ABSTRACT VERTICAL TRANSFER OF INSTRUCTION BASED ON (DGNITIVE STRATEGIES FOR A SEQUENCE OF GEOLOGIC TASKS by Fred Nelson Finley In this study an information processing approach was applied to design an instructional sequence which would effectively and efficiently teach students to classify igneous rocks, and to evaluate learning and transfer within the sequence. This approach involved content analysis to provide a three level description of the detail and structure of the knowledge related to igneous rock classification. The resulting description was in terms of an interrelated set of concepts, task descriptions, and task specific cognitive strategies. The instructional sequence was organized on the basis of compatible cognitive strategies. The sequence consisted of three tasks. The first task required students to compare the rock samples to a standard. The second task required students to classify the samples using a one variable, three cell classification scheme. The final task required students to classify the samples with a two variable, nine cell, geologic classifi- cation scheme. The design of an instructional sequence which shared conmon con- cept and task features was expected to (l) facilitate learning during Fred Nelson Finley instruction, (2) enhance task performance on a posttest, and (3) enhance the transfer of learning to the pretest for a related task. Instruction based on task specific cognitive strategies was expected to enhance learning and transfer to an even greater extent within the task sequence. The availability of the strategies in a student's memory was to serve as a mechanism which would enhance learning and transfer. Randomly selected students were assigned to three treatment groups . The Cumulative Strategy group was instructed on a cognitive strategy for each task. The Cunulative Feedback group was given feedback on the correctness of their performance for each task. The Isolated Feedback group consisted of two sets of students. Each set was given feedback instruction for the second or third task only. Observations of student behavior were made using coding systems based on the cognitive strategy models. Scores were defined to reflect students learning, use, and transfer of the strategies during the instruction, the posttests, and pretests respectively. Additional scores reflected the accuracy of performance and the amount of in- struction necessary to learn to perform the tasks. Data analysis (1) described the learning, use, and transfer of the cognitive strategies by students, and (2) evaluated effects attributable to instruction on the task sequence and effects attributable to strategy based instruction by comparing performances of the treatment groups. The findings of the study were: (1) Students learned the task specific strategies during instruction. (Z) (3) (4) (5) Fred Nelson Finley The students used components of the strategies they had been taught during posttests, and trans- ferred strategy components to the pretests for the next closely related task. Students did not use or transfer the complete strategies exten- sively. The performance results related to instruction on the task sequence and the strategy based instruction were mixed. Significant differences occurred at important times during the instruc- tional sequence, but did not occur consistently. The differences were generally not dramatic. The detailed representations of the knowledge students were to learn in conjunction with an information processing view of human thinking proved useful. The descriptions of the knowledge and learner guided both the selection and se- quencing of the content for instruction. The detailed representation of the knowledge led to collecting data which provided substantial insight into the manner in which students used and transferred that lmcwledge. The experimental design and the thoroughness of the observations generated a large volume of data which proved difficult and costly to Fred Nelson Finley collect, manipulate, and reduce to meaningful scores. Smaller scale studies would have provided some of the important findings more efficiently. VERTICAL TRANSFER OF INSTRUCTION BASED ON C(IZNITIVE STRATEGIES FOR A SEQUENCE OF GEOLOGIC TASKS By Fred Nelson Finley A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of IDC'IOR OF PHILOSOPHY Department of Secondary Education and Curriculum 1977 4 . . ,- —,‘ a H L, LL) DEDICATION To Alice and Ken ii ACKNOWLEDGMENTS Many people have contributed their time, energy, and expertise to this research. The faculty, students, and staff of the Science- Math Teaching Center at Michigan State University, provided an enjoy- able amd intellectually stimulating environment. In particular many thanks are extended to Dr. Glenn Berkheimer, Judy Dennison, and Rich Brandenburg for their guidance and friendship. I specially acknowledge the many contributions of my friend and colleague Dr. Edward L. Smith. As my research advisor he provided quality teaching, incisive critiques, and insightful suggestions during every phase of the study. I wish also to thank my family for their continued encourage- ment, support, and advice. Their contributions were both substantive and personal. A substantial portion of the editing was completed by Mrs. Fern E. Dyer, my wife's mother. My son provided much needed hummus and interesting interludes. Most importantly, my wife gave her love and mral support which made completion of this work possible, enjoyable, and worthwhile. iii TABLE OF CDNTENTS LIST OF TABLES ......................... LIST OF FIGURES ......................... Argunents Related to the Design of Instruction ..... The Knowledge to be Taught ............. Psychological Views of Learning and Transfer in Science Education .............. The Design of Instruction ............. Canponents of the Present Research ........... Analyzing the Knowledge: The Content-Task- Strategy mdel ................. Information Processing Psychology: A Dynamic View of the Learner ............... The Design Process ................. Overview and Direction of the Study ........... Research Questions . . . ................ II. REVIEW OF RELATED RESEAROI ............... The Structure of Knowledge ............... Content-Task-Strategy Lbdel ............ Content Analysis. . ..... - ........... Task Analysis ................... Strategy Analysis ................. Psychological Views of Learning and Transfer ...... iv Page xii WOALN £0 10 11 13 14 19 21 21 26 27 28 29 31 CHAPTER III. Information Processing Psychology ............ The Human.InfOrmation Processing System ...... Task Environment .................. Problem Space . . ................. Instructional Design .................. Content-Task-Strategy Analysis of the Classification of Igneous Rocks ........ . .......... Geologic Classification . ............. Content Analysis of Geologic Classification . . . . Task Analysis . .................. Skills or Strategy Analysis of Geologic Classification . ................ Design of Precursor Tasks and Strategies ...... Additional Related Research ............ RESEARCH METHODS .................... Overview. . .................... Research Subjects. . . . ................ sample. . . . . ................. Selection and Assignment .............. mteri als C C O ....... O OOOOOOOOOOOOO Miltiple Classification Pretest Boards ....... Rock Sets . . . . . ................ Task Boards .................... Procedures . . . .................... Instructor and Tester Training ........... Classification Pretest and Preliminary Instruction. Pretest and Posttest Instructions ......... Instructional Treatment and Treatment Groups. . . . Outcome Feedback Instruction ............ Strategy Instruction ............... Strategy Instruction - Task 1 Comparison to Standard ............ . ....... Page 36 36 39 4O 41 44 45 46 52 S4 64 72 77 77 78 78 78 82 82 83 85 85 85 86 88 89 90 91 Comparison to Standard Task: Single variable Classification Task: Strategy Instruction - Task 2 Single variable Classification ................. Strategy Instruction - Task 3 Double variable Classification ................. Strategy Instruction - Responses to Student Errors ..................... Design..... .................... Experimental and Comparison Groups ......... Control of Independent Variables by Design ..... Experimental Design . ..... . ......... Hypotheses ..................... Dependent variables ................... Raw Data. . .................... Scores. . ..................... Statistical Analysis .................. Comparative Analysis ................ Descriptive Analysis ................ RESULTS ......................... Research Questions ....... . ........... Strategy Results ..... Strategy Learning ................. Strategy Use. . . . . . . . ............ Strategy Component Use ............... comparison to Standard Task: Performance Results. . . . Pretest . . . . . . . . . ....... . ..... Facilitation of Learning .............. Task Perfbrmance .................. Strategy Results . Strategy Transfer ................. Strategy Components Transfer ............ vi Page 91 92 93 95 98 98 99 103 105 111 111 118 126 126 127 129 129 131 131 132 133 134 134 135 136 137 137 140 Page Strategy Learning . ................ 141 Strategy Use. . .................. 142 Strategy Components Use .............. 142 Single Variable Classification - Perfbrmance Results . . 145 Learning Transfer ................. 146 Facilitation of Learning .............. 147 Task PerfOrmance .................. 149 Double Variable Classification Task: Strategy Results . 151 Strategy Transfer ................. 151 Strategy Component Transfer ............ 152 Strategy Learning ................. 159 Strategy Use .................... 161 Strategy Component Use. . ............. 161 Double variable Classification Task: Performance Results . . . .................... 164 Multiple Classification Pretest Scores ....... 165 Learning Transfer ................. 16S Facilitation of Learning .............. 167 Task PerfOrmance .................. 169 SuImnary of Results . . . ................ 171 CONCLUSIONS AND DISCUSSION ............... 181 Study Overview . . . .................. 183 Limitations ....................... 185 Conclusions ....................... 186 Discussion . . ..................... 187 Initial Strategy Learning . ............ 187 Strategy Use and.Transfer . . . . . . ....... 188 Performance Results . . . . . . . . . ...... 193 Representation of the Content of Instruction. . . . 197 The Efficiency of a Large Scale Experimental Study. 200 Summary' ......................... 202 APPENDICES A. DEFINITIONS OF PRIMARY PROCESS ............. B. .MULTIPLE CLASSIFICATION.MATERIALS.AND PROCEDURES . . . . C. INSTRUCTIONAL PROTOCOLS ................. D. SCORE SHEETS ...................... BIBLIOGRAPHY .......................... viii Page 207 213 217 259 270 Table fiOWVO‘Sflfi 10. 11. 12. 13. 14. 15. 16. LIST OF TABLES Analytic and Systemic Concepts for Igneous Rock Classification .................... Description of Primary Infermation Processes ....... Responses to Student Strategy Errors During Instruction . List of Research Hypotheses ............... comparison to Standard Task - Raw Data Symbols ...... Single variable Classification - Raw Data Symbols . . . . Double variable Classification - Raw Data Symbols . . . . Comparison to Standard Task (I) Scores .......... Single variable Classification Task (11) Scores ..... DoUble Variable Classification Task (III) Scores ..... Strategy Scores Criteria ................. Strategy Learning Results: Trials to Criterion Scores for Cumulative Strategy Group Instruction ....... Strategy and Component Use Results: Comparison to Standard Task Posttest ................ t-Test fer Trials to Criterion Score: Comparison to Standard Task Instruction ........ . ...... t-Test fer Comparative Response Score: Comparison to Standard Task Posttests .............. t-Test fer Placement Accuracy Score: comparison to Standard Task Posttests .............. ix Page 48 58 94 106 113 114 117 119 120 121 124 132 133 136 137 Table 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. Page Strategy and Component Transfer Scores: Single variable Classification Task Pretest ......... 139 Strategy Learning Results: Trials to Criterion Score fbr Cumulative Strategy Group ............. 141 Strategy and Component Use Scores: Single variable Classification Task Posttests ............. 143 P1acement.Accuracy Results for Isolated Feedback Group: Single variable Classification Task First Pretest ........................ 145 Learning Transfer - Placement Accuracy Results: Single variable Classification First Pretest ......... 147 Learning Transfer - Planned Comparisons fer Placement Accuracy: Single variable Classification First Pretest ........................ 147 Facilitation of Learning - Trials to Criterion Results: Single variable Classification Task Instruction. . . . 148 Facilitation of Learning - Planned Cbmparisons for Trials to Criterion: Single variable Classification Task Instruction ...................... 148 Task PerfOrmance - Placement Accuracy Results: Single variable Classification Task Pesttests ........ 150 Task Perfbrmmnce - Planned Comparisons for Placement .Accuracy: Single variable Classification Task Posttests ...................... 150 Strategy Transfer Scores: Double variable Classification Pretest ........................ 152 Transfer of Comparison-to-Standards Components Scores: Double Variable Classification Pretest ........ 154 Transfer of verbal Response Component Soores: DoUble variable Classification Pretest ............ 157 Strategy Learning Results: Trials to Criterion Score for Cunulative Strategy Group. . ........... 160 Table 31 . 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. Strategy and Component Use Scores: Double Variable Classification Task Posttest ............. Learning Transfer - Placement Accuracy Results: Double Variable Classification Pretest ........ Planned Comparisons for Pretest Accuracy: Double Variable Classification Pretest. . . . . ....... Facilitation of Learning - Trials to Criterion Results: Double Variable Classification Instruction ...... Planned Comparison for Trials to Criterion: Double Variable Classification Instruction .......... Task Performance - Placement Accuracy: Double Variable Classification Posttest ........... Planned Comparison for Placement Accuracy: Double Variable Classification Posttest ........... Page 162 166 168 168 169 170 Smmary of Strategy Learning Results: Trials to Criterion Scores - Instruction ...... . .......... Sumnary of Strategy Use Results: Strategy Use Scores - POStteStS o o o o o o cccccccccccc Sumnary of Strategy Transfer Results: Strategy Transfer Scores - First Pretests ........... Sumnary of Facilitation of Learning Results: Trials to Criterion Scores - Instruction ........... Sumary of Learning Transfer Results: Performance Accuracy Scores - First Pretest. . .......... Sunmary of Task Performance Results: Posttest Performance Accuracy Scores . . . ........... Sumnary of Strategy and Strategy Components Use Results forPosttests. . . . . . . . ., ............ Sunmary of Strategy and Strategy Component Transfer Results for Pretests ................. Snmnary of Conclusions and Questions for Future Research . xi 172 173 173 174 174 179 203 LIST OF FIGURES Figure 1. b LN o o 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. Task-Content Matrix .................... Generalized Classification Scheme (Analytical Level) . . . Specific Classification Scheme for Igneous Rocks (1) . . . Double Variable Classification Chart ........... Flow Chart Symbols .................... Comparison Secondary Process ............... Classify Tertiary Process ................. Strategy fOr DoUble variable Classification Task ..... Single variable Classification Task Strategy ....... Single Variable Classification Chart ........... Comparison-to-Standard Chart ............... Comparison-to-Standard Task Strategy ........... Random Selection and Assignment of Students ........ Number of Students fOr Each Task ............. Mnltiple Classification Pretest - Sample Board ...... Testing and Instruction Schedule . . . . ......... Design to Control Major Independent Variables ....... Design to Balance Use of Sample Sets A and B ....... Experimental Design .................... Large and Small Shapes for Multiple Classification Pieces. xii Page 35 50 51 56 57 60 61 63 66 68 69 7O 80 81 82 97 101 102 104 216 CHAPTER I THE PROBLEM A major expectation of all schools is that students will learn what they are taught and transfer what they have learned to more com- plex situations. Science education students are expected to learn and to transfer knowledge and skills of the science disciplines. As the body of knowledge which constitutes any one discipline is large, those engaged in instructional design have two major responsibilities. The first is to select that knowledge which is most central to solving the problems of the discipline. The second, the problem of this study, is to design instruction to maximize the ease of learning and to enhance transfer of that knowledge to new, often more complex, situa- tions. In addressing these responsibilities instructional designers must be able to describe the knowledge to be taught, to model the think- ing of the learner, and to describe the manner in which the design should be accomplished. There are two components to the thesis of the study. (1) Instruction for the precursor tasks of a sequence will enhance performance of later tasks when the sequence is designed on the basis of analyzing the structure of the lonowledge to be learned and an information processing view of human thinking. (2) There will be a facilitative effect of instruction based on task specific cognitive strategies within the task sequence. The second statement was the major fecus of the study. The specific undertaking was to design an instructional sequence which would effectively and efficiently teach students to classify igneous rocks and to evaluate learning and transfer within the sequence. Students were given a number of rock samples to classify using a two variable classification scheme. These two variables were the size of the mineral grains and the relative amount of light and dark grains in the individual samples. The two variables were crossed, resulting in.a 3 X 3 matrix defining nine classes of igneous rocks. Each sample must be correctly placed in one of the nine classes. Rock classifica- tion was selected as particularly important to geologists in addressing a large nunber of problems within the discipline. The instruction was designed to facilitate the initial learning of the geologic classifica- tion and there should be direct evidence of transfer within the instructional sequence. For this study the following were done to meet the responsibilit- ies cited: ‘ I. The knowledge to be taught was described in detail. The description included the infbrmation to which the student could.make explicit reference, and that knowledge which was implicitly required to classify the rocks. This knowledge was described in.tenms of the constructs of the discipline. II. A psychological model was prepared which specified how knowledge of the discipline could be used in the student's reasoning as he classifies the rocks. III. The design process was made explicit. This included the way the knowledge of geology and.a model of a thinking student were combined to result in an effective instructional procedure. 'With respect to each of these undertakings, past arguments within science education point to several considerations or problems. The following section briefly describes those arguments. The second section Characterizes the present literature which will be considered. The final section presents an overview of the study including Specific research questions. Arguments Related to the Design of Instruction Science education over the past twenty years has debated.what students should be taught and how that infbrmation could be organized to facilitate learning and transfer. As pointed out by Shulman and Tamdr (1973), much of this discussion has focused on the notion of structure. Within this debate two lines of thought, often intermingled are important. The first is epistemological, the second psychological. .A third consideration is the process of designing the instruction. This has not been an explicit topic in the science education literature. These three considerations are outlined below. The Knowledge to be Taught The epsitenological arguments focused on what should be taught. The traditional answer had been to select the scientific laws, facts, principles, and definitions which were considered the stable truths of each discipline. The textbook served as the collection of content to be learned. The more recent response has been "enphasis on the nature, structure, and unity of science, and on the processes of scientific inquiry" (lClopfer, 1971, p. 565). In particular, the "processes of science" such as hypothesis formulation, data collection, classification, and inferring were constrasted with the previous "content" notion of what should be taught. Even though discussion of the value to be placed on content or process has abated, issues of what should be taught are unresolved. Most science educators would now agree that both content and process should be taught. However, the descriptions of how content and process are related have not been fully developed. Schwab has begun the description of these relationships using the parallel terms sub- stantive and syntactic structures of the disciplines. Schwab's work described the nature of disciplines. For Schwab "the structure of a discipline consists, in part, of a body of imposed conceptions which define the investigated subject matter of that disci- pline and control its inquiries," (1962, p. 199). He further de- scribes the types of structures named above. The first, substantive structures, is "a body of concepts--conlnitments about the nature of the subject matter functioning as a guide to inquiry." The second, syntactic structures, is "the pattern of its (the discipline's) pro- cedure, its method, how it goes about using its conceptions to attain its goal" (SChwab, 1962, p. 203). It is important to note that Schwab views these structures as "interrelated, capable of distinction in theoretical discourse but never in practice" (Shulman and Tamir, 1973, p. 1102). He further claims that the structures are particular to each discipline. Structures, be they content or process, which cut across disciplines should not be expected. This is an important point of Schwab's work unfOrtunately ignored by many curriculum developers. The integrity of flhe structures of a given discipline must be maintained, lest incomplete or inaccurate knowledge be in- cluded in curricula. Schwab's work clearly calls for the identification and description of specific substantive and syntactic structures. Hewever, there are few detailed analyses of this type in the science education literature. One reason fer this may be the lack of analytic models to help describe the intersection of syntactic and substantive structures. The structures of a diSCipline are many and complex. To do the analyses which should precede instructional design such analytic models are needed to simplify and organize the resultant infbrmation. Analysis and description of the knowledge to be taught not only avoids mis- representation of the knowledge,'but provides the designer with the major structures to be used in the design process. Psychological Views of Learning_and TranSfer in Science Education The second critical area fer the discussion of structure was psychological. The major question was how to best facilitate the learning and transfer of knowledge structures. The discussion centered on what knowledge can be best taught and the development of optimal organization of that knowledge. These questions were approached from a number of psyChological perspectives. The views most relevant to the present work are represented by Bruner and Gagné. For Bruner (1963) structures of a discipline were described as the principles and generalizations which related a range of phenomena. Bruner expected such structures to serve as mechanisms of learning and transfer. This kind of knowledge would be more easily retained and transferred more broadly. Furthermore, instruction to teach such structures was to proceed in such a way that students discover those general relationships. This was based on the view that learning is an "act of discovery" requiring the recognition of new knowledge, fellowed by the cognitive reorganization and verification of that knowledge (1961). Gagné (1970) claimed that instruction should be hierarchically ordered. The final task learning had to be supported by the prerequisite skills of simpler types of learning. The learning of principles was dependent on learning prerequisite rules which in turn depend on the learning of necessary concepts. Gagné posits suCh hierarchically organized skills, called capabilities, as internal to the learner. The capabilities are described in.terms of the behaviors the learner can perform. The work of Gagne, Bruner, and others established the necessity of considering the learner when designing instruction to facilitate learning and transfer. Bruner's concept of structures (principles and generalizations from.a discipline) as mechanisms of transfer and the "act of discovery" provide two guidelines for curriculum design, but little in the way of detailed description. The first points to considering that the nature of the knowledge influences the manner in.which the learner uses that knowledge. HOwever, Bruner does not propose a.way these structures can be systematically identified and described. The "act of discovery" notion clearly implies that there is an important internal cognitive processing of newly recognized knowledge. Hewever, little of how the knowledge structures are reorganized is specified. With a model of the way knowledge is cognitively processed, a great deal more infbrmation about the learner would be available to the curriculum designer. Gagne presented a more precisely defined and detailed set of constructs than did Bruner. This resulted in a more complete descrip- tion of the internal and external conditions of learning. However, the description of internal capabilities only in terms of behaviors that can be observed limits the richness of this description. Little is known of how knowledge is directly used or altered as an individual attempts to complete a task. By tying the psychological descriptions so closely to the overt behaviors, little is known about the dynamics of the thinking of an individual. What is required for instructional design is a more dynamic, precisely specified model of human thinking. This should describe the processing of the available knowledge struc- tures and reflect in detail the observable performance. The Design of Instruction Different conceptions of instructional design have been implicit in elenentary and secondary science education curricula. The notion that instruction is designed by deduction from a single psychological theory has been prominent in elenentary school curricula. For example, various psychological perspectives greatly influenced the Elementary Science Study (Bruner) and Science—A Process Approach (Gagne). Al- though much more attention was paid to the nature of the subject matter in the design of the Science Curriculum Improvement Study, the work of Piaget was highly influential. As Shulman arnd Tamir point out, this is inadequate to the task. "Psychological theories of learning and cognition renain far too weak a foundation to support any entire curricular program. No single theoretical formulation has yet demon- strated sufficient comprehensive validity to be trusted to this task." (1973, p. 1138). At the secondary level the reverse problen was the case. Knowledge related to learning and cognition was not fully utilized. Instead, extensive reliance was placed upon the structure of knowledge. New courses were designed in biology (Biological Science Curriculum Study), Chemistry ((1134 Study), and Physics (Physical Science Study Committee). These attempted to reflect more adequately the nature of science disciplines than had the traditional approaches. The result of this single factor design approach has been that relationships between the knowledge to be learned and the psychological mechanisms of learning are unspecified. The design process should integrate the epistemologic information gained from the careful analysis of the structure of the disciplines and our knowledge of the learner as he exhibits various performances. Without such integration, informa- tion valuable to the designer is lost, often in the confusion of psycho- logical and epistemologic constructs. A design process such as this re- quires epistemologic descriptions and psychological models which are compatible . Components of the Present Research The present work attempts to develop and evaluate an instruction- al sequence designed to facilitate learning and transfer. The design incorporates the detailed analysis of the knowledge structures and a compatible psychological model of the way students use the available knowledge to complete specific tasks. To do this the work of Schwab is extended, and a psychological model of cognitive performance, richer in descriptive power than nodels proposed by Bruner and Gagne is utilized. The following explanation briefly characterizes the model proposed by Smith (1974) for the analysis of disciplinary struc- tures and the information processing psychology of Newell and Simon. The major tenets of the design process adopted from the Science of the Artificial by Herbert Sinner (1969) are also described. 10 Analyzingfithe Knowledge: The Content-Task-StrategyiModel The model used in this study for the analysis of the disciplinary structures was developed by Smith to represent specified domains of learning in terms of concepts, tasks, and strategies. When taken together the resulting description represents the structure of some portion of a discipline (Smith, 1972, 1974). This model is particular- ly appropriate to meet the needs of this study. The descriptions of the knowledge to be taught are constituted in suCh a.way that Schwab's warning to maintain the relationships between the structures of the discipline is fellowed. Both substantive and syntatic structures and the relationships between them are made explicit in these descriptions. He has proposed three levels of analysis in the description of the learning objectives. Smith describes these levels of analysis as follows: "Content analysis involves (l) the identification of the types of conceptual systems Characteristic of a discipline or subdiscipline, (2) the fbrmulation of a paradigm or analytic network which represents the structure of each type of system and (3) the comprehensive identification and cataloging of the conceptual systems of discipline according to the analytic network they exemplify. Task analysis involves the identification or perfbrmance requirements relevant to a Specific type of conceptual system. These requirenents or tasks are described in terms of the corresponding analytic network. Skills analysis identifies alternative infbrmation processing strategies by which tasks can.be perfbrmed. These are descriptions of behavior at the psychological level and provide the basis for planning and predicting transfer among tasks." (1974, p. 2) The content analysis is viewed as a detailed description of Schwab's substantive structures. Task and skills (or strategy) analysis, 11 when taken together, describe important aspects of the syntax of the discipline. The tasks specify what is done with the substantive structures. The strategies described in psychological terms the way those tasks are carried out. In general, Smith views learning and transfer to be facilitated in an instructional sequence by the presence of shared concept, task, and strategy components. He argues particularly for the facilitative effect of the strategy component as follows: "The transfer effects of learning several tasks probably depend heavily on the strategies the student learns to use in performing both original and transfer tasks. This suggests that the design of instruction to optimize positive transfer must consider strategies which the student learns to use in performing the tasks." (1974, p. 11) The major focus of this study is the facilitative effect of in- struction based on task Specific cognitive strategies in a sequence of successively more complex tasks. Information Processing Psychology: A Manic View of the Learner The basic tenet of the information processing theories is that hunan beings are adaptive systems which behave according to the nature of the task with which they are confronted. Thus, the field of infor- mation processing psychology considers both the structure of the tasks to be performed and the cognitive processing of available information. This viewpoint is adopted for the present work as it offers a poten- tially rich description of a learner completing a task, and, accordingly, more information useful in instructional design. 12 In the design of instructional sequences the knowledge to be learned is Specific to and inherent within a discipline. Using the model proposed by Smith major structural components can be described in terms which represent the structures of the discipline. Within the infbrmation processing framework, such description can be used to describe what is called the task environment. This is the information to which the learner can.make explicit external reference. we can also represent the necessary and sufficient knowledge from the dis- cipline which is required within the learner to complete the specified performance. This additional knowledge refers to the content of the problem space, the mental world in which the learner perfbrms sequences of cognitive Operations with available knowledge to solve a given problem. The task environment and problem space are closely related. The structure and infbrmation in the task environment, in conjunction ‘with the existing knowledge of the learner, determines the problem space the learner adopts. Certain structural features of the task environment will be predominantly represented in the problem space. The problem space which is constructed by the problem solver may or nmy'not be apprOpriate fer solving a given.problem, This can be due to the influence of previous experience and missing knowledge. It is reasonable to expect that if the problem space contains relevant, well organized infbrmation, the prObability of correct task perfbrmance will be high. In particular, if the conceptual knowledge necessary fOr a specific perfbrmance and strategies which process that knowledge in 13 an organized way are available, and likelihood of correct performance is increased. Learning and transfer phenomena may be explained in terms of the availability in menory of concepts and strategies which can be utilized by a learner for performing a given task. The Des ign Process Simon views design as a science in its own right. He describes design as the develognent or courses of action which change existing situations into preferred ones (1969, p. 55). The result of such design is an artifact. The designer uses (1) knowledge of the goals which the artifact is to meet, (2) knowledge of the workings of the inner environment of the artifact, and (3) knowledge of the outer environment. The prenise is that to the extent the inner environment of the artifact is appropriate to the outer environment in which it Operates, the goals for the artifact will be attained. This view is extended by Simon to describe the hunan problen solver as an artifact in that he is an adaptive systen which can be changed and modified by learning. From this vieWpoint instructional design can be considered a matter of utilizing what is known about the knowledge to be learned (outer environment) and the inner environment of the learner to develop effective and efficient learning experiences. Design on this basis requires (1) descriptions of the knowledge to be learned (i.e. , the outer environment) and (2) a model of inner environment of the problem solver. Nbre particularly, the model of the problem solver needs to include a description of the knowledge and strategies which would constitute a problen space appropriate to the 14 outer task environment and a model of the way, the problem solver pro- cesses that information. The description of the knowledge taken from a discipline and potential matching problen Space is possible using constructs such as those proposed by Smith. Information processing psychology offers rich description of the problen solver. Overview and Direction of the Study The epistenologic argunents of Schwab's work imply a need to map a potential domain of learning before design of instruction, lest the selection and representation of knowledge be inaccurate. The integrity of the structure of the discipline from which the knowledge is drawn must be maintained. An information processing view indicates likewise. The task en- vironment and previous learning interact to generate a problem space the student uses to perform the given task. We need to know what information is given about a problen and what is required to solve it. Without such information the designer cannot forge appropriate instruc- tional procedures. To design and evaluate instructional sequences, we need to pr0pose psychological mechanisms of learning and transfer. In this study a conmon set of concepts and, in particular, task specific cognitive strategies, serve this function. The construct of a Strategy is psychological, but it is viewed also as a description of a syntax of task performance. The final knowledge to be learned can be reduced to simpler learn- ing episodes related by cannon features. These preliminary episodes 15 must be designed and sequenced, taking into consideration these structures of the final learning desired before a high level of per- formance can be expected. This study carried out the following: I. II. III. Mapped a potential domain of learning and transfer. 