A SYSTEM ADPROACH TO THE ANALYSIS OF THE TEQCI-{ER SUPPLY PROBLEM EN TLWSH SECONDARY E‘U-CA'E'ION Bissertafion for the Begree of Ph. D. B:Z£CHEGA=.‘€ STATE UNW‘ERSW {(EMALE’TIN AMEN 1974 lllllllllllllllllllllllllllllllllllllllllllllllll , z; .- 3 1293 00069 9136 Michigan ._,_c University This is to certify that the thesis entitled Systems Approach to Analysis of Teacher Supply Problem in Turkish Secondary School System presented by Kemalettin Akalin has been accepted towards fulfillment of the requirements for Ph . D . degree in Education n V. 7///”c’/ L ”lovAK'I’V/{flf7b< “r/ [uvr Major professor 0-7 639 ABSTRACT A SYSTEMS APPROACH TO THE ANALYSIS OF THE TEACHER SUPPLY PROBLEM IN TURKISH SECONDARY EDUCATION BY Kemalettin Akalin The Problem In spite of the struggle and of the requirement of the national develOpment plans to solve it, the problem of inadequate supply of secondary school core subject teachers (teachers for general education) has drastically grown in Turkey throughout the last score of years. The Purpose The purpose of this study was to examine the problem in order to search for an operational approach to solve it, and at the same time to demonstrate a new way of analyzing educational problems in general. The operational aim was to present a systems approach, useful in analyzing educa- tional problems in general, and to perform an application of the technique to the particular teacher supply problem of the country. Obviously, the need for scientifically processed data is essential to any effort to solve the problem through 5 “Air. ' Kemalettin Akalin ”a." {3'7 .3 (7 these kinds of studies. Hence another purpose of this study was to develop a tool, a mathematical model, as a means for obtaining information relevant to the problem. Conclusions Drawn from the Analyses A logical block diagram was developed in order to examine all events which either appeared to be involved in or to affect the teacher supply efforts and activities in the Turkish system. The overall conclusion drawn from the analytical examination was that the causal problem, which results in the shortage of secondary school core subject teachers, is essentially a resource utilization problem rather than a resource scarcity problem. In other words, the problem is caused basically by ineffective administra- tive decisions. In view of solid evidence that the administration has been supported and encouraged by the environment in its struggle for solution of the problem, the above mentioned ineffectiveness of decisions may be attributed to the inert state of the system, which cannot at present keep pace with the dynamic changes of the society. In order to cope effectively with the problem, needed basic operational measures which may be derived from the analysis of the problem may be cited as follows: 1. To change the traditional conservative concept of administration toward the productive modern concept of management. Kemalettin Akalin 2. To establish a modern data processing system, which seems to be an especially urgent need, because the education system has become too large and too complex to be managed adequately by the central Ministry of Education through continuing today's practice, lacking adequate flows of essential information. 3. To redesignate the teacher supply system in terms not only of its organizational structure but also its training programs, so as to better answer the needs of the changing society. The Tool DevelOped to Utilize Processed Data To accomplish the purposes of this study, a mathe— matical model was develOped to facilitate operational approaches for solution of the problem under consideration. The model consists of two main parts. The first part was devoted to a simulation model in order to illus- trate how alternative solutions are obtained and examined through manipulating parameters, and to illustrate what kind of data is needed in simulation for planning. The second part was developed as a descriptive model in order to define the state of the system at a particular point in time. Obviously the purpose of the second part of the model was to facilitate obtaining realistic parameters to be used in a simulation model. Kemalettin Akalin The model also facilitates cost analyses relevant Unopera- tional approaches for solution of the teacher supply problem. Application of the Model The model was applied to the province of Eskisehir, which was selected on a nonrandom basis. The criteria for selection of this province were: (a) to include all known variables, i.e., all kinds of secondary schools in Turkey, and (b) to facilitate data collection at minimum cost and effort. Since expected performance of the model was obtained from its application for this particular province, one logically deduces that similar performances could be obtained for other provinces through simple 100ping in the computer program. Although one should not generalize the findings in the Eskisehir application of the model for Turkey as a whole, implications of the results may be cited as follows: 1. Teacher supply and utilization problems exist in the province of Eskisehir, and the application demon- strates how the nature and dimensions of the problem may be apprehended. 2. Cost analyses indicate potential means for establishing criteria to facilitate improving the system Kemalettin Akalin with respect both to quality and quantity of service, through both short-range and long-range measures. It is hoped the success of this demonstration may encourage the Turkish National Ministry of Education to make greater use of systems approaches, to improve its flows of information, and to modernize its own adminis— trative structures based on the outcomes of research and planning. A SYSTEMS APPROACH TO THE ANALYSIS OF THE TEACHER SUPPLY PROBLEM IN TURKISH SECONDARY EDUCATION BY Kemalettin Akalin A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Secondary Education -‘ &(hurfluflnm .‘\_,_ . 1974 DEDICATED TO My wife and children ii ACKNOWLEDGMENTS The author wishes to express his particular appre- ciation to Dr. Wilbur B. Brookover, his academic advisor and chairman of his doctoral committee, who generously gave his time and encouraging advice throughout the struggles from which this present study originated. The author is very grateful to his professors for their help enabling him to bring other relevant disciplines to bear on this study. These include Dr. H. E. Koenig and Dr. Thomas J. Manetsch in systems science, Dr. Leonard H. Rail in economics, and Dr. Martin G. Keeney in systems science, computer science, and institutional research. Dr. Keeney served also as a member of the doctoral committee. The writer expresses his thanks to Dr. Cole S. Brembeck and Dr. MaryEllen McSweeney, who also served on the doctoral committee in many helpful ways. The author is grateful for the assistance of Dr. Ben A. Bohnhorst and Dr. Kenneth L. Neff who patiently read the manuscript and improved its style along with constructive criticisms. For their assistance in helping to gather and process the data, and to prepare graphs and figures, iii appreciation is extended to the writer's colleagues in the Ministry of Education. Sincere appreciation is extended to the Turkish Government and to USAID for providing scholarships which enabled the writer to carry out his proqram of graduate studies abroad. iv TABLE OF CONTENTS LIST OF TABLES . . . . . . . . . . LIST OF FIGURES . . . . . . . . . . Chapter I. INTRODUCTION . . . . . . . . . Statement of the Problem . . . Objectives . . . . . . Delimitation of the Study . . . Operational Procedure of the Study . Organization of the Study . . . . Definitions of Terms . . . . . . Summary . . . . . . . . . II. REVIEW OF LITERATURE . III. Introduction . . . . . Development of Systems Concept . . Application of Systems Concept Systems Techniques . . . . . . Management As a Control System Educational Administration . . . . Summary . . . . . . TURKISH SCHOOL SYSTEM AND THE BACKGROUND OF THE PROBLEM . . . . . . . . Operational Organization of the Turkish School System . . . . . Background of the Problem Making Use of Information in Administrative Decisions . . . . Evidences of Existence of the Teacher Supply Problem . . . . . . . Summary . . . . . . . . . Page viii CDHKOQONJE-H Hra 20 20 21 25 28 34 42 44 44 48 65 69 77 Chapter IV. VI. VII. Page IDENTIFICATION OF THE SYSTEM AND THE PROBLEM . . . . . . . . . . . . . 79 Identification of the System . . . . . 79 Identification of the Problem . . . . . 98 Discussions and Conclusions . . . . . 118 MATHEMATICAL MODEL FOR TURKISH SECONDARY SCHOOL SYSTEM . . . . . . . . . . . 132 PART 1. SIMULATION MODEL FOR TURKISH LYCEE TEACHERS . . . . . . . . . . 133 The Origin of the Model . . . . . . . 133 Objective (or Criterion) Function . . . 137 Student Submodel . . . . . . . . . 137 Teacher Submodel . . . . . . . . . 139 Cost . . . . . . . . . . . 144 Findings and Conclusions . . . . . . 146 Summary . . . . . . . . . . . . 152 PART 2. MATHEMATICAL MODEL FOR IDENTIFI- CATION OF THE TURKISH SECONDARY SCHOOL SYSTEM . . . . . . . . . . . . 153 Introduction . . . . . . . . . . 153 Notations . . . . . . . . . . . 153 Section 1 . . . . . . . . . . . 155 Section 2 . . . . . . . . . . . 159 Section 3 . . . . . . . . . . . 168 Summary . . . . . . . . . . . . 187 EVALUATION OF FINDINGS IN THE APPLICATION OF THE MODEL . . . . . . . . . . . 190 Introduction . . . . 190 Geographic and Demographic Circumstances of the Province . . . . 191 Procedures for Collecting and Processing Data . . . . . . . . . . 192 Evaluation of Findings . . . . . . . 197 SUMMARY OF THE STUDY . . . . . . . . 227 Introduction of the Problem . . . . . 227 Review of Literature . . . . . . . 229 The Background of the Problem . . . . 233 Identification of the System and the Problem . . . . . . . . . . . 236 vi Chapter Mathematical Model for School System . . Evaluation of Findings of the Model . . . Concluding Statement . APPENDIX A . . . . . . . APPENDIX B . . . BIBLIOGRAPHY . . . . . . . vii Page Turkish Secondary . . . . . . . 241 in the Application . . . . . . . 243 . . . . . . 244 . . . . . . 246 . . 268 . . . . . . 281 Table 10. 11. 12. LIST OF TABLES Development in Secondary School Teacher Training Institutions . . . . . . . . Planned Development of Education Institutes (1968-1972) . . . . . . . . . . . Estimation and Realization of Production of Teachers in 1961—1971 . . . . . . . . Produced Weekly Class Hours in General Secondary Public Schools and Aggregate Calculations for Average Weekly Class Hours Per Teacher . . . Frequency Distribution of Courses in Terms of Established Load of Teachers . . . . . . Frequency Distribution of Fields in Terms of Supply Rate . . . . . . . . . . . Various Combinations of Training Branches in Education Institutes . . . . . . . . Yearly Outcomes of the Lycée in Desired and Presented Systems in the 20th Iteration, Analogous to the 20th Year in a Planned Period . . . . . . . . . . . . Established Teaching Load of Secondary School Teachers in Class Hours . . . . . . Cost Schedule Per Student by Educational Level Established by State Planning Organization Groups of Municipalities With Their Demographic Characteristics in the Province of Eskisehir . . . . . . . Teacher Supply and Utilization Problems Occurring in Eight Municipalities in the Province of Eskisehir . . . . . . .. . viii Page 57 62 64 71 74 75 129 148 161 175 192 203 Table Page 13. Aggregate Calculation for Need and Supply of Secondary School Core Subjects Teachers in the Province of Eskisehir . . . . . . 207 14. Partial Results of Cost Analysis for Secondary Education in the Province of Eskisehir . . . . . . . . . . . 221 ix LIST OF FIGURES Figure 1. Block Diagram of the Operational Structure of Turkish Public Schools . . . . . . . 2. Indices of Increases in the Number of Students and Teachers in General Secondary Schools . 3. Basic Sources of Teachers in Turkey . . . . 4. Student/Teacher Ratios in Secondary Schools . 5. Indices of Increases in the Number of Students in Elementary and Secondary Schools and in the Population . . . . . . . . . 6. General Illustration for Turkish Education System Within the Society . . . . . . . 7. Organization Chart: The Position of Organiza- tion for Training Core Subjects Teachers Within the MOE . . . . . . . . . . 8. Block Diagram for Need and Supply of Teachers of Secondary School Core Subjects . . . . 9. Increases in Funds and Quantity of Students of Education Institutes . . . 10. Estimated Need for Education Institute Graduated Teachers and Realization . . 11. Block Diagram for the Lycée and Its Teachers in Turkey . . . . . . . . . . . . 12. Estimated Need and Supply of Mathematics and Science Teachers in Present and Desired Systems . . . . . . . . . . . . . Page 45 50 52 54 6O 81 84 86 104 126 135 150 CHAPTER I INTRODUCTION In this country, we suffer from the lack of the habit of thinking scientifically--a11 the way from the private life of citizens to the administration of the state. -—Ismail Arar Statement of the Problem Insufficient supplies of general secondary school teachers has been a problem in Turkey since the early fifties. Following the Revolution of May 27, 1960, Turkey undertook to manage its national development by means of national five-year plans. The first planning period began in 1963. Education was considered to be a prime factor in the development of the economy and the society, and it was given high priority among other planned activities. How- ever, in spite of the five—year plans and their yearly pro— grams, implementation has remained insufficient throughout the last decade. In particular, the shortage of general secondary school teachers, which was fewer than 3,0001 in 1Milli Egitim Bakanligi, Ogretirme Komitesi ve On Yillik Plan (Istanbul: Milli Egitim Basimevi, 1961), p. 82. the 1960-1961 school year, grew to more than 18,0002 in the 1970-1971 school year. This teacher shortage, which was readily apparent, manifested itself more and more year by year. The need to analyze the problem and to achieve effective control over it became increasingly urgent. Over the last twenty-five years, the present writer has been intimately concerned with the problem: in his capacities as a teacher and administrator of teacher training schools, and since 1959 in his work in the central Ministry (a) as an administrator in the general directorate for teacher training and (b) as a researcher on the staff of the Ministry's planning office (which will be referred to in this study by its initials PAKD--see footnote 2, below). In 1960 and 1961, this researcher was in charge of preparing a ten-year plan for meeting the need for elementary and secondary school teachers. On the basis of his experiences and his first-hand observations of implementation during the planned period, he developed the working hypothesis that a key to the problem might lie in the decision-making processes by which the system of pre- paring and supplying teachers was administered. The 2Source: Data supplied by the Planlama, Arastirma, ve Koordinasyon Da1resi (PAKD--the Planning, Research, and Coordination office of the National Ministry of Education in Turkey). V““ .ado- ...,- 5—w- §vrn ‘ >~ a.-. rising demand and aspiration in society for more general secondary educational opportunities exceeded the targets specified in the national plans. At the same time, the supply of teachers fell below the targets. The problem appeared to be more dynamic than the ability to COpe with it in the present administrative system. The researcher pursued this problem further in graduate study at Michigan State University. There he took up a study of systems analysis with a View to the light which might be shed by employing a systems approach to the problems of teacher supply in Turkey. Working Hypothesis Upon Which This Study Is Based This became the working hypothesis upon which the present research is based: that a systems approach to analyzing the processes of teacher supply in Turkey (a) might help administrators understand better the nature of the teacher shortage problem, (b) might better identify the points at which better decisions need to be made and the variables which need to be considered, and (c) might indicate new and better kinds of data needed. What the researcher learned was that a systems approach represents a new and general method of thinking. It recognizes that the operations of a particular part of a system are normally interrelated in complex ways with the simultaneous operations of other parts of the system. A systems approach is a comprehensive way of enabling the analyst to include in his thinking--in ways he might not otherwise be able to do——those other pertinent variables which also bear on the particular problem at hand. The present study therefore is a study in applied methodology. It attempts to demonstrate how a systems approach may be usefully applied--in this case, to the particular problem of teacher supply in Turkey. In addi- tion to the particular problem, the researcher hopes that the general usefulness of the approach also will become apparent. The problem of teacher supply is urgent and for that reason it was selected as the tOpic for application in this study. But the problem of teacher supply is only one part of the total complex of processes making up the , whole Turkish educational system. Application of the approach to other problems may promise also to offer useful results similar to the outcomes of the present study of teacher supply. Objectives There would appear to be a great opportunity for helping Turkish educational administrators by providing them with better analyses and better data. In this way their decisions may be more effectively based on scientific analyses and national understandings. In present practice, however, such help customarily is neither asked nor pro- vided. Decisions are made depending on personal, empirical estimations or on interpretations of aggregate statistical data which are frequently outdated, and inaccurate, or insufficiently analyzed. Any attempt to help administra- tors, therefore, should first of all attempt to facilitate the provision of sufficient data which has been scien- tifically analyzed. As indicated above, the primary aim of this study is to demonstrate one promising new way in which this might be done in terms of applying a systems approach to the problem of need and supply of secondary school teachers. The overall objective is to accomplish this aim through facilitating a more compehensive identification of the problem and its relevant variables. The following main objectives may be specified: 1. To utilize a systems approach in analyzing the education system under consideration in order to identify the relevant variables involved in causing an inadequate supply of general secondary school teachers, and to explore the interrelationship among these variables. 2. To develop a mathematical model for approxi- mating the state of the system related to demand and supply of secondary school core smflxfixfi: teachers at a given particular point in time. To be more specific, one may break down the above primary objectives into secondary ones, as follows: 1. In terms of identification of the problem: a. Isolate and identify the problem in terms of its internal structural and functional nature and its external environment. b. Illuminate possible interrelationships of vari- ables which maylxacausing the problem. 2. In terms of the system as it relates to need and supply<1fsecondary school teachers, identifytfluafollowing: a. Anatomy of structural elements in the existing situation in terms of need and supply of teachers. b. Existing functional relationships among vari- ables relatedtx3need and supply of teachers. c. Assessments of actual observed utilization of teachers in an existing situation. d. Opportunities for better utilization of teachers under existing circumstances. e. Assessments of the utilization of funds with respecttxithe observed utilization KO KO KO KO \O KO K0 K0 KO KO 5 ox m ox ox 0‘ 0 O o Ch 03 (D H H .H H H H H H H H H (*) Sources: State Planning Organization and State Statistical Institute. 