The Reforms in Mathematics Education for Grades 1 through 12 in Albania from 1945 to 2000
TABLE OF CONTENTS I INTRODUCTION 1 Need for the Study 2 Purpose of the Study 7 Procedures and Methods of the Study 8 Resources for the Study 12 Summary of the Introduction and Organization of the Remainder of the Study 13 II BACKGROUND FOR THE STUDY 15 Introduction 15 Early Development: Mathematics until 1945 15 The Albanian Communist Regime's Educational Reforms 26 The Democratic Reforms 29 III LITERATURE REVIEW 34 Past Research Studies focused upon Albania and Mathematics 34 The Worldwide Study of Mathematics Reform 41 Conclusion 43 IV METHODOLOGY 45 Theoretical Research Philosophy 45 Further Philosophical Influences 50 The Qualitative Research Approach 52 The Case Study 60 Summary of the Methodology Discussion 77
V RESULTS 78 The Historical Record 79 Experience Surveys 80 Case Study in Earlier Reform: The Development of the Algebra Curriculum 103 Case Study in Later Reform: The 1980s 113 Investigating Mathematics Textbooks 129 VI DISCUSSION 147 Discussion and Triangulation of Issues 147 Summary of the Discussion 152 VII CONCLUSION 156 Formal Answers to the Research Questions 157 Limitations of the Study 164 Validity and Reliability 173 Areas for Future Research 175 Interviews of subject matter experts and re-examination of the study material....l75 Personal Statement 180 The Current State of Education in Albania 181 Bibliography 182 Appendix 1: Research Questionnaire 188 Appendix 2: Historical Evidence 197 Lesson Plan, based on the program 1928 Primary Schools.... 197 Teaching Plan of the year 1933 for "The Feminine Institute Queen Mother" 198 Mathematics 1: Objectives and Lesson Plans 199 ii
List of Tables and Figures Table 1 Resources used for historical and secondary analysis 68 Table 2 Classification of study respondents 73 Table 3 Classification of study respondents 81 Table 4 Demographic and Experience Profile of Study Respondents 82 Table 5 Teacher preparation 85 Table 6 Perception of Albanian performance as compared to others 86 Table 7 Responses to question 9 88 Table 8 Responses to question 10 89 Table 9 Responses to question 11 90 Table 10 Unqualified mathematics teachers by district (Babamusta, 1998) 101 Table 11 Structure of Education in Albania 181 Figure 1 Theoretical Framework of the Research 49 Figure 2 Map of Albania 205 in
Acknowledgements The researcher has been fortunate to enjoy the support of many individuals throughout the process of engaging in this research and preparing the dissertation. Although all of this support, including scholarly, financial, and personal support, is gratefully to be acknowledged, four individuals deserve special mention and thanks. Henry O. Pollak, Ph.D. (Visiting Professor and esteemed professor of Information Theory), has served as not only my adviser through this process but also has imparted great amounts of mathematical knowledge from several courses I have taken with him. Bruce R. Vogeli, Ph.D. (Clifford Brewster Upton Professor and Director of the Mathematics Program in the Department of Mathematics, Science & Technology) provided the idea for the topic of the research. Matthew L. Jones, Ph.D. (Associate Professor of History) guided me in doing research in science and science history and assisted with the reading in several books which helped with the historical framework of this research. Petrit Muka (A Specialist with the Institute of Curricula and Training, Tirana, Albania) gave me many valuable resources for the dissertation, provided access to research subjects for the questionnaires, and helped to distribute and collect the questionnaires. My sincere thanks to these four individuals, as well as all other individuals, that have aided with this research and investigation. Their contributions to this research could not have been more valuable.