1. A portion of geology was identified as an important structure of that discipline. Specifically, the classification of igneous rocks was selected. This is an important procedure used in solving problens of the discipline. The substantive structures related to the classification were identified and charac- terized according to the nature of their fnmction in the discipline. This was done in terms of Smith's analytic networks. Proposed possible psychological mechanisms of learning and transfer. 1. Cannon conceptual structures and task specific cognitive strategies were hypothesized as mechan- isms for the learning and transfer of disciplinary S tructures . Designed a learning sequence across which learning and transfer can be expected to occur. 1. The knowledge to be learned was analyzed to determine precursor learning episodes which 16 are smaller, less complex components of the final episode. The learning sequence consisted first of learning concepts related to the classification of igneous rocks. Second, the sequence was a series of tasks, ordered according to the expectation that learning a strategy for one task would facilitate learning and transfer in the next task. E‘mpirically investigated strategy learning, strategy use, strategy transfer, task performance, and learning transfer within the task sequence. For purposes of this study these terms were defined as follows: 1. Strategy learning is the initial acquisition of a strategy inferred from students actions during the instructional trials. Facilitation of learning consists of fewer trials to criterion compared to an appropriate control group. Trials to criterion indicate the anount of instruction necessary to learn to perform a given task. Strategy use is the generalization of the strategy to new elenents (rock sanples) which is inferred from students actions on the posttests. Task performance is the effect of previous instruction on the accuracy of student performance in the posttests for a particular task. 17 5. Vertical strategytransfer is the use of the strategy for a previous task during the pretest attempt to complete a subsequent task in the sequence. 6. vertical learningtransfer is the cumulative effect of the previous instruction on the accuracy of student performance during the initial pretest attempt to complete the next task in the sequence. The unique aspect of the instructional sequence is the three dimensional representation of what was to be learned, i.e., the representation of the learning objectives. These were expressed in terms of the fOllowing: (1) interrelated sets of concepts, (2) task descriptions including the infbrmation given to the student and the perfbrmance outcome required, (3) cognitive strategies which are models of the cognitive processes a student could use to systematically act on the information available in completing the task. The relationships among these descriptions of what was to be learned were detailed in terms of common or compatible features in each dimension. The derivation, description, and organization of the objectives into an instructional sequence were based on the related features of eadh of these three dimensions of representation. It was further based upon the chosen design approach. The intent was to design in- struction which would generate an inner environment (problem space in the learner) potentially sufficient in an.encounter with the given outer environment (the task the learner is to complete). 18 The analysis of igneous rock classification resulted in a descrip- tion of the concepts and task requirements which characterize the outer environment. It further resulted in the identification of concepts and potential cognitive strategies which would be in a problem space appropriate for the task environment. Given the detailed three dimen- sional description of the final task, the design continued to develop related preliminary tasks which reduced the complexity of the learning. The closely related tasks are progressively smaller components of the final task. The use of smaller nunbers of identical concepts and less complex subroutines of the strategy, both taken from the final task, served as the basis for these preliminary tasks. The major features of the final task were maintained as smaller, logically related chunks of infbrmation to be learned. The attempt was to (1) optimize the amount of knowledge acquired during a single instructional episode and (2) to facilitate the fbrmation of a few large Chunks of infbrmation which could be processed from the limited capacity short-term menory. From this perspective, learning to solve a.particular task was considered the accumulation of the necessary knowledge and strategies so that a prOblem space apprOpriate to the task is generated upon en- counter with that task. Learning will be facilitated according to the degree to which a match between the problen space and task environment is attainedn The problem space is apprOpriate to the task environment to the extent that concepts and strategies of the learner fit the features of the task. It can also be expected that transfer of learn- ing to a new, more complex task can be expected if the previous task 19 shares conmon structures, and the learner has those structures available for use on the new task. RESEARCH QUESTIONS The preceding section outlines the steps taken to meet the epistemlogic and learning considerations previously described. The following is the translation of those considerations into researchable questions . I. II. III. IV. Strategy Learning: When instructed in a specific strategy within a task sequence, can the student learn to perform the task using that strategy? Strategy Transfer: Does a learned task-specific strategy transfer to a more complex task within a task sequence, that is, will a student automatically utilize the strategy learned for a precursor task in the nminstructed attempt to perform a related more complex task? Strategy Use: Following instruction on a task within a task sequence do students use the taught strategy to perform the task? Does strategy-based instruction improve the learning of a vertical sequence of tasks? More specifically: A. Learning Transfer: Does strategy-based instruction enhance the transfer of learning within the task sequence? 20 B. Facilitation of Learning: Does strategy-based instruction enhance the efficiency of learning cf the tasks within the sequence? C. Task Perfbrmance: Does strategy-based instruction fOr the sequence enhance posttest perfbrmance within the task sequence accuracy? The remaining Chapters describe the attempts to answer these questions. The second chapter (1) describes epistomologic, psycholog- ical and design issues which have been related to the constructing instructional sequences, (2) describes the literature utilized to address these issues, and (3) describes the manner in which the literature was applied in the present study. The third chapter describes the experimental procedures, specific research hypotheses and scores used to answer the research questions. The feurth chapter presents the results of the experiment. The final Chapter summarizes those results and intrepretes them in light of the initial premises and limitations of the study. CHAPTER II REVIEW OF RELATED RESEARCH The present chapter reviews the research considered in the develop- ment of this learning and transfer study. The chapter can be divided into five sections. The first reviews recent literature in which there have been attempts to describe the nature of the knowledge to be learned. The second reviews recent literature related to the learning and transfer of knowledge as argued by researchers who had a major influence in science education, The last portion of each of these sections reviews in some detail the literature directly utilized in the present study. The third section describes the view of instruction- al design whiCh guided the development of the instructional sequence. The fOurth section is the most important of the chapter as it describes the results of applying the reviewed literature to meet the goals of the study. The section includes the description of the knowledge to be learned in terms of concepts, tasks, and strategies. The final section briefly reviews science education studies and the basic work of Piaget related.to multiple classification. The Structure of Knowledge Schwab (1962), Phenix (1962), and others have argued that the var- ious disciplines must serve as the sources of knowledge to be included 21 22 in the curriculum. As noted earlier, Schwab has further argued that the nature of the structures of that knowledge are particular to each discipline. He asserts that the relationship between the substantive and syntactic structures within each discipline must be maintained if the curriculum is to accurately reflect the knowledge to be taught. Taken in total these points argue for a strong epistemologic foundation for instructional design. The argument for attending to the structure of knowledge has been made for work in both curriculum development and curriculum research. Robinson, in the "Philosophical and Historical Bases of Science Teach- ing" (1969), asserts that the elucidation of structure has been inadequate and, as a result, has been problematic in curriculum develOpment. "This lack of precision and comprehensiveness is seductive with respect to many who work in curriculum development because it promises great simplification in the overwhelming task of mastering the manifold realms of scientific knowledge. It creates the illusion of easily grasped solutions rather than hard scholarship for dealing with curri- culum problems" (1969, p. 460). Citing Hurd and Rowe, Robinson also argues that research efforts have suffered from a lack of analysis from an epistemologic base: ". . . researChers have lacked well-developed philosophic starting points and have tended to be contradictory, frag- mented, and unpatterned" (Robinson, 1969, p. 459). In concert with Robinson, Shulman and Tamir make the following recommendation, ". . . the structure of the subject matter must. . . 23 beCome an explicit facet of research design in the field of instruc- tional research" (1973, p. 1138). A variety of researchers have suggested ways of representing the knowledge to be taught. Many of these views (Bruner, Gagne, Schwab) have served as the basis for the development of particular science education programs. Bruner called attention to the necessity of attending to the nature of the knowledge. From a psychological perspective he cited four arguments for teaching the "fundamental structure of a sobject" (Bruner, 1960). l) "The first is that understanding fUndamentals makes a subject more comprehensible" (p. 23). 2) "The second relates to human memory. . . unless detail is placed into a structured pattern, it is rapidly fergotten" (p. 24). 3) "Dhird, an understanding of fundamental principles and ideas, as noted earlier, appears to be the main road to adequate 'transfer of training'" (p. 25). 4) "The feurth claim fOr emphasis on structure and principles in teaching is that by constantly reexamining material taught in elementary and secondary schools for its fondamental character, one is able to narrow the gap between 'advanced' knowledge and 'elementary' knowledge" (p. 26). For Bruner the fundamental structures were the principles and concepts of a discipline so basic and.important that they simplified and.made understandable a wide range of related phenomena. Bruner did not specify how the fundamental structures could be described or identified but called fer further research on eaCh of these four arguments . 24 Schwab described the nature of discipline structures in greater detail than had Bruner. His representation of the knowledge to be learned was dependent upon the conviction that "to identify the disciplines that constitute contempory knowledge and.mastery of the world is to identify the subject matter of education. . ." (1964, p. 11). On the basis of the review of some feur thousand researcher reports, Schwab characterized the disciplines as distinctive in terms of the substantive and syntactic structures which were used to guide their inquiries. This study has been cited by Robinson as the "most penetrating analysis of structure in the literature" (1969, p. 460). However, lest the sc0pe of this work be misinterpreted, Schwab him- self has described this work as prelimdnary investigation "of the nature, variety, and extent of human knowledge" (1964, p. 6). He expected later work to provide the detailed descriptions of specific structures. Gagne chose to represent the knowledge to be learned in terms of psychological descriptions of the tasks to be performed. The final task was analyzed by asking the question, "What do the students need to know befOre they can complete this task?" By successively asking this question, learning hierarChies were developed which specified the prerequisite knowledge. The hierarchies described the conditions internal to the learner which are necessary to complete the final task. The task descriptions are in terms of concepts, rules, and principles whiCh are defined as psychological constructs. For Gagne, the concepts, rules, and principles are classes of responses which indicate different types of observable perfbrmances. 25 The final tasks from which the learning hierarchies were derived were to be specified by subject matter specialists. HOwever, from that point on in the development of the hierarchy there is little or no con- cern for the structure nature or structure of the discipline. Gagne contended that ". . . difficulties in identifying the content of learning would be avoided if care were taken to put the emphasis where it belongs, which is on the attainment of the learners" (1970, p. 244). More recently within science education has been the work of Klopfer in the Handbook of Formative and Summative Evaluation (Bloom, Hastings, Madaus, 1971). KlOpfer used both desired student behaviors and a range of content fer elementary and secondary schools to generate a matrix representing science knowledge. The student behaviors were in part derived from the Bloom Taxonomy of Educational Objectives but also focused on categories relating to processes of scientific inquiry. The categories of content encompass "virtually all the content of school science instruction, both in traditional and modern courses, and reflects the divisions and subdivisions of the subject that are commonly accepted by contemporary science teachers and educators" (KlOpfer, 1971, p. 580). Such a.matrix implies scientific inquiry behaviors which cut across disciplines. .Although this is antithetical to Schwab's analysis, such a matrix does point toward the relationship between various student behaviors and the content of the subject matter. This view is preferable to the dichotomous content vs. process arguments which raged during the 1960's. It should be noted, however, that this classification scheme still is not a detailed analysis. For example, 26 a cell from the matrix is the Interpretation of Experimental Data and Observations (behavior) for Cell Structure and Function (content). A large quantity of knowledge remains unspecified within this category. The researchers reviewed above have offered a variety of important perspectives. The work of Bruner and Schwab pointed to the importance of structure. Bruner argued from a psychological perspective. SChwab argued from an epistimologic vantage point. Both provided broad initial guidelines about the nature of the knowledge to be taught. Neither provided a framework for detailed analyses to be used in the design of specific instructional sequences. Gagne points to the utility of detailed descriptions in instruc- tional designs. However, the purely psychological perspectives do not develop important epistemologic considerations as indicated by both Schwab's and Bruner's positions. KlOpfer also does not fully attend to the point that various disciplines are by their nature different and do not necessarily use common processes in their inquiries. How- ever, he did illustrate that the behaviors or processes and content of science are not separable. 1 ‘Within the literature epistemologic constraints have been dis- cussed. These constraints now must be applied in the descriptions of subject matter. Greater detail from the analysis of what is to be taught must be available fer purposes of instructional design. Content-Task-Strategy Model Smith has prOposed.a.model for representing the knowledge to be taught. The model was used in this study as an analytic tool to generate 27 the descriptions called fer in the previous section. The analysis provided the relatively fine grain descriptions used in the design of the instructional sequence. There are three components to the model; content, task and skills or strategies. Content analysis involved the identification and description of related concepts or sets of concepts. Task analysis results in descriptions of what infermation is initially given and ultimately required in the perfbrmance of the disciplinary tasks. Strategy analysis specifies at a psychological level how available infbrmation is processed in the performance of a specific task. Further description of these three components, the basic attending assumptions, and a brief elaboration are stated below. The final portion of the chapter describes the results of the analysis completed fer this study. This example will elaborate the brief descriptions presented here. Content Analysis Assumptions: (1) "Any discipline is built around a set of specialized conceptual systems. (2) Many of the specialized conceptual systems of a discipline fall into a small number of categories, each of which share a common logical structure" (Smith, 1974, p. 2). Description: "Content analysis involves l) the identification of the types of conceptual systems characteristic of a discipline or subdiscipline, 2) the formulation of a paradigm or analytic netwOrk which represents the structure of each type of system, and 3) the comprehensive identification 28 and cataloging of the conceptual systems of a discipline according to the analytic network they exemplify" (Smith, 1974, p. 2). The content analysis identifies sets of concepts which belong to a particular discipline. For geology such a set of concepts in- cludes sandstone, shale, limestone, and siltstone. These concepts are similar in that each names a particular rock type. For this set of content-specific concepts (called "systemic" concepts) a single "analytic" concept is generated which must be of sufficient generality to represent the function of all similar concepts within the discipline. For example, the analytic concept "class name" can be applied to all specific concepts listed above. A complete but relatively small number of such analytic constructs when taken together, constitute an analytic network which specifies the logical relationships between Specific or systemic concepts of the discipline. Task Analysis Assumptions : 1. "Most important competencies related to a discipline, at least from a general education point of view, can be presented as manipulations of conceptual systems." 2. "The level of mastery of a conceptual system may be adequately inferred from a defined set of observable behaviors" (Smith, 1974, p. 2). Description: "Task analysis involves the identification of performance requirements relevant to a specific type of conceptual system. These requirements or tasks are described in terms of the corresponding analytic network (Smith, 1974, p. 3). 29 IMore specifically tasks are defined by presenting the analytic concepts which represent the given information and the infbrmation which is required as output by the person executing the task. A geologic task represented within this framework may be defined at the analytic level as: Given: one class name Required: statement of relevant variables On the systemic level, the task could read: Given: the class name, sandstone Required: the variables, composition, texture, particle size Smith suggests one of the ways of identifying tasks within a discipline is by having someone familiar with both the discipline and the task analysis model list tasks important to that discipline. This technique was utilized in the present study. Strategy Analysis Assumptions: 1. "Common infermation processing strategies are applicable to the utilization of conceptual systems sharing a common structure" (Smith, 1974, p. 2). Description: "Skills analysis identifies alternative infbrmation processing strategies by whiCh tasks can be performed. These are descriptions of behavior at the psychological level and provide the basis for planning and predicting transfer among tasks" (Smith, 1974, p. 3). Skills or strategy analysis represents the psychological processes by which someone may complete a specified task. They are models of cognitive perfbrmance expressed as flow charts indicating the order or 30 sequence in which various hypothesized processes are executed. Smith carefully describes the purpose of these models and the criterion for evaluation. ". . . the infbrmation processing strategies. . . are not intended as a description of how students actually do perform such tasks. The question of whether these strategies are valid or invalid as descriptions is not relevant. They are conceived as a description of one feasible and reasonably efficient way of perfbrming such tasks, and as being trainable by some instructional procedures. The relevant criteria fbr evaluation ask: 1) Can instructional procedures be devised which result in acquisition of the intended strategies in a reasonable segment of instructional time? 2) Is the strategy effective, when carried out, in producing valuable behavior? and 3) Are the processing routines useful in predicting transfer relations among related learn- ing events? Whether or not the intended strategy is a valid description of behavior is a relevant question only in relation to Children who have received instruc- tion designed to produce the strategy" (Smith, 1972, p. 75). Each strategy consists of a sequence of primary, secondary and tertiary processes. "A.processing step involving a primary process represents what fer purposes of the analysis at least is to be con- sidered a unitary skill, e.g., decoding a variable name" (Smith, 1972, p. 148). Each process is defined in terms of the input and output of in- formation and the Operation.which changes that information. Additional and.more complex secondary and tertiary process are defined in terms of primary processes. Definitions of the primary processes and the detail‘ of strategies for the geologic classification task are described later in the chapter. Taken together the products of Content-Task-Strategy analysis represent the structure of a portion of a discipline. The description 31 consists of related sets of concepts (conceptual systems), specified tasks to be performed with those concepts, and strategies which model at a psychological level how the task can be performed. Psychological Views of Learning and Transfer Shulman and.Tamir have pointed out that within science education one of the major issues has focused on ". . . what is most learnable under given conditions, (and) what is most readily retained and trans- ferred to new situations. . ." (1973, p. 1105). A number of psy- chological perspectives were brought to bear on this issue, and science education programs developed on the basis of those perspec- tives. The major contributors were Bruner, Gagne, and Ausubel. Bruner viewed learning and transfer as dependent upon the struc- tures of the subject to be learned. He argued for learning the struc- ture in the sense that "to learn structure, in short, means to learn how things are related" (1963, p. 7). Bruner's particular interest was in what he called non-specific transfer, or the transfer of prin- ciples and attitudes. This type of transfer, in contrast to transfer of specific skills, is viewed as the most important way in which learn- ing serves the future. "In essence, it (non-specific transfer) consists of learning initially not a skill, but a general idea, which can be used as a basis fer recognizing subse- quent problems as special cases of the idea originally mastered. "The continuity of learning that is produced by the transfer of principles, is dependent upon mastery of the structure of the subject matter. That is to say, in order fer a person to be able to recognize the 32 applicability or inapplicability of an idea to a new situation and to broaden his learning thereby, he must have clearly in.mind the general nature of the phenomenon with which he is dealing. The more fundamental or basic is the idea he has learned, almost by definition, the greater will be its breadth of applicability to new problems" (1963, p. 17). Also important to Bruner's conception of the transfer phenomena was the notion of strategies or heuristics for inquiry and the poten- tially broad applicability of general strategies. In fact, Bruner argues that through extensive experience in discovery or problem solving situations one learns "the working heuristic of discovery. . . that serves for any kind of task one may encounter or almost any kind of task" (Bruner, 1961, p. 30). While Bruner argued that the general relationships were most important fer learning and transfer, Gagne was concerned with the learning detailed sequences of prerequisite capabilities. These capabilities are considered internal to the learner and are described in terms of the observable behaviors of the learner. Complex intellec- tual Skills are learned most easily when constructed from Simpler skills, hierarchically organized. Transfer to more complex tasks is dependent upon the learning of the simpler prerequisite components. This type of transfer Gagne labels vertical transfer. It "is observed.when a capability to be learned is acquired more rapidly when it has been preceded by previous learning of subordinate capabilities" (1970, p. 337). In.contrast Gagne describes lateral transfer. This is concerned with the way previous learning can.be used.in.new situations of approx- imately the same complexity. Gagne is less specific concerning meChanisms for lateral transfer than those for vertical transfer. He preposes 33 that the lateral transfer of a learned capability is enhanced by practice in a wide variety of situations, but he leaves open the question of whether the ability to transfer capabilities broadly is largely innate or learned. Ausubel (1965) contends that what is most easily learned is know- ledge of the subject matter and that this is what transfers. The knowledge is most easily learned if there is available in the existing cognitive structure concepts which can "subsume" the newly introduced material, thus providing a stable organizational framework to which the new knowledge can be anchored. Mnre specifically, learning is depen- dent upon the "organizational properties of the learner's subject matter knowledge (suCh as clarity, stability, generalizability, inclu- siveness, cohesiveness, and discriminability, not (the) degree of simil- arity between stimuli and responses in the two learning tasks" (1965, p. 108). In this point Ausubel takes issue with Gagne's common elements view. He furthermore disagrees with Bruner's view that non-specific transfer is limited to problem solving situations where principles can be used to recognize a particular problem as a special case of more inclusive structures of the subject matter. Ausubel clearly points out that reception learning of new content is affected either positively and/or negatively by previous experience and therefbre is also a transfer phenomena of'major importance. In more recent work, Smith (1972), has presented a view of learning and transfer which emphasizes shared concept, task, and skills or strategy components. In particular, he has emphasized the role of cognitive strategies. 34 He has defined lateral and vertical transfer as related to the content-Task matrix shown in Figure l. The various possible contents shown across the t0p of the diagram represent related conceptual net- works which function in similar ways within the discipline. The con- ceptual networks are considered structurally similar. vertically the matrix shows a set of related tasks described in terms of analytic constructs. These task descriptions reflectthe nature of the concep- tual systems and are statements of what is done with the related sets concepts. Tasks can be sequenced on the basis of shared strategy components where the strategies of simpler tasks serve as subroutines for the more complex tasks. Lateral transfer refers to the perfOrmance of the same task across different conceptual systems. vertical trans- fer refers to perfbrmance on a sequence of tasks within the same conceptual system. Smith argues that cognitive strategies may serve as a mechanism for learning and transfer. With respect to lateral transfer, Smith asserts that once a strategy fbr performing a task has been learned with one set of concepts, the learning of that task using a different conceptual system will be mediated by the availability of the strategy. The strategy serves as a stable organizing sequence of infbrmation processes which coordinate the use of parallel concepts. Whereas lateral transfer is dependent upon the use of the same strategy across various contents, vertical transfer occurs within the same set of concepts across different tasks. The facilitative effect of the strategy in this case is dependent upon the compatability of the TASK 3S CONTENT Conceptual Cbnceptual Conceptual Conceptual System System System System I II III Iv Lateral Transfer Task 3 Identical task and strate ; different sets of concepts 11 4‘3 m p E a Task 2 g: a b? .3 g. 3.5 Task 1 Identical c different t shared strat Figure l . Task-Content Matrix 36 strategies for less complex preceding tasks. "Once a strategy fer a task has acquired some degree of stability, it can function as a sub- routine in a larger strategy" (Smith, 1974, p. 12). If learning tasks within an instructional sequence have been arranged with due consider- ation for the common strategy components, learning and transfer within the sequence should be enhanced. It is this facilitative effect of cognitive strategies in a vertical task sequence that is the particular interest of this study. Information Processing_Psychology Smith's work is largely dependent on the broader field of infor- mation processing psychology. By reviewing the work of Newell and Simon (1969, 1971, 1972), the description of the role of strategies in task performance can.become more complete. In addition, a more complete picture of the human information processor is available fer use in the design of instruction. The review is divided into three sections: 1) the characteristics of the human information processing system, 2) the task environment, and 3) the problem space. The Human Information Processing_System The human information processor is dependent upon the manipula- tion of symbols. Those symbols designate the information available in the external environment and information available within the processor. One symbol can be a complex structure of other symbols organized by the use of simple logical relationships. 37 Upon receiving information from the external environment , it can be encoded as symbols and stored for future use. Symbols often refer to drunks of information, a chunk being the largest recognizable stimulus configuration. These chunks are learned patterns of information. Symbols may also reference programs or strategies for processing in- formation and conceptual krnowledge stored in memory. One other impor- tant type of symbol is the goal which controls the behavior of the information processor. The goal of obtaining a problem solution in a given situation is ultimnately a test which when executed results in a decision as to whether or not the problem has been solved. If the solution is not met, the next operations performed are responses to the existing differences between the present state of knowledge and the goal or final desired state. There are three central components to the information system. The first is the processor which consists of elementary information pro- cesses, a short term memory (STM) , and an interpreter. The second is a long-term memory (LTM) and the third an external memory (FM). Taken in total, the system processes the information within the STM which has been taken from either of the two memories. The processing is serial, that is, only one of the elenentary processes can be executed at a time. Within the processor, elementary information processes (eip's) operate on symbols. The eip's are a limited set of operations which can compare, designate, or alter an input symbol in a specified manner. The processes are simple in that only one or two symbols at a time are used. The behavior of the information processor is constructed from 38 organized sequences of these processes. These sequences of information processes, called strategies by Smnith (1974) are central to this study. Strategies can be constructed from the elementary processes within the attempt to solve a given problem or exist as symbol structures in long term menory to be recalled into STM and executed. Short term merory is the component which holds the inputs and out- puts of the elementary processes. Newell and Simon describe the character of STM as follows: ". . . STM holds about five to seven symbols, but only about two can be retained for one task while another unrelated task is being performed. All the symbols in STM are available to the processes, i.e., . . . there is no accessing or search of STM" (1972, p. 808). The character of STM is particularly important as it is a major re- straint on the capabilities of people to process information. The interpreter determines the sequence of the elementary processes to executed. It is described as a program or strategy which controls the cognitive action of the problem solver. This program can be constructed in STM strictly from elementary processes or simply be able to interpret other programs called into short term menory. The interpreter integrates the behavior of the information processor by organizing the sequence in which available symbols are processed. The second major component is long term metory (LTM). In this memory a virtually unlimited number of symbols or symbol structures can be stored. These symbols are organized as lists of lists. The organization of lists are maintained by various logical relations. The entering of new drunks of information into long term menory is a 39 relatively slow process taking from 5K to 10K seconds for meaningful chunks (Simon, 1969, p. 39). In addition to STM and LTM, a third merory, the external menory (BI) is associated with the processing system. This is "immediately available visual field" (Newell and Simon, 1972, p. 809). Information can be stored in and retreived from the external memory. Task Environment The processing system just described is relatively simple. Its capabilities are set by a relatively few limiting factors such as the 5-7 chunk limit of STM and the serial nature of the processing. The adaptive nature of the system reflects the ability to change, i.e. , to alter its behavior in response to the task which it is required to perform. It is the information and structure of the task which to a great extent demands or necessitates certain behaviors. Different tasks result in different behaviors from the same human information processing system. Newell and Simon use the term "task environment" to refer "to an environment coupled with a goal, problem, or task. . ." (1972, p. 55). The task environment consists of (l) the information immediately and externally available to the problem solver and (2) invariant structures which limit the range of possible behaviors. There are certain features of the environment which form the relevant structure of the environment and demand certain behaviors in the successful performance of a task. A demand of the task environment is "a constraint on the behavior of the problem solver that must be satisfied in order that the goal be 4O maintained" (Newell and Simon, 1972, p. 79). It should be emphasized that the goal, or required outcome of the task determines what are and are not demands of the environment. A change in the specified goal would make certain features of the environment demanding and others irrelevant. Thus, to understand the performance of an individual completing a given task requires careful and detailed description of the task environment. Even though as noted by Newell and Simon, the task environment cannot be completely objectively described, the analysis of that environment must precede the investigation of a problem solver's behavior. The major features are those available to any in- dividual confronting the task. This includes the information given in the initial presentation of the task and the logical relationships which place demands on performance. The features should be inherent in the task, not related to the nature of the problem solver. Problem Space The problem space is a mental construction of the problem solver. It contains information from the task environment and long term memory, and a goal which indicates when the task has been completed. The relationship between the task environment and problem space is important to consider. The structure of the task environment limits the range of possible information to be included in the problem Space. This does not imply that the adopted problem space will be an exact representation of the task environment. In fact, the problem space is an abstraction which will contain only a small portion of the 41 available information. This may or may not be sufficient to solve the problem at hand. However, it is clear that the better the problem space reflects the structure of the task environment, the more likely the individual will correctly solve the problem. Newell and Simon describe the relationship as follows: "A problem Space may contain more or less structure than the environment it represents. If it contains more. . . some of this structure will be spurious. It will be at best useless, and possibly harmful to the problem solv- ing process. If the problem space contains less structure than the environment, it may not permit maximum use of the structural information that is potentially available" (1972, p. 825). The above should not imply that the only infbrmation in the problem space is from the external environment. The individual includes in his representation of flhe task knowledge recalled from long term memory. The total construction of the problem space can be considered as the result of an interaction between the previous learning internal to the problem solver and the external task environment at hand. Instructional Design Gagne (1970), Bruner (1971), Scandura (1973), Merrill and Boutwell (1973) and others have developed sets of dependent and independent variables which should be considered in the design of instruction. Some variables have pertained to the learner, others to the content of instruction, and still others to the type or style of the instructional presenta- tion. Each viewpoint contains implicit assumptions about the manner in which these variables should be used in the process of designing instruction. The following reviews the work of Simon to explain the design process used in this study. 