61 Finding a solution to the supply of secondary school teachers was strongly recommended in the five-year national develOpment plans and yearly implementation pro- grams issued by the State Planning Organization after 1962. In the first plan, the existing situation in the early sixties was described as follows: The fact that the organization of education could not be adjusted to new developments caused imbalances in educational methods. The most important of these arises from the inadequate supply of teachers, and has led to a steady deteri- oration of student teacher ratios. In many branches there are serious gaps as regards both the numbers, quality and vocational branches of teachers. Other problems are the lack of administrative personnel in education and of closer COOperation between edu- cational institutions and the various ministries. Implementation between 1963-1970 remained inade- quate. The problem of supply worsened instead of improving. To try to mitigate the situation, the maximum load of teachers was increased by six hours. Thus a teacher could teach as many as 30 hours in a week. The situation after the mid-sixties was described in the second plan as follows: The insufficient number of teachers is limiting the progress and quality of education. At every level the student-teacher ratio is getting more and more out of proportion. In secondary schools there _are 45 students for every teacher graduated from a teacher college and in high schools there are 38 ‘students for every university graduated teacher. The scarcity of teachers is partly compensated for 57State Planning Organization, Republic of Turkey, First Five Year Development Plan 1963—1967 (Ankara: 1963), p. 402. 62 by non-professional people but this harms the quality of education. Methods which will provide the greatest benefit from teachers have not been developed and the teachers within Turkey are not evenly distributed. . . . In secondary schools an important bottleneck has arisen in quality and quantity. Even at this level, productivity has decreased. . . . In high schools the quality and productivity of education declines mainly because of inadequacies in build- ings and teachers.58 Targets for increasing the capacity of education institutes were given in the second plan as shown in Table 2. These figures proved to be too high to be realized in the given time. Perhaps the planners had simply counted the overall number of teachers needed to close the gap between demand and supply within the five years. However, in spite of the urgent need and the defi- nite requirements of the plans for more teachers, the number of students in education institutes decreased in the TABLE 2--P1anned Development of Education Institutes (1968-1972).59 First Total Number Years Registrations Graduates of Students 1968-1969 4,600 1,750 10,100 1969-1970 7,000 3,800 15,200 1970-1971 8,800 5,850 19,100 1971-1972 10,600 7,400 23,100 1972-1973 13,000 8,950 28,150 58State Planning Organization, Republic of Turkey, Second Five Year Development Plan 1968-1972 (Ankara: 1969), p. 178. 591bid., p. 191. 63 1967-1968 school year (see Table l on page 57). In the same year, the humanities and science branches of education institutes were again subdivided into Turkish, Social Studies, Science, and Mathematics, as they had been before 1946, and the training period for them also was extended from two to three years. These changes in the training pro- gram adversely affected the supply and utilization of teachers.‘ Although the number of education institutes and their students began to increase in the 1969-1970 school year as shown in Table 1, the rate still remained insuffi— cient to answer the need. After the 1971 announcement known as "The Ultimatum of March Twelfth,"60 education was again one of the high priority issues. A broad study of needed reforms in educa- tion took place in the Ministry of Education for the second time within eleven years. Thus, implementation in the planned period also has remained inadequate in terms of supply of secondary school 60On March 12, 1971, the military leadership of Tur- key issued a memorandum to the President indicating alarm and concern over the state of law and order and urging the gov- ernment to take immediate steps to correct the situation and to move forward with needed social reforms. The clear implication was that if satisfactory steps were not taken, the military would be compelled to assume control of the government. The Prime Minister and his cabinet thereupon resigned and since that date Turkey has been governed by a sequence of civilian coalition governments and cabinets whose main motives have been to restore civil order and to push ahead with reforms. 64 core subject teachers. Table 3 presents the outcomes of implementation as compared with the estimation in the MOE's Ten Year Plan for supply of teachers. The targets of the Ten Year Plan were exceeded by 3.5 percent in terms of training elementary school teachers and missed by a short-fall of 53 percent in terms of train- ing secondary school core subject teachers. The actual ,situation of supply in 1971-1972, after the period covered by the Ten Year Plan, was a small surplus of elementary school teachers and a shortage of approximately 20,000 general secondary school teachers. TABLE 3.--Estimation and Realization of Production of Teachers in 1961-1971. Normal Education Higher Teacher School Institute Training School Graduates Graduates Graduates Realization6l 110,338 19,037 1,768 Estimation62 106,625 36,842 7,744 Difference +3,713 -17,805 -5,976 61 _ Milli Egitim Bakanligi, Ogretmen Okullari Genel Mfidfirlfigfi, 1971-1972 Yilligi. 62Milli Egitim Bakanligi, Ogretmen Yetistirme Komitesi Raporu ve On Yillik Plan, op. cit. (Ministry of Education, Report of the Teacher Train- ing Committee and Ten Year Plan.) 65 Making Use of Information in Administrative Decisions Before the Planned Period Prior to 1960, data were mainly collected only for immediate uses in routine operations, i.e., usually simply to record the numbers of students, teachers, and schools in the concerned year. It was not customary to analyze data, evaluate implementations, or employ data in making decisions until the adOption of the concept of planning in 1960. In the late fifties a central bureau was estab- lished in the Ministry of Education to collect statistical data and one person was assigned to organize the bureau. However, after six months, apparently finding no need for such a bureau, the MOE then abolished it. In fact, the State Statistical Institute, as one of its legal responsibilities, was collecting and publishing statistical data related to fields of social activity throughout the country, including education. The data were tabulated for general purpose and were usually pub- lished some years after they were collected. Therefore the possibility of timely use of data by concerned educators was very limited. In the Planned Period When the problems were studied in the Ministry of Education after the Revolution, the need for statistical 66 data was recognized. Statistics and Planning branches were set up in the general directorates. However, there were no standards for evaluation or tabulation of data. Each of the offices had its own methods, which were empirical rather than scientific. Although extensive data were col- lected from institutions, a great proportion of them were neither used properly, nor were they retrievable once they were filed. In the early years of the planned period the need became apparent for a central office to establish effective cooperation between the MOE and the State Planning Organiza- tion and to coordinate planning operations among the Ministry's offices. A central "Budget and Planning Office" was established in 1964. Soon after, another office similar to the "Budget and Planning Office" was estab- lished under the Undersecretary for Vocational and Technical Education, and this tended to generate a competitive dualism within the MOE. This, along with reluctance of other offices to accept it, adversely affected the early development of organization and function of the "Budget and Planning Office." However, the responsibilities and personnel of this office have expanded nevertheless, and its service has come to be valued as the years have passed. In 1968, under a contract between Michigan State University and the Ministry of Education, the National Educational Research and Planning (NERP) Project was 67 initiated. The objective of the project was to give necessary assistance to the Ministry of Education through the Budget and Planning Office.63 The project provided 22 scholarships at Ph.D. and Master's levels. Two full-time advisors, and short-term consultants as well, came from the USA. The need for an effective data processing system was recognized at the outset, as stated in the project's "Second Semi-Annual Report" prepared by the two advisors: An efficient, high-speed storage and retrieval sys- tem is the key to a data bank. Speedy access to data is an essential feature of the system. Tragi- cally, the Government of Turkey expends vast amounts of money every year to collect data on its education system; data which are grossly underutilized. The Ministry of Education alone distributes over 370 forms; each Turkish school must complete, on the average, from 10 to 15 forms per year. The volume of information returned is so great that some of the general directorates can do nothing with much of it. In other cases, the staff can barely keep pace with the inflow because these data are laboriously trans- ferred, in written form, to one or another filing system in the Ministry. In almost no case is there a capability to go to those files and extract one or more categories of information for all schools in Turkey within less than six months time, if by then. Turkey has a great deal of data that it can not use productively. 6An electronic system can remedy this situation. 63Kemalettin Akalin, Prospectus of Utilizing Foreign Resources in the Educational Reform, Ankara, 1971, p. 11. (Mimeographed.) 64NERP, Second Semi-Annual Report, PAKD, Ankara, December, 1968, p. 10. (Mimeographed.) 68 In spite of the early identification of the problem and of the need for an effective data processing system, still satisfactory progress toward solving the problem was not achieved.65 In 1970, the former "Budget and Planning Office" was redesignated the "Planning, Research and Coordination Office" (PAKD) with the intention that all planning and research activities of the Ministry would be consolidated under the direction of this office. Then the effort to establish the intended central data processing system became an urgent issue. To help realize the establishment of the data processing system, a "Data Bank Agreement Project" with the computer center of Hacettepe University (SISAG) was initiated in January, 1971. However, this project failed after the first step. The situation was summarized in NERP's Seventh Semi-Annual Report as follows: A working agreement was reached with SISAG in January and a Data Bank Work Group was established in the PAKD. After an initial two-month trial period, however, it appeared that cooperation between PAKD and SISAG might prove difficult to maintain. The MOE did not yet have a clear enough picture of its own needs to be able to communicate effectively these needs to SISAG. SISAG proposed to assume greater responsibility for the project, but the MOE was reluctant to place too much power in the hands of a contracting organization. As a 65NERP, Eighth Semi—Annual Report, PAKD, Ankara, December, 1968, l. 15. (Mimeographed.) 69 result, SISAG's direct participation has been post- poned until the PAKD develops a better picture of its needs and can draw up adequate Specifications for SISAG to follow.66 As of the middle of 1973, PAKD had not resumed cooperation with SISAG. The establishment of an effective data processing system depends largely on the understanding and handling of the problem within the PAKD and the Ministry of Education. Evidences of Existence of the Teacher Supply Problem Though the fact is self—evident that there is a shortage of teachers throughout the country, nevertheless one needs to set forth specific evidence of its existence. Conceivably the shortage at some schools may be due to underutilization of teachers at other schools. If this were the case, the problem would become a problem in utilization rather than a problem of supply. Or perhaps both shortage of supply and underutilization may be impor- tant factors. Evidences of the Shortage of Teachers Direct data for actual demand and supply of teachers in the country are unavailable, but an aggregate calculation is possible through using presently available statistical 66NERP, Seventh Semi-Annual Report, PAKD, Ankara, June, 1971, p. 6. (Mimeographed.) 70 data. The curriculum of secondary schools is fixed throughout the country. The number of class sections at secondary schools by level and the number of supplied teachers by field facilitate aggregate calculation of the average ratio of class hours per teacher. If adequate ratios can be realized through an effective policy of utilization, there would not be an actual shortage in the quantity of teachers. Table 4 includes findings for 14 courses in three different years. Calculation for the table was done as follows: The numbercxfclass sections by level in a particular year was multiplied by weekly class hours of each course as fixed in the curriculum. The products for each level were summed up for each field. The sum, as the produced weekly class hours for the field in the particular year, was divided by the number of existing qualified teachers in the field. The quotients are the calculated aggregate average weekly class hours per teacher for each field for the year. Ranges of aggregate average weekly class hours per teacher for the 14 different courses are 11.6-56.7, 6.0-50.4, and 11.2-105.1 in the 1962-1963, 1965-1966, and 1969-1970 school years, respectively. The first impression of these findings is that there is a large difference in the rate of supply among the 14 fields and the maximum limits of the ratios can hardly be realized even if a 71 TABLE 4--Produced Weekly Class Hours in General Secondary Public Schools and Aggregate Calculations for Average Weekly Class Hours per Teacher. (*) 1962-1963 1965-1966 1969-1970 Courses Class Hours/ Class Hours/ Class Hours/ Hears Teacher Hour Teacher Hours Teacher aces Turkish 8,618 23.8 9,795 27.1 20,953 35.3 Philosophy 2,981 20.4 3,636 24.6 6,625 33.0 History. 3,793 12.4 4,387 11.4 8,921 16.8 Geography 3,419 11.6 3,646 6.0 8,023 11.2 Mathematics 9,072 56.7 10,345 42.4 21,929, 41.5 Biology ’ 3,825 15.3 4,226 14.9 9,235 25.0 Physics 4,882 41.4 5,769 49.3 12,175 63.0 Chemistry 4,475 38.9 5,258 44.9 11,142 105.1 MIDDLE SCHOOL Social Sub. 56,584 30.1 83,429 23.5 145,645 26.5 Science 66,518 32.0 96,205 31.8 168,378 26.8 TOGETHER (**) Drawing 17,586 43.0 24,354 50.4 44,859 71.8 Phys. Ed. 7,665 22.3 10,171 25.5 19,194 46.0 Music 7,665 33.8 10,171 41.7 19,194 66.2 Foreign L. 26,171 25.5 34,098 25.5 64,974 35.2 (*) Data were obtained from: MOE, General Directorate for Secondary Education. (**)Inc1udes lycees and middle schools. 72 perfect policy of utilization were possible. Even more convincing evidence comes from applying a proper criterion for the upper limit of a realizable ratio. In Turkish practice there is no means but human power for teaching. The traditional design of the system requires this and the gap between demand and supply of qualified teachers is filled by lay and unqualified teach- ers. There are no actual data for the total aggregate average loads of teachers. Calculations in a previous study by this researcher estimated this figure to be 19.2 hours per teacher.67 Another available criterion is the formally estab- lished load of teachers. Minimum and maximum limits of compulsory load for an individual teacher are 18-24 hours and 15-21 hours in the first and second cycle of secondary schools, respectively. It is possible these limits may be realized by individual teachers at larger schools but not as an aggregate average, because many schools are not large enough for Optimum utilization of teachers. In spite of this fact, accepting the established load of teachers as an optimistic criterion, an evaluation was made as follows: Calculated ratios in Table 4 were compared with the established loads of teachers. The 14 courses included 67Kemalettin Akalin, A Simulation Model for Turkish Lycée Teachers, Michigan State University, East Lansing, July, 1971, p. 9. (Mimeographed.) 73 in the table fell in three regions: over, in, and below the range of established loads. The frequency distributions of this operation for each year are seen in Table 5. One may conclude that an extensive problem of inadequate supply of teachers of secondary school core subjects does in fact exist in the country. No recent mitigation may be observed. Instead, the problem has grown as the years passed. The actual situation is probably worse than portrayed in Table 5 because the base criterion is probably too high to be realized as the aggregate average throughout the country. Effects of the Sources of Teachers on the Existence of the Problem There are two main sources which train teachers, and one might wish to compare the effects of these sources on the existence of the problem. For this purpose, the relationships between the two sources of teachers and the existence of the shortage of teachers were roughly com- pared, as follows (see Table 6): Table 6 simply tallies frequencies from Table 4. Thus, for example, in Table 4, opposite the subject "physics," there are three entries for each of three previous school years. The ratios of weekly class hours per teacher for physics are listed in Table 4 as 41.4, 49.3, and 63.0, respectively, for the three years. Since each of these ratios is above the formally established TABLE 5--Frequency Distribution of Courses in Terms of Established Load of Teachers. 1962-63 1965-66 l969~70 OVER THE RANGE (Under-supply) Number of courses: 9 10 12 Percentage : 64.3 71. 85.7 IN THE RANGE (Optimal supply) Number of courses: 3 Percentage 21.3 7 7.1 BELOW THE RANGE (Over-supply) Number of courses: 2 Percentage : 14.3 21. 7.1 TOTAL Number of courses: 14 14 14 Percentage : 100.0 100. 100.0 Implications of the above table may be summarized, as follows: a. Most of the courses were under-supplied, with the prOportions increasing as the years passed. b. The prOportion of optimally supplied courses was small, and decreased as the years passed. c. There were a few continuously over-supplied courses. 75 TABLE 6--Frequency Distribution of Fields in Terms of Supply Rate Origins and Fields of Frequency of Frequency of Frequency of Teachers Under-Supply Optimum Sup. Over-Supply UNIVERSITY: Physics Chemistry Mathematics Turkish Philosophy wawuw I I Biology History ~ - Geography - - TOTAL 15 3 6 PERCENTAGE 62m5 12.5 25.0 EDUCATION INSTITUTE: Drawing 3 - - Music 3 - - Science Group 3 - - Social Group 2 1 - Physical Ed. 2 l - Foreign Lang. 3 - - TOTAL 16 2 O PERCENTAGE 88.8 11.2 0 76 range (15-21 hours at second cycle secondary schools), the subject of physics may be said to have been undersupplied with teachers in each of the three years. Hence in Table 6, the "Frequency of Under-Supply" for physics is entered as "3." And since physics teachers are supposed to be supplied by universities (i.e., by higher teacher training school students who study at universities), the tally of "3" for physics is listed among tallies for the university as a source of supply. The other tallies in Table 6 were derived in the same way. The eight "lycee" subjects from Table 4 were all considered for Table 6 to be in the "university domain," while the six "middle school" and "together" subjects in Table 4 were all listed in Table 6 under the "education institute domain." Courses Taught by Teachers Trained in Universities In this domain there are consistently undersupplied fields, such as physics, chemistry, and mathematics; and geography is a consistently over-supplied field. The fre- quency of optimally supplied courses is very small in this domain. Courses Taught by Teachers Trained in Education Institutes Under-supply has existed in all courses with varying frequencies, but no oversupply was observed. Four courses in six are consistently undersupplied courses. 