Analyzing Mathematics High School State Examinations in Albania in the 1970s and 2006-2015

250 Pages·2017·2.1 MB·English

Analyzing Mathematics High School State Examinations in Albania
in the 1970s and 2006-2015: Two Decades, Two Historical Periods

Bukurie Gjoci

Submitted in partial fulfillment of the
requirements for the degree of
Doctor of Philosophy
under the Executive Committee
of the Graduate School of Arts and Sciences

COLUMBIA UNIVERSITY

2017
© 2017
Bukurie Gjoci
All rights reserved
ABSTRACT

Analyzing Mathematics High School State Examinations in Albania
in the 1970s and 2006-2015: Two Decades, Two Historical Periods

Bukurie Gjoci

This dissertation is devoted to the history of the Albanian system of education in
general, its mathematics education program in particular, and, specifically, the Albanian high
school mathematics assessment. Historical in terms of its research methodology, and
mathematical-pedagogical in terms of the objects of the study, this research explores and
compares the Albanian high school mathematics graduate examinations during 1970s and
2006 – 2015: two decades during two different historical periods. It analyzes the general
structure of the examinations, their mathematical task design, and the history of their changes
under the influence of political and social processes. The units of analysis here are the
questions of each examination, which are examined both individually and in context as part
of the examination, investigating the examinations’ topic coverage and comparing the latter
to the intended national curriculum.
This study was based on multiple primary sources, including documents from the
Albanian Ministry of Education, the Central State Archive of the Republic of Albania, the
Internet archive (http://www.arsimi.gov.al), memoirs of former teachers, high school
textbooks during the respective years, and other sources. The analysis showed that Albanian
mathematics education was not immune to political and social change: both its curriculum
and assessment were affected. Examination administration, format, topic coverage, and item
characteristics, even the pure mathematical problems, represented in some ways the Albanian
social, economic, and political views of the time.
TABLE OF CONTENTS

List of Tables ............................................................................................................. iii
Chapter I—INTRODUCTION .............................................................................................. 1
Need for the Study ..................................................................................................... 1
The Purpose of the Study .............................................................................................. 4
Procedure of the Study ................................................................................................ 5

Chapter II—BACKGROUND OF THE STUDY ................................................................... 8
Introduction ................................................................................................................ 8
History of Education in Albania ................................................................................. 10
Education During the Albanian National Renaissance (Mid-19th
Century-1912) ............................................................................................. 10
Education After the Declaration of Independence (1912-1928) ..................... 14
Education Under King Zogu ........................................................................... 17
The 1946 Education Reform ........................................................................... 21
The Reorganization of the Education System—The Long-term Measures .... 28
Education After Communism ......................................................................... 34
History of Mathematics Education in Albania ............................................................ 41
History of Examinations in Albanian Education ........................................................ 43
History of Examinations in Mathematics in Albania ...................................... 47
Summary ..................................................................................................................... 48

Chapter III—LITERATURE REVIEW .................................................................................. 53
Historical Research ..................................................................................................... 53
Education and Social and Political Change ................................................................ 55
Mathematics Education and Social and Political Change ........................................... 59
High-stakes Examinations and Social and Political Change ...................................... 61
Summary ..................................................................................................................... 65

Chapter IV—METHODOLOGY ............................................................................................ 67
Historical Research Methodology and Major Sources ............................................... 67
Examination Analysis Methodology ........................................................................... 70
General Structure of the Examinations ........................................................... 72
Item Characteristics ........................................................................................ 72
Topic Coverage ............................................................................................... 73
Alignment Analysis Methodology .............................................................................. 76
Examination Analysis—An Example ......................................................................... 78
Item Analysis .................................................................................................. 79
Item Analysis .................................................................................................. 81
Item Analysis .................................................................................................. 83
Item Analysis .................................................................................................. 85
The Examination Alignment Analysis ............................................................ 86
Summary ......................................................................................................... 86