42 Simon considers design as the development of courses of action which will change existing situations into preferred ones. An artifact is considered the interface between the outer environ- ment of the world in which it exists and its own inner environment. Both the outer and inner environments can be described in terms of the properties and laws which describe the interactions therein. The natural sciences often provide these descriptions. Most importantly, an artifact is designed to meet certain goals. An effective and efficient design is one which constructs the artifact so that the inner environment can respond to the outer environment appropriately. It would seem that construction of such designs could be facilitated by detailed descriptions of the major features of the inner and outer environments. Simon also argues that the human being is essentially an artificial system in that it can adapt to the demands of the outer environment. There is: ". . . evidence that there are only a few 'intrinsic' charac- teristics of the inner environment of thinking man that limit the adaptation of his thought to the shape of the problem environment. All else in his thinking and problem- solving behavior is artificial--is learned and is subject to improvement through the invention of improved design" (Simon, 1969, p. 26). The last sentence is the key to the design of instructional sequence in this study. As a result of having completed the specified instruc~ tional sequence the individual will have learned information necessary to the performance of the specified tasks. That is, the inner envi- ronment of the learner will be "altered so that it is appropriate to the 43 demands of the outer environment or nature of the task to be performed. The extent to which this is the result of instruction should be re- flected in the perfOrmance of the individuals being taught. The design of instruction, then, requires: 1) .A description of the outer environment, information to which the learner has explicit reference in per- forming a task. 2) A description of the general characteristics of inner environment of the problem solver. Instruction is viewed as the course of action taken to make available conceptual knowledge and strategies fer the construction of an appro- priate problem space. How, then, can the necessary descriptions be gained so that the instruction can be designed? As the content of instruction is to be taken from a discipline, the delineation of the structures of that discipline can provide the descriptions of the task environment and a model of an appropriate inner environment or problem space. Smith's model of content-task-strategy analysis described earlier will be used to provide these descriptions. These descriptions cannot be exact replicas of the real world or the world as it would.be viewed by any given problem solver. What is described are the major features used by those working in the discipline to classify igneous rock samples. These include the concept labels, logical relationships, and a goal or required outcome of the task environment, and the concepts and strategies of a model prOblem space. Smith's model was chosen as it provides an analytical 44 framework which facilitates obtaining these descriptions and maintains the relationships between the various structures of the discipline. Given these descriptions a sequence of instruction can then be designed by considering the general nature of the human infbrmation processor. The description includes the limits of short term memory, the time required to store "chunks" of infbrmation, and the serial nature of the processor. Each of these point to important considerations in design of instructional episodes. CONTENT-TASK-STRATEGY ANALYSIS OF THE CLASSIFICATION OF IGNEOUS ROCKS Within this section the analysis of igneous rock classification is presented in three parts. The first is the content analysis which identifies the set of related concepts which the discipline utilizes to classify the rock samples. The relationship of the concepts to each other is made explicit by use of the class member analytic network by Smith. This set of concepts will also serve in the description of the task environment and model problem space. Secondly, a task analysis describes in analytic terms the task which the students must learn to perfOrm when classifying igneous rocks. The task description is composed of the infermation initially given and the required outcome or goal. This further describes the task environment and problem space. The strategy or skills analysis results in a.model cognitive Strategy fer task perfOrmance. This describes one way the task can be perfbrmed. An appropriate strategy is to be considered a.potentially important problem space component. 45 The final section presents the design of the instructional sequence used to teach students to classify the igneous rock samples. This in- cludes Specification of pre-task instructions, the precursor tasks, and strategies for performing those tasks which were developed to facilitate learning of the final task. Geologic Classification Geology is the science of the earth, a major subdivision of which is physical geology. This portion of the discipline addresses, in part "the nature and properties of the materials composing the earth. . ." (Leet and Judson, 1965, p. 1). Central to these inquiries is the con- cept rock which could be considered the central unit of study for physical geologists. The classification of various rock types serves to organize the descriptions of the phenomena under investigation so that the scientific community can share infermation gleaned from their inquiries in a systematic and understandable manner. Furthermore, the field classi- fication of rock samples with which this study is concerned is closely related to the theoretical issues of the discipline. Field classifica- tion implies the use of variables which are visible in hand samples or rock outcrop as the basis of classification. Additional, more complex classification schemes are used as the observational technique becomes more saphisticated in.the laboratory. 46 Content Analysis of Geologic Classification The content analysis is to identify related sets of concepts and the relationships between those concepts. The meaning of any one concept is dependent on others with which it is systematically associated. In association with the concept rock are terms such as igneous, metamorphic, and sedimentary. This study is confined to the subsets of igneous rocks. In the analysis of concepts attendant to the classification of igneous rocks, the class-member analytic network described by Smith provides the organizational framework. In addition, the analytic constructs "elements" and "comparative" are taken from another analytic network, the variable-value Network. They are included as they are used in the definitions of the class-member constructs. This is possible as the two networks are logically related. The following analytic terms describe the character of specific concepts: 1. "element - the entities (objects, events, systems constructs, etc.) which are being studies" (Smith, 1972, p. 89). 2. "comparative - term representing the relation between the values of a single variable (or descriptions on a set of variables) which characterize two or more elements (or an element at different times)" (Smith, 1972, p. 89). This implies one value is greater than, equal to, or less than another value for the same variable. "Definition of the class-member analytic Network: 3. class - a designated set of elements 4. class member - an element of a class 47 5. class rule - a decision by which it may be determined whether or not an elemnent is a member of a class 6. class name - a name applied to an element as a result of its membership in a class 7. defining value - a value employed in a class rule 8. defining value name* - name which describes a particular defining value or the set of defining values included by a pair of defining values as specified by a class rule 9. relevant variable - a variable whose values are employed in the rule fer a class or a set of classes 10. partition - a set of mutually exclusive classes, i.e., superordinate class 11. partition name - a term or phase referring to a specific partition" (Smith, 1972, p. 119). USing these analytic concepts as guidelines, the fbllowing Specific geologic concepts are identified as related to the classification of igneous rocks (Table l). The symbols following the examples of specific geologic (i.e. , systemic) concepts correspond to those symbols used in Figures 2 and 3. These figures illustrate the relationships be- tween the various concepts. They are constructed at the analytic level to illustrate their generality of their use. The most general organization of these analytic concepts into a classificatory scheme is shown in Figure 2. Relevant variables are used to define each class. These may or may not be the same. The defining values indicate the limits between which the value for a *Note: The defining value name is added to Smith's original network as necessary to fully describe the concepts related to igneous classification. Table l. Analytic Concept element class members class class names relevant variables defining values comparative class rule 48 Analytic and Systemic Concepts for Igneous Rock Classification Systemic Concepts (Exemplars) any rock sample (e) individual rock samples belonging to a class a set of rock samples identified by the class names stated below granite (C1), diorite (C2), gabbro (CC) rhyolite (C4), andesite (C5), basalt (C6), glass (C7), obsidian (C9) grain size (A), amount of light grains (B) a1, a2 for the variable grain size; b1, b2 for the variable amount of light grains (These values are usually Specified by standard examples, not quantitatively.) the value for a rock sample (e) is greater than (>), equal to (=), or less than (<) the value for a particular standard For a given element (rock sample e), the value 'a' for the variable grain size (A), and the value 'b' for the variable amount of light grains (B) in conjunction with the set of class . rules below Specify class membership: Ifa1a1,andb:b1,theneeC1. Ifa_>_a1,andb2_<_b_a1,andb_b1,theneeC4. Ifa ao ~n~cn ‘m2H>wcn rr>2m‘mz~n>wm mayonn— Y L GHT HALF FEEHIY'DARK~ GRAINS LIGHT GRAINS GRAINS AWEIBH'OF LIGHT COLORED GRAINS Figure 4. Double Variable Classification Chart 57 U! I rock sample 5 - standard sanple v - value of a variable for a particular sample V - defining value for a standard NV - value name RV - relevant variable [:1 primary information process secondary or tertiary information process <> indicate a decision is required O indicates end of strategy Figure 5. Flow Chart Symbols are abstracted or taken directly from the references cites. LOCATE is the only process defined originally within the present study. The exact definitions of these processes are given in Appendix A. The following two flow charts define secondary and tertiary pro- cesses necessary to the strategy model for the geologic classification task. The first flow chart (Figure 6) describes a secondary process called COMPARISON first described by Smith, McClain, and Kuchenbecker. Table 2. 58 Description of Primary Information Processes ACT GKDSE 1 COMPARE DECDDE ENOODE LOCATE ORDER PLACE REPORT the process of acting on an Object to obtain a particular kind of input (e.g., color or temr perature infOrmation). The process requires the retrieval of an appropriate observation action (Smith, 1972, p. 153). Operates on a set of stimulus objects. A choice of one object is made on the basis of some salient criterion such as a particular feature of position (Padilla, 1975, p. 204). determines the comparability of two encoded units of infOrmation, e.g., the texture of two objects. The process determines if the objects are the same or different (Smith, 1972, p. 155). this process functions to gain access to the network of stored concepts. The network is entered by way of verbal label fOr one of the consistent concepts (Smith, 1972, p. 150). categorizes sensory non-verbal infOrmation which has been attended to in terms of pre- vious experience or creates a new category (Smith, 1972, p. 154). involves the searCh fOr a position logically or spatially related to a particular source of infOrmation in the environment. The input to the process may be another position, object, or verbal label. attends to and assesses the magnitudes of two different encoded units of infOrmation and orders them from lesser to greater (Smith, 1972, p. 156). the spatial placement of an element to indicate its membership in a set (Smith, 1972, p. 155). allows verbal responses to be made. The output is a verbal label. The input is a concept (Smith, 1972, p. 157). 59 Table 2 (Cont'd.) SCAN represents a rather cursory, largely visual exploration of the stimulus field to locate salient and/or relevant features (Smith, 1972, p. 152). SELECT sort relevant information from irrelevant. It filters out almost all information except for that related to the variable or var- iables of interest (Smith, 1972, p. 153). "This is a secondary process which takes as input a variable concept (i.e. , the node activated by decod- ing of variable name or an appropriate retrieval process) and an ordered pair of elements. It compares the elements on the given variable and outputs a comparative concept applicable to the ordered pair of elements. Thus, the C(MPARISON process does not produce a verbal report although it makes such a report immediately possible. Alternative steps might be carried out next instead. The identities of the elements and the comparison variable are maintained. (Figure 6) indicates a parallel execution of processing steps. This indicates the desirability of near SiJmnltaneous observation of the two elements. "Parallel processing" in the technical psychological sense is not implied. Further- more, feedback from the selecting and encoding steps to the ACI‘ Step undoubtedly occurs creating an active subsystem. Such feedback systems are very common, but to avoid excessive complexity, are not always diagrammed." (Smith, 1972, p. 161). The second flow chart (Figure 7) defines a tertiary process CLASSIFY defined for the present work. This process encorporates the (IMPARISON secondary process as a critical subroutine. The CLASSIFY process takes as input a variable name, an element to be classified, and some number of elements which represent the defining values Of a number of classes. Also given is a class rule which defines a class in which a sanple should be placed. The decision rule is implicit in the CLASSIFY process. 60 Input : relevant variable elemnent 5 (sample) element S (sample) » DEmDE variable name ] ACT ACT n element 5 n element 8 (sanple) (Standard) SELECT SELECT feature of feature of element 5 element S ENCODE ENCODE feature of feature of element 5 element S CINPARE element 5 to element 8 features ORDER elements Figure 6. Conparison Seconndary Process 61 Input: relevant variable element 5 (sample) element Sl-x (Standards) QBOSE 1 S1 (greatest) as Standard COMPARISON of sanple S 0mg]: next to Standard S Standard (S) SCAN board LOCATE LOCATE position at 1 side of S [11 Figure 7. Classify Tertiary Process position at < side of s l 62 The tertiary process ends where the class to which the element belongs has been unequivocally determined fOr a single variable. This occures when the appropriate position has been located because (1) the value fOr the sample is greater than or equal to the value of the standard or (2) no standards which define additional classes remain unused. Additional processing steps resulting in Specified outputs may fOllow. The next flow Chart (Figure 8) specifies the entire information processing routine fOr the Double variable Classification Task utilizing the CLASSIFY tertiary process. Reviewing briefly the task was described as fOllows: Double variable Classification Task Description Analytic Level Task Systemic (Concept)Level Exemplars Given: an element; two Given: an igneous rock sample; grain relevant variables; size, amount of light colored two defining values grains; two standards repre- fOr each variable; senting the defining values sex defining value fOr each variable; large grains, names; a set of small grains, about half light of class rules. grains, mostly dark grains; (See page 56) Required: The element placed Required: The rock sample placed in in the class of the class to which it which it is a belongs. member. The model includes the processes whiCh result in the necessary decisions and the outputs required by the task. In addition, verbal output is included in.the strategy whiCh are not required by the task. These are the verbal responses indicating the value name which corresponds to the classification decision made on each variable. Pilot study indicated that students could often not recall the 63 Input: relevant variables element 5 (sample), element 1 x (standards), value names CHOOSE 1 relevant variable PLACE ‘ S in appro- I priate position CLASSIFY * CHOOSE 1 sample next us1ng . variable 1 var1able LOCATE any I AL next Yes value name value name not located DECODE value name fOr located position LOCATE correspondingv—-%>1 Egggd position REPORT value name Yes I LOCATE SCAN appropriate board value name fOr first var Figure 8. Strategy fOr Double variable Classification Task 64 column or row in which the sanple was to be placed. The required verbal output facilitated the location of that position when it was needed near the completion of the routine. Design of Precursor Tasks and Strategies The process of designinng an instructional sequence which would result in students being able to classify igneous rock sanples attempted to follow Simon's view of design. As stated before, design is con- sidered the construction of an artifact with an environment appropriate to a particular outer environment. In this case the innstruction is to result in the formation Of an inner environment of the problem solver which is appropriate for accomplishing a particular task. The inner environment must contain information which enables the individual to construct a problem space in which a specified goal can be efficiently and accurately attained. The problem space must conform to the demands of the task environment in which the goal is imbedded. The problem space should be such that the infornmation available in that external environment and stored in long term menory are effectively integrated in the performance of the task. The necessity of designing the task sequence is dependent on a nunber of factors. First, it was expected that the task environment was too complex for students to be able to perfornm the task without instruction. Too many chunks of unfamiliar information would have to be coordinated for successful performance. Secondly, it is based on the assumption that the strategy just described was too long and 6S complex to be learned and applied in an unfamiliar task environment during a single session. These assumptions would be expected, consider- ing the slow encoding times of recognizable (let alone unfamiliar) chunks of information. The preliminary pilot study clearly confirmed these expectations. In the light of the information processing literature, an attempt was made to reduce the complexity of the final task to identify pre- cursor tasks which would form the instructional sequence. This was first done by a logical or rational analysis of the final task. The task was analyzed to identify additional tasks which were less complex in terms of the number of the specified inputs and outputs. The per- cursor tasks were also selected so that the logic of any preliminary task was consistent with the logic of the following task. This necessitated consideration of the class rules as identified during the context analysis. This analysis reduced the number of chunks of information to be learned in any sinngle instructional session. Following Smith's argument for expecting subroutines of a complex strategy to serve as mechanisms of learning and transfer, the strategy of the final task was also to be reduced to simpler components. Thus, the additional tasks had to be defined in such a way that major strategy components would be appropriate for the task. Learning of the concepts whidn serve as the inputs and outputs of the processing routines is necessary to perform any tasks. This information must be available in the long term menory of the task per- former. Without such information the connstruction of a problem space appropriate to the task would be difficult if not impossible. 66 element 5 (sample), elements S - Sx (standards), value 1 l CLASSIFY Sample S DECODE value name for located position I REPORT value name PLACE sample (5) in corresponding class Input: relevant variablej Figure 9. Single Variable Classification Task Strategy 67 The final task, classifying the rock samples on two variables, can be easily reduced to classifying the samples using only one variable. That is, the students are to place a given rock sample into one of three classes as delineated by the defining values and class rule. The content changes in that one variable and all attending value names are not utilized. The task is described below at both the systemic and analytic levels. The Single variable Classification Task board is shown in Figure 10. Single variable Classification Task Description Analytic Level Task Systemic (Concept Level Exemplars Given a set of elements, Given: a set of igneous rock one relevant samples grain size, variable and standard presenting defining values. the defining values of each class. Output: the elements correctly Output: eaCh sample correctly placed in the classes placed in the class of defined by the de- which it is a member. fining values. As just indicated the strategy fOr any precursor task must also be closedly related to the strategy fOr the final task. When compared to the strategy fOr the Double variable Classification.most of the strategy shown.in Figure 9 can.be seen as a subroutine of the more complex program. Analysis of the second task resulted in the Specification of a Comparison to Standard Task. The intent was to have students 1) make a number of discriminations by comparing samples to standard and 2) to fellow the class rule for comparison to any one standard when 68 LIGHT GRAINS AMQJNT OF LIG-IT COLORED GRAINS Figure 10. Single Variable Classification Chart placing the sample in a cell. The class rule was implicit in the task environment. For exanple, the comparative values "larger grains" and "same size grains" were listed together for one cell while "Smaller grains" was listed for the other cell. The board for this task is shown in Figure 11. The specification of this task is dependent to a great extent on the (DMPARISON secondary process being an important subroutine in the strategy for the Single and Double Variable Classification Tasks. The task was specified in such a way that students could learn this sub- routine in the context of task performance. The strategy for this task is Shown in Figure 12. 69 Comparison to Standard Task Description Analytic Level Task Systemic (Concept) Level Task Given: an element, relevant Given: variable, and de- fining value. Output: the value Of the var- Output: iable for the element in comparison to the defining value, i.e., greater than, less than, equal; the ele- ment placed in the corresponding cell. granite sample, grain size, standard exhibiting, fine grained texture. the granite is more course grained than the standard (defining value). ANDUNT OF LIGlT (DIDRED GRAINS IMORE OR SAME AWEXDH'OF LIGHT GRAINS MORE DARK GRAINS Figure 11. Comparison to Standard Chart 70 Input: Relevant Variable, element 5 (Sample), element S (Standard), 3 value names (Wr-vms) I CHOOSE 1 element S - as standard I make COMPARISON of sample 5 to standar (S) REPORT comparative value v > , = , < V m I corresponding value name (VNl, VNZ, or VN3) PLACE sanple (s) in corresponding class STOP Figure 12. Comparison-to-Standard Task Strategy 71 In sunmary, the design of the instructional sequence results in two additional tasks derived from the content-task-strategy analysis of igneous rock classification. The results are dependent on both the task and strategy. The three tasks can be more generally described as follows: Task III: IDUBLE VARIABLE CLASSIFICATION TASK The final task is the classification Of igneous rock samples using two variables, grain size, and the relative anounts of light and dark grains. The variables are crossed to form a 3 X 3 classification chart. Each row or column is defined by specific defining values. These are represented by standard sarples located on the boundaries of each row and column. Task II: SINGLE VARIABLE CLASSIFICATION The second task is the classification of the sanples using only one variable on a three cell classification table. Again, standard samples represent the defining values of each cell. Task I: CDMPARISON TO STANDARD The first task is the comparison of a single rock sample to a standard sarple requiring a verbal statement as to whether the variable values for the sanple are greater than, equal to, or less than the values for the standard. Also required is the correct placement of the sanple in one of two cells labeled greater than or equal to, and less than. Preliminary to any instruction on a task the content analysis and pilot study indicated a number of concepts were needed to under- stand the initial task instruction. In general there were the value names 1) large grains, small grains, glassy (for the variable grain size); and 2) mostly light colored grains, about half light colored grains, mostly dark grains (for the variable anount of light colored 72 grains). In addition, for both sets of value names it was necessary to teach students to identify individual grains within each sample. For the second set of value names "light" grain and "dark" grain had to be operationally defined. Other concepts identified by the content analysis were either already known by the students or learned in the context of the preliminary task instructions. In effect the preliminary concept instruction was done for those concepts necessary to make instructionns on the first tasks understandable by the students. Taken in total the preliminary concept instructions and initial task in- structions were intended to make available to the student in long term memory those concepts of the discipline which were necessary for task performance as indicated in the strategy models. Additional Related Research The study of classification within science education has not been previously investigated from the perspective adopted in the present study. The learning and transfer of classification has been addressed primarily as developmental studies following the work of Piaget. There has been a limited number Of studies which were directly compared with science content. In its place tasks taken directly from the work of developmental psychologists have been used. The studies have investi- gated the delineation Of hierarchies of logical classification structures (Allen, 1970), the effects Of a structured learning sequence on classification achievement (Raven, 1970) , the effects of response format of a classification learning sequence (Popp and Raven, 1972), the development of classification abilities in culturally disadvantaged 73 children (Raven, 1967-68), and the properties a child selects to classify pictures of various bottles (George and Dietz, 1971). TO borrow a conclusion from VOelker's review of the literature on concept learning: "Many studies could have just as well been done by a child development specialist. . . (p. 42). An inordinate amount of researCh still seems to be based on the notion that it is necessary tO determine how early in the curriculum certain concepts can.be in- serted. UnfOrtunately, the concern fOr introduction takes precedence over Optimizing learning"—TI973:_ET 41). JMore closely related to science education are the studies by Allen (1968) and Bridgham.(1969). The fOrmer investigated effects of an elementary science unit from.the SCIS program on students classificatory abilities; the later examined the relationship of the students under- standing classification to the learning of electrostactics. Bridgham's study in particular was important as it offers an apprOpriate perspective fOr science educators in utilizing the work of development psychologists. "If Piagets work is to be used apprOpriately in.making curricular decisions, attention must be fOcused on the effects of a childs dev- elopmental status on his approaCh to and learning of curricular content" (1969, p. 119). It is this viewpoint that points to the utility of developmental studies in the present investigation. The work of Piaget is related to the present study in that the structures of multiple classification would seem necessary to the performance Of the geologic classification task. The crucial com- ponent of this structure is the Operational coordination of two pro- perties which determine the intention of a class of Objects. Without this Operational structure the subjects would be likely to resort to the classification of a.rock sample on the basis of a Single variable. 74 The particular Piagetian task most like the geologic classifica- tion task is called simple multiplication or intersection and is de- scribed as fOllows: "(The subject) is presented with a row of green objects (a pear, a hat, etc.) and a row of leaves with various colours (brown, red, yellow, etc.) at right angles to it. An empty space is left at the point where they meet, and the subject is asked to fill the cell (the answer being in the fOrm of a verbal description, or a free drawing, or if necessary a choice out of several alternative pictures). He has to find the object that "fits in with everything" in.each of the two rows" (Inhelder and Piaget, 1964, p. 176). The responses of students fall into two groups. The subject either takes only one of the two rows into account when deciding the element to fill the empty cell, or he takes both. Inhelder and Piaget cite the fOllowing data (1964, p. 178). Age 5-6 7-8 9-10 Choice matches 1 collection 85% 42.5% 17.5% Choice matches 2 collections 15% 57% 82.5% However, for Piaget the ability to coordinate two variables does not fully define the structure fOr inclusion. In addition, the students must abstract the common property of a collection, i.e., determine its intention, and use the word "all" in response to questions about his choice. The later indicates the ability to consider the extension of the class. The reactions of students demonstrating both the ability to coordinate two prOperties and the extension--intention relationship of a class and its elements occured in the fOllowing proportions (1964, p. 184). 75 Age 5-6 7-8 9-10 12.5% 30% 50% The geologic classification task is similar in that the student must be able to coordinate two properties of class membership to correctly place a sarple. Thus, lest the lack of the development of those structures preclude the performance of subjects in the geologic task, the presence or absence of the structure related to simple multiple classification must be considered in the evaluation of student per- fornmance. Bridgham (1967) in the context of investigating the rela- tionship between childrens' classificatory abilities and their under- standing of electrostatics developed a simple multiple classification test. In the present study, this test was used in considering the development of the related classification structures of the students. In interpreting any relationship between performance on the two tasks, it must be kept in mind that the classification tasks are also different on at least two important dimensions. First the intention of the classes are obtained in two different ways. In the Piagetian task the intention is visible in a set of related Obj ects in perpendic- ular rows. In the geologic task the intention of the classes must be obtained from defining values of each cell as exenplified by the standard in combination with the class rule. Secondly , there are important differences in perception of the variables which define the class intention. The Piagetian tasks are developed in such a way as to explicate the existence of the operation- al or logical structures . They are, therefore, concerned with objects 76 that clearly present the variables and values Of those variables. For exanple, the variables are often size, shape, and color. The variable values for color may be blue, green, red, yellow, etc. Using such variables and values one encounters few problems with dis- crimination. Few children will have problems telling a blue square from a red triangle when working with the multiple classification task. The variables are well known and easily perceived by the students. In fact to select unfamiliar objects, unknnown variables, and nearly indiscrimninable values would greatly confonmd the major purposes in their study. However, within a disciplinary task such as geologic classification the discrimninations required are not so easily made, and the variables and values are often previously un- known to the student. These are often major problems in disciplinary classification tasks. Considering the foregoing comment, it is clear that the geologic classification is more complex in terms of the elements and concepts involved. However, because the same logical or Operational structures are required the development of those structures must be considered. CHAPTER III RESEARCHIMETHODS Overview Students were randomly selected and randomly assigned to one of four instructional groups. One of the groups was given instruction based on model cognitive strategies for the following tasks: Compar- ison to Standard, Single Variable Classification, and Double Variable Classification. The other three groups were given feedback about the accuracy of their responses. Of these three groups, one was in- structed on all tasks, one was instructed on the second task only, and one was instructed on the third task only. During the first contact each student received (a) innstruction on concepts used in the tasks and (b) a multiple classification pretest. The students were given a pretest-instruction-posttest sequence on each task. The posttest was given on the second day. During each contact with the students data relevant to specific hypotheses were collected for statis- tical analysis. The chapter includes description of the research methods of the study. There are Six major sections: (1) the sanpling of the subjects from the population and the assigment of the subjects to instruction- al groups, (2) the description of materials, (3) the procedures related 77 78 to the instruction of research personnel and research subjects, (4) the experimental design, including research hypotheses, (5) the dependent variables, and (6) the statistical analyses. Research Subjects Sample The sample for this study was taken from the fourth grade classes in four schools in a mmnlti-ethnic district with a wide range of family incomes. The twenty-three urban elementary schools of this district showed enrollments of 72% Caucasian, 17% Negroid, 9% Spanish (by surnamne), and 1% American Indian. The mean age was 117.0 months (5. D. 4.14 months). The four schools were selected because the researcher had pre- viously assisted them in a project unrelated to the present research. Practical problems of gaininng access to the schools for research necessitated the use of these schools. Students in two of the schools were in self-contained classrooms. The third school used a large single room for team teaching. In the fourth school the teachers taught specific snbject areas in separate rooms, and used a modular scheduling program. Selection and Assignment The random selection and assigment of students and instructors was complex but necessary to assure that irrelevant variables would not vary systematically across treatment groups. All random 79 assigment procedures were done using a table of random numbers. The assigment procedure is described below with aid of Figure 13. Assignment was made to one of four instructional groups. The sub- jects assigned to the first and second groups continued throughout the three tasks of the study. The third group was used during the sessions fOr the second task only and the fOurth group was used during the sessions fOr the final task only. .A total of twenty fOur students were chosen from each of the fOur schools. For the self-contained room schools twelve students were randomly selected from each of the two fOurth grade rOoms. Three of these twelve students from each room were randomly assigned to each of the four treatment groups. For the team.taught and.modular schedule schools the twenty fOur students were randomly selected from all fOurth grade students. Six students of each twenty four were assigned to each of the fOur treatment groups. Instructors and students were arranged in the fOllowing way. TWelve instructors were divided into fOur teams of three. Each team of three instructors was assigned to one school. The assignment of these teams of instructors to teams and schools met the sCheduling requirements of the instructors and the schools. From the self-contained room schools, one student from eaCh class- room and instructional group was assigned to a particular instructor. For the team teaching and modular scheduled schools, two children from each instructional group were randomly assigned to one of the three instructors. Each instructor was responsible fOr eight of the twenty- fOur students. 