77 In short, neither source of supply-~neither the universities nor the education institutes--appears to have been doing an adequate job of meeting the demand. Summary In the Turkish school system, academic, vocational, and technical schools at secondary and higher educational levels are separated from each other. Because of this practice, higher education of the individual is legally determined by the particular secondary school from which the individual is graduated. There are two groups of higher educational institutions--universities and higher schools. The former are autonomous and the latter either have academic autonomy or are entirely controlled by the Ministry of Education. Supply of teachers of secondary school core subjects has been a chronic problem in Turkey since the fifties. In spite of planned activities and requested measures in the national plans, no mitigation of the prob- lem has been observed. Among the fields taught in secondary schools, mathematics, physics, chemistry, Turkish, drawing, music, science group, and foreign languages are consistently under-supplied in the planned period, while geography is consistently over-supplied. There are two groups of institutions to train general secondary school teachers--universities and 78 education institutes. As suppliers of teachers, there is little or no difference between these two institutions-- both have been inadequate sources. Scientifically processed data for administration and planning were scarcely employed in the Turkish education system prior to 1960. However, in the planned period, the need for processed data was recognized. The responsi- bility for providing such data now belongs to the Planning, Research and Coordination Office (PAKD). Although there has been a struggle since the late sixties to establish a modern and scientific data processing and storing system, a practical solution to this problem has not been achieved yet. The next chapter presents an analysis of the causes of Turkey's teacher shortage. This analysis employs a "systems approach," and provides a more scientific basis for understanding the nature of the problem. In addition, it points to sorts of data needed in order to study the problem in detail. It is hoped that the following analysis will prove useful in both these ways: better scientific under- standing of the problem and better uses of data to study the problem. Moreover, it is hOped that the following "systems approach" may serve as a general example, showing how many other problems in Turkish education may be simi- larly tackled. CHAPTER IV IDENTIFICATION OF THE SYSTEM AND THE PROBLEM Merely to know the existence of a problem is not enough to cope effectively with it. An operational approach to solvingtflmaproblem requires one to scientifically identify the system and the problem along with their natures and environments. The aim of this chapter is to make these identifications with respect to the Turkish secondary school core subject teacher supply system. The chapter closes with discussion and conclusions concerning these identifications. Identification of the System In general, a system is a group of components which interact with one another to achieve a desired objective. Therefore a system can be defined in terms of its components, objectives, and interactions among components. An education system may consist of a small group of students, a class, a school, a group of schools, and so on up to the whole society. For any particular study, boundaries have to be chosen. In this study,tfluaboundary of the system will be defined in terms of the problem of secondary school core subject teacher supply. However, the entire system of 79 80 education of the society is illustrated in a simple form so that one can see the situation of the particular problem within the whole education system. Education System of Turkey Figure 6 is a simplified illustration of the Turkish public education system within the society at large as the universe. The system consists of educational administration including the Ministry of Education, all types and levels of schools subordinated to or controlled by the Ministry of Education, higher educational institu- tions which are independent of the Ministry of Education, and universities. According to Item 50 of the Constitu- tion, providing education for the people is one of the first responsibilities of the State. This responsibility is accomplished by the Ministry of Education on behalf of the State. Private schools are permitted at kindergarten, primary, and secondary levels, provided that they follow the patterns and standards established for the public schools. Private schools are controlled by the Ministry of Education. In Figure 6, the box for the Ministry of Education includes educational administrative units in the provinces and districts. The administration of schools is included in the box for schools which is represented by the letter S and includes all kinds and levels of schools controlled 81. FIGURE 6.--General Illustration for Turkish Education System Within the Society. __--_- -__"'_1 ..... A. 3 1 + I. 01 _ MINISTRY 11 L—+* or —°—> S 03 DAL. Is EDUCATION W 02 f F ., °s :— ...... 4 ..... 2.-———.2223::"°°S SCHOOLS A 3 A‘ I2 I3- 14 SYMBOLS FOR THE SYSTEM: A1: Manpower and information input to the MOE. A2: Manpower and information input to the university. A3: Manpower and information input to the schools controlled by the MOE. .A‘: Manpower and information input to the autonomous higher schools. As: Manpower stock of the society. D 1 Implementation decisions and policies of the MOE for education (includes money). F1: Information relationships between the MOE and the university. F2: Information relationships between the MOE and autonomous higher schools. 01: Flow of public school graduates to the university. 02: Flow of public school graduates to the autonomous higher schools. 03: Flow of outputs of public schools to the society's manpower stock. 0‘: Flow of outputs of the university to the society's manpower stock. 05: Flow of outputs of the autonomous higher schools to the society's manpower stock. 8 x All kinds and levels of schools controlled by the MOE. INPUTS TO THE SYSTEM FROM ITS ENVIRONMENT: 11: Money. 12: Law and legislative requirements (includes targets of development plans and policies of the government). 3: Demand of the society for education (includes public pressures). ‘: Professional requirements and pressures. Is: Feedback from the society at large. 16: Informal group pressures. 7: International affairs and effects. 8' Students enrolled in schools for the first time. H 82 by the Ministry of Education. For simplicity, a few schools which are under the control of other ministries are not separately represented in the figure. In terms of this study's purpose, to identify the problem of teacher supply, the existence of these other ministry schools do not significantly affect the situation. Other components of the system are universities and higher education institutions that are autonomous and independent of each other. Dotted lines between these schools and the Ministry of Education refer to informational connections. Inputs from the society to the system are repre- sented by eight arrows. Explanations of the arrows are provided below the figure. One of the eight arrows, 18, represents student input to anycnjmn:schools within the system. The flows of students among schools are repre- sented by the arrows O1 and 02. The capital sigma in the circle represents the pool of manpower at any given point in time. Varying fractions of manpower that are used by the components of the system are represented by arrows Al, A2, A3, and A4. Arrow A refers to the remaining 5 manpower in the society. The Organization for Core Subject Teacher Supply All entities which are directly related to the particular problem under consideration here must be included 83 in an analysis of the system of secondary school core subject teacher supply. The components of this system are: the General Directorate for Teacher Training Schools (control subsystem), teacher training schools, and the admission and training policy of the university, which is, as a whole, not in the teacher supply system but affects it through the admission and training policy for higher teacher training schools. In order to see the position of the General Direc- torate for Teacher Training Schools within the Ministry of Education, a simple organizational chart of the ministry is represented in Figure 7. As shown in the figure, various general directorates are subordinated to the Undersecretaries for General Educa- tion and for Vocational and Technical Education. These general directorates make implementing decisions for the several types of secondary schools. The duty of training elementary and secondary school core subject teachers belongs to the General Directorate for Teacher Training Schools. This implies that decisions which affect the need for teachers and decisions aimed at answering the need are made by separate officers which are legally independent of each other. Schools which are to train core subject teachers are represented by the box labeled "Teacher Training Schools" and are of two types: education institutes and higher 84 FIGURE 7.--Organization Chart: The Position of Organization for Training Core Subjects Teachers Within the MOE. (Rectangle B encloses the defined [Board of Education teacher supply system for core subjects.) . #_“ L. [MINISTRY OF EDUCATION] T ___‘ National Council of Education __‘- Undersecretary for General Education ___‘ ’ Undersecretary for Vocational and Technical Educatio [ General T Directorates A I l .L A I ‘ I I I I v I I General Directorates L A L l A l V D1 Tra Teacher ‘33 ining Universities] r"'-"r+-- '- P u b l i c S c h o o l S y s t e m EXPLANATIONS: A : Admission and : Core subjects : Decisions for B D D : Decisions for D : Decisions for 0 training policy of the universities. teacher supply system. general education. training teachers of core subjects. vocational and technical education. Product of teacher training schools for core subjects. (Trained teachers) T : General Directorate for Teacher Training Schools. (The control component of the teacher supply system.) 85 teacher training schools. The former are entirely under the control of the General Directorate for Teacher Training Schools, whereas the latter are also subject to control by the university through its admission and training policies. In order to provide a more complete analysis of this system, a logical block diagram is given in Figure 8. Secondary School Core Subject Teacher Supply System The secondary school core subject teacher supply system is included in the dotted rectangle in Figure 8. Although the two organizations--the Ministry of Education and the university--are essentially out of the defined system, they affect the system through their decisions, policies and implementations related to the need for training of teachers. The offices of the Ministry of Education other than the General Directorate for Teacher Training Schools affect the system in two ways, as follows: 1. Implementation decisions which include opening new schools, establishing curriculum, etc. These decisions are represented by B in Figure 8. The effects of these 1 decisions are included in the "need generator function" and the resultant of this function is represented in the figure by N, the need for core subject teachers. 2. Connection with the control component, the General Directorate for Teacher Training Schools. The 86 FIGURE 8.--Block Diagram for Need and Supply of Teachers of Secondary School Core Subjects. (Enclosed in the dashed-line rectangle is fhe system for supply of lonehers of secondary school core subjects.) H [—————J 1. 1 X] UNIVERSITY 1 F <4V—\ r"* B 1 A N 2 r..—- ——.—_‘ b—-Jp——- I I N": d1 I I 88. E ' I: E‘s 1" (:3 1".) J’. L a- . z I 2‘” 9 E E E 8 I h m C H x O c Q. a: In t. I" 9" I u a 3; D (I2 M -I H Inn.< I g g {I h 8 , 9308 ' “2 .1 EE := H 0 B I as" 0 d3 ctn N Z ; I U m 2' “I Ll Ea I I; L‘ '1“ I) 2 ’1: [.3 ‘4 C F) I‘ I.) QI U '_) h I IL‘ “I! | D. '1: 'v I ' (7 .‘I I I I I L_-_-__.._..-_ J Swims: A :Admission policy of the university. 1 A2:Traininq policy of the university. 81:1mplementation decision of the MOE {or secondary education. Bzzhdministrative and informational connections oetween offices of the HOP and the control component of the system. D :Control decision of lhc control component for training teachers. E :Feedback (Information). F :Need generator function. M :Demand of the society for secondary education. N :Number of needed teachers of secondary school core subjects. 01:Number of teachers trained in higher teacher training schools. OzzNumber of teachers trained in education institutes. 01:Number of teachers in the stock of private and other mInistrics' schools. OzzNumber of teachers who have left the profession in the previous year. R :Algebraic difference between numbers of needed and supplied teachers. 8 :Number of teachers employed by the public secondary school system. (Supplied teachers) T :Number of teachers hired by the public secondary school system {rem outside of the profession. y... T2:Number of secondary school teachers eligible to leach in teacher training schools. x1 X2:Number of students who apply in education institutes. gngnnsrsns FOR: :Number of students who apply to higher teacher training schools. a :student admission policy of the university. dlzcontrol decision for students to higher teacher training Schumlq, d :control decision for interactions in teacher training schools. (Includes funds, policies, training programs, regulations, etc.) d3zcontrol decision for students to eduCation Institutes. d4zcontrol decision for hiring teachers from secondary schools Io teacher training schools. p :percent of flow of higher teacher training school griduates to private and other ministries' schools. pzzpcrccnt of flow of higher icachcr trJInInq school graduates out of the profession. pzzpcrccnt of flow of educaIIon Inslltutc graduates lo prIyaIe and olhcl ministries’ schools. p4zpercent of [low of cducaIIon inulitule dradualrs out of the oroInwnIon. psrpercent of flow of higher Icachcr training Hrhnul quaduiios to puolnc schools. pail-(plip2) 4p‘) p6zpcrcent of flow of cdncalion Infilllule uraduatcn to puhllr wrhoois. p! l—(p 1 I 3 p72percent of flow of thnchvrn lo prIvaIv and olhvr MIHIGIrIvu' uchoolu. pflzpercent of flow of toachern ouI of tho profwanon. 87 connection arrow, B2, is the input to the control component and includes information in addition to what the component, as the part of the Ministry of Education, receives from the environments of the ministry (see Figure 6). As Figure 8 implies, the feedback information, which is a necessary component of a closed system, is transmitted to the control component by means of the offices of the Minis- try of Eflucation. Therefore, the expected function of the feedback in the secondary school core subject teacher supply system depends fundamentally on the effectiveness of the information transmission through arrow B2. The university affects the secondary school core subject teacher supply system in two ways also, as follows: 1. Admission policy which is presented by Al in Figure 8. Candidates selected for higher teacher training schools through the policy parameter of the control com- ponent, d take the university entrance examination 1’ which is represented by a. 2. Training policy which is represented by A2 in Figure 8. Those who pass the university entrance examina- tion are admitted as higher teacher training school students and trained at the university. Obviously, the production of higher teacher training schools, 0 in Figure 8, is controlled by the 1 university, which is autonomous and independent of the system under consideration. Therefore, in respect to 88 secondary school core subject teacher supply system, the number of higher teacher training school graduates, 01, is an uncontrolled variable. Control Component The control component of the system is the General Directorate for Teacher Training Schools. The control is practiced through implementation decisions that include regulations, priority decisions, administrative authority, established quota for students, etc. These implementation decisions are represented in the block diagram by D, i.e., the output of the control component. A part of D, namely d2, goes directly to the schools (the production component) as an input to them which includes established curriculum, regulations, administrative orders, funds, etc. Other parts of D are shown in the block diagram as parameters, as follows: d - decision parameter for selection of students for higher teacher training schools. Stu- dents are selected through either competitive examination or the school records. d : decision parameter for selection of students for education institutes. Students are selected by means of competitive examinations. d : decision parameter for assigning teachers from secondary schools to the faculties of teacher training schools. The Production Component The production component is composed of higher teacher training schools and education institutes. All 89 inputs to the production component, including regulations and curriculum, are controlled either by the control component or by the university. Therefore, the products of this component, i.e., trained teachers, are controlled outputs. These outputs are represented by O and O2 in l the block diagram. Production of the System Production of the system is trained teachers. In Figure 8, O and 0 represent numbers of teachers graduated l 2 from higher teacher training schools and education insti- tutes,respectively. In the real world, all of the teachers graduated from the schools do not go to teach at public schools. A fraction of them may go to teach at other ministries' or private schools. Another fraction may go into jobs other than teaching. Some may not work at all. This situation is discussed at more length below in the section on the pool of teachers. First, however, the fol- lowing mathematical expressions may be given for the outputs of teacher training schools: 01 = f(xl, A2,ea,D, T2, t) (l) 0w = 9(X2, D. T2, t) (2) 01: number of teachers graduated from higher teacher training schools, 02: number of teachers graduated from education institutes; a: parameter for admission policy of the uni- versity, 90 A : training policy of the university, D: implementation decisions made by the control component. (These decisions, which are related to each input, are represented by d's.) T2: number of secondary school teachers eligible to teach in teacher training schools, x : number of students who apply to higher 1 teacher training schools, x2: number of students who apply to education institutes, and t: time. Supply of Secondary School Core Subject Teachers, S At any point in time there is an existing pool of teachers. The magnitude of this pool is equivalent to the supply of teachers at that particular time. The pool is subject to change in the domain of time because of the continuous flow of trained teachersixux>and out of the pool (part-time teachers are not included in the pool). Variables forming the pool of secondary school core subject teachers are classified in four groups as follows: 1. Teachers Trained in Higher Teacher Training Schools All teachers graduated from higher teacher training schools do not go to teach in public schools. Some of them may go to teach in private and other ministries' schools and some go out of the profession. Therefore, teachers who and feed the where, TH TH: 91 graduate from higher teacher training schools pool can mathematically be written as follows: 1 p5 (3) quantity of teachers who go to teach in public schools after graduation from higher teacher training schools, quantity of teachers, graduated from higher teacher training schools as in Figure 8, percent of flow to public schools as in Figure 8. 