1 I INTRODUCTION Albania (Albanian: Shqiperi/Shqiperia, in Gheg dialect: ShqipnialShqypnia) is officially known as the Republic of Albania (Albanian: Republika e Shqiperise.) The nation is found on the Balkan Peninsula (refer to Figure 2, Map of Albania.) It extends across an era of almost 30,000 square kilometers. Between the years 1945 and 2000, the educational program of Albania has experienced significant reform orchestrated by two different political systems, the Communist government that was established following World War II and the post communist government that took its place within the last two decades (in early 1990's.) This research project was focused on the structure and outcomes of a series of rapid reforms in Albanian education during the latter half of the 20th century, particularly in regard to the mathematics curriculum and the outcomes from mathematics educational changes. These educational reforms have significance not only in a historical position, but also in terms of modern educational curriculum structure and performance. The Albanian government has undertaken tremendous reforms throughout its educational system since the ascension of the Communist government following World War II. In 1945, the country suffered from extreme illiteracy, poor mathematics skills, and low graduation rates. Within the years 1945 to 2000, the country implemented a long series of general reforms that, combined with specific changes to the mathematics curriculum, have generated positive results within the nation. What domestic and
2 international political, social, and cultural forces helped to shape these reforms? What further reforms must Albania accomplish in order to further strengthen the country's education of mathematics? This dissertation will focus upon the reforms undertaken in mathematics education for grades one through twelve in Albania between the years 1945 and 2000. Need for the Study Educational policy makers around the world have devoted considerable resources into the effective development and implementation of reforms in mathematics education. Leung et al. (2006) explained the present situation as: Mathematics reform is one of the most pressing areas of educational reform: "Policy makers recognize the importance of adjusting to the changing world and mathematics education reform movements can be found in many countries at this moment. A number of international studies have also taken place in the last decade to provide policy makers with information on the relative standing and effectiveness of their educational systems" (Leung et al., 2006, p. 6). The academic interest in mathematics reform has been bolstered by a growing negative public attitude directed toward the study of math (Allen and Johnson-Wilder, 2004). Interest in the reform of mathematics education has coincided with the increasing recognition of a pervasive "negative attitude" toward the study of math in the general population (Allen and Johnston-Wilder, 2004). In the United States, reform
3 has focused upon engaging and encouraging teachers of mathematics to help them develop programs geared toward the specific needs of their students (Brahier and Schaffher, 2004). In addition, standards-based reforms have sought to establish general competencies of specific mathematics concepts (Honig, 2006). The National Council of Teachers of Mathematics (NCTM) has been active in the development of new standards for mathematics curricula and teaching (Wilson, 2003). In Europe, the teaching of mathematics has also drawn concern over the need for reform. In Great Britain, the country's educational program has struggled with a shortage of qualified mathematics teachers (Allen and Johnston-Wilder, 2004). Reform efforts have centered on preparing qualified teachers and drawing more people to mathematics as a career. The Ministry of Education and Culture of Albania has chosen to develop its recommendations based upon outside observation by government officials and district heads. While this provides some information about how the classroom works, these studies neglect to include the opinions of teachers and students who are actually functioning within the system. In particular, a study that is focused upon the gathering of the opinions of teachers can provide qualitative, empirical knowledge about how Albanians have managed to adapt to the challenges found with teaching mathematics within an educational system that had undergone such extensive transformations over the period of time from 1945 to 2000. Learning from other countries is a valid means of researching and developing reforms in mathematics education (Leung et al., 2006). After the end of World War II, the state of education in Albania was in considerable disrepair. In 1945, the nation did not have any institution capable of supporting tertiary
4 education (Misja, Kalluli and Teta, 1996). The newly formed Communist government sought to improve the country's fractionalized educational system. The Educational Reform Law was passed in 1946. Destroying illiteracy was the focus of this system and by 1956, results demonstrated that the majority of Albanian citizens under the age of 40 could read and write (Gjonca, 2001). Mathematics education was another concern of this system. The Albanian Ministry of Education organized seminars introducing new courses, methods and materials to improve the technical and professional skills of teachers (Ministry of Education, "Arsimi Popullor", 1947; Shuteriqi, 1947). Further reforms continued in the subsequent decades, including another major series of reforms during the 1970's and 1980's. These changes included specific changes in mathematics that sought to modernize the teaching process (Polio, 1973; Tato, 1987). The reforms were praised for dramatically increasing the educational opportunities for individuals living in rural areas. "The number of kindergartens in urban areas increased by 112% from 1970 to 1990, while in rural areas it increased by 150%. The number of primary schools in urban areas, for the same period of time, rose 31%, and in rural areas, 24%. The total number of secondary schools increased by 291% and that of high schools, by 60%." (Gjonca, 2001, p. 27). Similarly, studies of graduation demonstrated progress. "The number of pupils who graduated from primary schools for the period 1970-1990 increased by 74.8%; for the secondary school, the number rose by 914.2" (Gjonca, 2001, p. 27).