80 3.5.55 no «5.5.372 at: 5:923" IRES. .m. 0.53". Cr: ‘I—h CF: 2 : c. carer—7.:— uoaucuws .8337...— / Star—7.... :28 3 M :36 35.... ~ 57v... baa—E..."— nlfl MIC VIA J/MNB : — >_ :— L .2 A. a... w... 95c: :28 O. c :33... 53:5. 39.3.. :23 IF: ¢~ ave—Ow. Eco-ES. /<\ z 5. 286m $8.3. 83.23. 5.3. =8 :35 3.8. ‘n: ‘fl: “I: n ~ .— uouoeams scour—an:— mmfiu 53 :8 96b. 53 [Eu — :23- 5.8.5 an n my? 3? 2....-. 96.. fine 3 n .593 2.815. mac—u 53 In... 2 woo—ow aqua—:3. /\ : .— 28.3 28.3 88 353.858. 81 While the total number of students was ninety-six (N = 96), a mazimum of seventy-two students were in the study at any one time. This resulted from the use of three groups of twenty-fOur students during the second and third task. The minimum number of forty-eight students resulted from the use of only two instructional groups dur- ing the first task. Figure 14 summarizes the number of students which were instructed on each task. Instructional Group Task I Task II Task III N .A 24 24 24 24 B 24 24 24 24 C 24 24 D 24 24 N 48 72 72 96 Figure 14. NUmber of Students fOr EaCh Task In addition to these students, six sUbstitute children were ran- domdy selected from.each school. For the self-contained classroom schools, again half these students were from each classroom. These students were used to replace those students originally selected in case of absense prior to the beginning of instruction on the first task. .After a student had begun instruction in the task sequence, appropriate instruction continued following any period of absence. 82 MATERIALS Multiple Classification Pretest Boards The multiple classification pretest develOped by Bridgham (1967) consisted of eight 18 inch x 18 inch white posterboard cards. Attached to each card were two perpendicular rows of posterboard shapes (triangles, squares, rectangles, circles and, cresents) which also varied in color and size. Each row had one characteristic (color, shape, or size) which was the same for all Objects in the row, and two which varied across objects. The object which would have occured at the intersection of the row was absent. Also on the board were five to seven Objects from which the students were to select the one which belonged in the Open space. Figure 15 is an example of one of these boards. Complete descriptions of these materials are included in Appendix B. 2:30“ (All Yellow) O(Red) A (Green) 0 (Blue) (Y elloW) D (Black) OOenow) L D (White) Figure 15. Multiple Classification Pretest - Sanple Board 83 Rock Sets The classification scheme selected for this study necessitated the selection of rock samples which could be classified on the basis of grain Size and the amount of light colored grains. Samples which had a.bimodal distribution of grain size could not be included. NO judgment could be made by a Student as to the classification of such samples using the given criteria. In addition, the rocks selected were intended to reflect the distribution of the various classes of igneous rocks. FOrty-eight field samples (1000-15,000 cm3) were selected. These field samples were divided into two sets labeled Set A.and Set B. TWO sets were necessary to minimize the students learning specific rock types. Each instructor used both sets, alternating them between testing and instructional sessions. The two sets were generated from the original fOrty-eight samples by randomly assigning the samples from each class to the sets. This resulted in the rocks being distributed among the eight classes as fellows: Set.A - 5 granites, 6 diorites, 2 gabbros, 4 rhyolites, 2 andesites, 4 basalts, 0 glass, 1 obsidian; Set B - 5 granites, 6 diorites, 2 gabbros, 4 rhyolites, 3 andesites, 4 basalts, 1 glass, 0 obsidian. One cell in the classification scheme had.no representatives. Within each of the sets rocks were judged as high, medium or low difficulty by three persons ranging in geologic experience from expert to novice. Difficulty was judged.primarily on the basis of how fine a discrimination was required.between the sample and the nearest standard for a given variable. The texture of the grains and lack of color constrast were also considered. 84 The initial random assigment to sets A and B resulted in one more highly difficult sample being assigned to Set A and one more low difficulty sample being assigned to Set B. Both being within the same class, the samples were switched to balance both sets for difficulty. The judgment Of rock difficulty was used in ordering the presen- tation of the samples in each set. The ordering was done to balance the rock difficulty across the twenty-four sanples. Without this precaution the trials to criterion measure, to be described later, could have been systematically influenced by the consecutive occurrence of a number of rocks which were easy or difficult to classify. One sanple from each difficulty category was assigned to one of seven groups of three. These seven groups were randonmly ordered. This accounted for the order of twenty-one of the twenty-four sanples. As two rocks of high difficulty and one of medium difficulty remained, an eighth identical group could not be generated. These samples were randomly assigned along the positions between the other seven groups. This procedure resulted in a set consisting of seven randonnly ordered groups of three sanples of varying difficulty, and three samples ran- domnly inserted in the sequence. Finally, twelve replicas of Sets A and B were made by fracturing the larger field samples into hand sample sizes (20-100 cms). These mmltiple sets were necessary to avoid the students remembering the correct placement of a sample on the basis of irrelevant criteria, such as an unusual shape. 85 In addition to the samples, four standards were required to represent the defining values for each cell. The two grain size standards and two amounts of light grain standards were selected so that samples placed by comparison to the standards would be geologic- ally correct. For the Comparison to Standard task only one of each pair was required. The standard exhibiting the maximum value was selected from the pair for each variable. Task Boards The three task boards are shown in Figure 4, 10, and 11 (previous chapter). Each board was constructed of tan tri-wall cardboard with printed variable and variable value labels on white posterboard attached. All lines consisted of 1/4 inch black posterboard tape. The cells for each board were 8 inches x 8 inches squares. Each letter- ing area was 5 inches in width. Procedures Instructor and Tester Training Eadn instructor received approximately three hours of instructions , aimed at developing an understanding of the questions and design of the study. This was expected to help instructors reach correct deci- sions to problematic Situations in the field. The next instruction (two hours per task) was in the specific use of the protocols and scoring procedures for each task. This included verbal explanation, denonstration by the researcher and dissertation advisor, and sinmnlation 86 where all instructors scored one expert trainer who was completing the task. Two hours of practice with peers acting as subjects was also completed for each task. Finally the instructors worked approx- imately three hours with children in practicing the protocols and scoring procedures for the first two tasks. This was not necessary for the third task due to the similarity of the second and third task pro- cedures and the field experience each instructor gained teaching children on the first two tasks. In total the instructor training, supervised by one or two expert trainers, required approximately eighteen hours. Throughout this training enphasis was placed upon the careful and complete use of the innstructional protocols. Addition- al personnel Similarly trained were utilized to posttest all students. Classification Pretest and Preiiminary Tns tructionT— The multiple classification pretest developed by Bridgham (1967) was administered to all children before any instruction associated with rock sanple or tasks. The students were asked to look at each of eight cards and identify one of a set of objects which Should be placed at the blank intersection of two perpendicular rows of objects. As described earlier, the Obj ects in a row varied on two of three pro- perties (color, size, shape) and was constant on a third property. The students were told that there were "two groups of things" and a space where "Something is missinng" (Bridgham, 1967, p. 147). They *Note: Complete protocols for all instructions are included in Appendix C. 87 were asked which of the objects from the other group should go in the blank space. Thus, to complete the task the students were required to decide the common characteristic of each row and to coordinate those two properties in selecting the object appropriate to filling the open space. The task scores were 0-8 depending on the number of cards for which the student selected the correct object. This score was to be used as a potential covariate with the scores for the Double Variable Classification Task. During this same session students were given the instruction on concepts necessary to understanding the task instructions. This in- struction was called systemic instrnxztion and focused on teaching the students about the rocks they were to be using. The students were taught to identify a mineral ggainj 13333 grain, §_p_al_l_ grain, glassy rock, _l_igh£ and gags grains. Except for the concept grain, the others were the descriptive terms identifying the value for the variables grain size and anount of light colored grains. These values were used in the labels for the cells of the task boards. To accomplish this instruction students were first shown a rock sanple exemplifying the concept of interest and three exanples of the concept were carefully pointed out to the student. Each student was then asked to identify three different exanples of the same concept in the given sample. A brief exanple of the instructions for the concepts grain and large grain follows to illustrate the above procedure. Included are the quotations from the actual protocols. 88 ". . . Before I have you start the task, there are some things I want you to learn about rocks." ". . . Rocks are made up of grains. look at these rocks and I'll Show you what a grain is." ". . . This rock has large grains." (A rock sarple with large grains is shown to the student and the instructor begins to point to three exanples of a large grain carefully outlining the boundary of each grain.) . . . This is a large grain." (point - repeat for three grainns.) ". . . Can you Show me three of the large grains in the rock?" (The student is handed the sarple and a pencil with which to outline the three grains.) The only exception to the above procedure was with the concept "glassy". This was operationally defined as grains which were too small to see, so the student could not point out examples. Instead, they were asked to state that rocks were called glassy when the grains were too small to see. If the student could not identify the different examples, or the innstructor had any doubts as to student understanding, the instruction was repeated. The understanding of these concepts was necessary lest a lack of these basic understandings interfer with per- fornmance of the prescribed tasks. Pretest and Posttest Instructions All students were pretested prior to instruction on each task. This pretest also served as the general task instructions. For each task, the pretest instructions were intended to accompl ish the following: 1) Z) 3) 4) 5) 6) 89 Inndicate what was required of the student in performing the given task. For the first task only, exaple values were shown to the students as a review of the earlier instruction. This was done prior to the task introduction. Direct the students to use the appropriate variable or, in the case of the third task, variables. Describe the function of the standards with respect to each variable value label. That is, the decision rule which defined the logical relationship between each standard and the contiguous value labels was described. One such protocol statement was, "Rocks with more or the same amount of light grains than this standard (point to standard) go in this square (point to square)." For the Double Variable Classification Task these instructions were repeated for the second variable. In addition, it was pointed out that each value label was for an entire row or column and not simply for the contiguous square. Indicate to the children they were to use what they had learned before to do the present task. Ask the students if they had. any questions. The protocols used to make the above explanations were read to the students as the instructor pointed to anpropriated portions of the task boards . For the posttest the protocols were exactly the same as those used for the pretest. Instructional Treatment and Treatment Groups There were two types of instructional treatments within the study. Strategy instruction was based on the model of the cognitive strategies 90 for each task. The other was outcome feedback innstruction. This was based on the correctness of a student's response. Both treatments were designed to assure that the, information concerning the requirements of the task and function of the classification chart were identical. In addition, both treatments provided equal opportunity for experience with the materials and practice on the task. The practice during instruction varied only as did the number of sanples each student required to reach the criterion of task performance. The following sections describe the instruction for the feedback and strategy treatments . Outcome Feedback Instruction Students given outcome feedback instruction were told they would be informed if they were right or wrong on the verbal response for the first task and placement of a sample for the second and third tasks. Two denonstration examples followed. Each exanple was placed in the appropriate cell. The placement was explained in terms of the comparative relationship between the sample and standards defining the boundries of each class for both variables. Following each placement, the innstructor responded. If the placement was correct the instructor said: "Good! This rock has larger/the same size/smaller grains than the standard and was put here (point)". If the placement was incorrect, the response was "No! This rock has larger/the same size/smaller grains than the standard and should be put here (point)." Thus, for errors the child was both told and shown what the correct response should have been. If the child made more than four successive errors, the demonstra- tion portion of the instruction was repeated. 91 Strategy Instruction The instruction for strategy treatment subjects consisted of initial verbal instructions describinng the major features of the strategy the child would be asked to learn. This was followed by a denonstration of the strategy which connsisted of two exanples which were 'talked-through' . That is, the instructor modeled the performance of the strategy and pre- sented a corresponding verbal explanation of the sequence of strategy steps and the decisions being made. The behavior or sequence of steps the children are expected to learn for each task follows. Reference to the classification charts (Figures 4, 10, and 11) may be helpful in reading the following descriptions . Strategy Instruction - Task 1 Comparison to Standard The instructions for the comparison to standard task were relatively simple. The student was required to place the sanple proximate to the standard and then to make a multiple mmber of comparisons between the two rocks. The pnn‘pose of the proximate placement was to have both rocks placed within the childs visual focus as nearly to simultaneously as possible. The multiple comparison assured the collection of suf- ficient infornmation on the relative values of the variable under consider- ation. Both proximate placement and multiple comparisons were to facili- tate the students making the correct discrimination between values . Strategy Instruction - Task 2 ingle arialile ClassificatiOn The strategy innstruction for Single Variable Classification Task 92 is contained in the description of the final Double Variable Classification Task. The only difference is that the sequence of steps is executed for only one variable. Strate Instruction - Task 3 IBuBle TarraEIe Class1f1catnon For the third task the sequence of actions began with the selec- tion of one of the relevant variables, grain Size. The student then compared the sample to the standard exhibiting the maximum value for that variable. The sanple had to be placed in close proximity to the standard. The decision to be made was whether the sanple has larger, the same size, or smaller grains than the standard. If the grains were larger or of equal size, the sample was to be designated as belonging in the row preceding the standard. If the grains were smaller, the next standard was to be used in the same way. Rocks with larger or the same size grains were to be designated as belonging in the second row. Rocks with smaller grains belonged in the bottom row. To facilitate encoding the decision, the child was asked to verbalize the label for the selected row. After the row was selected, the remaining variable, the amounts of light colored grains, was used. The above process is repeated until the correct column was located. By making a series of comparisons to standards sequenced according to the decision rules implicit within the task, the class of each sample could be located. Following correct use of the strategy and correct placement of a sanple, students were given feedback identical to that of the outcome feedback treatment group . 93 Strategy Innstruction - Responses to Student Errors The responses to various possible errors were more complex than in the Outcome Feedback Instructions. As both the correct use of strategy and correct placement were required, there were several classes of errors which resulted. Error '_Iype I - the students used the strategy correctly but made a discrimination error during one of the compar- isons to a standard. Error Me 11 - The student correctly placed the sanple but did not complete the strategy correctly. Error Type III - The student did not correctly place the sanple and did not correctly use the strategy. The responses to these errors consisted of two parts. The first concerned correctness of placement, the second with the strategy errors. As more than one strategy error was possible the instructor responded to the first error in the strategy performance for the sample. This was possible as the strategy use required a well defined sequence of actions. The exact responses can be best understood in terms of the actual protocols from the Single Variable Classification Task. The responses given in Table 3 are taken directly from the protocols and listed under the error type. 94 Table 3. Responses to Student Strategy Errors During Instruction Type I (If incorrect placement but child's strategy is consistent Error with response.) Response: No! This rock has mostly light/about half light/mostly dark grains. (Move the rock to standard where initial error was made.) Be sure to take time to carefull look back and forth between the rock and the standzgi (point back and forth). You should have. . . . --placed the rock here (place). OR --Checked this standard (point) too and placed the rock here (place). Type II (If correct placement and incorrect strategy. Error Response: "The rock was placed correctly but you forgot to. . ." (use 9333 of following for first of strategy errors.) Type III (If incorrect placement and incorrect strategy. Error Response: No, this rock has mostly light grains/ about half light grains/mostly dark grains and should have been placed here (place sanple in correct cell). You forgot to. . . (use one of following for first of strategy errors.) Error: Resme: Not proximate to first or "begin by putting the rock both standards. close to the first standard" (Move rock to first standard) Not proximate to seconnd stand- "move the rock close to the ard when required; i.e. , second standard." (Mme rock P2, P3 samples to second standard). 95 Table 3 (Cont'd.) --no verbal output "read large grains/small grains/ glassy outloud before you placed the rock in this square. *--uses second standard "to stop after you checked the when sample is correct in first standard. If the rock cell 1. has larger or the same size grainns as this standard (point) you do have to use the next standard (point). *This response is used only when cell 1 placement was correct. This does not count as an incorrect trial. The innstructors corrected strategy errors as they occured. This was to help the students develop the strategy by adding the smaller components a step at a time. This procedure was followed until the entire strategy had been learned by the students. As with the feedback students, the incorrect placement of four successive samples required a readministration of the denonstration portion of the protocol. Schedule The investigation began three days prior to instruction on the Comparison to Standard Task with the administration of the mmnltiple classification pretest and preliminary instruction. The preliminary instruction was to teach the concepts necessary to perform the task. Following the initial session the students began a pretest-instruction- posttest cycle. The students were pretested and then were instructed in a given task and variable on the first day of the week. A second 96 instructional session for the same task.and variable was given to students without a pretest if they did not reaCh criterion during the first session. The second late afternoon session was seldom required. The following day students were posttested by personnel blind to the treatment given individual students. This two day cycle was repeated on the third and fOurth instructional days using the same task, but using the second variable. The order of the variable pre- sentation was balanced within each instructional group. During the third instructional week when Double variable Classi- fication was the fOcus, this cycle was changed in two ways. First, a second day of instruction was sCheduled for students who did not reach criterion during the first instructional session. It was anticipated that this task was substantially more difficult to learn and would require additional instructional time. Secondly, there was no need to repeat the cycle twice as both variables were combined in the task. The complete instructional sChedule including the pretest, instruction, posttest, and task variable sequence is shown in Figure 16. 97 WEEK 1 WEEK 11 WEEK 111 Treatment Day N l 2 3 4 5 6 7 8 9 10 ll 12 Group.A 12 GS LG GS LG GS LG GS LG GS GL GS LG Strategy Instruction 12 LG GS LG GS LG GS LG GS LG GS LG GS Group B 12 GS LG GS LG GS LG GS LG GS LG GS LG Feedback Instruction 12 LG GS LG GS LG GS GS LG LG GS LG GS Group C 12 GS LG GS LG Feedback Instruction 12 LG GS LG GS Group D 12 GS LG GS LG Feedback Instruction 12 LG GS LG GS Session P1 P0 P1 P0 P1 P0 P1 P0 P1 12 PO KEY: VARIABLES SESSION GS _ grain size :5 : preéizgtand instruction LG - amount of light grain pos 12 - second instruction if required *During each of the first two weeks, second instructional sessions were completed in the late afternoon if necessary. Figure 16. Testing and Instruction SChedule 98 DESIGN The section on design is divided into three parts. The first describes the experimental and comparison groups necessary to evaluate the research questions. The second is based on two figures which describe the control of the various independent variables involved in the study. The third part explains the research design as related to the hypotheses of the study. This section also delineates the use of the three treatment groups to isolate the effects of the instructional sequence from the effects of the strategy based instruc- tion. Experimental and Comparison Gronps To evaluate the stated questions, three groups were required. TIwo comparison groups received the outcome feedback instruction, the third group received strategy instruction. The experimental group, called the Cumulative Strategy Group (CF), received the strategy-based instructional treatment in all tasks. The first comparison group, designated as the Cumulative Feedback Group (CF), also participated in the entire sequence of three tasks. When comparisons were made between the performance of this group and the Cumulative Strategy group both groups had conpleted the cumulative experience with the materials, concepts, and tasks. Differences in dependent measures were attributed to the strategy basis of instruction. The second comparison group was referred to as the Isolated Feedback group (IF). Within this group, different subjects were brought into the study for the second and third tasks. This group was required to 99 evaluate the effectiveness of the instruction in previous tasks, and they did not receive innstruction in previous tasks. This was to assure that the instruction on the vertical task sequence results in positive learning and transfer effects. Control of Indemndent Variables by Design Certain independent variables within the study were controlled by the experimental design. The relevant design considerations are presented in two diagram. The first (Figure 17) presents the rela- tionships between the independent variables treatment, school , instructor, and variable sequence which are briefly described below. It should be noted that for the first task, the Isolated Feedback treatment group (IF) was not in the study but was present for the Single and Double Variable Classification tasks. The relationships shown remained the same across all tasks. The number of subjects in each cell is included. The second figure illustrates the relationship between school, variable sequence, and rock set as the rock set used by the students changed across the instruction-testing sequence. The relationships shown were identical for each of the three treatment groups within each school. The independent variables cons idered were: Treatment: (TRT) The variable of major interest. There were three levels each represented by a particular experimental or comparison group: Cumulative 100 Strategy (CS), Cumulative Feedback (CF), Isolated Feedback (IF). School: There were fOur levels of school, selected as previously described. Instructor: (1) From a total of twelve instructors, three were assigned to each school. 'Variable (VS) This pertained only to the first two tasks in Sequence: the sequence. The Comparison to Standard and Single variable Classification tasks required separate instruction fOr grain.size and the amount of light colored grains. The order in which the variables were presented to the students was considered. The first variable sequence (VS 1) was grain size, then amount of light colored grains. The second sequence (VS 2) was reversed. As shown in Figure 17, treatment (TRT), the variable of major interest, was crossed with the schools to Obtain a balanced design. Without this balance, school treatment interactions could.have confOunded interpretation of treatment main effects. Instructors, also crossed with treatment, were, however, nested within the schools. The logistics of running the study precluded.the possib- ility of balancing the design fOr instructors and sChools. Differences among the instructors' perfOrmance were not expected. The possibility was minimized.by the extensive training and.use of precise protocols. It should be noted that instructors were not used to posttest students. 101 School I I I I I I IV Treatment I Numbers of Groups VS 1 2 3 4 5 6 7 8 9 10 ll 1 2 Students 1 l l l 1 l l l l l l 12 IF 24 2 l l l l l l l l l l l 12 1 l l l l l l l l 1 l l l 2 CF 24 2 l l l l l 1 l 1 l l l l l 2 l l l l l l l l l l l l 1 2 CS 24 2 1 l l 1 l l l l l l l 2 TOtals 6 6 6 6 6 6 6 6 6 6 6 6 72 72 VS - Variable Sequence 1 - Instructor Figure 17. Additional trained personnel were used to administer all posttest Design to Control bajor Independent Variables sessions , without knowing the treatment group to which students had been assigned. Each team of two testers were assigned to posttest all students in two schools. students from each treatment group in each school. Each tester collected data on one half (3) The variable sequence was crossed with the treatment to balance difference in the difficulty for grain size or the number of light colored grairns . difficulty. Pilot work predicted this difference in variable Figure 18 indicates the mnannner in which two rock sets were used in the study. The use of two sets of sanples was necessary to avoid 102 m Em < 30m 393 mo 3.: 858m 8 S38 .2 one: m < < m < m < m < m < m < m < m N m < < m < m < m < m < m < m < m N a m < < m < m < m < m < m < m < m N < m m < m < m < m < m < m < m < H H: m < < m < m < m < m < m < m < m N m < < m < m < m < m < m < m < m N z m < < m , < m < m < m < m < m < m N < m m < m < m < m < m < m < m < N H IE p H FEEEEF N8 033:; 235» Seats, 235, 282.5 BE 28% SE: 283 on“: eotmuaamma one StBtGBB 282a, 2855 8 its 288 - m 38... 29am - N one 5399.8 - H x89 103 the possibility that students could remember sanples from pretest to instruction or innstruction to posttest. The rock sets were rotated as shown across the tasks within each treatment group. Because it was anticipated that the order in which students encountered the variable may affect either initial or later task performance, the design was balanced for this effect. One independent variable not included in the diagram was rock set. Inwo sets of rock samples were utilized within the instruction and test- ing, Set A and Set B. The development of the sets, described in the materials section, was done to assure the sets were identical in difficulty. Furthermore, the use of the sets was balanced in the following manner. Within each school one half of the students in each treatment group were given set A, B, A for the first variable of the Comparison to Standard pretest, instruction and posttest respectively. For the second variable the sequence was B, A, B. The ordering of the set presentation was identical for the Single Variable Classification Task. The Double Variable Classification set order was A B (B) A with set B used for the second instructional session if required. The second half of each treatment group utilized the rock sets in exactly the Opposite order. Experimental Design The experimental design in Figure 19 beginns with the random assign- ment of subjects to treatment groups and describes all eleven contact sessions with the students. Not shown is the second variable sequence, in which half of the students in each group were presented with the variables 104 I I minnow I I l v g 31:31 nausea ' U I: O I _ 3 ..'- I 9‘ $3.10 ‘ ' - I 1:; § 8 E I c a C O J 1631:1133 m ,_ -_- norm-111.13 > t: 9: “01131.11“ U . ' ' o: '3 2 I E 3! 1 ° I x x b x J 03 SITE-U. J ' 2 :2 53‘ . i E 2 _; I sparrow E ' 1"- u v s use; 191m 3 ' I U c— c t c 8 X39103 6: F 913.115 I .(auroov ! _ . z x“; rsansod ,._ O _ ' E." g — u. on 94035 . " I a G O La <= 0 Barons ” . ': g . ' g '5 S . a :- uormn-o *“ '3 E E c 31521 “(aims-“I x x5 x?) 01 5131.11. —. c u.- g . .... Z I . r f - I manner I °° '3 r 2 mi 191624 :1. g D -' woos E c: C u C v 53318115 0 3 I buxom: .2 2 rise; 15311504 ;._ . o E .5 I— E V) sums . N . o g ° ‘3 =5— .(3312115 '7' n _. .2 at L“. L'- 9 W ,5 .. s: nonmsu -° - . upturn; u: E Z 31 l ' I x x 5 x8 ‘31 “FF-ll J L: c .0' WOW c ' 2 also; 153131,; a 5’; ' I c c b o 8 “1°35 «I , .{861u1s I bum I I 315:1, nausea ' 8. . m c: a; e 8 “”35 I E 0.113.119 N C If. I ‘3 3 ? :2 won an I .. “OT-131L123 n I; :2 I311 .141: (“a .313 01913111 __- _-_- .2 i I '5 if: minnow Q I ” "' I 31511 1:91:14 .. . I 3 O C O 8 533mg - 5 Marcus In '2 (an: I II 5 I an; 15311504 . ' n g- § c 5 c 8 “3‘05 of v v, 1 53:13:15 5 so no mas-u noting; n :3 I X '1' I I x If: x 8 0'1 "FF-1.3. ...‘ N I use), 19010.14 =13 c8 buxom: uormuun 1daouog spurns mumpad 9 I nsanaid uornaguseo atrium I I mounts-9v m I I m :25: 3 a E .o '5 .3 u 5 v P- 0 C- U "- g: F; 9 5'. 35: 3'5” 3 E 5 as l’xperimcntal nus ign Figure 19. 105 light colored grains and grain size fer the first two tasks. This was indicated in the previous section. In addition to describing the sequence of instructional and test- ing sessions, the diagram outlines the session during which data of the specified dependent variables was collected and the hypotheses stated at each session. Subscripts IF, CF, CS, denote the Isolated Feedback, Cumulative Feedback, and Cumulative Strategy instructional groups. The superscripts b, c for the isolated feedback indicate that individuals in Task 3 are different from those in Task 2. Hypotheses The hypotheses for the three tasks are stated below in two fbrms, a, and.b, bf. The 3 statement is the general fOrm.of the hypotheses. The b, bf form directly implies the comparisons which will be made between groups. The b_fbrm indicates the comparison used to evaluate the possibility of positive and.negative learning or transfer effects due to instruction on the task sequence. The bf form.shows the com- parison for evaluating the effects of strategy-based instruction within the prescribed vertical sequence. The hypotheses are listed by task and under the corresponding number of the research question stated earlier (page 19). The research questions are reiterated below to facilitate reading of the hypotheses. 106 Table 4. List of Research Hypotheses I . Strategy Learning: When instructed on a specific strategy within a vertical task sequence, can the student learn to perform the task using that strategy? I I . Strategy Transfer: Does a learned task-specific strategy transfer to a more complex task within a vertical task sequence, that is, will a student automatically utilize the strategy learned for a precursor task in the unin- structed attempt to perform a related, more complex task? III . Strategy Use: Following instruction on a task within a vertical sequence, do students use the taught strategy to perform that task? IV. Does strategy-based instruction improve the learning of a vertical sequence of tasks? More specifically: A. Learning Transfer: Does strategy-based instruction enhance the transfer of learning within the task sequence? B. Facilitation of Learning: Does strategy-based instruction facilitate the learning of the tasks within the sequence? C. Task Performance: Does strategy-based instruction enhance post- test performance accuracy within the task sequence? Oomparison to Standard Question II and IVA are not applicable to this first task as they address transfer phenomena. Question I. Strategy Learning 1 . (a) The students given Strategy Instruction will learn the strategy for Task 1. 