2. Teachers Trained in Education Institutes As in the case of higher teacher training school graduates, a mathetmatical expression for the teachers who go to teach public schools after graduation from education institutes is as follows: where TE: (4) quantity of teachers who go to teach public schools after graduation from education institutes, quantity of teachers graduated from education institutes as in Figure 8, percent of flow to public schools as in Figure 8. 92 3. Teachers Assigned From Outside, Tl Some graduates from the university or other higher schools may also apply to teach at public secondary schools. Some of them may have teaching certificates from the uni- versity. They may try to enter the teaching profession for various reasons, such as lack of opportunity for employment in their field, a preference for teaching, a desire to be located near their family, etc. The present over-supply of geography and history teachers is a result of teaching assignments which were given to applicants graduated from universities simply to provide some form of employment for them. In addition, those who have left but later return to the pool of public school teachers are counted in this group. Such entrants into the teachers' pool are represented by T1 in the block diagram. T1' the number of teachers assigned from outside, is thus a con— trolled variable controlled by the Ministry of Education. 4. Teachers Who Leave the Pool of Teachers A portion of the pool of public secondary school teachers also tends to leave the profession for reasons that may be classified in three categories, as follows: (a) Teachers may be assigned to teach at teacher training schools. This is represented in Figure 8 by * T2 d4. 93 (b) Like teacher training school graduates, some pool teachers may leave public secondary schools to teach at private or other ministries' schools. The parameter for this flow is represented by p7 in the block diagram. (c) A proportion of teachers in the pool leave the profession for a variety of reasons such as marriage, retirement, death, resignation, finding another job, etc. The parameter for the loss to the profession is represented by p8 in the block diagram. Male teachers who are drafted and discharged by the army can be counted in p8 and T respectively. 1! The available pool of teachers, i.e., the quantity of teachers supplied to public secondary schools at a particular time, is represented by the arrow S in Figure 8 and its mathematical expression is as follows: S = h(Oll 02! T1! T2! p51 p61 p7! p8! t) (5) where S = quantity of supplied core subject teachers to public secondary schools, 01: quantity of teachers graduated from higher teacher training schools, 02: quantity of teachers graduated from education institutes, p5: parameter for the proportion of the flow of teachers to the pool of public secondary school teachers after graduation from higher teacher training schools, 94 p6: parameter for the proportion of the flow of teachers to the pool of public secondary school teachers after graduation from educa- tion institutes, p7: parameter for the proportion of teachers who leave the pool for teaching in private or in other ministries' schools, p8: parameter for the proportion of teachers who leave the profession for any other reason, t: time. Need for Core Subject Teachers, N Need for secondary school core subject teachers is essentially a function of demand of the society for second— ary education and the implementation decisions of the general directorates of the Ministry of Education. These decisions include all items necessary to Operate schools, including the opening of new schools. However, utiliza- tion of teachers, established curriculum, school buildings, and the rate of failure of students at schools are impor- tant variables to define the number of needed teachers. All of these variables are included in the "need generator function" in Figure 8. This function may mathematically be stated, as follows: N = n(Bl, M, r, l, c, b, t) (6) where N: number of needed general secondary school teachers, 95 l: implementation decisions of general directorates for secondary schools, M: demand of the society for secondary education (this demand is partly answered through the decisions for opening new schools), b: size of classes (defined by the curriculum and the space of classrooms), c: established curriculum for secondary schools, p... utilization rate of teachers, r: percentage of failure of secondary school stu- dents (the greater the percentage of failure, the larger the number of needed teachers), t: time. The Effect of Need and Supply of Teachers, R R is the algebraic difference between numbers of supplied and needed teachers, as follows: where R: algebraic difference between the actual numbers of supplied and needed general secondary school teachers in Figure 8, S: actual number of supplied teachers as in equa- tion (5), and N: actual number of needed teachers as in equa- tion (6). The interpretation of the algebraic value of R, which may be considered as an error signal, is as follows: 96 —, shortage of teachers R = O, optimum supply of teachers (8) +, surplus of teachers In Turkey, the value of R has been persistently large and negative for a number of years. The aim of the present analysis is to try to identify the exact nature of this crucial problem. Feedback, E Feedback is a necessary component of a closed system. As seen in Figure 8, it is the channel of informa- tion from schools to the offices of the Ministry of Education. Each school sends information related to demand and supply of teachers to the office to which it is subordinated. The concept of feedback implies that output information is transmitted back to the input so that pro- duction is modified. It required adequate channels of communication, i.e., any information from sender to the receiver is transmitted by the channel of feedback without being subject to any change. Information related to demand and supply of teachers is regularly sent to the Ministry of Education by each school in predetermined forms and at specified times. Since schools are vitally affected by the problem of a shortage of teachers, one expects school administrators to send correct data, allowing for the possibility of chance error, to their superior offices in the Ministry of 97 Education. Then any insufficiency between R and the control component may be ascribed to inadequate transmission of feedback information between the General Directorate for Teacher Training Schools (control component) and other offices of the Ministry of Education. Summary In the Turkish secondary school system, numbers of both needed and trained teachers are controlled variables. Because of the organization of the education system and of the central Ministry of Education, the control action related to the need and supply of teachers is carried out by various organizations that are independent of each other. For example: the production of education institutes is controlled by the General Directorate for Teacher Train- ing Schools (control component of the teacher supply system); the production of higher teacher training schools is controlled by the university; and the creation of need for secondary school core subject teachers is controlled by at least five general directorates of the Ministry of Education. In other words,'on the one hand the need for teachers is created by offices which legally do not assume responsibility for training teachers, and on the other hand teachers are trained by the control component and the university which do not assume legal responsibility for satisfying the society's aspiration for secondary education. 98 This practice implies that in terms of need and supply of general secondary school teachers, the system works as an uncontrolled system although it should work as a closed, i.e., a controlled, system. Nevertheless, the system may be made to work as a closed system, provided that effective communications are realized which extend the feedback between the control component of the secondary school teacher supply system and the above mentioned organizations. Identification of the Problem The inadequate supply of teachers for secondary school core subjects appears on the face of it to be a serious problem in the Turkish education system. The fact is, however, that is is really the effect of some other problems, rather than itself being the actual problem. An Operational approach to solve the teacher shortage problem requires defining the location and the nature of the more basic causal problems responsible for the existence of the teacher shortage problem. Theoretically speaking, the teacher shortage problem might be solved through practicing adequate con- trols over either the creation of need for teachers or the training of needed teachers, or both. In a democratic society, however, the need for teachers, i.e., demand of the society for education, is hardly controllable. 99 Nevertheless, as was explained in Chapter III, control of the creation of need for teachers had been practiced in Turkey until the early fifties through putting restrictions on opening new schools. Since then, this practice has been loosened by public pressure. Therefore, to try now to practice strict controls in order to keep needed and supplied teachers quantitatively in balance is out of the question in the Turkish society. As to the number of supplied teachers, it has without any question remained a strictly controlled vari- able in the Turkish school system. One may therefore conclude that the existence of the problem of inadequate teacher supply is basically the effect of inadequate con- trol over the teacher supply process, rather than over the creation of need. That is to say, the causal problems Should be sought where the control action for teacher supply takes place. Problem Area To define the location of the causal problems under COIlsideration, entities related to teacher supply are IE‘Iiewed in terms of control action, as follows: P00 1 of Teachers In Figure 8, the letter S represents the quantity 0f the pool (stock) of teachers employed by the public mfiiool system.at a particular time. The quantity of the 100 pool is subject to change because of the continuous flow of teachers into and out of the pool in the domain of time. All variables and parameters to define this change take place betweentflmaproduction component (teacher training schools) and the pool of teachers in Figure 8. Among all these variables and parameters, 01 and 02 (the productions of teacher training schools) and the quantity of teachers assigned to teacher training schools (through the control parameter d4) are controlled by the control component. Obviously, the pool of teachers is fed fundamentally by 01 and 02 which are the controlled products of the teacher supply system. Therefore, causal problems responsible for inadequate supply of teachers should be sought in the process of production. Process of Production AS seen in Figure 8, the process of production takes place between D, decision of the control component, and O1 and 02. Since responsibility for the control of the process belongs to the control component, one should discover whether the inadequate production is due to ineffec- tive decision or to some uncontrollable constraint causing the control action to be ineffective. If such exist, they should be inherent in (a) inputs, (b) interactions, or (c) time related to the process of training teachers. 101 Inputs.--Figure 8 implies that all inputs to teacher training schools are controlled by either the university or the control component. The control exercised by the university is uncontrollable by the control compo- nent and therefore should be counted as a functional constraint on the control exercised by the control component. The two inputs, A and d are related to interactions and 2 2’ will be discussed under that topic. However, money input, which is included in d is reviewed here among other 2’ inputs as follows: Money: Money input to teacher training schools is not separately presented in Figure 8. It is included in d2 because of the following reasons: 1. Money is allocated from the national budget via the Ministry of Education rather than directly to teacher training schools (see I in Figure 6). l 2. Money and any physical asset appropriated to a particular type of teacher training school by the budget law can be transferred to another type of teacher training school by the control component, namely, the General Directorate for Teacher Training Schools. Therefore, without any change in the amount of money, the amount of appropriated money to a particular type of teacher training school may be changed through decisions made by the control component. Such decisions, which can be called "priority 102 decisions," are included in d2 and, in turn, in D in Figure 8. , 3. There is a legal way to transfer money from other items of the budget for the Ministry of Education to the item for teacher training. Such a transfer can be practiced after a joint decision by related offices of the MOE. Therefore, even the amount of money input to teacher training schools can be changed through priority decisions, which are included in B2 in Figure 8. Consequently, money input to teacher training schools is not only a matter of resource but also a matter of decisions which are made by the control component and/or by the Ministry of Education at large. Therefore, taking the real world into consideration, the means for money input to teacher training schools can be represented by B2, D, and d2, respectively. All in all, money is well known for its scarcity throughout the world, including Turkey. Nevertheless, in terms of training teachers, the country has not experienced a serious money problem, at least after 1960. Instead, training needed teachers has been encouraged by legisla- tors and planners who have a voice in appropriation of money from the national budget. In addition, as was explained above, there is a way to appropriate more money to a particular training school than is defined in the budget law. 103 Figure 9 reveals the fact that increases or decreases of the quantity of students in higher teacher training schools and education institutes are not strictly tied to the amount of money appropriated from the national budget. In fact, decrease of money happens after the _decrease of the number of students. In 1968 and 1969, for example, in spite of increases in the amount of money appropriation for cash expenditures, the quantity of education institute and higher teacher training school students decreased. Since there already were enough equipment and student stations to train more teachers, decrease in the quantity of education institute students cannot be attributable to the scarcity of money. Conse- quently, resources of money should not be counted as a functional constraint on the quantity of trained teachers. Students: As was explained before, lycée graduates who can pass the university entrance examination, especially for colleges of scientific subjects, do not usually choose teaching as a profession because of the scarcity of student stations in colleges and because of better payment in other professions. To find students for higher teacher training schools, a fraction of normal school students passed to the final grade are selected to train under the lycée final grade program in the preparation class. Because of contracts with the Ministry of Education, the preparation 104 FIGURE 9--Increases in Funds and Quantity of Students of Education Institutes. (*) 0 u v v 1 r I .' w r ‘y 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 (*) Source: MOE, General Directorate for Teacher Training Schools. 105 class graduates take the university entrance examination as candidates for higher teacher training schools. Less than one-fifth of the potential candidates are selected for the preparation class. Even if all students who pass to the final grade in normal schools were prepared under the lycée final grade program, a sig- nificant raise in the number of higher teacher training school students in needed fields would hardly be realized because of the competition for' preestablished (mustas of students for colleges. The competition among applicants to the university is extrmely high, such that, in recent years, only one-eighth of them have been admitted.68 For scientific subject colleges, the fraction is doubtless even less than that. In summary, inadequacy in the quantity of higher teacher training school students in needed fields is due to control actions practiced by the control component of the system and of the university (dl and Al, respectively, in Figure 8), rather than a scarcity in the source of potential students (X1 in Figure 8). One may conclude, therefore, that the admission policy of the university does constrain the control action of the control component. As to the student input to education institutes, it is strictly controlled by the control component. As an average over the last five years, only six percent of the ¥ 8Source: PAKD. 106 applicants were admitted to education institutes by means of competitive examination.69 Each year, the number of new students is decided by the control component on the basis of policy for training teachers (d3 in Figure 8). Therefore, the source of potential students to education institutes (X2 in Figure 8) is not scarce and, in turn, does not constrain control. Teachers of teachers: Teachers are assigned to teacher training schools by the control component from secondary schools. Every teacher assigned to teacher train- ing schools is a loss to the supply for public secondary schools. Therefore the decision to assign teachers to teacher training schools is a priority decision (see d4 in Figure 8). A governing rule of economics is that alloca- tion for production should be given higher priority than allocation for consumption, if there is no other choice and more production is required. There should not be a functional constraint on decisions for hiring needed teachers to teacher training schools. Interactions.--Interactions in the process of training teachers take place in the teacher training schools, which make up the production component of the system. Interactions are regulated by the training policy of the 69 Schools. Source: General Directorate for Teacher Training 107 university and by the control component (by means of A2 and d2, respectively, in Figure 8). A2 includes training programs and methods of the disciplines in which higher teacher training schoool students are trained. As to d2, it includes: money, school regulations, all administra- tive decisions and orders, professional training programs for both higher teacher training schools and education institutes, and the entire training program for education institutes. Therefore, interactions in higher teacher training schools are controlled partly by the university and partly by the control component. Interactions in educa- tion institutes, however, are entirely controlled solely by the control component. Consequently, control action of the control compo- nent for interactions in higher teacher training schools is constrained by the university, but for education insti— tutes it is unconstrained. Time.