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Chapter V—ANALYSIS ........................................................................................................ 88
The National Curriculum During the 1970s ............................................................... 88
The Teaching of Mathematical Content (Active Learning and
Problem Solving) ....................................................................................... 90
Teaching Through Real-Life Applications (Modeling) .................................. 93
Assessment ...................................................................................................... 96
Analysis of Examinations From the 1970s ................................................................. 96
General Structure of the Examinations and Item Characteristics ................... 97
Topic coverage ....................................................................................... 99
Subtopic representation .........................................................................103
Alignment of the Examinations’ Topic Coverage With Curriculum
During the 1970s .......................................................................................105
The National Curriculum During 2006-2015 ............................................................107
Curriculum Objectives ...................................................................................109
New Knowledge Introduction ........................................................................111
Knowledge Processing ...................................................................................112
Assessment .....................................................................................................114
Analysis of 2006-2015 Examinations ........................................................................117
General Structure of the Examinations and Item Characteristics ..................117
Topic coverage ......................................................................................119
Subtopic representation .........................................................................123
Alignment of the Examinations’ Topic Coverage With the Curriculum
During 2006-2015 .................................................................................124
Comparing Subtopic Representation Between the 1970s Examinations and
the 2006-2015 Examinations ................................................................126
Albania’s Social and Political Standing Represented Through Mathematical
Problems and Examinations ..................................................................132
Summary ....................................................................................................................135

Chapter VI—SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS ...................137
Summary ....................................................................................................................137
Conclusions ................................................................................................................141
Answers to the Research Questions ...............................................................141
Limitations of This Study and Recommendations for Further Studies ......................145

REFERENCES ......................................................................................................................147

APPENDICES .......................................................................................................................157
Appendix A – The 1970s Written Examinations ...................................................................157
Appendix B – The 1972 Oral question bank .........................................................................167
Appendix C – The 2006 – 2015 Written Examinations .........................................................169
Appendix D – Curriculum Framework ..................................................................................229
Appendix E – The required curriculum during 1970s ...........................................................231
Appendix F – The required curriculum during 2006-2015 ....................................................237

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LIST OF TABLES

Table

1 Curriculum Framework ............................................................................................... 75

2 General Structure of the 1970s Examinations ............................................................ 98

3 Mathematics Topics Detailed, Categorical Concurrence, and Range of
Knowledge for Each Examination, 1970-1979 ..........................................................100

4 General Structure of the 2006-2015 Examinations ....................................................118

5 Mathematics Topics Detailed, Categorical Concurrence, and Range of
Knowledge for Each Examination, 2006-2015 ..........................................................120

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ACKNOWLEDGEMENTS

It would require another dissertation to adequately express my gratitude and
appreciation for all of you who have aided and supported me throughout this journey. If you
are reading this, you know who you are, and though I cannot list all your names, rest assured
I will remember and pass on the nature of your kindness in my interactions with others.
Thank you, Dr. Alexander P. Karp, for your guidance, advice and honesty. Dr. Erica
Walker, Dr. J. Philip Smith, Dr. O. Roger Anderson and Dr. Patrick Gallagher, I appreciate
the time you spent reading my paper and am honored to have had the opportunity to discuss
my work with each of you resulting in invaluable comments and suggestions. Arta & Artur
Lika, Anduela Kaja and Naim Buci, I am thankful for your assistance in gathering resources
and materials. Also a special thank you to two mathematics teachers, Mr. Bashkim Muka and
Mr. Bujar Shehu; your answers to my questions were an irreplaceable source of information.
Brothers and sisters, thank you for providing a challenging “classroom” environment
by constantly engaging with me in riddle contests throughout our youth. Creation of new
riddles as necessary to survive these contests – most of which involved mathematics – dates
the beginning of my research to my childhood years. We were very fortunate to have parents
who through their selflessness, courage and foresight were able to free us from seemingly
insurmountable obstacles and restrictions to enable us for our futures. With great gratitude I
thank you, my parents, Zahide and Halit Gjoci.
Most importantly, I want to say thank you to my husband, Lami, and kids, Denis,
Kade and Danjel. Thank you for your support, encouragement and love you have given me!
You have literally gone through this journey with me, so this degree is as much yours as it is
mine. Thank you! I love you so much!
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Chapter I
INTRODUCTION