107 Table 4 (Cont'd.) Question III. 2. Question IV. Question IV. 4. Question I. 1. (b) Eighty percent of the students in the Strategy Instruction group will meet criterion of strategy learning fbr Task 1. Strategy Use (a) (b) The students given Strategy Instruction will use the taught strategy during the posttests fer Task 1. Eighty percent of the students given Strategy Instruction will meet the criterion of Strategy use during the posttests on Task 3 far 80 percent of the samples. Facilitation of Learning The Strategy Instruction will result in the greater facilitation of learning for Task 1. Students given Strategy Instruction fbr Task 1, will learn to perfbrm the task in significantly fewer trials than will the groups given Outcome Feedback Instruction on Task 1. Task Perfbrmance The Strategy and Outcome Feedback Instruction on Task 1 will result in greater accuracy of perfbr- mance on the Task 1 posttests. The students given Strategy Instruction on Task 1 will perform the posttests with significantly greater accuracy than the students receiving Outcome Feedback Instruction on Task 1. Single variable Classification Strategy Learning (a) (b) The students given Strategy Instruction will learn the strategy fbr Task 2. Eighty percent of the students in the Strategy In- struction group will meet criterion of strategy learn- ing fOr Task 2. 108 Table 4 (Cont'd.) Question IT. Strategy Transfer 2. Question III. 3. Question IV. 4. Question IV. S. (a) Cb) The strategy fbr Task 1 will automatically transfer vertically to the perfbrmance of Task 2. Eighty percent of the students given Strategy Instruction on Task 1 will meet the criterion of Task 1 strategy use during the first pretest on Task 2 fOr 80 percent of the samples. Strategy Use (a) (b) (a) (b) (a) The students given Strategy Instruction will use the taught strategy during the posttest fOr Task 2. Eighty percent of the students given Strategy Instruc- tion will meet the criterion of strategy use during the posttests on Task 2 fbr 80 percent of the samples. Learning Transfer The learning from.both the Strategy and Feedback Instruction of Task 1 will automatically vertically transfer to the performance of the first Task 2 pretest. However, the Strategy Instruction will result in greater vertical auto-transfer within the task sequence. The students instructed on Tasks l and.2 by Strategy and Outcome Feedback will perfbrm.the first Task 2 pretest with significantly greater accuracy than will the students who have not received instruction on Task 1. The students given Strategy Instruction for Task 1 will perfbrm.the first Task 2 pretest significantly more accurately than will the group instructed by Outcome Feedback on Task 1. Facilitation of Learning Both the Strategy Instruction and.0utcome Feedback Instruction for Task 1 will facilitate the learn- ing on Task 2. However, the Strategy Instruction will result in.the greater facilitation of learn- ing within the task sequence. 109 Table 4 (Cont'd.) Question IV. 6. Question 1. 1. (b) (a) 0)) Students given Outcome Feedback and Strategy Instruction for Tasks l and 2 will learn to perform Task 2 in significantly fewer trials than will the group given Outcome Feedback Instruction on Task 2 only. Students given Strategy Instruction for Tasks l and 2 will learn to perfbrm.Task 2 in significantly fewer trials than will the groups given Outcome Feedback Instruction on Tasks l and 2. Task Perfbrmance Both the Strategy and Outcane Feedback Instruction on Tasks l and 2 will result in greater accuracy of perfbrmance on the Task 2 posttests. Hewever, the Strategy Instruction will result in the greater accuracy of perfbrmance within the task sequence. The students given Outcome Feedback and Strategy Instruction on Tasks l and 2 will perfbrm the Task 2 posttests with significantly greater accuracy than.the group receiving Outcome Feedback Instruction on Task 2 only. The students given Strategy Instruction on Tasks l and 2 will perfbrm.the Task 2 posttests with significantly greater accuracy than the students receiving Outcome Feedback Instruction on Tasks 1 and 2. DoUble variable Classification Strategy Learning (a) (b) The students given Strategy Instruction will learn the Strategy fOr Task 3. Eighty percent of the Students in the Strategy Instruction group will meet criterion of strategy learning for Task 3. 110 Table 4 (Cont'd.) Question II. Strategy Transfer 2. Question III. 3. Question IV. 4. Question IV. 5. (a) (b) The strategy fOr Task 2 will automatically transfer vertically to the perfbrmance of Task 3. Eighty percent of the students given Strategy Instruction on Task 2 will meet the criterion on Task 2 strategy use during the pretest on Task 3 fbr 80 percent of the samples. Strategy Use (a) Cb) (a) Cb) 03') (a) The students given Strategy Instruction will use the taught strategy during the posttest fOr Task 3. Eighty percent of the students given Strategy Instruction will meet the criterion of strategy use during the posttest on Task 3 for 80 percent of the samples. Learning Transfer The learning from.both the Strategy and Feedback Instruction on Task 1 and 2 will automatically vertically transfer to the perfbrmance of the Task 3 pretest. However, the Strategy Instruction will result in greater vertical auto-transfer with- in the task sequence. The students instructed on Tasks l and 2 by Strategy and Outcome Feedback will perfbrm the Task 3 pretest with significantly greater accuracy than will the students who were not instructed on those tasks. The students given Strategy Instruction fOr Task 1 and 2 will perfbrm.the Task 3 pretest significantly more accurately than will the group instructed by Outcome Feedback on Task 1 and 2. Facilitation of Learning Both the Strategy Instruction and Outcome Feedback Instruction fbr Tasks l, 2, and 3 will facilitate the learning of Task 3. However, the Strategy'Instruc- tion will result in the greater facilitation of learning within the task sequence. 111 Table 4 (Cont'd.) (b) Students given Outcome Feedback and Strategy Instruction for Tasks l, 2, and 3 will learn to perform Task 3 in significantly fewer trials than will the group given Outcome Feedback Instruction on Task 3 only. (b ') Students given Strategy Instruction for Tasks l , 2 , and 3 will learn to perform Task 3 in significantly fewer trials than will the groups given Outcome Feedback Instruction on Tasks l, 2, and 3. Question IV. C. Task Performance 6. (3) Both the Strategy and Outcome Feedback Instruction on Tasks l, 2, and 3 will result in greater accuracy of performance on the Task 3 posttest. However, the Strategy Instruction will result in the greater accuracy of performance within the task sequence. (b) The students given Outcome Feedback and Strategy Instruction on Tasks l, 2, and 3 will perform the Task 3 posttest with significantly greater accuracy than the group receiving Outcome Feedback Instruc- tion on Task 3 only. (b') The students given Strategy Instruction on Tasks 1, 2, and 3 will perform the Task 3 posttest with significantly greater accuracy than the students receiving Outcome Feedback Instruction on Tasks l , 2 and 3. Dependent Variables Raw Data The raw data for each of the three tasks consisted of a sequence of coded responses to indicate the actions of students as they attempted to solve the task. The coded responses were selected to describe 1) 112 task responses, i.e., required responses such as rock sample placement on the task board, 2) strategy responses, i.e., actions required for executing the model strategy, and 3) general responses, i.e., addition- al actions a student might take while searching the task board for infonmation. This last category of coded response was somewhat general. For example, in the second task, the student might look at the left, middle, or right side of the board. This could.be recorded. However, whether the student was attending to the value labels, variable labels, standards, or logical relationships between the arrangement of the squares could not be reliably determined. Recorded on each answer sheet (Appendix D) fur the instructors was the sequence of symbols which would result if a child correctly exe- cuted the task using the model strategy fOr each rock sample. This allowed the instructor to accurately decide if the strategy had been utilized and if the placement was corrett. The instructor was to record in sequence all actions by the student in addition to or in place of strategy required actions. The symbols instructors were to record, and a brief explanation of each are shown in.Tables S, 6, and 7, one fer eaCh task. The symbols are arranged under the previously mentioned categories. FOllow- ing the figure for each task are examples illustrating how these symbols were utilized. The Comparison to Standard Task requires that students verbally state the comparatiVe value greater than, equal to, or less than. This 113 Table 5. Cemparison to Standard Task - Raw Data Symbols Task Response ‘Vl-3 Student responds verbally with comparative value greater than (1), equal to (2), less than (3) fer comparison of sample to standard on a given variable. Pl-Z Student places sample in cell labeled greater than, equal to (l), or less than (2). Strategy Response Al-x Student places sample in proximity to standard grain size fOr comparison lasting 1 to x seconds counted by the instructor. A.is the standard fbr grain size, C the standard fer the amount of light Cl-x colored grains. amount of light grains General Response b Student looks at board for information, the detail of which cannot be observed.by the instructor. Sl-x The student looks at the sample for l-x counted 3 seconds. ' described the relationship between the sample and standard on a given variable. .A coded sequence of symbols described the actions of students in perfbrming the task. For example, the recorded sequence 84 V3 b P2 for grain size would indicate that the students had studied the sample for 4 counted seconds (S4), responded smaller grains (V3), looked at the board (b), and placed the sample in cell 2 (P2). If the student had correctly followed the strategy, the coded sequence fur the same 114 sample would have been S4 A5 V3 b P2. The only difference being the symbol AS indicating the student placed the sample proximate to the standard for S counted seconds. This coded sequence of symbols can be used also to describe more varied students' actions. An example would be S4 A2 b 81 A4 b Vl P2 P1 where the student repeated a look at the sample, a comparison to the standard and a look at the board before giving the verbal response, placing the sample in cell 2 and finally moving the sample to cell 1. Such extended sequences for the first task were quite unconmon . Table 6. Single Variable Classification - Raw Data Symbols Task Response Pl-3 Student places sample on cell labeled large grains (1), small grain (2), glassy (3) for grain size; or mostly light grains (1), about half light grains (2), mostly dark grains (3) for the amount of light grains. Strategy Response A, B. Student places sample proximate to one of the grain size two standards which define the limiting values or of the three cells. C, D amunt of light grains V1-3 The student reads or states the value label for the cell where the sample is to be placed. General Responses Sl-x The student looks at the sample for l to x second oounts . The second count was only recorded for the students first look at the sample. L,M,R. The student looked to the left, middle, or right portion of the board. 115 The Single Variable Classification Task required the correct placement of the rock sample in one of three cells (P1, P2, or P3) de- lineated by the standards and variable value labels, such as mostly light grains, about half light grains, mostly dark grains. The students instructed to use the strategy were also required to place the sample proximate to certain standards (A, B or C, D) and provide a verbal response indicating the value label where the sample was to be placed (V1, V2, V3). The instructors recorded additional data when students examined the sample (Sl-x) and looked to various portions of the board (L, left; M, middle; R, right). Students were not required to state a comparative value relating the sample to each standard as they were in the first task. Examples of correct strategy sequences for grain size would be: (1) §_l_0 AbVl Pl (2) SbABMVZ P2, or (3) SiABV33P3. These sequences would reflect the use of the strategy as designed for the sample which should be placed in cells 1, 2, or 3 respectively. The underlined symbols indicate those actions which were not required to meet the criteria for correct strategy use. The looks to various parts of the board would not be necessary or expected after the student has learned the value labels. A variety of other sequences were recorded varying from one as simple as 82 P3 to an extended sequence S3 A B S L R A V1 V2 P2. In the first sequence the student simply looked at the sample and directly placed the rock in the third cell of the board. The more complex set of symbols indicated the student looked at the sample (S3) made 116 proximate comparisons to both standards (A, B) looked to both ends of the board (L, R) , checked standard A a second time, and changed his mind about the correct verbal response (V1 V2) before placing the sample in the cell consistent with the last verbal response. The Double Variable Classification Task required the correct place- ment of the sample in one of the nine specified cells (Pl-9). The strategy model required proximate comparison to 2 to 4 standards (A, B, C, D) and verbal responses which indicated the variable value label for the row and colum in which the sample belongs (VI-6). The general re- sponses included the student looking at the sample (Sl-x) and searching for information associated with variables (G, grain size; L, amount of light colored grains). The sequence of symbols indicating the use of the exact strategy model for a sample belonging in the center class of the matrix (P5) is given as an example. This shows student actions when the use of all four standards was required. Again, the underlined symbols were not required components of the strategy. The sequence is S7 A B _G_ V2 C D b VS P5. The student looked at the sample for seven second (S7) counts and made proximate comparisons to both grain size standards (A, B) before looking at the board (G) and stating the grain size value label "small grains" (V2). Comparison to both standards for the amount of light grains (C, D) preceded the look at the board (L) to read the label "about half light grains" (VS) and the placement (P5). Sequences showing no use of the standards (SS L S G L P4), use of standards for one variable (S8 AB V2 L P), out of sequence verbal re- 117 Table 7. Double Variable Classification - Raw Data Symbols Task Response Pl-9 Student places the sample in one of the nine classes on the 3 x 3 classification scheme. 213] 4 516] 7 8]§] Strategy Response A,B,C, or D Student places sample proximate to one of the two standards for each variable: A, B for grain size; C, D for the amount of light colored grains. V1-6 The student reads or states the value label for the row (VI-3) or column (V4-6) where the sample is to be placed. General Responses Sl-x The student looks at the sample for l-x second counts . The second count was recorded for the student's first look at the sample. G, L The student looked at the side of the board Where information related to the grain size variable (G) was located or to the bottom of board where information related to the variable, amount of light grains (L) was located. sponses ($17 A C V_l_ V4 Pl) , and nunerous other sequences were possible. One of the more complex responses recorded was 810 V4 S G S G S G S L S L G S G S B Vl Pl. 118 Scores This section defines the scores generated from the raw data. There were four general types of scores used to evaluate the various types of hypotheses. For each type there were specific scores based on the criteria apprOpriate to eaCh task. The types of scores are de- scribed below. The specific scores are described in.Tables 8, 9, 10. l. Perfbrmance Accuracy_Scores indicate the degree to which the students correctly meet the task requirements such as correct placement of the rock samples. 2. Strategy Transfer Scores indicate the use of the strategy fer the previous task during the first attempt to perfbrm the subsequent task. 3. Strategy Use Scores describe the extent to which students utilized the strategy taught for that task. 4. Facilitation of Learning Scores indicates the extent of instruction necessary fOr students to learn to correctly perform a given task. 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Each of these related to questions which arise during or after instruction. For learning-transfer and strategy-transfer hypotheses only, scores denoted by V1 are apprOpriate. The evaluation of transfer questions occurred only on the first pretest as the observations must precede instruction on the new task. FOr the scores describing perfbrmance of the Double Variable Classification Task the above need not be considered. The use of both variables was required in that task. The strategy use and strategy transfer scores require additional comment. First, the criteria fOr the two scores are different. The criteria fOr the strategy transfer scores was taken from the previous task and observed on the first pretest fbr the next more complex task. The criteria for strategy use, on the other hand, was based on the model strategy for the task under consideration. This score was obtained from any test following the first instruction. The detail of the criteria for strategy use and strategy transfer scores for each task are given in Table 11. Second, in eaCh of these descriptions the term "required" has a specified.meaning. "Required" indicates that Observed student actions were those whiCh would have been evident had the model strategy been executed to gain the students' placement of the sample. For strategy transfer scores the corresponding model strategy was from.the previous task. For strategy use scores the model was for the task being perfbrmed. The actions had to be consistent 123 with the student's placement of the sample. This may or may not have been correct. Discrimination errors were possible during comparisons to standards which were not errors in strategy performance. The criteria fOr these scores were very stringent as they require the use of strategy as an algorithm when they perform the task. The strategy transfer scores were eSpecially stringent as the students must have utilized the strategy learned fOr a previous task to develop another strategy for the more complex task. The more complex strategy must have been consistent with the requirements fOr the new task. For example, the Double Variable Classification Task required that both grain size and the amount of light colored grains be considered to classify a sample. The previous task required only consideration of one variable. The strategy transfer measure required the Single Variable Classification Strategy be applied to both variables. In effect, the student must not just have transferred the simpler strategy but utilized it as a chunk of information in constructing a strategy for the new task. Examples of how the scores were derived from the raw data will clarify the criteria and how they were applied. One example for each of the strategy use scores is describeda The strategy transfer scores are not exemplified as they are similar to the strategy use scores of the previous task. The simplest of the strategy use scores was from the comparison to Standard Task. .A raw data sequence such as S4 A5 Vl b Pl indicated the samples were compared to the standard fOr more than 4 second counts, Table 11. 124 Strategy Score Criteria Task Comparison to Standard Single Variable Classification Double Variable Classification Strategy Use Sample was placed proximate to the standard fOr at least fOur second counts while making the comparison. The sample was placed.pro- ximate to the required number of standards. The value label corresponding to the placement was re- ported following the com- parison to the last required standard. The sample was placed pro- ximate to the required number of standards. The value label corresponding to the placement was re- ported for each variable. The verbal report occurred fOllowing comparison to the last required standard for each variable. Strategy Transfer (not applicable) The sample was placed proximate to the required number of standards for at least fOur second counts. The sample was placed proximate to the re- quired number of stand- ards. The value label corresponding to the placement was report- ed fbllowing the com- parison to the last required standard. This was done fOr both variables. the verbal response (V1) followed directly with the placement (Pl) being made consistent with that response. The proximate comparison to the standard for at least 4 second counts was the single criterial feature of the strategy use. Strategy use fOr the Single Variable Classification Task was some- what more complex. The fOllowing pairs of raw data sequences illustrate the critical features of correct strategy use: (la) A'Vl P1; (1b) B A V1 Pl; (2a) A B‘VZ Pa (2b) B a‘VZ P2; (3a) A B'V3 P3 (3b) B V3 P3. The pairs included only the critical features of the strategy use for 125 placement of the samples in the first, second, and third classes respectively. The second sequence of the pair was simply the reverse of the first. This reversal of direction was the only allowed differ- ence from.instruction. NOt illustrated were additional extraneous actions such as glances at various parts of the boards and the use of a second standard.when it was not needed to place the samples in the first or third cells. It should be noted that the four second count require- ment was not included in the strategy instructions and thus is not a requirement for strategy use. For the Double variable Classification Task the following illus- trates correct sequences: (l).A B V3 C D‘V4 P1, (2) A.B V2 C D VS PS, (3) D'V6 B ALVZ P6, (4) A B V3 C D'V4 P7. The first two sequences show no deviation from the strategy. In both cases the student checked the number of standards required in the strategy and gave the verbal response following the decision fOr each variable. The third sequence was correct but reversed. The student began at the minimum value standard fOr the amount of light grains (lower right standard on the board) instead of the maximum value standard for grain size (top standard on left side of board). The fOurth sequence illustrates that a second standard (D) was used.when only the C standard was needed to make the decision (V4) indicating the sample belonged in the left column (mostly light grains) on the board. This use of the extra standards was allowed as correct strategy use. In addition to the strategy use and transfer scores which were used to directly evaluate the stated hypotheses there is another 126 extended series of scores not described in this section. These are used to describe student behaviors in terms of portions of a strategy used or transferred in performing a task. For each component, such as the placement of a sample proximate to standards or the statement of a value label, a series of progressively less stringent more sensitive scores were computed. As the number of these scores is large they are best described in the context of discussing the various hypotheses for each task in Chapter 4. Statistical Analysis The statistical analysis was separated into two areas. The first involved the various comparisons between groups. The second con- cerned learning, use, and transfer of the strategy by those given strategy instruction. Comparative Analysis The comparative analysis of the Comparison to Standard task data considered only task perfOrmance and facilitation of learning hypotheses. In addition there was only one comparison to be made between the performances of strategy and Feedback students. The comparison was made using Student's t-statistic. The Single and Double variable Classification Tasks necessitated a planned comparison analysis to evaluate hypotheses involving learning transfer, task performance, and facilitation of learning hypotheses fbr each task. The two comparisons were: (1) The mean of the Cumulative Feedback and Cumulative Strategy Cumulative groups vs. the Isolated Feedback group and (2) the mean of Feedback vs. Cumulative Strategy treatment groups. 127 These comparisons allowed evaluation of the following statements: (1) If the average of the two groups receiving instruction on all tasks exceeded the performance of the isolated feedback group, then it can be stated that the effects of the cumulative instruction positively affected student performance. This comparison also guards against the possibility of negative transfer effects. (2) If the strategy feedback group performed better than the outcome feedback group, then it can be stated the better performance was due to the strategy-based in- struction within the task sequence and not simply to cumulative experience with materials and outcome feedback. Completing the analysis using the above comparisons was selected as the effects of interest were specified prior to beginning the investigation. The analysis was a ONEWAY ANOVA for the a priori constrasts as calculated using the Statistical Package for the Social Sciences (Nie, gt EL, 1975) program. The alpha level was set at a = .05. This was considered sufficiently large to detect differences between mean scores and yet was sufficiently small to protect against incorrectly supporting the hypotheses. Descriptive Analys is There were no comparison groups involved in the analysis related to the strategy learning, use, and transfer hypotheses. The hypotheses 128 were concerned only with the perfbrmance of those students receiving the strategy based instruction. However, some scores are reported for other treatment groups as an indication of whether other students are perfbrming the task using the model strategy or strategy com- ponents. ‘Mean scores, standard deviations, and frequency distributions are sufficient descriptive statistics fOr eaCh of these scores. The criteria for supporting the various strategy hypotheses required 80% of students to meet the strategy learning, use, or transfer criteria fer 80% of the samples. As there were 24 students in each instructional groups this means that 19 students must have give a correct perfbrmance on 19 of 24 samples for a hypothesis to be supported. Nineteen of twenty-fOur samples or subjects is 79% whereas twenty of twenty-fOur samples or subjects is 83%. The fOrmer was se- lected as closest to the 80% stated in the hypotheses. CHAPTER.IV RESULTS The questions reiterated below indicate two major areas of investigation within the study. The first three questions (I, II, III) were concerned with ability of the students given strategy based instruction (the Cumulative Strategy Group) to learn, use, and trans- fer the taught strategies. The related premise was that the strategy fer each task would.be learned, used in a posttest, and transferred to the next task in the sequence as a chunk of information. The second area of investigation was related to the accuracy of task performance. It was predicted that the availability of the strateg- ies in long term.memory would facilitate learning to perfbrm.the task accurately, enhance the posttest performance accuracy, and enhance the pretest perfbrmance accuracy of the next task (Questions IV. B, C, and A, respectively). Research Questions I. Strategy Learning When instructed on a specific strategy within a vertical task sequence, can the student learn to perfbrm.the task using that strategy? II. Strategy Transfer 129 130 Does a learned task-specific strategy transfer to a more complex task within a vertical task sequence, that is, will a student automatically utilize the strategy learned fer a precursor task in the uninstructed attempt to perfbrm a related, more complex task? III. Strategy Use Following instruction on a task within a vertical sequence do students use the taught strategy to perfbrm the task? Iv. Task PerfOrmance Does strategy-based instruction improve the learning of a vertical sequence of tasks? .More specifically: A. Learning Transfer Does strategy-based instruction enhance the transfer of learning with the task sequence? B. Facilitation of Learning Does strategy-based instruction facilitate the learning of the tasks within the sequence? C. Task Performance Does strategy-based instruction enhance post- test perfbrmance accuracy within the task . sequence? These questions were asked for eaCh of the three tasks in the instructional sequence: Comparison to Standard, Single variable Classification, Double variable Classification. The last task is the most important because learning to correctly classify igneous rock samples is central to developing a students knowledge of geology. The results fOr eaCh task are reported in two sections. The first addresses the hypotheses related to strategy learning, use, and transfer. The strategy use and transfer results included two types of scores: (1) scores whiCh directly assess the use or transfer of the complete strategy, and (2) scores which further describe the students’ 131 behavior as it reflects their use and transfer of components or parts of the strategy. These components are related to the proximate place- ment of samples to standards and/or the verbal response by which students reported value labels from the task boards. The second section addressed the facilitation of learning, learning transfer, and the task performance hypotheses. The reported results are the comparisons made among the Cumulative Strategy (CS), Cumulative Feedback (CF), and Isolated Feed- back (IF) groups. Comparison to Standard Task: Strategy_Besults Strategy Learning The hypothesis* related to Question I is: l. (a) The students given Strategy Instruction 'will learn the strategy fOr Task 1. (b) Eighty percent of the students in the Strategy Instruction group will meet criterion of Strategy learning fOr Task 1. The Trials to Criterion Score (lTC)** indicates that 92% of the twenty-fOur students given strategy instruction learned to perfbrm the Comparison to Standard Task correctly using the appropriate Strategy. The students reached the criterion fOr learning with an over *The (a) statement is a general fbrm.of the hypothesis while the (b) statement(s) represents a specific predictions. **Note: For the first two tasks instruction was given on each of two variables. The average score for performance on both variable is reported except fbr scores related to transfer questions. Transfer scores are calculated from data for the first pretest of each task. 132 all mean of 10.50 trials (samples) or slightly more than 3 samples greater than the minimum number (7) in which criterion performance could be reached. No students required a second instructional session (i.e., more than 24 samples). The data shown in Table 12 clearly support the stated hypotheses. Table 12. Strategy Learning Results: Trials to Criterion Scores for Cumulative Strategy Group Instruction (n = 24) % of Ss learnfng the strategy correct- Trt Score Score 1] in the indicated number of samples Grp Name Label Mean S.D. 7-17 13-18 19-74 > 24 Samples Samples Samples Samples CS TRIALS TO CRITERION" l'I‘C 10.50 3.53 75 21 4 0 Strategy Use The hypothesis related to Question III is: 2. (a) The students given Strategy Instruction will use the taught strategy during the posttests for Task 1. (b) Eighty percent of the students given Strategy Instruction will meet the criterion of strategy use during the posttests on task 1 for eighty percent of the samples. The Strategy Use Score (lSU) most directly evaluates the students use of the taught strategy on the posttests (Table 13). Only one student (4%) used the strategy exactly as taught on more than 80% (19) of the samples. The mean score of 5.94 (S.D.=-S.24) indicates *Note: All scores which are used to directly assess a hypothesis are presented in capital letters on the tables. Scores related to strategy components are presented in lower case letters. 133 that students utilized the strategy on approximately 25% of the samples. The results fOr this score do not support the hypothesis. Table 13. Strategy and Component Use Results: Comparison to Standard Task Posttest (n's = 24) % of Ss using the strategy or compon- Trt Score Score ent for the indicated % of samples Grp Name Label Mean S.D. f 25% 26-50% 51-75% 76-100% Samples Samples Samples Samples STRATEGY lSU 5.94 5.24 58(13)* 30 8 4 USE CS Standard lSDU 13.71 9.49 24(17) 21 17 37 Use STRATEGY lSU 2.50 5.09 88(50) 8 0 4 USE CF Standard lSDU 4.96 7.44 75(25) 12 0 13 Use * % Of students using strategy or component on 0% of samples. Strategy Component Use Further description of student performance is indicated by the Standard Use Score (lSDU) in Table 13. This score is the number of samples placed proximate to the standard.without requiring the minimum fOur second-counts which were part of the Strategy Use Criterion. The comparison of'a sample to the standard is considered.a major component of the strategy. The mean score (13.71 samples) indicates that students used the standards for approximately 57% of the samples. Furthermore, nine of the twenty four sUbjects (37%) compared the sample to the standard more than 80% of the time. 134 The results fer the Standard Use and Strategy Use scores indicate a substantial number of students were placing at least one sample proximate to the standard but not fOr the 4 second-count required in the complete strategy. Comparison to Standard Task: Perfbrmance Results Pretest The data reported fer the first pretest for Task 1 provide some description of initial task difficulty. TWO scores are reported, the Comparative Response Score (CRrv1)* and the Placement Accuracy Score (PA4Vl). The mean score for CR4V1 for the Cumulative Strategy Group was 15.54 (S.D. = 4.06) samples correctly compared to the standard. The mean fer Cumulative Feedback group was 16.67 (S.D. = 4.17) samples. For the placement of the samples on the classification chart (PA- v1) the strategy students correctly placed an average of 19.25 samples (S.D. = 2.47) and the cumulative feedback students averaged 19.42 (S.D. = 2.16) correct placements. The consistently greater place- ment score is probably a result of judgements that a sample and standard are the "same" when the judgement "greater" was correct. The placement would be accurate for either decision. *the: The symbol v1 following any score label indicates the score pertains to the students first encounter with the task, i.e. , the first variable. 135 Considered together the 48 students correctly compared approximately 67% of the samples and correctly placed approximately 80%. The level of performance indicates the task is fairly easy to perform. Facilitation of Learning The hypothesis related to Question Iv B. is: 3. (a) The Strategy Instruction will result in the greater facilitation of learning for Task 1. (b) Students given Strategy Instruction on Task 1 will learn to perform in significantly fewer trials that will the group given Outcome Feed- back instruction. The difference in the Trials to Criterion Score between the Cumulative Strategy Instruction group (CS) and the Cumulative Feedback group (CF) indicates the extent to which the strategy based instruction facilitated the learning of the Comparison to Standard Task. The data shown in Table 14 are the results of the t-test analysis of the scores. Table 14. t-Test for Trials to Criterion Score: Comparison to Standard Task Instruction Trt Standard t 2-Tail Grp n 'Mean S. D. Error value D. F. t-Prob. CS 24 10.50 3.53 0.72 CF 24 10.10 2.51 0.51 0'45 46 0'656 The results do not support the hypothesis. The CUmulative Strategy group needed slightly more trials to criterion than the Cumulative Feedback group, but the difference was not significant 136 (p = 0.656). There is no differential facilitation of learning attributable to the instruction given either group fOr the first task. It is also apparent from the mean scores for both groups that the task is easy to learn to perfOrm. Only a mean of three samples more than the possible minimum of 7 are required by either group of students. Task Performance The hypothesis related to Question IV. C. is: 4. (a) The Strategy Instruction on Task 1 will result in greater accuracy of perfbrmance on the Task 1 posttests. (b) The students given Strategy Instruction on Task 1 will perfonm the posttests with significantly greater accuracy than the students receiving Outcome Feedback In- struction on Task 1. Both the Comparative Response Score (lCR) and the Placement Accuracy Score (lPA) are related to the students' ability to perform the task following instruction. The first score indicates the students' ability to correctly discriminate between the sample and the standard. The results of the t-test analysis are shown in.Table 15. The 2- tailed prObability is given as the results were in the direction Opposite to that stated in the hypothesis. Table 15. t-Test for Comparative Response Score: Comparison to Standard Task Posttests Trt Standard t Z-tail Grp n Mean S. D. Error Value D. F. t-Prob . CS 24 18.31 1.71 0.349 CF 24 18.98 1.54 0.31s ”1'42 46 0°163 137 The results indicate that students receiving strategy instruc- tion did not discriminate between the variable values for a sample and a standard in a manner significantly different (p = 0.163) from those receiving feedback on their performance. The results fer the second score (lPA) reported in Table 16 indicate the accuracy of sample placement on the task board by both groups. Table 16. t-Test fOr Placement Accuracy Score: Comparison to Standard Task Posttests Trt Standard t 1-tail Grp n Mean S. D. Error Value D. F . t-Prob. CS 24 20.35 0.93 .189 CF 24 20.35 1.31 .267 0 46 0'50 The analysis did.not indicate any significant differences (p = 0.50) in perfbrmance between the two groups. Single variable Classification Task: Strategy Results Strategy Transfer The Single variable Classification Task is the first in the sequence where hypotheses related to transfer phenomena are addressed. Because the transfer scores reflect the criteria fOr strategy use from the previous task, discussion of the results fOr the strategy transfer question (II) precede discussion of the results fOr the strategy learning question (I). The hypothesis related to Question II is: 138 2. (a) The strategy fer Task 1 will automatically transfer vertically to the performance of Task 2. (b) Eighty percent of the students given Strategy Instruction on Task 1 will meet the criterion of Task 1 strategy use during the pretest on Task 2 for 80% of the samples. The Strategy Transfer Score (2ST-v1) was calculated from data observed on the first pretest (i.e., the pretest for the first variable) fer the second task and are reported in Table 17. The score is a stringent measure in that students must use the standards sequentially fOr four second-counts while placing the sample. The mean score was low (§'= 1.21, S. D. = 1.91). Only one student applied the entire strategy to more than 25% of the samples. The results do not support the stated hypothesis. The Comparison to Standard strategy did not transfer as a complete chunk of information which was used in a more complex strategy based on the sequential use of the standards. One additional strategy transfer score was calculated. The strategy count score (ZSC4v1) is the number of samples for which students place the sample proximate to one or both standards fOr the fOur second counts. It is less stringent than the Strategy Transfer Score in that the students were not required to use the standards in any particular sequence. However, this score also indicates a very limited transfer of the first task strategy as only 8% of the students scores correctly for more than 25% of the samples. 