--Time is naturally an uncontrollable variable and the flux of time cannot be manipulated. Usage of time, however, is controllable, and because of that the size of a particular job and/or the magnitude of a specified production within a given period of time can be varied by manipulating related controllable variables and conditions Of interactions. That is to say, there should be a best Combination of inputs and conditions of interactions for 108 an optimum rate of a specified output within a given period of time. In many cases, however, delay time (the period of time required to yield a specified production) is inde- pendent of the magnitude of inputs and outputs. Institutional education is an example. For each type and level of schools, regardless of the quantity of students and teachers, there is a definite period of time (delay time) to accomplish the training program, designed for that school. In a plan to yield more production than the school currently produces, the time delay should be taken into consideration as a functional constraint. Obviously, to construct new school buildings and to train new teachers in order to increase the rate of output also will require additional periods of time before an increase in output will be achieved. If a future need for more output of a particular school is unpredictable, then necessary measures for satisfying that need can be put into effect only after the existence of the need has become manifest. In such a case, the delay time for additional output is a func- tional constraint on the measures and should be accounted for in making decisions to satisfy the need. If the need can be predicted and estimated to some degree sufficiently LDrior to its emergence, one can put necessary measures into 109 effect in advance to satisfy the need on time. In this case, regardless of whether the necessary measures are put into effect on time or not, one should not consider the delay time as a constraint. That is to say, whether utilized or not, if there exists a possibility of yielding more production to be needed in the future, the delay time required for the production should not be counted as a constraint on answering the need. Now, taking the above explanations into considera- tion, one can conclude that time has not been a functional constraint on control actions for training more teachers of secondary school core subjects, for the following reasons: The problem of a shortage of teachers has existed since the early fifties. Especially after 1960, the trend of the need and required measures to satisfy the need have been put forth through the ten-year plan and the develop- ment plans. There has been enough time if not to solve, then at least to mitigate the problem. In summary, training teachers in higher teacher training schools has been constrained by the admission and training policy of the university. Therefore a part of the causal problem stands with the university. Neverthe- less, one cannot see any functional constraint on the control action of the control component for the process of training teachers in education institutes. Therefore, 110 decisions of the control component (D in Figure 8) seem to be chiefly responsible for the inadequate quantity of teachers for core subjects trained in education institutes. After this conclusion and in order to discover the causal problems responsible for ineffectiveness of the control decisions, one should make an investigation into the entire process of making decisions to control teacher training. Such an investigation requires a review of all the entities which may affect the control decisions. These mentioned entities may enter the process at any point in Figure 8 from the control component through to the extreme left of the figure, i.e., within the Ministry of Education at large. Decisions which control teacher training (D in Figure 8) are the outputs of the control component. This output is the product of the input B2 which is subject to interactions within the control component in the time domain. Therefore, causal problems responsible for the ineffectiveness of the control decision D may be due to the input, or to interactions, or to time under considera- tion. The time domain in the Turkish instance includes more than a score of years throughout which control deci- sions have been ineffective. Since control decisions are sgenerally made on a yearly basis, the decisions are not (Zonstrained by time. In other words, throughout more than 111 twenty years, one has had opportunities to make effective decisions if inputs and interactions are sufficient to do so. That is to say, the ineffectiveness of the control decisions should be due to input and/or interactions rather than to time. Input B2 is a complex of variables which can be classified in three categories, two of which are as follows: (a) All inputs including funds, related to train- ing teachers of elementary schools and secondary school core subjects received from the society by the control component via the Ministry of Education (see Figure 6). (b) All other information bearing on the scope of responsibility of the control component which reaches the control component indirectly. The first two inputs above do not include pressure aimed at limiting the quantity of trained teachers for secondary school core subjects. On the contrary, they represent pressures to train more teachers. The demand for more teachers has been encouraged and requested con- sistently by both the environment and the superior offices of the MOE. Funds are scarce inputs but, as was explained before, the problem has been inadequate decisions on how to use them, rather than inadequate resources. One may conclude that inputs included in the above first two items are not responsible for ineffectiveness of decisions which regulate teacher training. 112 As to the third category, it includes information received by the control component from other offices of the Ministry of Education excluding the superiors who are overall policymakers. This third sort of information may be classified in two sub-categories, as follows: Feedback information: As was explained before, feedback is a necessary component for a closed system. The system supplying teachers of secondary school core subjects is a closed system, for which, therefore, feed- back is vitally important. Theoretically, the concept of feedback implies a sufficient. channel <1f information within the system. In the real world, however, the feedback (E in Figure 8) is established via a multiplicity of channels between schools and various offices in the Ministry of Education at large, rather than directly with the control component. The reasons for this is that each school sends information related to need and supply of teachers to its particular superior general directorate, not to the General Director- ate for Teacher Training Schools. This practice in the real world may create a problem if the information received from subordinated schools is not sufficiently transmitted by the general directorate to the control component. Then the system for supply of teachers of secondary school core subjects fails to function as a closed system, and decisions 113 for controlling teacher training are made in uncertainty. This practice can be counted as one of the causal problems under investigation here. Activity information: This includes any decision made by general directorates which indirectly entails creating additional needs for teachers of core subjects, such as decisions to open new schools or to extend exist- ing schools (represented by B1 in Figure 8). In the real world, each general directorate makes its own decision-- which may create additional needs for teachers--without consulting with the General Directorate for Teacher Training Schools. If the control component is not informed in time about decisions, its control decisions are made under uncertain conditions. Such conditions may, again, cause the control decisions to be ineffective. In short, there is a possibility that input B2 can be a location of causal problems responsible for the ineffectiveness of control decisions. Interactions in the control component.—-As for the interactions which produce the control decisions through using the inputs labeled B2, they are arranged and con— ducted by the control component. It appears evident that these interactions over the past twenty years have not been sufficient, perhaps because of the following reasons: 114 First of all, if B2 should not include sufficient information to make effective control decisions, it would be the task of the control component to ask for more information needed to make effective decisions. There can be no excuse for trying to accomplish the responsi- bility of supplying teachers for the entire school system of the society wihtout having had sufficient information for more than a score of years. But it appears that the control component was not deprived of information needed to make effective decisions. The aforementioned Ten Year Plan, which was prepared by the control component, and the five year development plans, which had the force of law, included necessary basic information along with requests to train needed teachers. One might even suppose that these plans may have been ignored in the making of control decisions to train teachers of core subjects. Consequently, another location of the causal problems responsible for ineffective decisions may be in the control component and the interactions which occur there, between it and the B2 inputs it receives. Basic Characteristics of the Problem The preceeding analysis reveals possible locations of causal problems responsible for the existence of the current teacher shortage problem in the Turkish secondary 115 school system. The problem is generated at points where measures might be designated for solving the problem. The analysis may begin to suggest why the problem has been growing without mitigation for more than twenty years. A systems approach elucidates relationships which otherwise might never be understood and locates specific points of causation which might otherwise remain hidden behind the glaringly apparent surface problem. After defining its locations, one needs to specify further the characteristics of the problem in order to facilitate an operational approach to tackling the problem. We have seen that there are two basic inadequacies in the teacher training system: (a) structural inadequacies which allow uncontrolled components to operate within what should be a closed system, and (b) inadequacies in decision making for teacher training. Since these decisions are outputs which combine input 82 and interactions in the control component, the inadequacy of decisions may be due either to the input or to the interactions, or to a combina- tion of both. If the inadequacy is due to input B2, one may attribute it to inadequate administrative organization of the MOE at large. As was explained before, 82 includes feedback and activity information which may not be ade- quately transmitted to the control component, thus causing its decisions to be inadequate. 116 If the inadequacy is due to interactions in the control component, one may count it as inadequate man- agement in the control component. Here the term management is used, rather than administration, because the task of the control component can better be defined by the term management which implies: ". . . the decision making, planning, and implementing that must underlie effective utilization of manpower, money, materials, facilities, information, knowledge, and time which constitute the pro- ductive resources. . . ."70 Probably the causal problems should be counted as both inadequate administrative organization of the MOE and ineffective management in the control component. The control component should find a way of getting needed information if it assumes the responsibility for answering Turkey's need for teachers, and indeed the Ten Year Plan and the five year development plans included such informa- tion. At the same time superior offices and other offices in the MOE should find an effective way of communicating feedback and activity information to the control component. Consequently, an operational approach to solve the teacher shortage problem would seem to include solu- tion of problems related to (a) administrative organization 70James L. Pierce, "The Planning and Control Con- Cept," in Administrative Control and Executive Action, ed. by B. C. Lemke and J. D. Edwards (Columbus: Charles E. Merrill Books, Inc., 1961), p. 8. 117 of the MOE, (b) management in the offices of the control component, and (c) the structure of the teacher supply system. Summary Shortage of teachers of core subjects in the Turkish secondary school system is an effect resulting from certain causal problems. The quantity of the supplied teachers is drastically less than the quantity of needed teachers. The quantity of needed teachers is increasing constantly and is the inevitable result of Turkey's grow- ing population and the rising aspirations of its society. The teacher shortage problem is therefore fundamentally a teacher supply problem. There is no free market of teachers, and the Constitution assigns the task of supply- ing needed teachers to the Ministry of Education in Turkey. In the final analysis the teacher shortage problem is fundamentally a teacher training problem--that is, a production problem. In order to meet a defined need, there are two fundamental problems to be solved in the process of pro- duction--resources, and the utilization of resources. Analysis of Turkey's teacher shortage problem reveals that limitations on resources to train needed teachers (namely, students, funds, teachers of teachers, and time) have not created unsolvable problems, but the utilization 118 of the resources (decision making, planning, and imple— menting) has been inadequate throughout the last twenty years. Inadequacies in utilization of resources may be traced to three "locations" in the teacher supply system: inadequate coordination and control between MOE policies and the policies of the university regarding teacher training, inadequate organization of the Ministry of Education for supplying inputs to the control component, and inadequate management in the control component of the teacher supply system. These three may be counted as causal problems. It appears, however, that the problem is generated at points where measures to cope with it can and should be designated. Discussions and Conclusions The preceding analysis implies that an operational approach to solve many problems in the Turkish education system necessitates c0ping first with certain basic admin- istrative problems in the Ministry of Education. Analysis of these administrative problems and their effects on the education system are beyond the scope of this study. Nevertheless, a brief characterization of administration in the Ministry of Education may help the reader to under’ stand the paradoxical dilemma of the inadequate teacher supply. 119 Ministry of Education and Problems TheorEtically, every organization strives to ful- fill its objectives, but the Ministry of Education evidently fails in many ways to fulfill its objectives. Blame is usually placed on the inadequacy in organization. Indi- vidual authorities thus tend to feel free from personal responsibility for the failures. Nevertheless, in spite of many studies and recommendations, no basic reorganiza- tion of educational adminsitration has been put into effect overtimepast twenty years. The central Ministry Of Educa- tion suffers from the characteristics of the innovation- resisting organization, as stated in the following quotation: An organization is itself an innovation, but most organizations of the past have been designed to be innovation-resisting. . . . To ensure reli- able repetition Of prescribed Operations, the organization requires strong defenses against inno- vation. Efforts to innovate must be relegated to the categories of error, irresponsibility and insubordination, and appropriate corrective action taken to bring the would be innovators "back in line." Any change is likely to run counter to cer- tain vested interests, and to violate certain territorial rights. Sentiments of vested interest and territorial rights are sanctified as delega- tions of legitimate authority in traditional organizations, thus guaranteeing quick and effective counteraction against disturbance. In theory, the innovation-resisting organization is not resistant to innovations issuing from the top Of its authority structure. 71Herbert A. Shephard, "Innovation-Resisting and Innovation-Producing Organizations," as quotedeINewton Margulies and Anthony P. Raia, Organizational DevelOpment Values, Processes and Technology (New York: Mc—Graw Hill Book Company, 1972), p. 50. 120 In addition, the Ministry of Education operations are often characterized by their extremely personalized character of administration, such that the personality of the individual Often is not differentiated from the posi— tion within the organization. Institutional authority is erroneously equated withtflmapower of the individual. The absence of job descriptions and objective criteria for selection of individuals to administrative positions encourages and facilitates staffing the organization on the basis of personal preferences Of the authorities. Under these circumstances, administrative activities tend to be governed by highly personalized concepts. Different admin— istrators may or may not be seriously careful about organizational Objectives. They may have highly indi— vidualized perceptions Of their roles. Arising perhaps mostly from an element Of uncer- tainty, a particular emotional climate is usually associated with such personalized administration. Accordingly, rela- tionships among individuals and groups are often disrupted by unpredictable complications of misunderstanding, unnecessary competition, jealousy, under—handed tricks, etc. Instead of fostering scientific thinking, creativity, initiative, and the taking of responsibility, the climate encourages sheer Obedience as the secure way of work performance. This situation is mentioned also by 121 Dr. Ziya Bursalioglu, in his article devoted to the question of reorganization of educational administration.72 In addition, the more recent book by Edwin J. Cohn73 sheds light on educational and administrative problems of concern here. These observations may help one to under- stand why the administration Of the MOE seems to be so overly occupied with daily routine, at the price Of ignoring planned activities, scientific studies, and follow-up implementations. In general, personalized administration cannot tolerate rigorous, Objective programs which are oriented toward the long range unless higher authorities insist on it and follow up by controlling the organization. Moreover, unscientific attacks on existing problems only serve tO generate new additional problems through more inadequate or improper decisions. All in all, the Ministry of Education stands in a state Of inertia, while by con- trast educational problems are spreading in a state of restless expansion, arising from unmet demands of the changing society. The result is extensive and chronic prob- lems. This is the dilemma to be overcome. 