5 While such data demonstrates an impressive trend toward overall educational completion, the figures do not show the great variance that occurs between regions within the nation. "A regional division exists for trends and levels between the northeast and southwest of the country" (Gjonca, 2001, p. 27). Several factors likely contributed to this regional variation in positive results, such as "the level of urbanization, tradition, religion, and age structure" (Gjonca, 2001, p. 27). The quality of these reforms is also questionable. These schools suffered from a lack of specific resources, such as textbooks, and overcrowding (Gjonca, 2001). Albania's focus upon self-reliance prevented the country from forming partnerships or similar educational relationships with systems outside of the country, so that Albania did not benefit from foreign advancements in education. Same as in other areas, Albania suffered from a shortage of specialists for the teaching of mathematics, too (Gjonca, 2001). Woodrow (2001) has demonstrated how philosophies and politics have influenced the development of mathematics education in various countries, for example the influence of Marxism in eastern European countries and the influence of politics and religion in the Islamic countries. "In the last decade, the international community of mathematics education researchers has increasingly recognized the importance of studies on the social dimensions of mathematics education" (Valero and Zevenbergen, 2004, p. 1). In some European nations, mathematics education has been tied to the support of democratic ideals. The Danish Ministry of Education states that "The teaching of mathematics should help students experiment and recognize the role of mathematics in society and culture. In order to be able to take responsibilities and to participate in a democratic
6 community, students should be able to understand the ways in which mathematics is used" (Skovsmore and Valero, 2001, p. 38). Such a conclusion has far-reaching implications upon the teaching of mathematics in a non-democratic nation, such as Albania. Mathematics education is both a social and political practice. The extent of support and availability of mathematics education says much about a culture and political system. "The recognition of the different and multiple positions that social actors can adopt in relation to and with the use of (school) mathematical knowledge is at the core of discussions of equity, social justice and democracy in mathematics education. The politics of mathematics education is essential to an understanding of mathematics education practices in large social contexts and form this broader understanding of the social" (Valero and Zevenbergen, 2004, p. 2). Several studies have explored the influence of trends and developments within the field of mathematics on the development of mathematical curricula (Fauvel & Maanen, 2000; Kline, 1953). Sriraman and Tomer (2007) compared the mathematics curriculums in Germany, France, England and other European countries. Various studies, monographs and articles have been produced concerning specific experiments, program studies, syllabi, school texts, methodologies, etc., but no broad study of the development of mathematics curricula, the conditions of teaching and learning, the infrastructures of the mathematics teaching staff, etc., has been undertaken by any scholar over the last 55 years anywhere. Unfortunately, no study
7 has specifically been conducted within Albania. Information on Albania is lacking even in the studies of UNESCO (Bishop, Hart, Lerman, & Nunes, 1993). This dissertation adds to the current body of literature by conducting an in-depth study of the reforms initiated by modern Albania in the education of mathematics. The time period between 1945 and 2000 is an important era for research because it represents the Communist government's duration of political control of Albania. Demonstration of the effectiveness of the educational reforms might demonstrate some evidence of the legitimacy of Communism. Conversely, the examination of the publicly available literature, when combined with survey data, may demonstrate a strong state-controlled force for propaganda that claimed reforms were more effective than they truly were. Purpose of the Study This study has answered the following questions: a) What were the reasons given for the education reforms initiated by the Albanian government during the period 1945-2000? What domestic and international political, social, and economic entities influenced the reform process? b) How was the mathematics curriculum determined, who was involved in making that determination, and what were the major components? c) Were assessments made of the results of the mathematics education reforms? How were these assessments taken into consideration when developing further improvements in mathematics education?