139 Table 17. Strategy and Component Transfer Scores: Single Variable Classification Task Pretest (n's = 24) % oers transferring strategy or Trt Score Score component fOr indicated % of samples Grp Name Label IMean S.D. §_25% 26-50% 51-75% 0176-100% Samples Samples Samples Samples STRATEGY ZST—VI 1.21 1.91 96(54)* 4 0 0 TRANSFER Strategy ZSC-Vl 3.29 4.30 92(46) 8 0 0 Count CS Sequential ZSPS-v1 7.29 7.82 67(25) 4 13 16 Proximate Standard Proximate ZPS-Vl 10.00 9.47 45(21) 17 13 25 Standards (lor2 std) STRATEGY ZST-Vl 0.54 1.51 100(83) 0 0 0 TRANSFER Strategy ZSC-V1 1.82 4.38 96(71) 0 0 4 Count CF Sequential ZSPS-Vl 3.08 3.56 79(46) 13 8 0 Proximate Standards Proximate ZPS-Vl 4.87 7.10 71(38) 17 4 8 Standards (lor2 std) STRATEGY ZST-Vl 0.21 0.83 100(92) 0 0 0 TRANSFER Strategy ZSC-V1 0.58 2.08 96(88) 4 0 0 Count IF Sequential ZSPS-v1 1.00 3.30 96(79) 0 4 0 Proximate Standards Proximate 2P84V1 1.62 3.79 96(67) 0 4 0 Standards (lor2 std) *'% of students transferring strategy of component for 0% ofsamples. 140 Strategy Commnents Transfer 1m additional scores useful in describing the students' actions are reported in Table 17. They serve to indicate the influence of various requirements and the transfer of strategy components. These are the Sequential Proximate Standard Score (ZSPS-Vl) and the mei— mate Standards Scores (ZPS-v1). The first score (ZSPS-Vl) is the number of samples for which the standards are used in sequence but without any time limitation. The mean Sequential Proximate Standards Score, which deletes the time requirement, was 7.29 samples (S.D. = 7.82). The seventy five percent (75%) of the students who sequentially used the standards for at least one sample averaged 9.72 samples (40%). When the minimum time requirement is eliminated a substantial anIber of students used the standards in sequence for a limited number of samples. The limiting effect of the time requirement is not surprising as it was seldom met during the Comparison to Standard posttests. The Proximate to Standards Score is the number of samples the student placed proximate to one or both standards. This is the least stringent measure in that there is no time or sequential use of standards requirement. The mean Proximate Standards Score was 10.00 samples (S.D. = 9.47). Nineteen students (79%) averaged 12.6 samples (52%) placed proximate to at least one standard for a brief time. This result indicates that the placement of samples proximate to standards trans- ferred to a moderate extent as a chunk of information or strategy component . 141 Strategy Learning The hypothesis related to Question I is: l. (a) The students given Strategy Instruction will learn the strategy for Task 2. (b) Eighty percent of the students in the Strategy Instruction group will meet criterion of strategy learning for Task 2. The mean Trials to Criterion Score (2T‘C) for students receiving strategy instruction was 12.05 samples (S.D. = 4.21). All students reached criterion, i.e. , learned to place the samples accurately using the strategy with a ZTC score less than 23 samples. The above hypothesis is supported by the data. This does not indicate that all students reached criterion during the sample instructional session (i.e. , > 24 samples) for both variables. Tm students (8%) required a second instructional session for the first variable, and one student required a second session for the second variable. However, all three students averaged less than 24 samples for the two variables combined. Table 18. Strategy Learning Results: Trials to Criterion Score for Cum11ative Strategy Group (n = 24) 1% of Ss learning the strategy correct- Trt Score Score ly in the indicated # of samples Grp Name Label Mean S.D. 7-12 13-18 19-24 >74 Samples Samples Samples Samples CS TRIALS TO ZTC 12.04 4.21 58(4)'* 30 12 0 CRITERION 7% of students learning strategy correctly in fewest msfible samples (7). 142 Strategy Use The hypothesis related to Question III is: 3. (a) The students given Strategy Instruction will use the taught strategy during the posttest fOr Task 2. (b) Eighty percent of the students given Strategy Instruction will meet the criterion of strategy use during the posttest on Task 2 for eighty percent of the samples. The posttest use of the Single variable Classification strategy by the Cumulative Strategy group was extensive, but not sufficient to confirm the hypothesis. The results for the Strategy USe Score (Table 19) show fifty eight percent of the students used the strategy as taught fOr more than 80% (19) of the samples. All students used the strategy fOr at least one sample. Strategy Components Use The Single variable Classification Strategy is composed of two major observable components. The first is the use of the standards in deciding the correct classification. The second is the verbal re- sponse. The reSponse is the report of an appropriate value label such as "large grains". The results of two scores for each component provide a closer look at the students' strategy use (Table 19). The Sequential Standards Use Score is the number of times the student placed.a sample proximate to the required number of standards in specified sequence. The Mean Score of 16.62 samples (S.D. = 6.67) is only slightly higher than the Strategy Use Score. This indicates that the use of the required standards is extensive. 143 Table 19. Strategy and Component USe Scores: Single variable Classification Task Posttests (n's = 24) % of 55 using strategy or component Trt Score Score fOr indicated % of samples Grp Name Label Mean S.D. fi.25% 26-50% ‘51-75% 76-100% Samples Samples Samples Samples STRATEGY ZSU 16.31 6.74 8(0)* 21 13 58 USE Sequential ZSSU 16.62 6.67 8(0) 17 13 62 Standards Use CS Standard ZSDU 19.06 5.97 0(0) 17 16 67 Use (lorZ stds) Sequential ZSVR 18.98 7.82 4(0) 17 12 67 Verbal Response verbal 2VR 23.06 2.67 0(0) 4 0 96 Response STRATEGY ZSU 3.00 5.07 83(33) 4 13 0 USE Sequential ZSSU 3.48 5.43 83(29) 4 l3 0 Standards Use CF Standards ZSDU 5.12 6.90 75(21) 8 4 13 Use (lor2 stds) Sequential ZSVR 4.25 6.66 79(21) 4 8 8 Verbal Response Verbal 2VR 18.75 8.32 13(4) 12 4 71 Response STRATEGY ZSU 0.43 1.13 100(75) 0 0 0 USE Sequential ZSSU 2.21 3.60 88(42) 8 4 0 IF Standards Use 144 Table 19 (Cont'd.) Standards ZSDU 3.17 4.90 88(42) 4 8 0 Use (lor2 std.) Sequential ZSVR 0.65 1.76 100(71) 0 0 0 Verbal Response Verbal 2VR 8.25 9.58 54(33) 17 8 21 Response * % offistudents using strategy or component for 0% of samples. The Standards Use Score is the number of samples for which the students used at least one standard. The mean was 19.06 samples (S. D. = 5.97). Eighty three percent of the students used the standards in some manner for more than 50% of the samples. Comparing the two Standards Use Scores indicates use of the standards in ways other than that prescribed by the instruction. The second component of interest was the verbal response. The Sequential verbal Response Score indicates the verbal reSponse was given fOllowing comparison of a sample to a standard and preceding the placement on the board. The students reported a value label in sequence for an average of 18.98 samples. Seventy-nine percent did so fOr more than half the samples. If the sequence of the response is not considered, the mean Verbal Response score was 23.06 (S. D. = 2.67). That is, 96% of the students reported a value label at some point for more than 80% of the samples. Comparing the two verbal response scores shows students were often giving a verbal response at times other than that consistent with the taught strategy. 145 Sipgle variable Classification - Performance Results This is the first task where the Isolated Feedback (IF) compari- son group is added to the study. Any comparisons between various scores involve three groups of students. The planned comparison analysis isolates the effects of the instructional sequence (Cumulative Strategy and Cumulative Feedback vs. Isolated Feedback) and then the effects due to strategy based instruction within the sequence (Cumulative Strategy vs. Cumulative Feedback). Prior to discussion of the results related to the hypotheses, it is possible to gain some indications of the task difficulty by examining the Placement Accuracy Score fOr the Isolated Feedback group recorded on the first pretest (Table 20). Table 20. Placement Accuracy Results for Isolated Feedback Group: Single Variable Classification Task First Pretest (n=24) %'of“Ss correctly plac1ng the Trt Score Score indicated % of samples Grp Name Label IMean S.D. §_25% 26-50% 51-75% 76¥100% Samples Smmples Samples Samples Iso- P1ace- 2PA4VI 16.83 3.61 0 8 50 42 Feed ment back Accuracy The results show that students new to the task can correctly place 70% of the samples following the concept and general task instructions. As this group was randomly assigned to the treatment, the results can serve as a reference point to which the later perfbrmance of this and the other groups can be compared. 146 Learninngransfer The hypotheses for Question IV. A. are: 4. (a) The learning from both the Strategy and Feedback Instruction on Task 1 will automatically vertic- ally transfer to the perfbrmance of the Task 2 pretest. However, the Strategy Instruction will result in greater vertical auto-transfer within the sequence. (b) The students instructed on Tasks l by Strategy and Outcome Feedback will perform the Task 2 pretest with significantly greater accuracy than will the students who have not received instruction on Task 1. (b') The students given Strategy Instruction for Task 1 will perform the Task 2 pretest significantly more accurately than will the group instructed by Outcome Feedback on Task 1. The Placement Accuracy Score fOr the first pretest (2PA4V1) measures the performance accuracy of the various groups. For hypothesis b the analysis evaluates the learning transfer effects by comparing the Cumulative Strategy and Cumulative Feedback per- fermance to the Isolated Feedback perfOrmance. Hypothesis b' is evaluated by comparing the performance of Cumulative Strategy and CUmulative Feedback groups. The results shown in Table 21 and 22 indicate no significant differences fOr either comparison. Even though the differences in performance are in the predicted directions the results do not support the hypotheses. No significant transfer of learning advantage is evident for those who were instructed on the first task, and no significant advantage within the task sequence accrues to those re- ceiving strategy based instruction. 147 Table 21. Learning Transfer - Placement Accuracy Results: Single variable Classification First Pretest Trt Group .Mean 8. D. n 95% Confidence Interval CS 18.54 3.23 24 17.18 to 19.91 CF 17.37 3.45 24 15.92 to 18.83 IF 16.83 3.61 24 15.31 to 18.36 Total 17.58 72 Ungrouped 3.46 16.77 to 18.40 Data Table 22. Learning Transfer - Planned comparisons fOr Placement Accuracy: Single variable Classification First Pretest Difference Standard Between Error of 1-tail Contrast Means Difference t-value D. t-Prob. CS+CF_ -——Z——. IF 1.17 0.99 1.17 69 0.121 CS:CF 1.12 0.86 1.31 69 0.097 Facilitation of Learning The hypotheses related to Question IV. B. are: 5. (a) Both the Strategy Instruction and Outcome Feedback Instruction for Task 1 will facilitate the learning for Task 2. However, the Strategy Instruction will result in the greater facilita- tion of learning within the Task sequence. (b) Students given Outcome Feedback and Strategy Instruction for Tasks l and 2 will learn to perform Task 2 in significantly fewer trials than will the group given Outcome Feedback Instruction on Task 2 only. 148 (b') Students given Strategy Instruction fer Tasks 1 and 2 will learn to perfbrm Task 2 in significantly fewer trials than will the groups given Outcome and Feedback Instruction on Tasks 1 and 2. The Trials to Criterion Score (ZTC) measures the facilitation of learning effects. The planned comparisons were the same as those for the preceding learning transfer hypothesis. The results of the analysis are given in Tables 23 and 24. Table 23. Facilitation of Learning - Trials to Criterion Results: Single variable Classification Task Instruction Trt Group .Mean S. D. n 95% Cbnfidence Interval CS 12.04 4.21 24 10.27 to 13.82 CF 10.60 3.35 24 9.19 to 12.02 IF 11.29 3.84 24 9.67 to 12.91 Total 11.31 72 Uhgrouped 3.80 10.42 to 12.7068 Data Table 24. Facilitation of Learning - Planned Comparisons for Trials to Criterion: Single variable Classification Task Instruction Difference Standard’ Between Error of 2-tail Contrast Means Difference t-Value D. F. CS+CF, -——7——. IF 0.031 0.95 0.033 69 0.974 CS:CF 1.437 1.10 1.306 69 0.196 149 The hypotheses are not supported in that the differences between means are in the Opposite direction to that predicted. HOwever, the differences are not significant. There is no advantage or disadvantage for those students who receive instruction fOr the first task. Similarly, there is no significant advantage or disadvantage fOr the students who received strategy based instruction within the sequence. Task Performance The hypotheses related to Question Iv. C. are: 6. (a) Both the Strategy and Outcome Feedback Instruction on Tasks l and 2 will result in greater accuracy of perfOrmance on the Task 2 posttest. However, the Strategy Instruction will result in the greater accuracy of perfOrmance within the task sequence. (b) The students given Outcome Feedback and Strategy Instruction on Tasks 1 and 2 will perform the Task 2 posttest with significantly greater accuracy than the group receiving Outcome Feedback Instruction on Task 2 only. (b') The students given Strategy Instruction on Tasks 1 and 2 will perform the Task 2 post- , test with significantly greater accuracy than the students receiving Outcome Feedback Instruction on Tasks l and 2. Placement Accuracy (2PA) is the single measure used to evaluate the above hypotheses. The results of the planned comparison analysis are given in Tables 25 and 26. Hypothesis b is evaluated by the com- parison of the combined Cumulative Strategy and Cumulative Feedback group to the Isolated Feedback group. The hypothesis b' is evaluated by comparison of the Cumulative Strategy to Cumulative Feedback group performance . 150 Table 25. Task PerfOrmance - Placement Accuracy Results: Single variable Classification Task Posttests Trt Group ‘Mean S. D. n 95% Confidence Interval CS 19.02 1.92 24 18.21 to 19.83 CF 18.85 2.11 24 17.96 to 19.75 IF 18.73 1.62 24 18.04 to 19.41 Total 18.86 72 Ungrouped 1.87 18.43 to 19.31 Data Table 26. Task PerfOrmance - Planned Comparisons for Placement Accuracy: Single variable Classification Task Posttests ‘Difference Standard Between Error of l-tail Contrast Mean Difference t-value D. F. t-Prob. CS:CF: IF 0.208 0.47 0.440 69 0.331 CS:CF 0.167 0.55 0.305 69 0.381 Neither hypothesis is supported. There is no significant advantage gained on the second task from previous instruction in task sequence. Furthermore, within the task sequence no significant advantage accrued to those students who received the strategy based instruction. 151 DOUble variable Classification Task: Strategy Results The results discussed in this section begin with the strategy transfer results (Question II) as the criteria for strategy transfer are related to those for strategy use from the previous task. The strategy learning (Question I) and strategy use results (Question III) fOllow. The discussion of all strategy results pertains only to scores for the students in the Cumulative Strategy Group. Strategy Transfer The hypothesis related to Question II is: 2. (a) The strategy fOr Task 2 will automatically transfer vertically to the performance on Task 3. (b) Eighty percent of the students given Strategy Instruction on Task 2 will meet the criterion of Task 2 strategy use during the pretest on Task 3 for eighty percent of the samples. The results of the Strategy Transfer Score (3ST) shown in Table 27 do not support the above hypothesis. Only 12% of the students reached the criterion of placing 80% of the samples by using the second task strategy for both of the variables involved in the Double Variable Classification Task. The mean score (x'= 3.00, S. D. = 7.10) further indicates the Single variable Classification Strategy does not become incorporated into a third task strategy as a complete chunk of information. The Strategy Count Score (38C) also shown in Table 27 is a second, less stringent strategy transfer measure. It is the number of samples fOr which students applied the second task strategy to at least one of the two variables. The group average was 6.79 samples (28%) on this 152 Table 27. Strategy Transfer Scores: Double variable Classification Pretest (n's = 24) % of Ss transferring the Strategy Trt Score Score indicated % of samples Grp Name Label IMean S. D. §_25% 26-50% 51175% C76¥100% Samples Samples Samples Samples STRATEGY 3ST 3.00 7.10 88(7l)* - 0 0 12 TRANSFER CS Strategy 33C 6.79 8.89 71(46) 4 4 21 Count STRATEGY 3ST 0.12 0.61 100(96) 0 0 0 TRANSFER CF Strategy 3SC 0.62 2.30 96(88) 4 0 0 Count STRATEGY 3ST 0.00 0.00 100(100) 0 0 0 TRANSFER IF Strategy 38C 0.00 0.00 100(100) 0 0 0 Count * % of students tranSferring the strategy fOr 0% of samples. measure. Only 21% of the students used the strategy on at least one variable for more than 80% of the samples. Even this less stringent score indicates that the strategy was not transferred to the extent anticipated. Strategy Component Transfer As the complete Single variable Classification strategy did not transfer, further description of the students' behaviors is infOrma- tive. This section includes results which indicate how two compon- ents of the strategy transfered. The components are the use of the standards and the verbalization of the value labels. 153 The students' placement of the samples proximate to standards is important in that the standards represent the values which define the classification matrix. The transfer of this component is reflected in four scores. These scores differ in two ways: (1) whether or not the sequence of use of the standards is considered and (2) whether or not the standards for both variables is considered. All fOur scores are reported in Table 28. The two scores which reflect sequential standard use are the Double Sequential Standards Scores (3DSS) and the Sequential Stand- ards score (3S8). The former (3DSS) is the number of times a sample is placed proximate to the required number of standards for both variables. The latter score is identical except that the use of the required standards is counted when applied to one or both variables. In this way it is less stringent. The 3DSS Scores (i'= 5.17, S. D. = 8.43) shows that 46% of the students who used all required standards for at least one sample averaged 11.2 samples (47%). This indicates a moderate use of the standards in sequence. However, the Sequential Standard Score (385) indicates that a much larger number of students transferred the compari~ son-to-standards component in some fOrm. Eighty-three percent (83%) of the students placed an average of 15.4 samples proximate to the required standards fOr at least one variable. The comparison of these twO scores indicates students did not frequently use the standards sequentially for both variables, but did so to a moderate extent for one variable. 154 Table 28. Transfer of Comparison-to—Standard Component Scores: Double Variable Classification Pretest (n‘s = 24) % of Ss transferring the component Score fOr the indicated % of s les Label Mean S.D. < 25% 26-50% 51-75; 76-100% Samples Samples Samples Samples Trt Score Grp Name CS Double Sequential Standards (Both variables) Sequential Standards (1 or 2 Variables) Double Standards (Both variables) Standards (1 or 2 variables) Double Sequential Standards (Both variables) Sequential Standards (1 or 2 variables) Double Standards (Both variables) 3DSS 3SS 3DS 3S 3DSS 3SS 3DS 5.17 12.87 6.17 20.37 0.25 2.96 1.21 .43 .87 .02 .17 .85 .08 .46 71(54)* 29(17) 71(46) 8(4) 100(88) 83(58) 96(75) 8 13 8 25 13 33 21 80 155 ' Table 28 (Cont'd.) Standards 38 4.37 8.16 79(63) 0 0 Cbunt (l or 2 Variables) Double 3DSS 0.12 0.61 100(96) 0 0 Sequential Standards (Both Variables) Sequential 358 0.66 1.28 100(63) 0 0 Standards (1 or 2 variables) IF Double 3DS 0.04 0.20 100(96) 0 0 Standards (Both Variables) Standards 35 3.25 6.01 83(67) 8 0 (1 or 2 Variables) r%’of'students transferring component fOr 0% ofrsamples. The last two measures of the use of the standards to not consider 13 the order in which the standards were used” The Double Standards Score (3DS) is the number of samples fOr which the students used at least one standard on both variables. The second, less stringent, score requires the proximate placement of a sample to at least one standard fOr one or both variables. This is the Standards Score (38). The mean 3DS score (x r 6.17, S. D. = 9.02) is very similar to the 3DSS score described above. Likewise the distribution of the scores is nearly identical. .A total of 54% of the students used at least one standard for an average of 12.2 samples. This indicates 156 that if students used the standards on both variables, it was done in the required order. The mean 38 score is 20.37 samples (8. D. = 7.17). Eighty per- cent of the students used at least one standard on the board to place more than 80% of the samples. Comparison of this score to the Sequen- tial Standards Score (x = 12.87) indicates there was a substantial use of the standards in ways other than that implicit in the strategy instruction. Comparison to the 3DS score (x'= 6.17) again indicates students are not using the standards on both variables, but are doing so for one variable. The second strategy component of interest is the verbal response. This component was added to the strategy fOllowing the pilot work. Students encountered difficulty recalling which row/column they had decided the sample should be placed for one variable after deciding the column/row fOr the second variable. The reporting aloud of the value label (large grains, mostly light grains, etc.) was included on the pre- mise it would facilitate retention of the first row/column decision in short term memory. As with the placement of the samples proximate to the standards, the four verbal response scores fall into two categories. The first pair of scores necessitates that the response be given immediately following the students' comparison of the sample to the last standard. The second scores simply required that a response be given. The re- sults fOr all scores are shown in Table 29. Table 29. 157 Transfer of verbal Response Cbmponent Scores: Double variable Classification Pretest (n's = 24) Trt Score Grp Name CS CF Double Sequential verbal Response (Both Variables) Sequential verbal Response (1 or 2 Variables) Double Verbal Response (Both variables) verbal Response (1 or 2 variables) Double Sequential verbal Response (Both Variables) Sequential Verbal Response (1 or 2 variables) Double verbal Response (Both 'Variables) Score Label Mean 3DSVR 3.37 3SVR 8.29 3DVR 11.25 3VR 16.21 3DSVR 0.25 3SVR 0.92 3DVR 7.67 S.D. 7.77 9.58 11.18 10.85 1.03 3.32 10.84 % of Ss transférring the component fOr the indicated % of samples g_25% 726150% 51¥75% 761100% Samples Samples Samples Samples 83(71)* 59(42) 50(42) 29(29) 100(92) 96(83) 67(63) 4 16 0 13 25 50 67 29 158 Table 29 (Cont'd.) Verbal 3VR 10.37 11.31 50(46) 9 4 37 Response (1 or 2 Variables) Double 3DSVR 0.00 0.00 100(100) 0 0 0 Sequential verbal Response (Both Variables) Sequential 3SVR 0.00 0.00 100(100) 0 0 0 verbal Response (1 or 2 Variables) IF Double 3DVR 2.08 6.61 92(83) 0 0 8 Verbal Response (Both Variables) Verbal 3VR 2.83 7.04 88(67) 0 4 8 Response (1 or 2 variables) 3‘ % of students transferring component for 0% of samples. The Double Sequential Verbal Response Score (3DSVR) is the number of samples for whiCh the student gave a verbal response at the correct time fOr both variables. The second score, Sequential verbal Response Score (3SVR) is identical except that it required one or both responses be made. The 3DSVR results indicate that 29% of the students gave both responses in the correct sequence for one or more samples. Students clearly did not transfer the required verbal responses to both variables. 159 Considering the response for one or both variables the 3SVR score indicates a total of 58% gave the required verbal response for at least one variable for one or more samples. These students average 14.21 (58%) samples. This is interpreted as a moderate degree of transfer of the verbal response strategy component to at least one variable in sequence. The second pair of scores consists of the Double verbal Response (3DVR) and Verbal Response (3VR) scores. They are the number of samples for which the students gave a verbal response at any time fOr both variables or at least one variable respectively. Comparing these twO scores indicates that the verbal response was used more extensively on at least one variable than on both variables. Seventy- one percent of the students gave the response on at least one variable fOr an average of 22.8 samples. Fifty-eight percent gave a verbal response on 19.28 samples on both variables. Comparing the scores which required the verbal response in sequence with those that did not (3DSVR vs. 3DVR, 3SVR vs. 3VR) indicates that the verbal response frequently did not fellow the final placement of the sample proximate to a standard as taught. For example, the mean number of samples where a response was given in sequence fOr at least one variable was 8.29 whereas the mean fOr giving a response out of sequence fOr at least one variable was 16.21 samples. Strategy Learning The hypothesis related to Question I is: 160 l. (a) The students given Strategy Instruction will learn the strategy fOr Task 3. (b) Eighty percent of the students in the Strategy Instruction group will meet criterion of strategy learning fOr Task 3. This hypothesis relates to whether students could learn to use the model strategy to perfOrm the Double variable Classification task accurately. The Trials to Criterion score (Table 30) indicates that all students receiving strategy instruction reached criterion ' within the two instructional sessions. During the first instructional session eighty-three percent (83%) of the students met criterion by correctly placing 7 of 9 consecutive samples using the taught strategy. Thus, the hypothesis is supported. The mean Trials to Criterion was 17.17 samples fOr the Cumulative Strategy group. The increased number of trials required in compari- son to the previous twO tasks (lTC = 10.50, ZTC = 12.04) indicates increased difficulty in learning to accurately perfOrm the task using the corresponding strategy. Table 30. Strategy Learning Results: Trials to Criterion Score fOr Cumulative Strategy Group (n = 24) % Of Ss learning strategy correctly Trt Score Score in the indicated number of samples Grp Name Label Mean S.D. 7-12 13¥18 19-24 > 24* Samples Samples Samples Samples CS TRIALS TO 3TC 17.17 9.79 38 37 8 l7 CRITERION *NOte: Greater than 24 samples implies students required a second instructional session. 161 Strategy Use The hypothesis related to Question 111 is: 3. (a) The students given Strategy Instruction will use the taught Strategy during the posttest for Task 3. (b) Eighty percent of the students given Strategy Instruction will meet the criterion of strategy use during the posttest on Task 3 for 80 per- cent of the samples. The Strategy Use Score (3SU) results fOr the Cumulative Strategy group (Table 31) do not support the hypothesis. Only 25% of the students used the strategy on more than 80% of the samples. The mean number of samples fOr the entire group was nearly half (i'= 11.67, S. D. = 8.66) with only 3 students (13%) not using the strategy on any samples. Fifty percent of the students used the strategy on more than 50% of the samples. This indicates a moderate use of the strategy by a.moderate number of students. Strategy Component Use The first strategy component of interest is the students' use of the standards. The first of two scores is the Sequential Standards Use Score (3SSU) which is the number of samples the students place proximate to the required standards fOr both variables in the taught sequence. The mean score of 13.50 (S. D. = 8.25) shows students used the required standards fOr 56% of the samples. Only twO students (8%) fail to use the required standards on any samples, while 37% did so for more than 80% (19). This indicates that the students used the required standards to a moderate extent. 162 Table 31. Strategy and Component Use Scores: Double Variable Classification Task Posttest (n's = 24) % of 85 using strategy or component Trt Score Score fOr indicated % of samples Grp Name Label Mean S.D. §_25% 26-50% 51-75% 7764100% Samples Samples Samples Samples STRATEGY 3SU 11.67 8.66 38(13)* 12 25 25 USE Sequential 3SSU 13.50 8.25 25(8) 21 17 37 Standards Use Standards 3SDU 17.04 8.86 21(8) 8 8 63 CS Use (1 or 2 stds. fOr both variables) Sequential 3SVR 14.83 9.86 33(13) 4 4 59 Verbal Response verbal 3VR 21.62 6.57 8(4) 0 0 92 Response STRATEGY 3SU 0.00 0.00 100(100) 0 0 0 USE Sequential 3SSU 1.12 4.52 96(88) 0 0 4 Standards Use Standard SSDU 1.46 5.15 92(88) 4 0 4 Use (1 or CF 2 stds. for both Variables) Required 3SVR 0.00 0.00 100(100) 0 0 0 Verbal Response verbal 3VR 10.92 11.61 50(50) 4 0 46 Response 163 Table 31 (Cont'd.) STRATEGY 3SU 0.00 0.00 100(100) 0 0 USE Sequential 3SSU 0.21 0.66 100(88) 0 0 Standard Use IF Standard 3SDU 0.42 1.21 100(88) 0 0 Use (1 or 2 stds. for both Variables) Sequential 3SVR 0.04 0.20 100(96) 0 0 Verbal Response Verbal 3VR 3.42 7.80 83(75) 4 0 Response ii% of students using strategy or component fOr 0% of samples. 13 The second score for examining the proximate placement of samples to standards is the Standards Use Score (3SDU). This is the number of samples fOr which students used at least one standard on both variables. This score is independent of the standards being used in any particular sequence. On the basis of this score the use of the standards in making placement decisions can be considered extensive. The mean score was 17.04 samples (8. D. = 8.86). Sixty-three percent scored correctly on more than 75% of the samples. The comparison of 3SSU and 3SDU indicates students were placing samples proximate to standards in ways other than that dictated by the taught strategy. The second component of interest is the verbal response. The first score addresses the question of whether the verbal response was given in sequence. The Sequential verbal Response Score (3SVR) 164 is the number of samples for which a student gave the verbal response directly fOllowing the last comparison to a standard for both variables. The mean score was 14.83 (S. D. = 9.86). Fifty—nine percent of the students gave both required responses in sequence on more than 80% of the samples. This again indicates a moderate use of this strategy component as required by the model strategy. The verbal Response Score (3VR) simply requires that students give both verbal responses regardless of sequence. As with the use of standards, there is a substantial increase in the mean of this less restricted score. The 3VR.mean was 21.62 samples (S. D. = 6.57) with 92% of the students stating two value labels fOr more than 80% of the samples. This indicates extensive use of the verbal response component but only to a moderate extent within the sequence specified in the model strategy. Double variable Classification Task: Performance Results With respect to the design of the study there are two reminders. The task now utilizes both variables simultaneously to form the classification matrix. Thus, there are no scores which are an average of the twO variables separately as there were with the first two tasks. Secondly, the students in the Isolated Feedback group were students who had not participated in instruction on previous tasks. Considering the initial pretest perfOrmance of the Isolated Feedback group it is again possible to gain some indication of the task difficulty. The students averaged placing 8.50 samples correctly. 165 The difficulty of this task is substantially greater than that of the previous two tasks where comparable groups of students correctly re- sponded fOr 16.1 and 16.8 samples respectively. Multiple Classification Pretest Scores The original plan for the analysis called for using the Piagetian Pretest Scores as a covariate for the Double variable Classification Task Placement Accuracy Scores. As indicated in the second chapter a positive relationship be- tween the scores was expected. However, the Pearson Correlation Co- efficient across all subjects was 0.075 and non-significant (s = 0.23). As a result Piagetian Pretest Score was not used as a covariate fer the analysis comparing group perfOrmance. Learning Transfer The hypotheses related to Question IV. A. are: 4. (a) The learning from both the Strategy and Feedback Instruction on Task 1 and 2 will automatically vertically transfer to the performance of the task 3 pretest. However, the Strategy Instruction will result in greater vertical auto-transfer within the task sequence. (b) The students instructed on Tasks 1 and 2 by Strategy and Outcome Feedback will perfOrm the Task 3 pretest with significantly greater accuracy than will the students who were not instructed on those tasks. (b') The students given Strategy Instruction for Task 1 and 2 will perform the Task 3 pretest significantly more accurately than will the group instructed by Outcome Feedback on Task 1 and 2. 