The History of Hebrew Secondary Mathematics Education in Palestine During the First Half of the Twentieth Century Inbar Aricha-Metzer 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 2013 © 2013 Inbar Aricha-Metzer All Rights Reserved ABSTRACT The History of Hebrew Secondary Mathematics Education in Palestine During the First Half of the Twentieth Century Inbar Aricha-Metzer This dissertation traces the history of mathematics education in Palestine Hebrew secondary schools from the foundation of the first Hebrew secondary school in 1905 until the establishment of the State of Israel in 1948. The study draws on primary sources from archives in Israel and analyzes curricula, textbooks, student notebooks, and examinations from the first half of the 20th century as well as reviews in contemporary periodicals and secondary sources. Hebrew secondary mathematics education was developed as part of the establishment of a new nation with a new educational system and a new language. The Hebrew educational system was generated from scratch in the early 20th century; mathematical terms in Hebrew were invented at the time, the first Hebrew secondary schools were founded, and the first Hebrew mathematics textbooks were created. The newly created educational system encountered several dilemmas and obstacles: the struggle to maintain an independent yet acknowledged Hebrew educational system under the British Mandate; the difficulties of constructing the first Hebrew secondary school curriculum; the issue of graduation examinations; the fight to teach all subjects in the Hebrew language; and the struggle to teach without textbooks or sufficient Hebrew mathematical terms. This dissertation follows the path of the development of Hebrew mathematics education and the first Hebrew secondary schools in Palestine, providing insight into daily school life and the turbulent history of Hebrew mathematics education in Palestine. TABLE OF CONTENTS Chapter I: INTRODUCTION .........................................................................................................1 Need for the Study ...........................................................................................................................1 Purpose of the Study ........................................................................................................................3 Procedures of the Study ...................................................................................................................4 Analysis of Primary Sources ....................................................................................................4 Analysis of Periodicals .............................................................................................................5 Analysis of Secondary Sources ................................................................................................5 Chapter II: BACKGROUND OF PALESTINE—JEWISH HISTORY AND CULTURE ............6 The Ottoman Empire........................................................................................................................6 World War I .....................................................................................................................................9 The British Mandate ......................................................................................................................10 Chapter III: LITERATURE REVIEW..........................................................................................15 History of Mathematics Education: Research of Methodological Interest ....................................15 History of Mathematics Education: Research Perspectives from Different Countries..................20 Research on the History of Education in Palestine and Israel .......................................................30 Summary ........................................................................................................................................37 Chapter IV: METHODOLOGY AND SOURCES .......................................................................38 Rationale for the Methodology ......................................................................................................39 Time Period ............................................................................................................................39 Schools ....................................................................................................................................39 i Textbooks ...............................................................................................................................40 Britain and Germany ...............................................................................................................40 Data Collection ..............................................................................................................................41 Data Analysis .................................................................................................................................41 Chapter V: HEBREW SECONDARY EDUCATION IN PALESTINE ......................................44 The Objectives of Hebrew Secondary Education ..........................................................................44 The Circumstances of the Foundation of the First Hebrew Secondary Schools ....................44 Secondary School Objectives .................................................................................................46 Graduation Examinations and the Hebrew Diploma .....................................................................51 The Language of Instruction ..........................................................................................................62 General Education Versus Specialized Learning ...........................................................................66 Chapter VI: THE OBJECTIVES OF MATHEMATICS INSTRUCTION AND THE DEVELOPMENT OF HEBREW MATHEMATICAL LANGUAGE .........................................69 The Objectives and Means of Mathematics Instruction ................................................................69 The Development of Hebrew Mathematical Language .................................................................74 Arithmetic and Algebraic Notation ........................................................................................79 Geometric and Measurement Notation ...................................................................................80 Chapter VII: CURRICULA AND EXAMINATIONS .................................................................86 Curriculum Analysis ......................................................................................................................86 Arithmetic Curriculum ............................................................................................................87 Algebra Curriculum ................................................................................................................87 Geometry Curriculum .............................................................................................................88 ii Calculus Curriculum ...............................................................................................................90 Comments ...............................................................................................................................91 British and German Influence .................................................................................................92 Textbook Analysis .........................................................................................................................97 Analysis of Algebra Textbooks ..............................................................................................97 Analysis of Geometry Textbooks .........................................................................................115 Notebook Analysis .......................................................................................................................130 Two Geometry Notebooks of Yehoshua Grinbaum (Ninth Grade, 1944-1945) ..................131 Algebra Notebook of Yehoshua Grinbaum (Ninth Grade, 1944-1945) ...............................134 Graduation Examination Analysis ...............................................................................................136 Procedures for Developing and Administering the Examinations .......................................137 Topics ...................................................................................................................................139 Appearance in the Curriculum ..............................................................................................147 Structure ................................................................................................................................150 Analysis of the Questions .....................................................................................................152 Summary ...............................................................................................................................163 Chapter VIII: CONCLUSIONS AND RECOMMENDATIONS...............................................165 Summary ......................................................................................................................................165