8 Procedures and Methods of the Study In order to answer the above questions, the research for information began with the identification of educational documents specific to Albania. These documents were found in Albania, in other nations, or on the Internet. The focus was on gaining information from a variety of different sources whenever possible. Answering Question A focused upon the factors that determined the need for educational reform during this time period. The research project specifically searched for and catalogued particular social, economic, and international movements that may have influenced policymakers in their assessment and design of educational reforms. Such factors included economic problems in the country due to lack of education and the desire of the newly appointed Communist government to demonstrate its effectiveness through the implementation of educational reform. Consideration was given to fit the specific reform of mathematics into the context of broader national education reform efforts. Answers to Question B were found by specifically searching for articles pertaining to mathematics reform during the particular time period. This included major educational administration appointments and curriculum development. The Ministry of Education's Arsimi Popullor (People's Education) was especially valuable in determining the answers to this question. Also, the researcher investigated several textbooks, Albanian Aritmetika 2 (Arithmetic textbook for the second grade) for the 1960s, 1970s and 1980s, which were found at the National Library in Tirana, Albania and compared and contrasted them with the Grade 2 Mathematics textbooks of Russia and United States of the same period of time.
9 Question C required a combination of the analysis of publications and survey data that demonstrated the real impact of reform efforts. The researcher searched for articles specifically studying the impact of reform efforts and the use of this data in the implementation of new reforms. The researcher further looked for political activities that might have spurred these reforms to see if political action and public reporting of reform efforts were consistent. Respondent survey data aided in the assessment of local school reform efforts that supported or denied published materials. Evaluating the quality of mathematics education in Albania was difficult because of the lack of unbiased data. Students were required to demonstrate mathematics proficiency through the successful completion of an examination in order to graduate from the eighth grade (Fiszbein, 2001). However, the reliability of these test scores has been criticized, because the tests were typically graded by teachers from the students' schools (Fiszbein, 2001). The passage of these tests was considered to be reflective of the teachers' abilities and therefore they had an interest in seeing as many students successfully pass the mathematics examination as possible. This situation has resulted in "an ongoing distortion of grades and granting of passing scores" (Fiszbein, 2001, p. 21). This demonstrates that research cannot depend upon schools self- reporting alone because of the high likelihood of skewed results and the impact of bias. The same problem of bias was found in governmental sources. Several studies were conducted by authors working in governmental institutions before school reforms were to be undertaken. (In Albania, education has long been considered to be in the process of reformation.) However, these studies were politically motivated, and the authors were not free to produce independent, objective analyses. Usually the
10 authors identified the failures of the previous methods and projected the future successes of current reforms, but they did not present a full or accurate portrait of the development of mathematics education in Albania. Mathematics education, like education in general, was influenced by the political, economic and social conditions of Albania, by the traditional culture of the country, by the country's geographical position and geopolitics, and by the political and financial institutions that supported the county's educational system. These factors highlighted the importance of the present study since it was undertaken independently, beyond the influence of the Albanian government and during a period of greater freedom of information. The study further traced the changing interpretations of mathematical truth in relation to a broader cultural context rather than just criticized, evaluated or interpreted the ideas being advocated. This approach gave the opportunity to clear up some abnormalities which have infected other previous investigations. These gathered documents were classified according to their content (curriculum, goals, administration, preparation of mathematics teachers and their continuing training, final examinations and the assessment of the student results, physical conditions of the classrooms, available teaching materials, teaching plans, etc.) The documents were further divided according to the historical periods that they referenced. While the study was not primarily historical in nature, it was important to develop a chronological history of the reforms and their subsequent policies in order to help understand the factors that led to these actions. The selected documents were studied and reclassified as the outline for the dissertation was refined. Based on the preliminary conclusions drawn from this