166 The Performance Accuracy Score (3PA) for the third task.was used to evaluate the transfer of previous learning within the task sequence (hypothesis b) and specifically the effects on performance attributable to the strategy based instruction (hypothesis b'). Table 32 presents descriptive statistics fOr each of the instructional groups separately. The results of the planned comparison analysis are shown in Table 33. Table 32. Learning Transfer - Placement Accuracy Results: Double Variable Classification Pretest Trt Group Mean S. D. n 95% Confidence Interval CS 13.54 4.88 24 11.48 to 15.60 CF 12.37 4.21 24 10.60 to 14.15 IF 8.50 4.62 24 6.55 to 10.45 Total 11.47 72 Ungrouped 5.01 10.30 to 12.65 Data Table 33. Planned Comparisons for Pretest Accuracy: Double Variable Classification Pretest Difference Standard' Between Error of l-tail Contrast ‘Means Difference t-Statistic D. F. t-Prob. CS+CF, ——7——a IF 4.458 1.44 3.896 69 0.000 CS:CF 1.167 1.32 0.883 69 0.190 167 The comparison between scores of the combined strategy and feed- back treatment groups and the iso-feedback group was significant at p = .000 indicating transfer effects of cumulative instruction within the task sequence were not chance occurences. However, the comparison between the scores fOr strategy and feedback children were not significant (p = 0.190). Thus, no added advantage was found in the accuracy of sample placement fOr the strategy based instruction when students attempted to apply the previous learning to the new task. Facilitation of Learning The hypotheses related to Question Iv. B. are: S. (3) Both the Strategy Instruction and Outcome Feedback instruction for Tasks l, 2, and 3 will facilitate the learning of Task 3. However, the Strategy Instruction will result in greater facilitation of learning within the task sequence. (b) Students given Outcome Feedback and Strategy Instruction for Tasks 1, 2, 3, will learn to perform task 3 in significantly fewer trials than will the group given Outcome Feedback Instruction on Task 3 only. (b') Students given Strategy Instruction fOr Tasks l, 2, and 3 will learn to perfOrm Task 3 in significantly fewer trials than will the groups given Outcome Feedback Instruction on Tasks 1, 2, and 3. The planned comparison analysis supports the first hypothesis but not the second (Tables 34 and 35). The difference between the Trials to Criterion Score fer the Cumulative Strategy and Cumulative Feed- back groups when compared to scores of those not having instruction or previous tasks was significant (p = 0.004). However, the compari- son between the scores fOr the Cumulative Strategy and Cumulative 168 Table 34. Facilitation of Learning - Trials to Criterion Results: Double Variable Classification Instruction Trt Group Mean S. D. n 95% Confidence Interval CS 17.17 9.78 24 13.03 to 21.30 CF 15.50 6.54 24 12.74 to 18.26 IF 22.83 11.95 24 17.79 to 27.88 Total 18.50 72 Ungrouped 10.058 16.14 to 20.86 Data Table 35. Planned Comparison for Trials to Criterion: Double variable Classification Instruction Difference Standard’ Between Error of Cbntrast Mean Difference t-Statistic D. F. t-Prob. 9%93: IF -6.500 2.42 -2.684 69 0.004 (l-tailed value) CS:CF 1.667 2.80 0.596 69 0.553 (2 tailed value) Feedback students was in a direction opposite to that predicted. The Cumulative Strategy students required more trials than did the Cumulative Feedback students, but that difference was not significant (p = 0.553). It is evident that the cumulative effects of instruction on the structurally similar precursor tasks facilitated the learning of the more complex task. NO differential facilitation of learning 169 effect, either positive or negative, is evident between the cumulative strategy and cumulative feedback instruction. Task PerfOrmance The hypotheses related to Question Iv. C. are: 6. (a) (b) (b') Both the Strategy and Outcome Feedback Instruction on Tasks l, 2, and 3 will result in greater accuracy of performance on the Task 3 posttest. However, the Strategy Instruction will result in the greater accuracy of perfOrmance within the task sequence. The students given Outcome Feedback and Strategy Instruction on Tasks l, 2, and 3 will perform the Task 3 posttest with significantly greater accuracy than the group receiving Outcome Feedback Instruc- tion on Task 3 only. The students given Strategy Instruction on Task 1, 2, and 3 will perfOrm.the Task 3 posttest with significantly greater accuracy than the students receiving Outcome Feedback Instruction on Tasks 1, 2, and 3. The results of the posttest placement accuracy analysis are shown in Tables 36 and 37. Table 36. Task PerfOrmance - Placement Accuracy: Double variable Classification POsttest Trt Group Mean S. D. n 95% Confidence Interval CS 16.25 2.83 24 15.05 to 17.45 CF 13.79 3.80 24 12.19 to 15.49 IF 13.83 3.13 24 12.51 to 15.15 TOtal 14.62 72 Ungrouped 3.43 13.82 to 15.43 Data 170 Table 37. Planned Comparison fOr Placement Accuracy: Double variable Classification Posttest Difference Standard Between Error of l-tailed Contrast Mean Difference t-Statistic D. F. t-Prob. CS+D . 2 Not carr1ed out because CF was not larger than IF CS:CF 2.46 0.946 2.579 69 0.005 CS:IF 2.42 0.862 2.750 69 0.004 Examination of the mean scores revealed that, contrary to the prediction, the Cumulative Feedback (CF) group did no better than the Isolated Feedback (IF) group. As a result the comparison of the combined Cumulative Strategy (CS) and Cumulative Feedback scores with the Isolated Feedback scores would not be infOrmative. Instead the CS group by itself was compared to the IF group as well as to the CF group. As indicated in Table 37, the CS group mean was significantly greater than the means of both the CF and IF groups. These results do not support the first hypothesis as stated since feedback instruction on the task sequence did not improve posttest performance. However, strategy instruction on the sequence did improve posttest perfOrmance. The second hypothesis was supported. The strategy based instruction on the task sequence did result in better posttest performance than feedback instruction on the task sequence. The conclusion is that no advantage in posttest accuracy accrued to the students having instruction fOr the entire sequence unless they re- ceived the strategy based instruction. 171 Summary of Results This section summarizes the results just presented. The results which.most directly address the research questions are given first and summarized in Tables 38-43. Results related to students' use and transfer of strategy components are given next and summarized in Tables 44 and 45. The results related to the research questions support the following statements: 1) 2) 3) 4) 5) 6) The students learned to correctly place the rock samples using the appropriate strategy during instruction for all tasks. The complete strategy was not used on the posttest(s) as extensively as predicted. The strategy was used to a moderate degree for the Single Variable Classifi- cation Task and to a lesser extent for the Double variable Classification Task. The complete strategy fOr precursor tasks did not transfer to the more complex tasks in the sequence. However, components of the taught strategy did transfer to a moderate extent. The students who had participated in the entire task sequence did learn to perfOrm.the more complex Double Variable Classification Task more easily than students who did not. However, there was no facili- tation of learning effect due to the strategy based instruction for any of the three tasks. The students' ability to perfOrm the more complex second task prior to instruction was not enhanced either by instruction on the simpler comparison to standard task or by the strategy based instruction within the sequence. However, transfer of learning to the final classification task is enhanced by instruction on the previous two tasks. There was no posttest task perfOrmance advantage fOr any group during the first two tasks. On the final task there ‘was a task performance advantage fOr those students receiv- ing strategy based instruction with the task sequence. 172 Table 38. Summary of Strategy Learning Results: Trials to Criterion Scores-Instruction % 55 Learning Task Trt Score Mean S.D. strategy in Results Grp fi_24 samples Comparison to CS ITC 10.50 3.53 100 55 learn to Standard perform stra- tegy accurate- 1y Single variable CS ZTC 12.04 4.21 100 55 learn to Classification perform strategy accurately Double Variable CS 3TC 17.17 9.79 83* 55 learn to Classification perform strategy accurately ifAll students learnecf the strategy in :41 samples Table 39. Summary of Strategy Use Results: Strategy Use Scores - Posttests Task Trt Score Mban S.D. % $5 with Results Grp Score 3_80% Comparison to CS 180 5.94 5.24 8 Complete Standard strategy was not used. Single variable CS ZSU 16.31 6.74 58 Complete Classificafiion. strategy was used.moder- ately. Double variable CS 380 11.67 8.66 25 Complete Classification strategy was used moder- ately. 173 Table 40. Summary of Strategy Transfer Results: Strategy Transfer Scores - First Pretests Task Trt Score Mean S.D. % 85 with Results Grp Score _>_ 80% Comparison to CS Transfer question is not applicable to task. Standard Single Variable CS ZST- 1.21 1.91 0 Complete Classification v1 strategy '! did not transfer Double Variable (B ZST 3.00 7.10 12 Complete Classification strategy did not transfer Table 41. Summary of Facilitation of Learning Results: Trials to Criterion Scores - Instruction Trt Score ‘Mean S.D. Comparison t-Prob. Results Grp Task 1: Comparison to Standard CS lTC 10.50 3.53 CS:CF 0.656 No strategy instruction (2-tailed) advantage. CF lTC 10.10 2.51 Task 2: Single variable Classification CS 2TC 12.04' 4.21 CS+CF : IF 0.974 No task sequence CF 2TC 10.60 3.35 2 (Z-tailed) advantage. IF 2TC 11.29 3.84 CS:CF 0.196 No strategy instruction (2-tailed) advantage within task sequence. Task 3: Double variable Classification CS 3TC 17117' 9.78 CS+CF, CF 3TC 15.50 6.54 '_7?_—’ IF 0.004 Task sequence advantage (l-ta11) IF 3TC 22.83 11.95 CS:CF 0.276 No strategy instruction (2-tailed) advantage within task sequence. 174 Table 42. Summary of Learning Transfer Results: PerfOrmance Accuracy Scores - First Pretest Trt Soore Means S.D. Comparison 1-tailed Results Grp prob. Task 1: Comparison to Standard (Transfer Question is not applicable to this task) Task 2: Single Variable Classification 2PA4V1 18.54 3.23 CS:CF: _ IF 0.121 No task sequence CF ZPA v1 17.37 3.45 2 advantage IF 2PA-V1 16.83 3.61 CS:CF 0.097 No strategy ad- vantage‘within task sequence. Task 3: Double Variable Classification CS 3PA 13.54 4.88 CS+CF : IF 0.000 Task sequence CF 3PA 12.37 4.21 2 advantage IF 3PA 8.50 4.62 CS:CF 0.190 No strategy ad- vantage within task sequence. Table 43. Summary of Task PerfOrmance Results: Posttest PerfOrmance.Accuracy Scores Trt Score Mean S.D. Comparison l-tailed Results Grp prob. Task 1: Comparison to Standard CS 1CR 18.31 1.71 , CF 1CR 18.93 1.54 CS.CF 0.163 NO strategy (2-tailed instruction value) advantage. 175 Table 43 (Cont'd.) Task 2: Single variable Classification CS 2PA 19.02 1.92 CS+CF , . IF 0.331 No task sequence CF ZPA 18.85 2.11 2 advantage. IF ZPA 18.73 1.62 CS:CF 0.381 No strategy ad- vantage'within task sequence. Task 3: Double variable Classification g: g3: 13.33 g'gg CS:IF 0.004 Cumulative strategy ' ° 1nstruct1on advantage IF 3PA 13.83 3.13 CS:CF 0.005 Strategy advantage within task sequence As indicated in the second and third statements above students did not use and transfer the complete strategies as extensively as predicted. However, they did use and transfer components of the strategies as described below. To facilitate the summary the following convention is used. The possible range of all strategy related soores is divided into upper (17-24), middle (9-16), and lower thirds (0-8). The terms extensive, moderate, and limited are used to describe the mean of each score. Strategy use and strategy component use scores are summarized in Table 44. It is important to recall that there are twO types of strategy component use scores. One type indicates that the components occured in the required sequence. The other indicates simply that the use of the component occurred. 176 The strategy use (150) fOr the first task was limited. This is possibly due to the 4 second oount requirement which was seldom achieved. The students did make the comparisons to standard (lSDU) to a moderate extent. For both the Single and Double variable tasks the strategy use (ZSU, 350) was moderate. The use of standard component in the required sequence (ZSSU, 3850) was also moderate fOr both tasks. Not considering a required sequence of actions, the use of standards was extensive (ZSDU, 3SDU). The pattern of scores for the verbal response component differs only in that the response was given in the required sequence extensively (ZSVR) during the second task. For both tasks the verbal response scores were greater than the comparable use of standards component scores. The important point is that scores which were not restricted by the requirement of sequential actions showed an extensive use of both components for both tasks. The strategy and strategy component transfer scores are summarized in Table 45. The first task strategy transferred only to a very limited extent to the Single variable Classification Task. The strategy count score (3SC-v1) indicated the strategy limited transfer to even one of the twO standards. The transfer of the proximate-to- standard component was limited if its use with required number of standards is the criterion. However, there was a.moderate transfer of this component to at least one standard. The strategy for the Single variable Classification task transferred only to a limited extent to both variables (3ST) or to one variable 177 (38C) of the Double Variable Classification task. For discussion of the transfer of the components to this final task it is best to separ- ate the results into two groups. The first contains the scores which required the component be transferred to both variables on the classification scheme. The second contains scores which required the component to be transferred to only at least one variable. With respect to the former group, the standards (3DSS) and verbal response (3DSVR) occurred in the required sequence only to a limited extent. The component transfer was also courted without considering a required sequence of actions. The comparison-to-standard components (3DS) transferred to a limited extent to both variables. Verbal responses (3DVR-Vl) transferred to a moderate extent. However, the second category of results indicates students were using the required standards (385) and verbal responses (3SVR) for at least one variable to a moderate extent. Not considering a required sequence indicates extensive use of at least one standard for at least one variable (38). The same is true for the verbal response component (3VR). There are two important points to note. First, there was a moder- ate transfer of the comparison-to-standard component from the first task to the second task for at least one of the twO standards which could have been used. However, the component was not transferred to the num- ber of stmrdards which would have been required by the class rules if the strategy the students were using was a sequential repetition of the first task strategy. Second, there was a moderate transfer of the 178 second task strategy components to at least one variable fOr the third task. However, the components were not transferred to both variables. The students did not sequentially apply the components to both variables as if the Double variable task was composed of twO Single variable tasks. Table 44. Summary of Strategy and Strategy Components Use Results fOr Posttests Task Score Soore Description Mean Extent of Use Comp to lSU Samples placed 5.94 limited strategy use Standards proximate to standard fOr 4 sec-counts lSDU Sample placed proxi- 13.71 moderate component mate to standard use Single var. ZSU Samples placed.by 16.31 ‘moderate strategy use Classification use of complete strategy ZSSU Samples placed by 16.62 moderate component use use of required standards ZSDU Samples placed by 19.06 extensive component using at least use one standard ZSVR verbal response 18.98 extensive component given in required use in sequence sequence. 2VR ‘Verbal response 23.06 extensive component given. use Double var. 3SU Samples placed by 11.67 moderate strategy use Classification use of complete strategy 179 Table 44 (Cont'd.) 3SSU 3SDU Samples placed by use of required standards Samples placed us- ing at least one standards fOr both variables. Both verbal re- sponses given in sequence Both verbal re- sponses given 13.50 17.04 14.83 21.62 moderate component use in required sequence extensive use of component moderate component use in required sequence extensive use of component Table 45. Component Transfer Results for Pretests Summary of Strategy and Strategy Task Score Score Description Mean Extent of Use Single var. ZST4Vl Samples placed by 1.21 limited strategy Classification transfer of proxi- transfer mate placement to required standards for 4 sec-counts. ZSC-Vl Samples placed by 3.29 limited strategy transfer of proxi- transfer to one mate placements to standard at least one standard for at least 4 sec-counts. 25PS4V1 Samples placed by use 7.21 limited transfer of of required standards component in sequence ZPS-Vl Sample placed by use 10.00 moderate component of at least one standard. transfer Double var. Classification 180 Table 45 (Cont'd.) 3ST 3SC 3DSS 3SS 3DS 3S 3DSVR 3SVR 3DVR Sample placed by transfer of second task strategy to both variables. Samples placed by transfer of second task strategy fOr at least one variable. Sample placed by use 5. of required standards for both variables Sample placed by use 12. of required standards for at least one variable. Sample placed by use 6. of at least one standard on both variables. Samples placed by 20. use of at least one standard on one or both variables. Both verbal re- Sponses given in sequence. Verbal response given 8. 1n sequence fOr at least one variable. verbal response 11. given fOr both variables. verbal response 16. given for at least one variable. 3. .37 21 limited strategy limited strategy transfer’of’the variable lhmited transfer of component in sequence on both variables. MOderate transfer of component in sequence for one variable limited use of component on both variables Extensive use of component on one variable Limited use of component in sequence fOr both variables. MOderate use of component in sequence on one variable Moderate use of component on both variables Extensive use of component on one variable. CHAPTER'V CONCLUSIONS AND DISCUSSION The present study applied an infOrmation processing approach to the problem of designing instruction in geology. This approach com- bines detailed content-task analysis with an infOrmation processing view of the learner. Smith (1974) argues the utility of such an approach to effectively improve new learning and especially to enhance transfer of learning. The study had three major goals. The first was to design an instructional sequence whiCh would effectively and efficiently teach fOurth grade students to classify igneous rock samples. The second was to evaluate learning and transfer within the sequence. The third was to begin evaluating the selected approaCh to instructional design. The design approach used a concept-task-strategy analysis procedure to provide a way of representing the detail and structure of the knowledge related to igneous rock classification. This approach enabled the use of guidelines fer the design of instruction suggested by an infOr- mation processing view of the learner. The application of the design approach provided a three dimensional representation of the knowledge to be learned. The description was in terms of an interrelated set of concepts, task descriptions including the infOrmation given to the 181 182 student and the required performance outcomes , and a cognitive strategy for performing the task using the available information. The infor- mation processing view of the learner suggested teaching limited amounts of information during an instructional sequence and sequencing the instructional episodes on the basis of the cognitive strategies. The thesis of the study was stated in Chapter I as follows: (1) Instruction for the precursor tasks of a sequence will enhance performance of later tasks when the sequence is designed on the basis of analyzing the structure of the knowledge to be learned and an information processing view of human thinking. (2) There will be a facilitative effect of instruction based on task specific cognitive strategies within the task sequence. In particular, the design of instruction as a sequence of tasks which shared common concept and task features was expected to (1) fac- ilitate learning during instruction, and (2) enhance task performance on a posttest, and (3) enhance the transfer of learning to the pre- test for a related task. Further, instruction based on task specific cognitive strategies was expected to enhance learning and transfer to an even greater extent within the task sequence. The central focus on the study was the effect of the strategy based instruction on learning, use, and transfer. The availability of task specific cognitive strategies in the students memory was expected to serve as a mechanism which would enhance learning and transfer. 183 The premise was that the complete cognitive strategy for a task would be learned during instruction, used during posttest fOr the same task, and transferred to a new task which shared common concept and task features with the precursor task. For this reason the learning, use, and transfer of the cognitive strategies were carefully described. Study Overview The classification of igneous rocks was selected as the knowledge to be taught to the students. The analysis of the knowledge identified the related concepts, described the task, and developed a cognitive strategy by which the task could be performed. The task required students to correctly place a number of rock samples on a given classi- fication scheme. The Double variable Classification scheme was formed by two variables which were crossed to form a 3 X 3 matrix defining nine classes of igneous rocks. The two variable names (grain size and the amount of light grains), a label for each row or column (e.g., large grains, about half light grains), and two rock standards fOr each variable were given on the classification board. The rock standards represented the values which defined each class. (See Figure 4, Chapter 3). The strategy fOr performing the task consisted of twO major components. One was the successive comparisons of a sample to standards to decide the row and column in which the sample was to be placed. The other was a verbal response which was the label associated with each row and column immed- iately fOllowing each decision. An instructional sequence including the 184 Double Variable Classification Task and two less complex tasks -- a Single variable Classification and Comparison to standard task -- was designed on the basis of the content, task, strategy analysis. The design also attempted to take into account the limitation of the learner as an information procesor as described by Newell and Simon (1972). Randomly selected students were assigned to one of three treat- ment groups. The Cumulative Strategy Group was instructed on the cog- nitive strategy fOr each of the three tasks. The Cumulative Feedback Group was given feedback on the correctness of their performance for each of the three tasks. The Isolated Feedback Group consisted of two sets of students one of which was given feedback instruction for the second task only, the other set was given feedback instruction fer the final; geologic classification task only. Exact instructions as to how to complete the task (i.e., strategy instruction) was not given to either the second or third group. Observations of student behavior were made using specially designed coding systems based on the cognitive strategy models. On the basis of these observations, a number of scores were defined to reflect students' learning, use, and transfer of the strategies during the instruction, the posttests, and the pretests respectively. Additional scores were defined to reflect the accuracy of performance on the pretests and posttests, and the amount of instruction necessary to learn to perform the tasks. Data analysis (1) described the learning, use, and transfer of the cognitive strategies by students given the strategy based instruction, and (2) evaluated the effects attributable to instruction on the task sequence and those effects attributable to strategy based instruction. 185 Limitations There are three major limitations of the validity and generaliza- bility of the conclusions related to this thesis. The first, as with any study, relates to the experimental procedures. The conclusions of any investigation are valid and generalizable only to the extent the procedures described were following and are reproducible by others. The observations of the researcher and limited number of reported problems or errors indicated the procedures were closely fOllowed. The second is that the conclusions can be directly extended only to the population from which the subjects were sampled. To the extent this population of Lansing, hfichigan fourth grade students is repre- sentative of students from other populations, the generalizations are valid for those populations. An indicated in Chapter 3, the Lansing School population is representative of a broad range of ethnic backgrounds and three different school settings. The final limitation is related to the content or the knowledge that is being taught. It would be inconsistent with the epistemologic arguments presented in Chapter 2 to argue that these conclusions are applicable to widely different content domains. However, the results of parallel experiments can be expected to be similar to the extent that (l) the structure of the knowledge in these areas is similar to that under consideration, (2) the learner is accurately represented by the described infOrmation processing view, and (3) the design of the instruction correctly relates the knowledge to be learned and the learner. 186 There is also an important limitation on the interpretation of the results. Little base line data is available with respect to the learning, use, and transfer of cognitive strategies. This resulted in a somewhat arbitrary assignment of criteria on which hypotheses related to strategy performance were supported or rejected. Slightly more or less rigorous criteria could alter portions of the interpretation. The interpretation would be more meaningful if baseline data for strategy learning, use, and transfer in other instructional situations were available. Conclusions This section is a summary of the findings of the study. The next section is a discussion of each finding including the implications and questions fOr future research. (1) Students were able to learn the task specific cognitive strategies as evidenced by their actions during instruction. (2) The students encorporated components of the original strategies they had been taught (a) in a later perfOrmance of the same task on which they had been instructed, and (b) in their perfOrmance of a new task which was similar to the precursor tasks in several features. (3) The performance results related to instruction on the task sequence and the strategy based instruction were mixed. 187 Significant differences occurred at important times during the instructional sequence but did not occur consistently. The differences were generally not dramatic. (4) The detailed representations of the knowledge the students were to learn in conjunction within an infOrmation process- ing model of human thinking proved useful. The description of the knowledge and the description of limits of the learner as an infOrmation processor guided the selection of the content to be included in each instructional episode and the sequencing of the instruction. The detailed representation of the knowledge led to collecting data which provided substantial insight into the manner in which students used and transferred that knowledge. (5) The experimental design and the thoroughness of the obser- vations generated a very large volume of data which proved difficult and costly to collect, manipulate, and reduce to meaningful scores. Preliminary smaller scale studies could have provided some of the important findings of the study more efficiently. Discussion Initial Strategy Learning The results for the students given the strategy based instruction indicate it is possible to teach task specific cognitive strategies. The 188 strategies for each task were learned within relatively limited amounts of instructional time. All students learned to perform the strategies accurately within three and five trials past the possible minimum of seven fOr the Comparison to Standard and Single Variable Classification Tasks. Even the larger, more complex strategy for the Double variable Classification Task was learned well within the twenty-fOur trials for the first instructional session. This result indicated the strategies had been learned and implied they would be subsequently available fOr use by students during their posttest perfOrmance of the same task. Furthermore, the implication was that students would have available this knowledge for transfer to the pretest for a new but closely related task. The results also indicate it is neither difficult or time consum- ing to teach task specific cognitive strategies. This implies it is reasonable to consider strategies as a type of knowledge to be included in the instruction of students. The value of including strategies as instructional content remains to be answered by results related to performance accuracy. Strategy Use and Transfer The students were expected to use the strategy they had been taught for each task when they performed the same task somewhat later. The prediction was that if they had learned a sufficient strategy they would recall and use that strategy. Furthermore, students were expected to transfer the strategy fOr one task to the next. The tasks shared "an Ewen. 189 common features which would allow the perfOrmance of the more complex task by the repeated use of the recalled strategy for the previous task. The students did not use or transfer the strategies to the extent predicted. The use of the complete strategies during the posttests was moderate, and the transfer of the complete strategies to the pre- test performance of the next task was very limited. The riCh descriptions of the students' behavior collected on the basis of the strategy models indicated that the learners frequently encorporated components of the original strategies as they developed their own way of performing both the posttests fOllowing instruction and the pretest for the next task.* Partial descriptions of the student performances are possible. The two major components of the strategy were the overt comparison of the samples to the standards and the verbal response indicating the value label on the board fOr each row or column. Those components were used and transferred either in the sequence as taught or in some other sequence not recognizable as part of the taught strategy. The later type of component use on task posttests was extensive and con- sistently greater than the moderate occurence of components in sequence. With respect to the transfer of these same strategy components to a new task, the pattern was identical to that fOr the use of the strategy *Note: Only the Single and DOUble variable Classification Tasks are considered here. Results related to the Comparison to Standard Task are given in Chapter 4. They are not included as the strategy was not complex enough to yield a variety of performances. 190 components. That is, the students transferred the components in an invented sequence of their own more frequently than in the sequence which was taught. However, the students were not applying the components as if the tasks could be completed by the repetitive use of strategy com- ponents. For example, the transfer of either strategy components, in sequence or not, to both variables of the Double Variable Classification Task was limited. The pattern of component transfer occurred for only one of the two variables. The strategy use results are parallel to the findings in other studies related to how students use what they have been taught as they perform a task following instruction. After reviewing those studies Resnick suggests the following: ". . . most people -- even quite young children -- use environmental feedback to simplify performance routines. They do not accept the routines they are shown as "givens" but rather as starting points. They invent even when we teach them algorithms" (Resnick, 1976, p. 76). To this can now be added evidence that students use their knowledge of a strategy in a similar manner on transfer tasks which are structurally related to the instructional task. The findings of this study suggest at least two alternative inter- pretations. The first is suggested by Resnick's reference to the students use of environmental feedback. It is that students learned the strategies during instruction but only used the strategies and/or com- ponents under certain conditions. For example, on the posttests they may be using the strategy on difficult samples only. This would imply a selective or intelligent use of the strategy. Students would be V. a... 191 utilizing the more complex and logically exacting strategy only when a simpler approach was not adequate. A similar hypothesis can be put forth with respect to both the use and the transfer of the strategy components. In performing the Double variable Classification Task the students may be consistently omitting the application of the strategy or components if they can immediately determine the correct row or column for one variable. As they decide the correct row or column fOr any one variable they may have eliminated one of the three rows or columns immediately by anticipating the single standard at which the decision will be actually made. These actions would imply the students were constructing a strategy which was more efficient. The possibility of students constructing such abbreviated strategies was suggested by the observation that students often expressed frustration at having to complete the whole strategy when they "didn't need to use it all." The second alternative is suggested by the infOrmation processing view that students can rehearse information in short term memory without storing that infOrmation in long term memory. The supposition would be that students did not actually learn the complete strategies during instruction but instead (I) learned the components and (2) with the help of repeated instructional cues rehearsed the sequence in which they were to be executed. During the delay between instruction and posttest, the sequence would have been fOrgotten. Upon confronting the identical task the students may have constructed a new although not necessarily different sequence for using the strategy components. During the per- fOrmance of the next more complex task the students may have created 192 sequences for using the strategy components which would reflect the sequence of component use only for that portion of the new task which was nearly identical to the previous task (e.g., the transfer of the comparison-to-standard component from the Single variable Classification Task to only one variable of the Double variable Task). This inter- pretation is more tenuous than the first in light of the studies cited by Resnick (1976, p. 68) and the strategy learning data from this study. However, it is plausible and should be considered. In either case a series of strategy models inferred from student actions are needed to describe in greater detail how students were modifying the strategies they had been taught. Additional analysis of data from the present study could provide substantially more complete descriptions of the students' learning, use, and transfer of the strategy components in two ways. One description would relate the use and transfer of components to the accuracy of sample placement. A second would identify the particular circumstances under which the strategy and strategy components were used and transferred. For example on the final task were the components utilized fOr one of the two variables, for difficult samples, or at the immediate point in their thinking when a row/column decision was being made. Knowing in some detail what infOrmation the students initially learned and then utilized following instruction could contribute sub- stantially to the instructional design. Instructional sequences based on task specific cognitive strategies may be more efficient and effec- tive if the strategies generated by the students served as the basis 193 for develOping and sequencing tasks. Those strategies may be small, simple, and based on conditional statements related to particular circumstances within the task. Instructional sequences of this type would have to be tested against sequences based on a more "complete" strategy. Teaching the more elaborate, complex strategies such as those used in the present research may help the students comprehend the task and the function of the components in a way not accomplished by teaching the smaller strategies. Performance Results A third major finding of the study has to do with the effects of the instruction on the learners' performance of the classification tasks. The central research predictions were: (1) students would efficiently learn to classify igneous rock samples accurately if instructed on a sequence of tasks which shared common concept, task, and strategy ele- ments, and (2) the effect of teaching cognitive strategies for each task would be even more effective in improving perfOrmance. The perfOrmance results were mixed.but interesting. The predicted effects of instruction on the task sequence and the added effects of the strategy based instruction were not observed at all until the final Double Variable Classification Task. The effects attributable to instruction on the task sequence were Observed in the pretest and during instruction for the Double variable Classification Task. The effects of the strategy based instruction were observed only on the posttest. 