72Ziya Bursalioglu, "The Need for Reorganization in Turkish Educational System," in The Turkish Administrator, a Cultural Survey, ed. by Jerry R. Happer and Richard I. Lewin (Ankara: Public Administration Division, USAID, 1968), pp. 265-84. 73 Edwin J. Cohn, Turkish Economic, Social and Political Change--The Development of a More Prosperous Open Society (New York: Praeger Publishers, 1970). 122 In brief, the assumption of this researcher is that an Operational approach to secure an effective solution of the problems currently confronting the society's educational development will necessitate coping first with the person- alized character of administration. The following two examples may serve to justify this assumption. They indi- cate how administrative shortcomings apply to teacher production problems (1) in higher teacher training schools, and (2) in education institutes. Higher Teacher Training Schools As was explained before, higher teacher training schools are subject to the general policy for admission and training of the university, but the university does not assume responsibility for the supply of teachers. There— fore the quantity and quality of teachers trained in these SChcxals are out of the control Of the control component, WhiCfli is responsible for the supply of teachers. The results of this dualism may be summarized, as f0110ws: (a) Because Of limited quotas for faculties Of scierltific disciplines, lycée graduates who pass the uni— verSCLtyentrance examinations do not usually choose teaching as a profession. (b) Candidates for teaching who nevertheless trairl at the university under the same programs as do 123 candidates for other professions, especially in scientific fields, often leave the teaching profession for better paying jobs. As an approach for solution of the problem, as was explained before, normal school students have been trained under the lycée program in the preparation class since the 1959-1960 school year. Since 1959, greater numbers of students have been able to go into teacher training through the higher teacher training schools by means of the change in policy and practice already mentioned above. Since that date normal school graduates also have been admitted, first to one-year "preparation" classes, and then they have been allowed also to follow the same training pro- grams as the regular lycée graduates. This approach may have been successful in the short run but it could not continue to succeed in the long run. Because of increasing requirements of competency, to put the needed number of students under needed programs became each year more difficult than before. Moreover, the problem of retraining trained teachers in the profes- sion continues to exist. For example, the number of chemistry teachers in lycées was 115 in 1962-63 and 140 in 1971-72, whereas the respective numbers of teachers needed were approximately 220 and 700. Clearly the approaches taken are incompatible with the characteristics of the problem. From a systems point 124 of View, the problem has until now been dealt with as a regional constraint (i.e., a scarcity of the student resource), although in fact it is a functional constraint (i.e., a function of the organizational structure of the system). In other words, while the legal responsibility for the supply Of teachers belongs to the MOE, at the same time the supply is subject to the admission and training policy of the autonomous university which does not assume responsibility for the supply of teachers. An Operational approach to solving the problem should include a change of structure in the system so that at least the following two conditions are realized: a. Student stations in higher teacher training schools should be controlled by the component which is responsible for the supply of teachers. b. There should not be a large number of teachers in needed fields who leave the profession for other jobs. There may be several ways to realize the above- mentioned two conditions. One may expect, however, that the basic problem with respect tO higher teacher training schools will remain unsolved as long as the structure Of the system remains as it is. Education Institutes Education institutes are wholly controlled by the MOE. Nevertheless, an inadequate supply of teachers from education institutes has been a growing problem since the 125 fifties. The persistence of the problem might lead one to suspect the presence of an unassailable functional con- straint, preventing the administration from effectively coping with the problem. Our analysis above concluded, however, that the problem is due to inadequate resource utilization. That is to say, the functional constraint itself resides in tflmn: self-same administration which is responsible for solving the problem. Figure 10 indicates that the quantity of trained teachers has lagged far behind the targets of the plans. Indeed, the need for thousands Of new teachers is self- evident in the schools. The slope Of the curve for trained teachers (for realization) has declined since 1967-68. The estimated number of teachers needed for the four years following 1967-68 was 18,800 in the Five Year Plan and 17,548 in the Ten Year Plan. The number of teachers trained in the same period, however, was 6,596. In the preceding four years, 10,251 had been trained (see Table 1, page 57). In 1967-68 the number of education institute students was reduced by about one thousand, even though all resources necessary to admit more students were then available and a shortage of teachers was then creating a bottleneck in the secondary school system. Moreover, the second Five Year Development Plan had called for an enroll- ment of 10,100 in education institutes for the 1968-69 126 FIGURE 10--Estimated Need for Education Institute Graduated Teachers and Realization.(*) 40,000‘ t;- ’0 N Q, 35,000. a a? .5, OJ A 4‘ "" 30,000« 0 ‘~ 25,000-1 20,0001 15.000‘ 10,000. 5,000# o.N é» . . . . . e e . a ‘5’ ‘5’ §$$§$$$$$$ r-I N m V In \D 1‘ GO ON O H N (*) Sources: a. Tables 1 and 2, b. Milli Egitim Bakanligi, Ogretmen Yetistirme Komitesi Raporu ve On Yillik Plan, (National Ministry of Education, Report of Teacher Preparation Committee and the Ten Yer Plan), Istanbul, 1961. 127 school year. The actual decrease in the number of education institute students in 1967-68 is nevertheless understandable. This decrease in the quantity of trained teachers after 1967-68 seems to have resulted from two measures which were put into effect in the 1967-68 school year: 1. In 1966-67 it was decided to divide each of the two main branches of training (humanities and sciences) into four branches (humanities into "Turkish" and "social sub- jects," and sciences into "mathematics" and "sciences"). 2. In addition, the training period for these branches was raised in 1967-68 from two to three years. These two measures, which were ostensibly aimed at improving the quality of training, had adverse effects, not only on the quantity but also on the possible utilization Of trained teachers, as follows: (a) To divide two training branches into four means that four teachers instead of two should be assigned to each school. But in the real world the number of small secondary schools in Turkey with fewer than 200 students has until now always been more than one-third Of the whole number of schools. Hence the capacity of schools to utilize teachers in the additional fields was seriously affected adversely by the above mentioned measure. In effect, the needed number of qualified teachers was indirectly expanded drastically. 128 (b) To extend a period of training from two to three years obviously requires fifty percent more resources, such as funds, school facilities, teachers of teachers, and time. A three—year program produces fifty percent fewer teachers to be trained through using the same available resources. This is another reason for the decline of the slope for trained teachers after 1967-68. In other words, using the same available resources, the new subdivided three-year training program reduced the quantity of trained teachers by up to one-third in compari- son with the previous two—year program. The adoption of the above measures is a good example of how important decisions may be made without a sound understanding of systems implications. The drastic impact of these measures on the Turkish system can be tabulated in terms of fields and training periods as follows: In 1946-47, there were five separate branches of training in the education institutes--Turkish, social subjects (history and geography), mathematics, physical sciences (physics and chemistry), and biology. Since that date these branches have been subject to varying combina- tions and subdividings. The effects of these combinings amd re-combinings, in terms Of resource utilization, may be calculated in man-years. For instance, if training is divided into five fields as above and the training period 129 is two years, then five teachers have to be trained in two years, and the result is 10 man—years, i.e., the product of five and two. If these five subjects are combined into two branches and the training period is again two years, the product is four man-years. Using this procedure, changes in the Turkish system relating to the combinations of the above five fields and to the training periods involved may be summarized since 1946-47 as shown in Table 7. Notice that in two years, between 1966—67 and 1968-59, the man-year requirements for training a teacher in each required branch jumped from 4 to 12. Meanwhile, the actual shortage Of teachers was a serious bOttleneck in the education system. TABLE 7.--Various Combinations Of Training Branches in Education Institutes. NO. of Years Of Man-Years School Year Training Required (Branches Branches Training times years) 1946—47 5 2 10 1949—50 1 2 2 1966-67 2 2 4 1967-68 4 2 8 1968—69* 4 3 12 *Continuing to the present. 130 Of course, measures aimed at improving the quality of teachers should not be opposed, provided that necessary protections against their negative effects on the supply may also be designated and put into effect. There is a need for finding scientific ways Of maintaining balance between the quantity and the quality of teachers on the basis of the country's need. One should not sacrifice either quantity or quality to the extent that the system as a whole ceases to function effectively. Summary Analysis of the problem indicates that the teacher shortage in the Turkish secondary school system is the result Of inadequate resource utilization rather than resource scarcity. The causal problem is fundamentally an administrative problem. An Operational approach requires first of all that the administrative problems be solved. Subsequent measures for solvingtflmaproblem should facilitate fulfillment of the following requirements: (a) An effective control in terms of systems concepts over the teacher training process. (b) A realistic plan, including assessment of the quantity of needed teachers in each field, requirements of the profession, and curriculum to train teachers on the basis of the society's needs and of the characteristics Of the schools. 131 (c) Appropriate conditions to retain trained teachers in the profession. CHAPTER V MATHEMATICAL MODEL FOR TURKISH SECONDARY SCHOOL SYSTEM The main purpose Of this chapter is to present a mathematical model to identify the state of the system at a particular time in terms of demand and supply of second- ary school teachers. Obviously, to develop a descriptive model would be in vain unless its outcomes are utilized in planning for solution oftfimaproblem under concern. That means to say, the descriptive model presented here is developed to show what kinds of analyses need to be made in order to provide accurate information to be used in planning for solution Of the problem. With accurate data in hand adequately analyzed, the planner would then require a corresponding simulation model to search for best solu— tions. Developing a simulation model for planning was not covered by the objectives in this study. However, in order simply to demonstrate what needs to be included in a complete set of systems procedures applicable to solution of an educational problem, an abridged version of a 132 133 previously prepared simulation model is presented at the outset of this chapter. Therefore, this chapter consists of two parts. Included in the first part is the above mentioned abbrevi- ated illustrative simulation model with its outcomes. It is presented simply to show that simulation can lead to optimum solutions. The descriptive model is the chief contribution of this chapter, as required by the second objective of this study. It is presented in the second part. Results of a pilot application of the descriptive model to the province of Eskisehir are reported in the next chapter. PART 1 SIMULATION’MODEL FOR TURKISH LYCEE TEACHERS The Origin of the Model The aggregate simulation model presented in this part was originally prepared by the present researcher at Michigan State University in July, 1971. Available data were inadequate to establish needed parameters and variables for running the model through the MSU computer, so parameters and initial variables were either obtained from what data were available or were established on the basis of educated assumption and guesses. 134 Therefore, at least some of the simulated values might, most probably, not be precisely accurate approxima- tions of the future behavior of the system. Nevertheless, the relative relationships which are discovered among the variables do appear generally to reflect interrelationships in the real world. The model was develOped to experiment with alterna- tives for planning the supply of Turkish lycée mathematics, physics, cheimistry, and biology teachers. Two basic alternatives were chosen: "present system" and "desired system." To these alternatives, two further alternatives in each case were included--thus making a total Of four alternatives in all, as follows: 1. Present system a. Supply of teachers with regular training, and b. Supply of teachers with regular and inservice training. 2. Desired system a. Supply of teachers with regular training, and b. Supply of teachers with regular and inservice training. In terms of the best alternative, i.e., desired system with inservice training, the problem would be solved in twenty years. The logical block diagram for the model is intro— duced in Figure 11. "GU" unblock Diagram for tho Lycoo and It. Teachers in Turkey. (student Flow, Touche: demand and supply, and Coat) Produced 'class hours I Demmd / for teacher Certlfled F humanities tea as —-—-— ° S’ Supply cl humanllles teacher! Investmerlt cost + z Shortage ll ‘ r—9 96 * E {I I! " 2 -g V ‘ ° 0 Current cos! ‘ ' 3.8. ¢ * £9 Teachers' salary Id . , X R E1 . z - Z a Z - ’ z - O 0 4 + 4 x x In t Tn 173 F n), z z 1.", = n 2 9 e - ~ - - drop d drop rap 1: IL EITHER E1:1,E2=O 0R E1=0,E2=1 136 Explanations for Parameters and Abbreviations in Figure 11 A8,BB: Parameters for student distribution from grade 1 to grade 2 literature and science divisions respectively in lycée. C1: Unit cost per student in lycée. C2: Average salary of lycée teachers. C3: Unit cost per teacher in-service training. C4: Unit cost per student in teacher training school. CS: Unit building and equipment cost per lycée student. C6: Unit cost of training humanities teacher. C7: Unit cost of building and equipment per student in teacher training school. D1: Amortization rate of school building and equipment. D2: Amortization rate of expenditures on training teachers. E1,E2: Regulators for inputs to teacher training schools in present and desired systems. 1: Function to calculate student input to lycée. F F : Function to calculate supplied humanities and science teachers. F3,F4: Functions to calculate student inputs to teacher training schools in desired and present systems respectively. F :‘Function to calculate teachers as input to in- ‘service training. H: Realized average teaching load of teachers. INLl: Student input to lycée. ININTl: Input to in-service teacher training. INT1,INT2: Correspond to the first and second year programs for in-service teacher training respectively. K1,R2,K3,K4,K5: Parameters for converting number of students into number of produced class hours by grades and by subjects. Ll: First grade of lycée. L2A,L3A: Second and third grades of lycée under the literature programs. LZS,L3S: Second and third grades of lycée under the science programs. R1,R2: Percentages of leave of the profession for any reason. TT1,TT2,TT3,TT4: Correspond to the grades of teacher training schools. X1: Number of potential students eligible to attend to lycée. x2,x3: Numbers of students who apply to desired and present teacher training schools respectively. x4: Teachers who apply to in-service training. 137 The model is presented here avoiding details and as three submodels, such as: (1) student, (2) teacher, and (3) cost. Throughout this part, indices are used without any change in identity, as follows: n = l, 2, 3, . . ., 20 (corresponding to the number of years) k = l, 2, 3, 4, 5 (corresponding to the number of grades with area) i = l, 2, 3, . . ., 16 (corresponding to the number of subject matters) Objective (or Criterion) Function U = U(xl, x2, . . ., Xr) (9) where U denotes the supply of teachers meeting demand and being subject to the constraints. Student Submodel Assumption 1: Increase in the number of lycée students will take place in such a pattern that about one-half of the age group will be in school after twenty years. Assumption 2: The rate of student flow in lycée is directly related to the percentage of supply of qualified teachers. (However, the rate Of student flow is not over 90 percent even if the supply of teachers is one hundred percent.) Constraint 1: In the Turkish school system, a one hundred percent student flow can hardly be achieved. Dropouts and the large pool of repeating students constitute a heavy constraint on the enterprise. 138 1 i R i L (10) where R1: student flow ratio, 1 : minimum student flow ratio, and L : maximum student flow ratio. Student Input to Lycée (11) where I : number of newly enrolled students to the first grade, and A: the ratio in increase. .l9-T/100 if 0 i T i 13 .06 if T > 13 Student Flow (Intermediate Inputs and Outputs * yk = B xk (12) n n * Dk = c xk (13) n Fk = Yk + Dk (14) n n n * .— Ik = B xk 1 if k > 1 (15) n n-l 139 k_l. _ In — In If k — l (16) k_k k k Xn — Xn-l Fn-l + Inn (17) where Y: number of students passed the grade, B: ratio for the pass, X: number of students enrolled in the grade, D: number of dropouts, C: ratio for droptouts, F: number of students flowed out of the grade, and I: number of students enrolled in the grade. : _. ‘k ‘k 'k C Rl(l Rl c) b c = 'k _ B b R1 0 where R1: percentage Of supply of teachers as explained in Constraint 1, b and c: parameters for differences in flow rates among grades. Teacher Submodel The teacher submodel consists Of two sections: demand and supply. Demand 140 Aggregate estimation for demanded teacher is calculated by dividing produced class hours by the average load of teachers. where Assumption 3: In the "present system," calculated average teaching load (19.2 hours per week) remains as it is. In the "desired system," however, the policy of utilization of teachers will be improved such that the load will be increased by 0.15 hours each year (3.0 hours after 20 years). Constraint 2: Smallness of school size and narrow- ness of teachers' fields are constraints on improving utilization of teachers. 1 £ R 3 L (18) R : hours of average teaching load, 2 12: minimum hours of teaching load, and L2: maximum hours of teaching load. Produced Class Hours where (19) H: number of produced weekly class hours, X: number of students, L: average number of students in classes, and W: number of weekly class hours of the course in the curriculum. 