11 collected material, a list of questions was developed. The researcher travelled to Albania several times to complete this research. He submitted a questionnaire to those most active in mathematics education in Albania. The test population included senior teachers. Respondents were hand selected according to a variety of characteristics. First, long-standing educators with long teaching experience and high qualifications were chosen as respondents from each of the 37 districts. These teachers were considered to be members of the most highly qualified and skilled nuclei of teachers within each region, and many of these teachers were key participants in one or more mathematics educational reforms in the recent past. The division according to districts and cities was in order to ensure that a mixture of opinions and experiences was represented within the study, ranging from educators in small towns and rural districts to educators in large schools in big cities. These individuals were not randomly picked in any case, but were selected from the Institute of Education's files according to the same characteristics as established for the regional teacher respondents including distribution and experience. Naturally, these respondents were mathematics educators by preference due to the focus of research in this case. The purpose of this survey was to confirm the data collected through the press and governmental sources. This step was made necessary because the press in Albania has been heavily censored and the available documentation would have not provided a realistic picture. Te data were augmented by an additional survey. Two focus groups were organized in Tirana, the capital of Albania. These focus groups were composed of teachers, particularly senior teachers, and others who were in a professional position to directly observe and assess the effectiveness of the mathematics education reforms
12 conducted during these years. Then, the results of the national and international assessments of mathematics education reforms in Albania were studied. Once the first draft was produced, it was submitted to two authorities for review. Special attention was paid to identifying any documentation or other sources of information that had been overlooked in producing the first draft. Resources for the study Fortunately, several sources of information were available to help support this research project. The bibliography presented at the end of this repor reflects some of the most important institutions and documents that were used in this dissertation. These included the following: a) The Ministry of Education of Albania has published the monthly magazine Arsimi Popullor ("People's Education") since just prior to World War II. This magazine has published all of the decrees and government decisions relating to education during this period, as well as speeches given by political leaders, criticisms of education reforms, inaugurations of the most important education institutions and announcements of special events in the field of education. This magazine has also published the decisions of high party and government officials who have played important roles in education. b) When the Institute of Pedagogical Studies was founded in 1970, Arsimi Popullor was discontinued and the Revista Pedagogjike ("Pedagogical Magazine") began publication. This magazine continues to be published today, although the name of the institution was changed to the Institute of Curricula
13 and Standards in 2005. The Institute also possesses valuable unpublished studies. c) Many documents and studies concerning the early preparation of mathematics teachers are available through the Center for Training and Qualifying Teachers. This center also possesses valuable unpublished studies. d) The Faculty of Natural Sciences at the University of Tirana and other local universities (The University of Shkodra and The University of Elbasan) possess libraries containing information concerning the local development of mathematics education. e) The National Library possesses copies of all publications produced in Albania during the entire focus period, as well as copies of all defended dissertations and a great deal of foreign literature. (According to Albanian law, every publisher must provide the National Library with five copies of any published book or defended dissertation.) Furthermore, the National Library archives several Albanian Arithmetic textbooks for the second grade, belonging to different periods of time, which the researcher compared and contrasted with the Grade 2 Mathematics textbooks of Russia and United States. Summary of the Introduction and Organization of the Remainder of the Study This introduction has provided an overview that details the reasons for examining this area of research as well as providing an insight into the particular research problem. The development of further information regarding the historical background and outcomes is in Chapter II, Literature Review. Chapter III,
14 Methodology, expands on the methodology in use in the research and the philosophical underpinnings that the researcher has used to explore this information. Chapter IV, Discussion, presents the results of the study and the outcomes of the historical and thematic analyses. Finally, Chapter V, Conclusions, presents final discussion and answers to the research questions, an analysis of the limitations of the study and potential biases, a discussion for future research, and analysis of conclusions for further research as well as a critical examination of the outcomes in the study. Supplementary materials are included in Appendices at the end of the paper.