194 The accuracy with which the students who were instructed on the entire sequence performed the pretest and the ease with which they learned to perform the task was significantly better than for those students who were given feedback instruction on the final task only. The students instructed on the sequence correctly classified 52% (4) more samples and were placing 54% of the samples correctly on the pre- test. The difference is statistically significant while the level of performance is moderate. The same students learned to perform the task in 29% (6.5 samples) fewer trials than did students instructed on the final task only. The difference is again significant and in absolute terms is substantial. There were no effects attributable to the strategy based instruction within the sequence during the pretest or instruction on the Double Variable Classification Task. The pattern of results was different for the posttest on the final task. Feedback instruction on the sequence was not effective, while the strategy based instruction within the sequence was effective. The Isolated Feedback group learned to perform the task as well as the Cumulative Feedback Group which was given instruction on the entire task sequence. The groups correctly placed 58% of the samples (13.83 and 13.79 samples respectively). The improvement of the Isolated Feedback group from pretest and posttest was substantial (63% or 5.33 samples). The Qmulative Strategy Group performed the task signi- ficantly better than either the Crmrulative or Isolated Feedback groups. The students given the strategy based instruction performed the task approximately 18% (2.45 samples) better than the other groups. The 195 accuracy of their placement was 68% (16.25 samples). While the differences were significant and percentage differences substantial, the results are not dramatic in absolute terms. The findings are substantial enough to continue research under the present design approach. The differences in performance which were evident did occur at the important point in the instructional sequence, that is, during the students performance of geologic classification task. The strategy based instruction did result in superior final performance. These differences were not likely to have occurred by chance. However, the findings were not consistent across tasks or even within the pre- test, instruction, posttest cycle for the final task. In addition, the absolute differences were not dramatic. These two points would argue against beginning the design of instructional sequences which were based on the present approach on any substantial scale without further research. The most promising avenue of research would be on the effects of strategy based instruction for longer sequences of more complex tasks. This is suggested by (l) the occurence of all effects on the final most complex task, (2) the late emergence of effects related to cumulative strategy based instruction. If there is a cumulative strategy effect, modest differences could develop into very important and large dif- ferences over a longer sequence of more complex instruction. There are several research questions directly related to the line of research suggested above. (1) What effects would occur by changing the present sequence of tasks? For example, would instruction on only one of (2) (3) (4) 196 the precursor tasks affect student performance? WOuld strategy based instruction fOr the Double variable Classification Task only result in perfOrmance as accurate as that exhibited by students given strategy based instruction throughout the sequence? Are the various instructional effects related to the complexity of the tasks? The effects observed during this study occurred only during the most complex task. It is quite possible that the effects of strategy based instruction will only be evident when relatively complex performance is required. Will the effects attributable to instruction on similarly designed instructional, sequences and strategy based instruction within the sequence change across the pre- test, instruction, posttest cycle as they did in the present study? The answer may contribute to understand- ing when the effects of a particular type of instruction can be expected to occur. What are the long term effects of the present instructional design or a modified version of that design? The effects of the instruction on the task sequence and strategy based instruction may be more or less dramatic than is indicated in the present study. 197 Reppesentation of the COntent OfwlnstructiOn Central to the present design approach was the representation of the knowledge the students needed to learn. This guided the design of the research and led to detailed descriptions of student behavior. These descriptions provided substantial insight into the manner in which students used and transferred the knowledge they had been taught. The attempt was to provide a theory of what the students should know to classify igneous rocks. The discipline (geology) served as an important source fOr identifying this knowledge. The knowledge (or inner environment) of the learner was viewed as composed of an inter- related set of concepts and a cognitive strategy which utilized the concepts as inputs and outputs. In infOrmation processing terms, the concepts and strategy constituted the infOrmation necessary and suf- ficient to meet the requirements of the external task environment. Effective performance was expected to the extent that the learner's knowledge was apprOpriate for that task environment. The descriptions of the task requirements and the theory of the sufficient knowledge were gained by applying the content-task-strategy analysis (Smith, 1974) and the information processing view of human thinking (Newell and Simon, 1972). The importance of having a detailed description of the desired learners' knowledge is best demonstrated by considering the role the strategy mode1(s) played in designing the instructional sequence and research procedures. The example also illustrates important guide- lines the infOrmation processing view provided the present approach to design. 198 The strategy for the Double Variable Classification was based on the notion that geologists used mental models or standards when classi- fying rock samples. The final strategy was designed knowing what concepts would be available as infOrmation to be processed and the required outcome. This made possible the description of a strategy sufficient for classifying the rock samples. The infOrmation processing view indicated that human information processing is basically serial in nature and that only a very limited amount of information could be held in short term memory. This necessita- ted a strategy which used information output from one process as input for the next process as much as possible. Otherwise, important infor— mation could have been fOrgotten, over the course of executing the strategy. The rather lengthy and complex strategy which resulted represented part of the knowledge sufficient to perfOrm the classification task. The relatively long times required for storing infOrmation in long term memory indicated that to teach the strategy all at once would be very demanding on the students memory. Smith's work suggested that strategies for less complex tasks could become subroutines in larger strategies and serve to reduce the memory load since the details of the subroutines would have been already learned as a units or "chunks." Given the detailed description of the strategy fer the final task, it was possible to identify potential subroutines. Precursor tasks were selected and sequenced in part because they could be perfOrmed using these compatible subroutines. 199 The strategy model for each of the three tasks in turn guided the develOpment of instructional protocols to teach the strategies. The models were the basis for the system of collecting raw data and translating that data into meaningful scores which would adequately and accurately represent the students' use and transfer of the strategies. The models insured that relevant behavioral data were collected" These data were useful in inferring use of components of the strategy as well as use of the entire strategy or originally planned. The methodology of the study became in large part a matter of translating the strategy models into protocols, a data collection system, and a set of meaningful scores. The resulting description of the students' learning, use, and transfer of the strategies provided a very rich description of student behavior. Theories of a student's knowledge such as the strategy models of this study are useful in instructional design and research. With a detailed task specific representation of students' knowledge as a frame of reference it becomes possible to predict specific student behaviors and collect extensive empirical evidence to test the predictions. If the predictions are not supported, the rich descriptions of behavior make available new knowledge about the students thinking. This knowledge can serve as the basis for alternative predictions to be used in researCh and the design of other instructional sequences. In fact, many of the alternative predictions, future research questions, and alternative proposed instructional sequences stated throughout this chapter were possible only because rich descriptions were available. They would 200 not have been possible if the only available information was related to perfOrmance accuracy and trials to criterion scores. The sub- stantial benefits of gaining a representation of the content or know- ledge to be taught in terms of concepts, task requirements, and strategies in the instructional design and research has been argued above. However, one caveat is necessary. Such analysis was not simple and straight fOrward to accomplish for two reasons. First, it was initially difficult to understand and to apply Smith's analytic constructs in the analysis of the content. Second, the time required to produce such an analysis is substantial as the product is a large number of highly interrelated pieces. While these difficulties should be anticipated, anyone attempting such analysis should not be deterred as the benefits appear to outweigh the costs. The Efficiency of a Large Scale Experimental Study The final finding is related to the benefits, cost, and efficiency of conducting a large scale experimental study such as this one. A study of this magnitude has the advantage of providing infOr- mation related to the effectiveness of the instruction and the detailed description of student perfOrmance at the same time. Without a study of this scale it would have been impossible to assess the effects attributable to instruction on the task sequence and the strategy based instruction within the sequence. However, the experimental de- sign required a large number of trained personnel (approximately 20), several supporting peOple, and daily contact with seventy-two students 201 for over three weeks. The thoroughness of the observations generated a very large volume of data which proved difficult and costly to collect, manipulate, and reduce to meaningful scores. The large scale experimental study is probably not an efficient way to proceed without the benefit of preliminary, more intensive, small scale studies. Smaller studies could have provided the same strategy performance information, guidance in the development of the instructional sequence, and baseline information to be considered in the interpretation of the results. TWO types of studies are suggested. The first is intensive study of a few individuals given strategy based instruction across tasks. This would probably have revealed that students were not using and transferring the complete strategies. Such infOrmation.would have modified this central premise of the present study. With fewer subjects it would have been possible to use the process tracing techniques to establish more complete models of their strategy perfOrmance. This additional step would have pro- vided the detailed descriptions of the students strategies which must now be sought post hoc from data obtained at a high cost. It would have been possible to establish if students were reformulating what they had been taught into one of a limited number of strategies, if strategies (or components) were being used under identifiable circum- stances, or if the strategies were entirely idiosyncratic. Models of their thinking could have been used to modify the initial strategy or develop an alternative more compatible with the students inclina- tions. This then could have become the basis fer the design to be examined with a large scale experimental study. 202 A second type of small scale study is also needed. Baseline studies would have provided information useful in the instructional design and in guiding the research procedures. Baseline data on task difficulty fer uninstructed students could have provided standards against which to gauge the effects of two types of instruc- tion and within each type of instruction the effectiveness of alternative instructional protocols. Baseline studies on strategy use and transfer could also have helped established as somewhat less arbitrary assignment of criteria on which hypotheses related to strategy performance were accepted or rejected. An additional benefit of both types of studies would be the opportunity to develop on a small scale protocols, scoring procedures, and programs for the analysis of the scores. The insight gained from the smaller studies would have assured the collection of the necessary and sufficient data during the larger study. Furthermore, the availability and use of limited sets of representative data in devel- Oping both scores and analysis procedures would have been more cost effective. 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ACT —- "This is the process of acting on an object in such a manner as to obtain a particular kind of input (e.g., color or temperature infer- mation). This might involve orientation of the required organs, explor- atory movements such as visual scanning or tactile exploration, and/or manipulation of objects such as hefting or squeezing. Perfbrmance of ACT requires a prior retrieval of the appropriate action from long-term memory, i.e. , activation of the observation action node in an associative network. This activation makes available the infOrmation from which a control program.can be reconstructed. For present purposes, no dis- tinction will be made between the construction and execution of the program.and ACT will be treated as a primary process. It may eventually prove necessary or useful to break it down further. The input fer ACT includes the observation action concept and the differentiated Object on which the action is to be performed. The output is the resulting input to the individual. Analysis of the input is carried out by other processes." (Smith, 1972, p. 153). CHOOSE 1 "CHOOSE l is a primary process similar to CHOOSE in nature, but differing from CHOOSE in that some criterion is used for the choice. 207 208 CHOOSE implies a certain randomness Of choice, or at least a choice based on such non-salient factors as proximity to the chooser or visual accessibility. CHOOSE 1 implies a choice which is non-random, which is based on some salient criterion CHOOSE 1 might compare a value for one element which is encoded and stored in short term memory to a series Of perceived values Of elements and choose the one element from the series which best approximates the value Of that one element. In this case CIDOSE 1 has provided an approxinutien of the value Of the original element." (Padilla, 1975, p. 204). C(MPARE ”This primary process determines the comparability Of two encoded units Of information, e.g., encodings Of texture information for two objects. (IMPARE essentially monitors the node or nodes activated as a result Of the encodings. If the same node is activated on both occasions, a judgment Of comparability is made. If different nodes are activated, a judgment Of non-comparability is made. The output Of COMPARE can itself be viewed as the activation Of a node in a network. This network includes nodes corresponding tO the concepts "same" and "different" (and perhaps others). The activation Of one of these nodes makes inmediately available certain Operational alternatives including verbal output. The particular alternative to be executed, if any, is determined by some controlling mechanism which represents the strategy being employed by the individual." (Smith, 1972, p. 155). 209 DECODE "This is the primary process by which an associative network is entered by way Of a verbal label for one of the constituent concepts. The input for the process is the verbal label. Decoding Of the label results in the activation Of a concept or node in the network. This does not necessarily result in the reconstruction Of images, actions, or verbal entities. In effect, the DEOODE process Opens the way to many possibilities, but it remains for the next step(s) to take advantage Of one or more Of them. The possibility that the individual is set to perform another step which then follows automatically from the decoding need not concern us here. The point is that access tO the storage network must be gained as a result Of processing the verbal label. This is the function Of the DECDDE process." (Smith, 1972, p. 150). ENCDDE "This primary process analyzes the detail information which has been attended to, e. g., as a result Of SELECT. The general nature Of the information has already been determined (note the nature Of ACT and SELECT) and it remains for ENCODE to make a determination about this specific case. For example, ENmDE might be preset tO analyze texture information. ACT and SELECT has made such information available. ENCODE determines whether or not the texture information is novel and, if not, categorizes it in some manner based on previously experienced texture information. If the information is novel, a new category is created. Thus, ENCDDE involves long-term memory. In terms Of an associative network, the analysis Of texture information activates a node representing 210 a texture value concept or else fOrms a new node paralleling other tex- ture value nodes. The input fOr ENCODE is selected non-verbal sensory infOrmation. The output is a value concept (the activation Of a node). Undoubtedly, some additional contextual information about the experience will enter short-term memory. Some may also enter long-term memory." (Smith, 1972, p. 154). LOCATE This primary process involves the search for a position logically or spatially related to a particular source Of infOrmation in the environment. The input to the process may be another position, Object, or verbal label. ORDER "This is a primary process which attends to and assesses the magnitudes Of two differing encoded units Of infOrmation. ORDER sequentially evaluates the two magnitudes and then hierarchically orders them from lesser to greater. This primary process then basically monitors the nodes activated as a result Of the encodings. The COMPARE secondary process usually precedes and determines whether or not different nodes were activated during encoding. If this results in a judgment Of non- comparability, it is the fUnction Of ORDER to evaluate the two nodes successively and tO seriate them.appropriately. The output Of ORDER can itself be viewed as an ordinal concept, i.e., the activation Of a node in a network. This network includes nodes corresponding to the concept of ”more" and "less" (and perhaps others). The activation Of one 211 Of these nodes makes immediately available certain Operational alternatives including verbal output and appropriate serial positioning Of the elements. The particular alternative tO be executed, if any, is deter- mined by some controlling mechanism.which represents the strategy being employed by the individual." (Smith, 1972, p. 156). PLACE "This primary process involves a spatial placement Of an element to indicate its membership in a set. The criterion for placement is unspecified in the process itself although it will usually be retained in short-term memory from earlier steps. The input tO the set is an element currently attended to and an affirmative result from.the appli- cation Of the criterion fOr set membership. The output is the element in its new spatial location. A variety Of contextual information placed in short-term memory usually enables the individual to recognize the subset previously set aside by PLACE." (Smith, 1972, p. 153). REPORT "This is the process by which verbal responses are made. The input is a concept. The output is a verbal label fer the concept embedded in an appropriate linguistic context (not necessarily a complete or correct sentence)." (Smith, 1972, p. 157). SCAN "This is a primary process which represents a rather cursory, largely visual, exploration Of the stimulus field. It establishes a figure-ground differentiation Of Objects and detects a few salient 212 features which may enter short-term store. However, only partial in- formation is Obtained, even in the visual modality. Detection Of certain salient and/or relevant features usually terminates the SCAN process, or at least relegates it to a background role, and triggers some attentive processing. Thus, the input tO SCAN is undifferentiated stirmilus information while the output is one or more differentiated perceptual Obj ects. In most cases, many features which are relevant from a formal point-Of-view are not detected by SCAN." (Smith, 1972, p. 152). SELECT "This is a primary process which sorts relevant information from irrelevant. In particular, it filters out almost all information except for that for the variable (or variables) judged relevant to the task at hand. Thus, the input is undifferentiated input and the variable concept. The output is information on the relevant variable about the perceived Obj ect. Actually, the process is not simply a next step following complete execution Of ACT. Rather, along with ACT it forms an active system with a feedback capability which allows modification Of the detailed functioning Of ACT mtil the appropriate input has been made available. This represents a monitoring function Of SELECT. Such feedback mechanisms are probably involved in many primary processes. The large number makes it cunbersome tO make them all explicit in the task routine. This aspect Of the primary process is probably important tO keep in mind, however." (Smith, 1972, p. 153). APPENDIX B MULTIPLE CLASSIFICATION MATERIALS AND PROCEIIJRE APPENDIX B MULTIPLE CLASSIFICATION MATERIALS AND PROCEDURE The multiple classification pre-test administered tO all students was develOped by Bridgham (1967). The test consisted of eight cards. Each card presented a vertical row and a horizontal row Of geometric pieces which intersected in a blank space. All the pieces in one row shared one or two class properties (color, shape, size). The pieces in the other row shared a different class property. Also on each card was a separate group Of alternative figures which could be placed at the blank intersection, The correct alternative had the property common to all pieces Of the horizontal row and the property common tO all pieces Of the horizontal. Students were asked to select the correct piece from the alternatives. The procedure is given below as stated by Bridgham. The only change was tO omit the line which is given in parentheses. Show first card. Here are two groups Of things: Point. You can see there's a space here where something_is missing. Point. Down here are some things which mightggo in the space. ‘POint. Which of these things do jou think should go in this space?_uRecordCChOice. (Why didTyou piCk that eneT) ’If 8 changes his mind, recordithe second’ EhOice, third choice, etc. Score on the basis Of the last choice. Show next card. Here are two more 5 Of thin 5. Point. Which Of these thing§_Ep01nt) should gO in this space?"POint. Record choice as aBOve. (Why did you pick that one?) Re- peat this procedure fer all succeeding cards. 213 214 The cards and pieces were made from poster board. The cards were white and 16 inches square. The shapes Of the various pieces are shown in Figure 20 fer the large (1-1/2 inch) and small (2-1/2 inch) sizes. The arrangement, color, shape, and size of each card is listed below. The descriptions are identical tO those given by Bridgham (1967). The alternative pieces were separated from the rows by 1/4" black poster tape. Card 1 Harizontal row: Vertical row: Alternatives: Card 2 Hfirizontal row: Vertical row: Adternatives: Card 3 Horizontal row: vertical row: Alternatives: Card 4 Horizontal row: Vertical row: Alternatives: (All pieces small) yellow pieces--triangle, square, ring, circle, blank blank; rectangles-~red, blue, black white yellow circle, red rectangle, green triangle, yellow ring segment, yellow triangle*. (All pieces red) squares-~1 inch; 3 inch; 2 inch; 2-1/2 inch; blank l-l/Z inch pieces--rectang1e, ring segment; blank; circle; triangle. 1-1/2 inch square*, 2-1/2 inch square, 1-1/2 inch circle, 1-1/2 inch ring segment, 2 inch ring. (All triangles) green triangles--l-l/2 inch, 2 inch, 1 inch, 3-1/2 inch; blank blank; 2-1/2 inch triangles--red, white, blue, black blue 3 inch triangle, green 3-1/2 inch triangle, blue 1 inCh triangle, red 2-1/2 inch triangle, green 2-1/2 inCh triangle*. (All large pieces) circles--orange, white, red, yellow; blank blank; blue pieces--triangle, triangle, ring segment, square blue rectangle, orange square, blue circle*, yellow circle, yellow rectangle. Card 5 Horizontal row: Vertical row: Adternatives: Card 6 Horizontal row: Vertical row: Alternatives: Card 7 Hfirizontal row: Vertical row: Alternatives: Card 8 Horizontal row: Vertical row: Alternatives: 215 (All squares) l-l/Z squares--yellow, blue, white, green; blank. red squares--4 inch, 1 inch, 3 inch, 2 inch; blank 1-1/2 inch blue square, l-l/Z inch green square, l-l/Z inch red square*, 2 inch red square, 3 inch blue square. green piences--2 inch circle, 2-1/2 inch ring segment, 1-1/2 inch square, 2-1/2 inch triangle. 1-1/2 inch rectangles--blue; blank; yellow, orange, red. blue l-l/Z inCh rectangle, green 2-1/2 inch ring segment, blue 2-1/2 inch triangle, green 2-1/2 inch rectangle, green 1-1/2 inch rectangle*, red 2 inch circle, yellow 1-1/2 inch rectangle. ring segments--yellow 3-1/2 inch, white 2-1/2 inch, green 3 inch, red 1-1/2 inch; blank. 2-1/2 inch orange pieces--circle, tri- angle, square, blank; ring green 2-1/2 inch square, yellow 2-1/2 inch triangle, orange 2-1/2 inch ring, white 3-1/2 inch ring segment, red l-l/Z inch ring segment, orange 2-1/2 inch segment*. blue circles-~2-l/2 inch, 1 inch, 3-1/2 inch; blank; 3 inch. l-l/2 inch pieces--green square, black ring segment, red rectangle, yellow triangles; blank. blue 3 inch circle, green 2-1/2 inch triangle, blue 1-1/2 inch circle*, blue 3-1/2 inch circle, yellow l-l/Z inCh triangle, green l-l/Z inch rectangle, white 2 inch ring segment. 216 9 .> Figure 20. Large and Small Shapes for Multiple Classification Pieces APPENDIX C INSTRUCTIONAL PROTOQXS APPENDIX C INSTRUCTIONAL PROTOCOLS The following pages are the complete protocols used during the re- search. Protocols fer the instruction on systemic concepts, comparison tO standard task, Single variable Classification Task and Double variable Classification Task are included. For the first two tasks there are two sets Of protocols, one fOr the variable grain size, the other fOr the variable amount Of light colored grains. The first Of these protocols is related to the systemic instruction. Before instruction on any task, all students were taught tO identify mineral grains, variable names related to grains size (large grains, small grains, glassy rocks) and the variable names related tO the amount of light grains (mostly light grains, about half light grains, mostly dark grains). Instructors pointed to examples and asked student tO identify additional examples fOr each concept. The remaining protocols were read by instructors as they explained and demonstrated the task. The protocol fOr each task consisted Of the general task instructions and strategy or outcome feedback instructions. The general task instructions were given tO all students as pre-test and post-test instructions. The strategy or outcome feedback instructions were given immediately fOllowing the pre-test depending on the treatment tO which the student had been assigned. Both the strategy and outcome feedback instructions were composed Of initial instructions and error responses to be made by the instructors for various types Of errors. 217 218 SYSTBIIC INSTRUCTION (Note: Be sure to point tO the outline Of each grain as you demonstrate. Have the students do the same if you have any doubt Of their understanding . ) Systemic Ins truction --Before I have you start the task, there are some things I want you to learn about rocks. --Rocks are made up Of grains. Look at these rocks and I'll show you what a grain is. I'll also show you about the size and color Of the grain. Sample A --This rock has large grains. --This is a grain (point) (Repeat for three grains). Can you show me three Of the large grains in the rock? Good! This rock has large grains. Sample B --This rock has small grains. --This is a grain (point) (Repeat for three grains) Can you show me three grains in this rock? Good! This rock has small grains. Sample C --The grains in this rock are so small you just see them. Each Of these small sparkles is a grain. This is a small grain (Repeat for three grains). Can you show me three small grains in the rock? Good! This rock has small grains. 219 Sample D --In rocks like these the grains are so small that you can't even see them. When the whole rock is made Of grains this small we call them rock glassy. --When do we call a rock glassy? (Student response.) 220 --I also want you tO learn what is a light grain and what is a dark grain. Sample A --This rock has mostly li ht colored grains. Only the grains that are black are callgd dark grains. --Even the grey grains like this (point) are light grains. --Is this (point) a light or dark grain? (Repeat for several light and dark grains. Include a grey grain) --GOOd! This rock has mostly light grains. Sample B --This rock has about half light and half dark grains. --Is this (point) a light or dark grain? (Repeat for several light and dark grains) --GOOd! This rock has about half light and half dark grains. Sample C --This rock has mostly dark grains. Each Of these small sparkles is a grain. --Can you show me three dark grains? --GOOd! This rock has mostly dark grains. Note: Understanding by the student is critical. If you must continue to be assured Of their understanding, do so by repeating relevant portions Of protocol before going on. 221 COMPARISON TO STANDARD Pretest and General Task Instructions Amount Of Light Colored Grains --For this task, I want you to lOOk at the amount Of light colored grains. Rehember only the grains that are black are dark grains. All other grains are light grains. Example A--Remember, these are light grains (point to 3) and these are dark grains (point to 3) --This rock is a standard (point). I want you to lOOk at the amount Of light colored grains in the standard and in the rock I hand you. --First, tell me if each rock I hand you has more light grains, the same amount of light grains, or more dark grains than the standard. --Then, place the rock in the square where it belongs. (point to squares) --The rocks with more light grains gr_the same amount Of light grains as the standard go here (point tO square). --The rocks with more dark grains than the standard gO here (point to square 2). --(Pause) --Remember, tell me if each rock I hand you has more light grains, the same amount of light grains, or more dark grains than the standard. --Then, place the rock in the square where it belongs. INSTRUCTOR NOTE: If this is the pretest instruction fer the second variable fOr this student, use the following. --Remember, what you learned last time. I want you tO use what you have learned to dO this, but be sure you use the amount Of light colored grains. --DO you have any questions about what I want you tO do? 222 CI»EMJUSON TO STANDARD Strategy Instruction Amount Of Light Colored Grains --I want you to do this again with some new rocks. Remember tO look at the amount Of light colored grains. Tell me if the rock I hand you has more light grains, the same amount Of light grains, or more dark grains than the standard. Then, place the rock where it belongs. --Before you begin, I want to show you a way to do this. --First, remember what a light grain is and what a dark grain is. --Then, move the rock very close to the standard. (point tO standard) Take some time to lOOk back and forth between the rock and the standard several times. --After you have checked carefully, tell me about the amount Of light colored grains the rock has. --Next, lOOk at the labels on the board (point to labels) tO find the correct square. --Then place the rock where it belongs. DEMONSTRATION DIALOGUE (Use examples A and C) --Watch while I demonstrate this for you. Example A: --First, remember what a light grain is and what a dark grain is. --Nbve the rock very close tO the standard (move rock). --Take some time tO look back and forth between the rock and the standard several times (point back and forth). --Then, tell me whether the rock has more light grains, the same amount Of light grains, or more dark grains than the standard. This rock has more light grains than the standard. --Then lOOk at the labels on the board to find the correct square. This rock has lighter grains than the standard (point tO "lighter") so it goes in this square (place in square 1). If a rock has the same amount Of light grains as the standard, I would also place it here. 223 COMPARISON TO STANDARD Strategy Instruction (Continued) Amount Of Light Colored Grains Example C: --Here is another example. --First, remember what a light grain is. - PS 1 10 I CC 1 V1 P1 2 , 8 I I f 3 IC L V1 3 I 16 I I {C D! M - P2 4 13 I C L WI PI 5 21 C 7.. V1 PT 6 so I I C D M V? W? ‘ 7 L 13 I C C L V1 P1 [ a I 2 , I C D 71 $3193 9 I 23 I A C L VIIPl lO 7 If D M V2 ‘52 ll 19 D R V3 F3! 12 15 C 1. V1 P1 13 14 A IC D Y 'I P1? 14 24 I I I C D R V3 PS I 15 I 3 I t' I? D \1 NZ 3’ I 16 17 I I I i C L VIWI I 17' 20 C D M V? P“! 13 I 30 A C D W '3 FPS 19 9 I I I . IC D T 12 N3 .133 ’ C 20 12 I I I I If L V1331 v 21 I 25 J I C D H [V2 92 22 11 L L I ' r T D M V? P2 I I 23 s I I I C D 72 VS #8 24 1 I I I I I I KEY: S - Looks at sample Student V - Verbal reSponse (response ‘) P - Places rock (square I?) Tester Date C, D - Looks at sample proximate to standard C, D Pretest Instruction Post test L, M, R - Looks at left, middle, right Strategy Feedback Iso-feedback of board SINGLE VARLXBLE CLASSIFICATION TASK Amount of Light Colored Grains—Set A 266 Order RockI Passed No. No.I Sequence of Actions Trial? Comments 1 10 I IC D R "3 MI * 2 8 I IC L V1 Pl 3 I 16 I IC L 11 P1 I I C D M - 2 . 2 4 18 I I I IC L WM 5 ¥ 2]. I v I 5 1 ' » 1 ' ” *C D W V2 92' 7 I 13I I I I I I I 3 I *C L V‘IIPII I s 2 . I 3 C D “WTvStPII 9 2 . 1 C If‘ L Vl-Pl . 10 A 7 I I I C D \r v.2 :32 11 19 1 I I ' C D R 11.".15' C 12 1sI 1 I JI J I I C L 11131 ' 13 14 I I I I I I I 'C ' 3 Wivfpz. 14 24 L I I I I L I ' C 11 R vsmsI I 13 I 3 I I I I IC D I \I IVE 193 I I I 16 . 17 L. ._ I L I IL. L I VIPI I I I 1'. 20 _1 I L 1 I EC . :1 WW? P’I' - 13 I 30 ' I I '“ IC I D R Ivsifis L f 19 9 I I I , I I I 1 I W I D: was I I: 1C ‘ L 1'1 .731 . 21 I 25 I I I I I C Ic 1 :1 SI ‘1': pz 22 u I I I I I 1 I ‘ C ' D M V2 Pl‘ I 23 I s I I I I I _I I I IIICIDIRI’IWII I KEY: S - looks at sample Student V - Verbal res nse (res nse *) P - Places roclpro(square If)> Tester Date C,D-bookst’.l “.t: staidargmcbepmxm e o Pretest Instruction L, M, R - Looks at left, middle, right Strategy Feedback Isa-feedback of board 267 SLVGLE VARLKBLE WIFIQTION TASK Amount of Light Colored Grains-Set 3 OrderI Rod-(I Il’assedI No. I No.1 )Sequence of Actions '.‘ria.l'?l Comments I I IC D M 'I’Z IPZ I 1 i 38? I. I I I; I l 2I31I ILIDLRIVJIPJ I 7 7C L ”PM 3 I 35I I I I I I I I I 1 IC D I )4 'v2 P2 6 4 I 42 I I I I I 5 I 49 IL. A BL IIII3I'P3 f 7C U ' .‘1 W7. P2 6 I 6E I I I I I I I 7" V I 7 39I ICILIMLpl I I I I ! IC ' L ' ITPl ' 8 I 44L I I LI I I I I I I5 I L I W'Pl ' I 9 :9I I I I I I L A IOIISI I I I I A mid VIUIIII’IWI I I I :C I ' 71 W‘ 12 I 40I I ILI I I I I if I L VlIPl 13 I 361 I i I " D \1 .172 ?2 14 I 33I IL I I I~ I T T C ' Lffi'l Pl Is I ISI I I vI I I I I IC 5 R IV? "93 I 16 46 I I I I I 1 I C T TI: .W "‘2 P2 ' I 1’ 47 I I II I I I C VI \1 W2 172 I 18 37 I L I I I I I. IS IL I 1191 ' I I I 19 48: 1 I I I I . 1 I C I: I-Irl'rl ' i 20 34 I I I I l I I T T I' I 21 271 IC D I R II.) PT L I If D I 31 'V2 IPZ I 1‘! 7“ ‘ A ' . l 23 32I IC II JIMI I L I I? W RII°IP°I I I I Key: S - Looks at sample Student V - Verbal response (response 1) P - Places rock (square ’) Tester Date C, D ‘ 1 k5 t - I_‘ . . t U020 simdafiffgv‘lim e Pretest Instruction Post test L, M, R - Looks at left, middle, right Strategy Feedback lso-feedoack of board 268 'ON TASK FICATI v 1 DOUBLE VARIABLE SET A Comments Passed Trial? Order Rock} ?5 P3 Sequence of Actions No. No. P4 VS I..l:'- l [P1 Pf FW' I L ID. i VftC {A l 'T ’A ! A 14 16 KEY: Student S - Looks at sample V x - Verbal response (response 4*) Post test {so-feedback Instruction Feedback Tester P - Places rock (square ‘) A, B, C, D - Looks at sample proximate Strategy Pretest to t. Gns. V L. Standard A, 3, C, D G, L - Looks at En 32./Amt. part of board 269 DOUBLE VARIABLE CLASSIFICATION IASK SET 8 S m m C a? 1 5a 5.1 pn Ill 5 S S P D. D. 3 4 7. 4 2 1. 1+ 6 S 6 Wu.) 6 .9- 4 “Wilmllrmlllm; llanulllp p p p m 6 1 6 T l .S l B 5 I 6 C A5 is. 1» a0 .4 .4 S 4 6 «D D we fir‘ll. [IIILYIIIIIIAWIIIIL 7 I‘L‘WVIIVIV'LN‘IWV‘LW V V {IL IIII'IA 0 4 1w W :4 .4» ailnjv pirlwi D V D U V D “u rL no r. r. F» F. n. F» Po no F. no «u rc FL ”L XL wililli l-..i,..s.--..l-..fi. : 1. A. . 3 2 g SCWCCWWwC WCWVC C CWCWWCW A -I.IJ Val-0L 3!; III-1..-} OtllL In]; L ii... i [J ll will a A w V. w. V m n n V n m. w w ArllfvillLllll ..Vlll4ull'411llii'l Ill. 1: B 1. _B H B _B To ro B B To B .l... Tl II E Illi IILTIVLVIVI III AAAAAAAAAAAAAAAARAAAAAFA :ill! 101:. Ill A III. -..lli I‘ll I|||A -...Ili llllk ...llliwlll. .flr" JTllllg I'll IIHIIILVIII TIL It‘ll! IIIIL l l'ni .10.; .IIIJLWIIIIATIV’AI‘- VI' . , 7 8 q. 2 2 6 mmnnxnwewuwwumxnumvsiuzzs: r gr.;.sV i a I 2 3 4 mmizsaso,agmnuuuumummmnzzz Iso-feedback Date Post test Instruction Feedback Pretest Strategy Student Tester (ins. part of board stamdard A, B, C, D P - Places rock (square 5) A, V, D, D - Looks at sample proximate to G, L - Looks at Gn. Sz./Amt. Lt. S - Looks at sanple V x - Verbal response (response ‘) KEY: BIBLIOGRAPHY BIBLIOGRAPHY Allen, Leslie R. "A Scalogram Analysis of Classificatory Behavior." Journal of Research in Science Teaching, 7 (1970), 43-45. 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