141 Demand for Teachers where P. = H. /R2 (20) P: number of demanded teachers, H: number Of produced weekly class hours as in equation (19), and 2: teaching load of teachers as in Constraint 2. Supply_of Teachers where Assumption 4: At most, 50 teachers from each field will be put under inservice training each year if the shortage of teachers in that field is over 100. Assumption 5: The number of new enrolled students In the first grade of teacher training schools will be: (a) in the "present sytem"--25 more students than the number of graduated students from the field in the previous year; (b) in the "desired system"--the base for calcula- tion for student input is the demand for teachers for the field concerned. Constraint 3: Training lycée teachers through inservice training is limited by the need for junior high-school teachers and by training facilities. (See Assumption 4.) Constraint 4: Both available student stations and teachersT teachers in teacher training schools are constraints on new enrollment in the first grade. 1 i R g L (21) 1 ° minimum number of new enrollment, R - number of new enrolled students, and L ° maximum number of new enrollment. 142 Student Input to Teacher Training Schools I. = G. + D (22) where I: number of new enrolled students, G: number of graduated students, and D: an additive parameter to utilize Assumption 5. Supply of Teachers t = _ * Zi,n Gi,n-l + (1 r1) Zi,n-1 + Gi,n-1 (23) s ._ * + (1 r2) Zi,n-1 I z = 2 z. (24) n i=1 1,n where number of trained teachers, G : number of teachers trained in teacher train- ing schools, Zt: number of the stock of lycée teachers trained in teacher training schools, r1: ratio of those who leave the profession (for teachers trained in teacher training schools), r2: ratio of those who leave the profession (for teachers trained through inservice training programs), GS: number of teachers trained through inservice training programs, 143 S ’ I Z : number<1fthe stock of lycee teachers trained through inservice training programs, Z3 = O in "present system." Supply of Humanities Teachers Because it is not a serious problem, the supply of humanities teachers is not included in planning through the simulation model. However, in calculation for the cost, humanities teachers should be counted. Therefore, though not differentiated by field, humanities teachers are included in the calculation for cost by utilizing the following equation: ph = p - p5 (25) n n n where h P : number Of supplied humanities teachers, P: number of the entire stock of teachers, and PS: number of supplied science teachers. Shortage of Teachers V. = P. - Z. (26) where V: number of the shortage of teachers, P: number of demanded teachers, and Z: number Of-supplied teachers. Notice: Objective (or criterion) function requires V = 0. 144 Cost Assumption 6: A11 expenses for teacher training are counted as investment to the lycée. Assumption 7: Purchasing power of Turkish money will remain as it is now. Assumption 8: There is no constraint on provision of needed funds. In this section, L denotes Turkish lira, equivalent to 1/14 dollar. Cost of Training Teachers : t - t * t‘k 5* Ll (Sn Sn-l) q1 + Sn q2 + Sn q3 (27) h h + _ * (Pn Pn-l) q4 where Ll: investment in training teachers, St: number of students enrolled in teacher training schools, SS: number of teachers under inservice training, Ph: number of humanities teachers, ql: unit cost of building and equipment of teacher training schools per student, q2: current cost per teacher training school student, q3: current cost per teacher under inservice training program (in the a "present system," 9=0), and q4: unit cost of training per humanities teacher. 145 Cost of the Lycée LG = C1n + C2 + c3 (28) where L2: cost of lycée, Cl: cost of teaching, C2: cost of school operation, and C3: cost of school plant and equipment. Actual Current Cost of Lycée L = C1 + C2 + A1 + A2 (29) n n n n n where L: actual current cost of lycée Cl: cost of teaching as in equation (28), C2: cost of school operation as in equation (28), A1: prorated cost of school plants and durable goods, and A2: prorated cost of training teachers. Unit Cost Per Lycée Student and Graduate LSn = Ln/S (30) where 146 LS: unit cost per student, LG: unit cost per graduate, S: number of students, and G: number of graduates. Findings and Conclusions The preceding model is an abridged version of the author's original model. This new version was abbreviated by either ignoring certain original alternative equations and adopting particular ones or by combining a few equa- tions which were in the original model into one equation. Nevertheless, the presented model is expected to serve in demonstrating how a simulation model may be utilized. Evaluation of findings in an application of the model shows not only the possible future behavior of the system under given circumstances, but also the kinds Of data needed in utilization of such models. In this section, illustrative findings of the original study through computer simulation are presented in three subjections, corresponding to the preceding three submodels, as follows below. Students Student input (new enrollment) to the lycée is treated as an exogenous variable in the model. Since initial values are constant and the values for student inputs are originated by the same equation, changing values 147 of numbers of new enrolled students in each of the alterna- tive systems are necessarily the same for the same year. Therefore, any difference in exogenous variables related to students in the varying systems should be attributed to the differences included in the design of the system. The differences included in designing for alterna- tive systems are only the rate of teacher supply. Then, Assumption 2, "the better the teacher supply, the better the student performance," is utilized in simulation. The better performance of students is counted as a higher passing rate (larger flow) Of students. These were included in the computer program in this way: The actual differences in the passing rates among various grades were presented as parameters. The general base for calculation was established as the percent Of supplied science teachers in terms of need. However, if the percent Of supplied teachers was less than 70%, it would be counted as 70%, and more than 90% would be counted as 90%. As a result of utilization Of Assumption 2 and a varying rate of teacher supply, calculated values for the variables of total enrollment, dropouts and graduates in the best alternative system differed from others after the 13th iteration. This means, even in the best possible system, the supply of science teachers could exceed 70 percent of need after 13 years under the assumed circum- stances. 148 The outcomes in the 20th iteration (i.e., at the end of the assumed planned period) in the two systems are presented in Table 8. Consequently, if falling pupil-teacher ratios is 74 an indicator of a better performance of students, the simulation model performed here helps to discover the long- range outcomes of a better teacher supply. A more precise approximation requires real data which were unavailable at the time this demonstration was performed. Demand and Supply of Teachers Demand and supply of science teachers are treated as endogenous variables in both present and desired systems. TABLE 8.--Yearly Outcomes of the Lycée in Desired and Presented Systems in the 20th Iteration, Analogous to the 20th Year in a Planned Period. Desired Present Difference Variables System System (a) (b) (a-b) Number Of tOtal 1,499,207 1,580,118 -80,911 students Number of graduated students 406,896 272,349 +134,547 Number of dropouts 56,849 165,137 -108,288 74 Hugh Philp, "The Evaluation of Quality in Educa- tion," in Qualitative Aspects of Educational Planning, ed. by C. E. Beeby (Belgium: UNESCO, 1969), p. 288. 149 Demand for teachers is defined by the number of students, average class sizes, and average teacher load. Because of Assumption 3 average teacher loads differ slightly from one another in present and desired systems. In the "present system," the supply Of teachers is defined in this way: The number of new students enrolled in a program is 25 more than the number of students graduated from the same program. In the "desired system,’ however, the number of new students is defined by the shortage of teachers. TO eliminate a sharp increase in the number of students, a smoothing parameter was utilized in calculation. The results of iterated calculations are presented by graphs in Figure 12. There are two situations to be noticed in Figure 12: (a) the gap between demand and supply is increasing as years pass in the "present system," and (b) the demand curve for the "desired system" is smoother than for the "present system." In other words, demanded number of teachers in the "desired system" is less than for the "present system." The difference between numbers is 3,800. In other words, improvement in the rate of teacher utilization and of teacher supply saves approxi- mately one-fifth of the number of teachers needed otherwise. Constraint 2 is taken into account in improvement of the teacher utilization and supply in the "desired system." 150 FIGURE 12--Estimated Need and Supply of Mathematics and Science Teachers in Present and Desired Systems. Thousands 21 I 2 . ° 0 e? 19 9'" r 9.; '0 .18 . Go 17. i (7' \‘Q .0... I, 16 ' 3.0 '..o" I O «” Years 1 23 4 56 7 89101112131215161718'1920 151 922.: Varying costs in the two systems are treated as endogenous variables. That is, what is needed is assumed to be available because Assumption 8 eliminates financial constraint in concerned systems. Iterated calculations reveal that salary and training of teachers require more money in the "desired system" than in the "present system." As to investment in school facilities for lycées and current expenditures on the operation of schools, the "present system" is more costly than the "desired system." The entire cumulative expenditure throughout 20 iterations is .008 more in the "desired system" than the "present system" simply because more money is invested in teacher training to close the gap between demand and supply. Thus, the entire yearly actual cost of the system, including teacher training, is less in the "desired system" than the "present system" after the eighteenth iteration. Cost per student is slightly higher but cost per graduate is significantly less (4 percent and 34 percent, respec- tively, in the twentieth iteration) in the "desired system" than in the "present system." This is an important finding in terms of the economical aspect Of improvement of an educational system. 152 Summary Simulation models are utilized whenever the future behavior of the system under given circumstances is under consideration. For a realistic approximation of the future behavior of the system, accurate actual data is necessary. However, as performed in this part, the trend of the future behavior of the system can be detected even in the absence of real data. This is an important contribution to planning for a socioeconomic system. The overall conclusion derived from the presenta- tion in this part is that, regardless of the numerical comparison, an educational system is expected to be more productive and economical if an optimum teacher supply is realized. Obviously, this conclusion is true only if a better teacher supply facilitates a better student per- formance and/or a better teacher utilization stated as assumptions 2 and 3 are true in some degree. One may derive another conclusion from the preceding presentation. Accurate real information needed in simula- tion of the model facilitates a rather realistic approxi- mation. That is the core of the theme Of this present study. The model in the preceeding part was developed as a tool so that information needed in planning for the supply of secondary school teachers could be identified, and then be collected and processed. 153 PART 2 MATHEMATICAL MODEL FOR IDENTIFICATION OF THE TURKISH SECONDARY SCHOOL SYSTEM Introduction This part is devoted to a mathematical model for identifying the Turkish secondary school system in terms of need and supply of teachers at a particular time. The model is exclusively for the Turkish system rather than a general one. The primary aim of building the model was to set forth the situation of need and supply of teachers. However, cost of secondary education is included in the model because financial feasibility is always an essential condition to be considered in trying to solve the teacher supply problem. The model is expected to facilitate computer-based data processing from the level of an individual school up to the level of the whole system. Any desired combination of schools, or districts, or provinces, etc., in between the individual school and the entire national system is possible through the use of the coding system in the com- puter program. Notations In order to facilitate notations, varying combina- tions of capital letters are used for variables. Calcula- tions are specified with the school year, subject matter, 154 grade level, and the type of school whenever needed. Indices that are used for these purposes consistently throughout the model without any change in identity are as follows: i: l, 2, 3, . . ., I (corresponding to each subject matter in curriculum), 0 < I < 33. j: 1, 2, 3, . . ., J (corresponding to each grade level), 0 < J < 8. k: l, 2, 3, . . ., K (corresponding to each type of secondary school such as lycée, middle school, etc.), 0 < K < 11. n: corresponds to time, in school years. The model was built to utilize data collected from schools. Therefore, any information related to a particular school in the scope of this model can be Obtained through uses of the model. However, in terms Of utilization of teachers as well as need and supply of teachers, a munici— pality with one or more secondary schools, rather than an individual school, was adopted as the basic unit because a teacher at a secondary school is, by law, compelled to teach in his field at another school in the same munici- pality whenever needed. Because notations in equations are not extended beyond the school level, calculations for a municipality or for any desired unit other than a school can be done through uses of codes in the computer prOgram. As was mentioned in Chapter I, the model was applied for the province of Eskisehir to demonstrate its 155 utility. To facilitate following the application together with related equations, table and column numbers of printouts in Appendix B are shown in parentheses right after the headline for each equation. In addition, without violating the logical order for calculations, equations are presented in three sections corresponding to the three types of tables in Appendix B. Section 1 includes equations to calculate raw data to be used in subsequent equations. Section 2 is devoted to equations to calculate functional relationships of variables in terms of need and supply of teachers. Section 3 includes equations related to the cost Of secondary education. Section 1 Calculated results of equations in this section are presented in Table 1 in Appendix B. Number Of Students (At the Top of Table l) The Turkish secondary school system has two kinds of students, daytime and boarding. Boarding students are provided free accommodations, clothes, books, etc., in addition to educational services. In the Turkish system, students are assigned to classes which follow fixed programs designed for each grade for a particular school throughout the country. Therefore, students are not identified by 156 subject matter but by grade and the type of school. Sex of students is not needed in this study. However, it may be identified through coding. STk(n)=. J [SDj k(n) + SBj'k(n)] (31) l I ”MCI where ST: number of all students, SD: number of daytime students, and SB: number of boarding students. Number of Class Sections (At the Top of Table l) 'Number of class sections is one of the two variables to calculate produced class hours. Because Of the fixed curriculum, the program for a class section is latent in the level of grade and the type of school. Therefore, the index for subject matter is not included in identification of class sections. CSk(n) = ”MC-I 1 CSj,k(n) (32) j where CS: number of class sections. Number of Teachers (Table 1, Columns 1 and 2) In the Turkish system, school administrators are counted as teachers. However, compulsory teaching hours for administrators are fewer than for teachers. 157 Identi- fication of sex of teachers is left to coding and not included in the equations. Teachers are identified by fields and by types of schools, not by grade levels. Ti,k(n) = TTi,k(n) + TAi,k(n) (33) where T: number of all teachers, TT: number of teachers without administrative status, and TA: number of teachers with administrative status. Produced Class Hours (Table l) Produced class hours imply the need for assignment of teachers. Since a fixed curriculum is followed, pro- duced class hours is the sum of the products of the number of class sections times the number of weekly class hours in a particular field summed over grade level in a particu- lar school, as follows: J _ * HPi,k(n) jél csj k(n) Hwi'j’k(n) (34) where HP: number of weekly produced class hours by existing schools, CS: number of class sections as in equation (32), and HW: number of weekly class hours in curriculum. ll 11lIIIIII( I Illa!!! III I.’ lllllr f ’l 158 Supply of Teachers (Table l) In the Turkish system, there is no means by which to provide substitute teachers. However, the shortage of teachers is partly compensated through assigning semi- qualified, unqualified, or lay teachers to classes. If none of these are available, the class is left teacherless. In other words, the class time passes without a teacher. The following equation was prepared to facilitate calcu- lation for the situation of the supply of teachers with respect to produced class hours. Since teachers are not identified by grade levels, j is omitted in the equation. HPi k(n) = HQi,k(n) + HSi’k(n) + HUi,k(n) I (35) + HVi'k(n) where HP: number of weekly produced class hours as in equation (34), HQ: number of class hours taught by qualified teachers, HS: number of class hours taught by semi-qualified teachers, HU: number of class hours taught by unqualified teachers, and HV: number of teacherless class hours. 