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 i 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