Need for the Study
Academic assessment is considered one major way of analyzing and improving the
educational process. Reforms in elementary and secondary education, which are in the forefront
of the public mind and on the agenda of elected officials and educators, rely on testing (Barton,
1998). High-stakes examination scores have a direct impact on a student’s life options and
opportunities (Lester, 2003; Moses & Nana, 2007), directly influence many education policies,
help refine programs, channel funding, and identify the roots of success (Cizek, 2001). Written
examinations were historically among the most important tools of assessment. They have been
used internationally and over time as a practical way to measure a person’s knowledge of an
academic subject.
Although academic testing in various countries originated from different historical roots,
they have three main functions: selection, placement, and certification decisions. In most countries,
the significance of testing is the greatest at the transition from secondary to postsecondary
schooling (U.S. Congress, Office of Technology Assessment, 1992). The American school system
has been viewed as the public “thoroughfare” on which all children journey toward productive
adulthood; by contrast, however, the role of the school system and of tests in many European
countries has remained principally one of “gatekeeper,” especially in the transition from high
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school to postsecondary (U.S. Congress, Office of Technology Assessment, 1992).
Thus, it is not surprising that written examinations have been studied nationally and
internationally. Key publications on the topic have been written by Azar (2005), Black (1992),
Dossey (1996), Gandal et al. (1994), Karp (2003, 2007), and Wu (1993). Because the success of
standards-based education systems depends on strong standards and assessments that measure
what the standards expect (Rothman et al., 2002, p. 1), many studies have been conducted on the
alignment of the examinations with the curriculum, namely, Al-Sadaawi (2007); La Marca,
Redfield, Winter, Bailey, & Despriet (2000); Martone and Sireci (2009); Nasser et al. (2014);
Polikoff, Porter, and Smithson (2011); and Webb (1997, 1999, 2002).
Indeed, the analysis of national written examinations has provided a deeper
understanding of the educational goals not only of the educators themselves, but also of the
government and society, and the practical ways in which these goals were meant to be
accomplished. However, this has not been the case for Albanian examinations, which have been
scarcely considered, much less analyzed, in any available sources. Albania has experienced a
dramatic history, both politically and educationally. For most of their history, Albanians have
undergone invasions, followed by occupations of foreign armies, during which time they were
prevented from developing their own educational system. Even though the earliest known book
written in Albanian, Meshari by Gjon Buzuku, dates back to 1555, the first official Albanian
school was only opened in 1887, and attempts to democratize education took place only after the
country’s declaration of independence in 1912 (Kola, 2014). In 1944, the communist regime
came to power in Albania, as it did in many other eastern European countries. The
implementation of compulsory primary education began in 1945 as part of the radical reforms
that were taking place in the creation of a new communist state with socialist features, which was
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achieved in 1952 (Kola, 2014). Assessment, as part of the education system during that time,
developed to a national level as well, and high-stakes examinations in general, and mathematics
examinations in particular, have become a formal part of the system. One of these examinations
is the High School State Graduation Examination; Dobrushi (2013) has called “Matura
Shtetërore” (The State Matura—the High School State Graduation Examination) one of the most
important procedures of the Albanian education sector, because of its impact in shaping both the
path of a student’s future education and the quality of higher education itself. The results of these
examinations represent one of the most important indicators of the education system’s
performance, particularly in connection with preparing students with the skills they need to face
present and future challenges (Golemaj, 2013).
An analysis of these examinations will provide a better understanding of Albanian
education in general and mathematics education in particular by describing the routes it has taken
and how it has been influenced over time, especially given that, to some degree, challenging,
high-stakes examinations drive the educational systems of their respective countries (Dossey,
1996). It will be of national interest to present information on the curriculum and discuss how
these examinations measure the knowledge they require, and whether they have evolved in a
coherent way, i.e., if they are broad enough to include key concepts and processes that will
maximize students’ opportunities for success in the 21st century (English, 2002). Internationally,
the examinations can be viewed as experiments based on methods that differ from those typically
used in other countries (Dossey, 1996).
This discussion of the historical evolution of these examinations, presented as a
comparison of two decades with two different political regimes—examinations from the 1970s,
when Albania was under the communist regime, and examinations from 2006-2015, when
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