15 II BACKGROUND FOR THE STUDY Introduction This chapter provides a brief history of mathematics education from 1887 to 2000 and a review of the theoretical and empirical documents devoted to this period. This historical period is divided into the following sections: • Early development: Mathematics until 1945 • The Albanian Communist Regime's Educational Reforms • The Democratic Reforms Early development: Mathematics until 1945 From the period of the opening of the first Albanian school till the end of the Second World War in 1945, there is little documentation related to the development of mathematics in Albanian school. The book The History of Education and Albanian Pedagogical Thinking, sponsored by the Albania's Ministry of Education and Science and published in 2003, in Tirana, which was the major source for the next several pages, provides some history to the nation's educational system. Until 1887, the nation's population was very diverse and the nation could be divided into four main groups who organized their own schools: the Medrese (Holy place where Muslims worship God), i. e. the Turkish, the Greek, the Serbian and the Bulgarian schools. The first official Albanian school was opened in the city of Korea in 1887, named "Mesonjtorja e pare Shqipe e Korces" (The first Albanian school of Korea). The school was opened with 35 students and one teacher. The school (Mesonjtorja) was a common
16 school for students of different beliefs and it did not depend upon support from one particular religious institution. The school had both male and female students. The students came from all segments of the population and they were allowed to attend without paying a school tax. This school served as the model of the Albanian educational system. The school taught the Albanian language and reading, geography and mathematics. The opening of the school demanded considerable interest from many monthly magazines as: "Drita" (Light) and "Diruria" (Knowledge) and exactly the news item "Numertarja" (Numerator) and "Numeratorja" written by Jani Vreto. These magazines were interested in the school because it was the first of its kind, and because it promised a new way of education in Albania that was not based in the older ways of religious affiliation and gender discrimination. After some years, in Bucharest were published some other books. It's important to stress that the Mesonjtorja was a school for students of different beliefs and that it did not depend on religious institutions. "Schools, where the Albanian language was learned and schools opened by the Albanians existed before 1887, even long time before. However, the opening of the Albanian school of Korea indicated prosperity in the development of our national education. The Albanian Mesonjtorja of Korea was the first elementary school with full national physiognomy, laic and democratic" (Dedja, B. et al., p. 133). Also, four years later, in 1891, the first school for girls was opened in Korea, with teacher Sevasti Qiriazi. "In 1988, sister of Gjerasimi, Sevasti Qiriazi, was sent for undergraduate studies in the American School of Istanbul, with an aim to dedicate herself to the education of the Albanian females..." (Dedja, B. et al., p. 141). In the first day of school only three girls appeared, but by the year's end it increased to twenty seven.
17 "During the first year, the main attention was concentrated in teaching, writing and reading in Albanian and arithmetic" (Dedja, B. et al., p. 142). The teaching of mathematics spread rapidly with the development of the nation's schools. The demand for books caused the establishment of new publishing offices in Albania. The great demand for books caused the opening of a printing office in 1908 that published the nation's first known mathematics textbook. Monastery City also became the home for the "National Educational Congress of Elbasan," which eventually became responsible for the preparation of teachers for the nation's primary schools. The education of the nation's teachers was approved by the Albanian Congress. The Congress specifically sought to elevate the nation's mathematics core to equal that of Europe. Mathematics included a strong focus upon geometry and logics. The government also pursued options to have Albanian teachers trained abroad in order to improve their preparation. On November 28th, 1912, Albania was declared an independent country, which was recognized from the Conference of London's Ambassadors in July 29th of 1913. At this time in Albania there were 250 primary schools and a very limited "whole schools" that addressed a broad range of subjects. There were some schools which existed only in foreign languages where instruction was offered in Turkish, Greek or Italian. At the time, the nation's Minister of Education was Luigj Gurakuqi. Education and culture became important factors in securing and upholding the Independence of Albania. One part of the equation was nationalism. The creation of an independent Albanian country was the main political aim for the organization on advanced basis of the country's inner life, for a faster national education and culture. Many advocated the