -0.3333 -0.3333 C2. CONTROL VS. SPECIAL Basis Vector =-0.3333 0.6667 -0.3333 237 Part l’- Experimental versus Special Control F-ratio for the multivariate test of equality of mean veCtors = 0.2795, df = 3 and 40, p less than 0.8399. TABLE N5 Mean Squares Between, Step-Down F's, and Probability Statements Associated with the Variables Under Part 1 (E vs. SC) VARIABLE BETWEEN MEAN SQ STEP-DOWN F P LESS THAN NT3 0.0694 '0.4670 0.4982 FT3. 0.0111 0.0115 0.9151 FFT3 0.0174 0.3780 0.5422 DEGREES OF FREEDOM FOR HYPOTHESIS = 1 DEGREES OF FREEDOM FOR ERROR = 42 TABLE N6 Hypothesis Mean Products Matrix Associated with Part 1 (E vs. SC) NT3 FT3 FFT3 NT3 69.444444-003 FT3 27.777778-003 11.111111-003 FFT3 -34.722222-003 -l3.888889é003 17.361111-003 238 Part 2 - Special Control versus Control F-ratio for the multivariate test of equality of mean vectors = 5.6897, df = 3 and 40, p less than 0.0025. TABLE N7 Mean Squares Between, Step—Down F's, and Probability Statements Associated with the Variables Under Part 2 (SC vs. C) VARIABLE BETWEEN MEAN SQ STEP-DOWN F P LESS THAN NT3 0.9294 6.2504 0.0165 FT3 0.0183 1.1109 '0.2981 FFT3 0.7233 8.3658 0.0062 DEGREES OF FREEDOM FOR HYPOTHESIS = 1 DEGREES OF FREEDOM FOR ERROR = 42 TABLE N8 Hypothesis Mean Products Matrix Associated with Part 2 (SC vs. C) NT3 FT3 FFT3 NT3 0.929449 FT3 0.130241 0.018250 FFT3 0.819928 0.114894 0.723313 1293 0 1 3 " F.“ T“ All-I." T“ u ” I'll ”-