159 Section 2 Equations in this section were prepared for calcu- lations of functional relationships among variables in terms of the need and supply of teachers. If there be any, the possibility of better utilization Of teachers can be detected through utilization of related equations. Because, by law, a teacher is compelled to teach in his field at another school in the municipality, equations in this section were prepared for such a municipality. Findings through utilization of equations in this section for the province of Eskisehir is included in Table 2 in Appendix B. Ratios (Table 2, at the Top) Student/teacher, teacher/class section, and student/class section serve to establish bases for estima- tion of needed teachers. For this reason, the above mentioned ratios were included in this section, as follows: ‘2‘ ii RS(n) = ST (n) / T. (n) (36) k=1 k k=l i=1 l'k ii If RT(n) = 'T. (n) / CS (n) (37) k=l i=1 l'k k=1 k K K RC(n) = E STk(n) / Z CSk(n) (38) k=1 k 1 160 where RS: student/teacher ratio, RT: teacher/class section ratio, RC: student/class section ratio, ST: total number of students as in equation (31), T: number of teachers as in equation (33), and CS: number of class sections as in equation (32). TeachingfiLoad Teaching load is one of the important variables which directly affects the number of needed teachers. It may usually be expressed as an average value. Theoretically, one would expect teaching load to fall within the legally established limits. It is empir- ically known however that, in practice, this is not true in Turkey. Inefficient utilization of teachers, smallness of schools, narrowness of the licensed field of teachers, and in some cases teachers also having administrative status, all work to lower teaching load below the estab- lished prescribed limit. Therefore, the teaching load is assessed according to the following two categories: Established Teaching Load Established teaching load is formally prescribed by law as given in Table 9 on the following page. 161 TABLE 9--Established Teaching Load of Secondary School Teachers in Class Hours. thhnmtTamiunglxmflsEEIWaflflyCHassltmms ina££(afieadmus (9335*Phflwmfllmibehwfl (1) (2) (3) (4) (6) (6) (knenfl.amd\kcathxmfl EHuafldonlhaduns First Cycle : 18 6 24 6 30 15 Second Cycle: 15 6 21 9 30 12 Workshop Teachers: 20 20 40 4 44 -- Administrators : 6 -- 6 12 18 12 Explanations for the Above Columns: (1) Compulsory in return for the base salary. (2) Optional if the teacher has more than 25 years of experience, compulsory otherwise. (3) Total of columns (1) and (2). (4) Optional for every teacher. (5) Total of columns (3) and (4). (6) Maximum class hours that may be taught by a teacher who is not certified in the subject. These hours are Optional and are permissible only if there is no vacant class in the teacher's own field and provided that the sum of columns (5) and (6) should not exceed 30 class hours a week. NOTE: Teachers are paid hourly honoraria for the loads included in columns (2), (4), and (6). 162 Observed Teaching Load The precise rate Of utilization Of secondary school teachers in Turkey is unknown. It is empirically known, however, that secondary school teachers in Turkey are underutilized. A previous study (using the simulation model presented in Part 1) by this researcher revealed that the realized (observed) average load of secondary school core subject teachers was 19.2 class hours in the 1968-1969 school year, notwithstanding the fact of the chronic and severe shortage of teachers. Observed teaching load can be obtained for each municipality through actual data from schools. Conforming with the established teaching load, the equations for Observed teaching load were prepared in two categories, i.e., with and without administrative status. Observed average teaching load Of administrators (Table 2, columns 4-9).-- K K LATi(n) = kél HAl,k(n) / kgl TA ’k(n) (39) K K LAQi(n) = kZl[HAi’k(n) - HAUi'k(n)] / kZlTAi’k(n) (40) K K LABi(n) = : [HAi'k(n) - HAHi,k(n)] / Z TAi’k(n) (41) where columns LTTi(n) LTQi(n) LTSi(n) where 163 LAT: number of class hours as average teaching load in qualified and unqualified fields of school administrators, LAQ: number of class hours as average teaching load in qualified fields of school admin- istrators, LAB: number of class hours as average teaching load in return for base salary of school administrators, HA: number of total class hours taught by school administrators. HAU: number of total class hours taught by school administrators in unqualified fields, HAH: number of total class hours taught by school administrators as honorarium, and TA: number of teachers with administrative status as in equation (33). Observed average teaching load of teachers (Table 2, 12-17).—- K K = kElHTi,k(n) / k:lTTi’km) (42) K K = k:l[HTi’k(n) - HTUi’k(n)] / kZlTTi'km) (43) K K = E [HTi’k(n) - HTHi’k(n)] / Z TTi,k(n) (44) k 1 k 1 LTT: numbercmfclass hours as average teaching load in qualified and unqualified fields of teachers, 164 LTQ: number of class hours as average teaching load in qualified fields of teachers, LTS: number of class hours as average teaching load in return for base salary of teachers, HT: number of total class hours taught by teachers, HTU: numbercflftotal class hours taught by teachers in unqualified fields, HTH: number of total class hours taught by teachers as honorarium, and TT: number of teachers without administrative status as in equation (33). Need for Teachers Need for teachers is in general the quotient of produced class hours divided by the average teaching load. Produced class hours is constant for a particular school in a particular year as long as the curriculum and the number of class sections remain unchanged. As to teaching load, the situation is different. The number of assigned teachers, which is not as stable as the number of class sections and the curriculum, defines teaching load. In other words, the numberwxfproduced class hours is inde- pendent of teaching load but the number of needed teachers depends on realized teaching load. Therefore, the number of needed teachers is inversely related to the size of realizable teaching load. The higher the degree of utiliza- tion of teachers, the smaller the number Of needed teachers. 165 Consequently, calculation for the number of needed teachers is done in terms of observed and possible best rates of utilization, as follows: Need for Teachers in Terms of Observed and Best Rates of Utilization (Table 2, Columns 18 and 19) K TDOi(n) = kElmpi’km) - HAQi’k(n)] / LTQi(n) + c (45) K TDBi(n) = kZlmpi’km) - HAQi’k(n)] / LTBi(n) + C (46) where TDO: number of needed teachers in terms of observed rate of utilization, TDB: number of needed teachers in terms of best rate of utilization, HP: number of produced class hours as in equation (34), HAQ: number Of class hours taught by school administrators qualified to teach, LTQ: average observed hours of teaching load as in equation (43), LTB: hours of teaching load in terms of best utilization of teachers, and C: constant to round the fraction. Teachers Expected to Leave the Profession in the Near Future To make an appropriate estimation for teachers needed in the future, one should know all possible 166 information related to the loss of teachers in the future. One can get actual information on two kinds of loss of teachers expected to happen in the near future. One Of them is retirement. By law, a teacher has the right to get a pension after 25 years of service. Therefore, to know the number of teachers who may leave the profession for pension in any year in the near future helps to take necessary measures in advance. The other is a temporary loss. Every male teacher should be drafted by the army by the age of 31. Although this loss is compensated by discharged teachers, there is a possibility of the number of discharged teachers to be smaller than the number of drafted teachers because of the time difference. In addi— tion, the discharged teacher may not ask for a teaching job at public schools. Therefore, the number of above described teachers are counted by means of the following equation: Expected Loss of Teachers in the Near Future (Table 2, Columns 22 and 23) K TLi(n) = E [T25i’k(n) + TMi’k(n)] (47) where TL: number of teachers expected to leave teaching in the near future, 167 T25: number of teachers with more than 25 years of experience, and TM: number of teachers who are not yet drafted by the army. Shortage or Surplus of Teachers DEFINITION: where D: number S: number Because need of observed and best -, surplus D - S = 0, best supply +, shortage of needed teachers and of supplied teachers. for teachers was calculated in terms utilization rates of teachers, shortage or surplus of teachers is also calculated in the same way, as follows: Shortage or Surplus of Teachers in Terms of Observed Rates of Utilizations (Table 2, Columns 20 SOi(n) SSi(n) where TDOi(n) - TDBi(n) - and Best and 21) "MN TTi k(n) (48) k 1 ’ TTi,k(n) (49) ”MN k 1 SO: number of shortage or surplus of teachers in terms of observed rate of teacher utilization, 168 SS: number of shortage or surplus of teachers in terms of best rate of teacher utilization, TDO: number of needed teachers in terms of observed rate of teacher utilization as in equation (45), TDB: number of needed teachers in terms of best rate of teacher utilization as in equation (46), and TT: number of supplied teachers. Section 3 This section is devoted to the cost of secondary education. Obviously, financial feasibility is a necessity for implementation in education. For this reason, cost of secondary education is included in the model, which is expected to be used to facilitate decision making on plan- ning and implementation for secondary education. This section is prepared in five categories, as follows: 1. Cash expenditures, 2. Prorated cost, 3. Current cost, 4. Unit cost per student, and 5. Unit cost per class hour. All values to be assigned to variables representing cost in subsequent pages are in Turkish liras. Cash Expenditures (Table 3, Columns A, B, C, D) Cash expenditure is the money paid for services and for consumer goods. All possible cash expenditures 169 from the budget in the Turkish secondary school system are included in four categories, as follows: Salary for Professional Services (Table 3, Column A) Included in this part are teachers, school admin- istrators, lay teachers, and school service personnel such as doctors, psychologists, counselors, etc. K I SPS(n) = Z .2 [BSPi’k(n) + SHTi’k(n) + SLTi’k(n) k=1 i=1 (50) + SESi,k(n)] where SPS: salary of professional manpower, BSP: base salary of professional manpower, SHT: honorarium, SLT: salary of lay teachers, and SES: salary for extra services such as workshop, administration, etc., and other payments such as children allowance, etc. Salary for Nonprofessional Services and Miscellaneous Personnel Benefits (Table 3, Column B) In this part, salary for nonprofessional personnel, such as clerks, employees, etc., and occasional personnel benefits of professional and nonprofessional manpower, such as medical treatment, etc., are included. 170 SNS(n) II II MN [BSNk(n) + SEPk(n) + SPPk(n)] (51) k 1 where SNS: salary of nonprofessional manpower and all occasional payments to all manpower, BSN: base salary of nonprofessional manpower, SEP: extra payments to nonprofessional personnel, such as overtime, children allowance, etc., and SPP: all occasional payments, such as medical treatment, travel expenses, etc. Cash Expenditures for School Operation (Table 3, Column C) In this part, cash expenditures for all kinds of needs for operation of schools except manpower are included. Through the uses of the items in the budget law, the (equation for general purposes is prepared, as follows: K CDS(n) = Z [cok(n) + CTk(n) + CVk(n) + CRk(n) k=1 (52) + CMk(n) + CLk(n) + CEk(n) + CPk(n)] where CDS: cash expenditures for school operation exclud- ing manpower (if there are boarding students in the school, X in equation (53) should be used as a multiplier for the equation), CO: cost of utility, such as electricity, etc., 171 CT: cost of transportation and communication, CV: cost of vehicle, CR: cost of renting, CM: cost of material, CL: cost of library, CE: miscellaneous cost, and CP: cost of minor repairs. Cash Expenditures for Boarding Facilities (Table 3, Column D) The above equation can be used for a school without boarding students. If the school has boarding students, however, there is no direct way to separate certain kinds of costs common to both educational services and boarding facilities, such as electricity, water, heating, etc. However, one can make an approximate separation by estab- lishing a base in terms of experiences, or uses of practiced ways in preparation of the budget, or of any appropriate representative cases. In any case, a means is needed to separate the costs for educational services and for board- ing facilities. The following equation is prepared to facilitate separation of educational costs from the whole cost, including the boarding facilities. As the multiplier of the operation cost, the equation is correct whether or not the school has boarding students. Therefore, it is used as a regular multiplier in calculation for the 172 operation cost without a need for the check statement in the cOmputer program. The equation for the multiplier is as follows: K K X(n) = 1/ [1 + [ 2 58 (n)) / 2 ST (n)] * c (53) _ k _ k k—l k—l where x: parameter for separating boarding expenses from the melded school Operation cost, SB: number of boarding students, ST: numberCertification Neither of the above The foreign language which you know best, if any: a. Name: ..................... b. Degree of mastery: I can speak a little bit. I speak fluently. I understand what I read through using dictionary. I understand what I read without dictionary. How many total hours are you teaching in a week for which you are paid in the form of and honororium either in your regular school or in other schools. 262 16. Please fill out the table below with all courses you teach either in your own school or in other schoolts). (If you teach in any other school, please write the name of the school on the dotted line.) 0:: not on: any sign In the cells below Name of the course Cycle l Cycle ll 1 Total [_Llllll LIIIIAI] Llllll] [JIIIIW IN YOUR 0'" SCHOOL [lllllj "IIIIQ' 0 00000000000 FIIllll IN OTHER SCHOO L TOTAL Note: If there were any expressions that you found to be unclear or difficult to understand, please cite them below by refering to numbers of items and I certify that this form was filled out accurately. May ... 1972 (Signature) sections. It is certified. May ... 1972 School Director 263 MINISTRY OF EDUCATION Planning, Regearch, and DATA COLLECTION FORM : P2 Coordination office (Nonprofessional Personnel) Please fill out the table below so as to represent the circumstances exactly on May 2, 1972. Those who filled out Form Pl will not be included in this table. TO BE FILLED OUT BY THE SCHOOL DIRECTOR. .mufl' 8330 3"” "mm 0' cation 0: Educational dependent serial no. my status Name Deg,” Step chlldten nay ... 1972 Director Of the school: 0 0 0 0 0 0 0 0 0 0 0 0 264 Planning, Research, and Coordination Office DATA COLLECTION POEM: 01 NOTICE: 1. 2. 3. TO BE FILLED OUT BY THE SCHOOL DIRECTOR a. This form will be filled out so as to represent the circumstances exactly on May 2, 1972. b. Please answer the items below through either filling out the dotted lines or putting an x in the cells to the left. Location of the school: a) Province: ................................ b) District: .......................3........ c) Sub-District: ............................ d)v1113980rt°m. 0000000000000000000000000 "an. at th. .ChOOI' 0000000000000000000000000 Shift status: B One shift C] Double shift 0 Triple shift 4. Composition of student body: 0 Coeducat ion [3 Girls only C] Boys only 5. Status of students: D Day students only D Boarding students only D Both day and boarding students 265 6. Please fill out the table below. NOTE: 1) Do not fill out the first column if the first cycle of the school is composed of three grades and there is no preparation class. 2) For lycee, data for LITERATURE sections should be entered firstI to the left of data for SCIENCE sections at each grade level. FIRST CYCLE SECOND CYCLE Class. Levels Total Total Numberoi Class Sections F Day-time Students N F Free Boarding Students M F Paid Boarding Students N Scholarship F ' Students I F Halt Boarding Students I F Total I . Grand Total 266 -.. 7. In the table below, please show the status of teacher supply for all courses, including selective courses, formally established extra courses, or workshops which may exist in your school. NOTICE: In the column for “Lay Teachers," please enter data only for those teachers who are not members of the regular staff. STATUS OF SUPPLY 13 Total of _, Names of Teachers of Teacher from Lay Teacher- Course ‘53 the Courses the School Other Schools Teachers less Hours 0 Class in the Certli. Uncert. Certli. Uncert. Certii. Uncert. H00" School Turkish Social Sublects Mathematics Sciences FIRST CYCLE erce, Agriculture Religious Engflsh French German PhyslcaI Ed. COMMON Drawing, Handicrait Home Econ Music Literature Philosophy History Arts History Geography Mathematics SECOND CYCLE Biology Physics Chemistry Vocational TOTAL Note: National Defense course will not be included. 8. Please fill out the table below on the basis of the explanations provided with each. 267 (Do not include kurus) durable goods for the 1970 and 1971 fiscal years. a. The table below will be filled out using the official records for VALUE OF DURABLE GOODS Carried over to 1971 from 1972 Written off in 1971 Purchased in 1971 Carried over to 1972 Used only for boarding students Used (or all othter needs TOTAL GENERAL EXPENDITURES the 1971 fiscal year excluding durable goods and salaries. b. The table below will be filled out using the official records for EXPENDITURES FOR BOARDING STUDENTS FROI NATIONAL BUDGET Klnds of expenditures Lira Kinds or expenditures Lira Library Food Utility Clothing Transportation and Communication Total Provided (Tam sonic? Rent other than the budget Supplies Transportation iiinor Repairs Social security benefits Personal Expendlt. it Iscelianeous Bonus Vehicle Operation Total Total Provided‘irom sources' other than the budget APPENDIX B 268 269 >Ofikm "WP: on itmh w>UnoU0 > w.:mwr mduum.uo> .m.wc n2¢.ou.uc> .rum Jnrnwz:.uo> >uhmwsm1u mu~m>la >omau_m 1 I III MinHh s Jkd! >lndwmumo mVM4 uU >unhm~1 >«o»m~r ‘1’ .um >Jommc.~1a mwaaz an on ON hm 0N mN 4N mm mm Am ow ad ma mmowu .mswa» dc mc:_o.mi. mawhbdlihanmDm cz_a¢ao:»u<~u_oz¢4 uo.az oo crow «wipe acoiucw» no .macpaaem.z~soa no.¢2 ~o mowiuaw» do «moan, so mamiuam» do mosm_u a mwsqz mucou JCFOh hm mmmw14 mm a J¢h0»twam NM orumoxuwb m4¢~¢t10- um Mbud ED >¢Ohm—1 >¢Dhm~1 >cha00wc ma:»1n orumoruw» m>0mrzo~heuc> on rescue orum mao~u_4warzo_»auo> o~ ruzwnu .rum rm~azch ozq wucws100iuc> ow rmubwzm .rom narcotizo_»aoc> aw zo_o_sma cacao >xaomc4_:a o~ moawxxourwczesrooaoq cxwrurmu~m>za mm mo~w>1a cm >¢hmutwru MN mu_m>zar.r»¢s - Nimu_»0040—m ON mmxaz mwoou diorpaxrmu2m_um u meZwuuw imu~»«swrhaa wwuhuzq #02 :mr uwuiuuu wqu» aw uw>u itzsmcwdxm 1p“: amalgam» du.02 yu.p< ”dun; Pmum u; v.uvk 2» vuvha~aaapg uu mammn z” fiuuhd~mayha no wawur :— TOMrANrd‘PJ -’.rd\so ‘. a,BCtC' in >xq4nm Loam nod zispma zuru ornzuqup 3.1.3.6 so .257; o:_:uth nu—uudauo‘a v2»0aduz» auhopro mewrquw do.oz:d >casUm:0u> .:Um maoaauamMIVOa oXUmoaror 0¢< wuawttuuruo) Lawn» m Janupoan N O P :3 1. 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ApQ-wanvw-nwfirA.c-cwiaitlaoccncufinocon .mnzude\.AMfiDAw.q .mo nonhuu Ampqdw-uvu «AAwmAxwucmu¢~)0¢A 280 nw***uufianuuna§§§h§§§¢§fiannnnuunawauaoq«a§*»§§9§9§u§quuuuvau§aa}§¢§¢§a§uuoafiaacaau§nuoanauaauaunu¢unuaunuuaauuaauu.a a om.mm u chohm u Am.mm v Acohm a owoec a m¢oc a oo.o a m~.om » u a a o 5 a u c 5 ache» 9 z o z u A n unngauuuuuunuunuunnauanun»*«*nuu*uuunnuu«aununu«auunuunnfianauufiauuoufiafiuo§a§uua¢uu4na§aunu§uuoau§§§ununnaonaunnfiunu «Dc: mmqau awn hmou hAz: .m§ uwfluwunnufifluwnfiwfi .flu.ufiwfi§unfiuw§u3nflflfl§flflflififlififlflfi§§flflflflkfiflflflflflfiflflfihfiflfiflflfifl§fi§fl§fl§fl§flflflflfl§fi§fiflflflfl§§§fl#flflflflfiflflflhflflfiflflflflflunflfi“53¢.“ .. * ¢m.mmoA a AcohmmA u mm.oomo¢mwm a mmocecmw¢m n m>.¢om>m¢mm u a x a 5 # Jakob a A a I « #n*«**unuunuaun«an»unflannunuuuuuuannfiuun«an»anuuunuéanauuanuanuuunuauufiu«an»«uununun«uuuauaauuuannonunuuuuuuunuunuuu pzmoahm awn hmou hAznocfi hmou hzwaasu .ru ununfinnunnunnn«nununnnaanuunuan«unann»ua§§§*§§#«§§u§a*aunaanunuaunnuu*uu§u§nannnnnunnunauuuuvonu§nanoaauaunnunauauuu » ¢¢o¢m~ommm Q mmoc>¢mmm 5 oo.wm~Ammm § mm.mmon> u Neoo~>o¢m~ n n Jahcp a o u A<»C»QDm * u u m a wanna»nununuaun«auuaunuuéflaaunauunu*«§#§«anafiuannuuuufinnfiaaéfiu§§u*uauauuuuuaouonuunnuaunnaauoaauoanunauoaaauuunnuuun hmou awhdmoma .no ”*nunaufi‘u%u*u«§ununflauannunuunQuufia fi§naunnufluaannnuuéauuaununun»nunuu§§anuufiea§«anuaa§nuan¢o¢¢9a«ananan§nuonnaunaq a mw.¢hooco¢m "geomoommom a mmoovohmAm o oo.ooAmA¢m « omoowhhmmc «accomwmmcew a u Jakob a o o AGda mwu. 1m; 1.9:. ..AA A #26 NN..mn m4ndk BIBLIOGRAPHY 281 BIBLIOGRAPHY Ackoff, Russell L., and Sasieni, Maurice W. 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