Mathematics Education in Mozambique
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Paulus Gerdes MATHEMATICS EDUCATION IN MOZAMBIQUE Papers from the Early 1980s Paulus Gerdes Copyright © 2014 by Paulus Gerdes www.lulu.com http://www.lulu.com/spotlight/pgerdes Paulus Gerdes Mathematics Education in Mozambique: Papers from the Early 1980s 2014 Paulus Gerdes Title: Mathematics Education in Mozambique: Papers from the Early 1980s Author: Paulus Gerdes C. P. 915, Maputo, Mozambique [email protected] Proofreading: Lesira L. Gerdes Publisher: ISTEG-University, Boane, Mozambique International distribution (Printed version and eBook): www.lulu.com/spotlight/pgerdes Copyright © 2014 Paulus Gerdes Mathematics Education in Mozambique Contents Page 0 Introduction 9 1 Changing Mathematics Education in 11 Mozambique 0 Introduction 11 1 History of Education and of Mathematics 12 Education in Particular 1.1 Traditional 12 1.2 Colonial 13 1.3 In the Liberated Areas 15 1.4 Since Independence 16 2 The Training of Mathematics Teachers 20 2.1 Historical Retrospective 20 2.2 The Teacher Training Courses 20 2.3 Further Training for Teachers 25 2.4 Professional Situation 28 3 National Seminar on the Teaching of 30 Mathematics 4 Open Questions 35 Notes and references 37 2 The First Mathematics Olympiads in 41 Mozambique Esselina Macome’s Autobiography 41 0 Introduction 42 1 Why Mathematics Olympiads were introduced 44 in the People’s Republic of Mozambique 1.1 Necessity to Popularise Mathematics 44 1.2 Looking for Ways to Popularise 45 Mathematical Knowledge 2 Learning from other Experiences 46 9 Paulus Gerdes 2.1 Objectives 46 2.2 How to Achieve these Objectives? 47 3 The First Maputo Mathematics Olympiad 48 3.1 Mature Situation 48 3.2 Realization 49 3.3 Correction 49 4 Analysis of Results 49 4.1 Distribution 50 4.2 Social Background 53 4.3 Composition by Gender 53 4.4 ‘A Great Success’ 54 5 Extension 55 6 The Future 56 7 Postscript 1983 56 Appendix 1: Short Autobiographies of Some 60 Winners in the First Mathematics Olympiads 1 Abdulcarimo Ismael 60 2 Lourenço Lázaro Magaia 62 3 Fernando Victor Martins Saide 64 Appendix 2: Problems in the Maputo Mathematics 66 Olympiad (1981) at the Level of the 10th and 11th Grades Appendix 3: Problems in the Maputo Mathematics 69 Olympiad (1982) at the Level of the 7th, 8th and 9th Grades References 70 Notes 71 3 Conditions and Strategies for Emancipatory 73 Mathematics Education in Underdeveloped Countries Point of departure: mathematics education cannot 73 be neutral Mathematics education for emancipation. How? 74 10 Mathematics Education in Mozambique Problematizing reality in classroom situations 75 Creating confidence 79 A. Cultural strategies 79 B. Social strategies 85 C. Individual-collective strategies 85 Concluding remarks 87 References 89 4 Culture, Mathematics and Curriculum 91 Development in Mozambique 0 Confrontation 91 1 Education-policy in Mozambique 92 2 The fight against mathematical 95 underdevelopment: some lessons from other Third World countries Curriculum transplantation 95 Selective perspective 96 Necessity of adaptation to local culture and 97 needs Profound criticisms of actual mathematics 98 education 3 Towards a socialist mathematics-education- 100 policy 4 Incorporation of mathematical traditions into the 104 curriculum First example 106 Second example 110 Third example 112 References 115 Appendix 1 119 Books in English by the same author 121 11 Paulus Gerdes 12 Mathematics Education in Mozambique INTRODUCTION The book Mathematics Education in Mozambique contains four papers from the early 1980s. The first paper, CHANGING MATHEMATICS EDUCATION IN MOZAMBIQUE, was published in 1981 in the international journal Educational Studies in Mathematics (Dordrecht / Boston, Vol. 12, 455-477). It is a modified version of the text Mathematics Education in the People’s Republic of Mozambique, elaborated in accordance with the questionnaire ‘Comparative study of the development of Mathematics Education as a professional discipline in different countries,’ organised by Gert Schubring (University of Bielefeld, Germany) for the Fourth International Congress on Mathematical Education, Berkeley, USA, 1980. The paper presents a brief description and analysis of mathematics education in different phases of the history of Mozambique, in pre-colonial and colonial times, during the National Liberation Struggle and after its Independence in 1975. The successes and problems that still had to be resolved in the post-independence period constitute the second part of the article, where particular attention has been given to teacher training and the first National Seminar on the Teaching of Mathematics. The second paper, THE FIRST MATHEMATICS OLYMPIADS IN MOZAMBIQUE, was published in 1984 in Educational Studies in Mathematics (Dordrecht / Boston, Vol. 15, 149-172). It explains why Mathematics Olympiads were introduced in the People’s Republic of Mozambique. It contains a description and analysis of the results — distribution of scores, types of problems, social background and composition by gender of participants and winners — of the first Mathematics Olympiads, together with short autobiographies of some winners. These autobiographies offer some insight into the social aspects of the development of their mathematical talents. The third paper, CONDITIONS AND STRATEGIES FOR EMANCIPATORY MATHEMATICS EDUCATION IN UNDERDEVELOPED COUNTRIES, was published in 1985 in the international journal For the Learning of Mathematics (Montreal, Vol. 5, No. 1, 15-20). It resulted from the revision of an invited paper 9 Paulus Gerdes presented at the Caribbean Conference on Mathematics for the Benefit of the Caribbean Communities and its Reflection in the Curriculum, organised by the Inter-American Committee on Mathematical Education, Paramaribo, Suriname, October 18-21, 1982. The paper was reproduced in the books Is mathematics teaching neutral? (University of Cape Town, 1987, 10-15), edited by Chris Breen, and Mathematics Education: Major Themes in Education (Routledge, London, 2010, Volume 1, 179-189), edited by Alan J. Bishop. In the paper, I reflect on my experiences in Mozambique. I present examples of problematizing reality in mathematics classroom situations and suggest some conditions and strategies for mathematics education to become emancipatory in ‘developing’ countries; in particular, some cultural, social, and individual-collective strategies for creating confidence among teachers and pupils. The fourth paper, ON CULTURE, MATHEMATICS AND CURRICULUM DEVELOPMENT IN MOZAMBIQUE, is the short version of an invited paper presented at the Seminar “Mathematics and Culture”, Bergen, Norway, September 26-28, 1985. This version was published in the book Mathematics and Culture: A seminar report (Caspar Forlag, Rådal, 1986, 15-42), edited by Stieg Mellin-Olsen and Marit Johnsen Høines. The paper discusses the education policy in Mozambique and the fight against mathematical underdevelopment. It draws some lessons from other developing countries regarding curriculum transplantation, selective perspective of curricula, and the necessity of incorporating local culture and needs. Furthermore, the paper stresses the need for incorporation of ‘mathematical traditions’ into the curriculum, and presents several examples for reflection by mathematics educators. Naturally, the book, Mathematics Education in Mozambique: Papers from the Early 1980s, reflects the cultural, social and political contexts in which the papers were written. Nevertheless, I express the hope that the reproduction of these papers may stimulate among its readers an interest in some critical issues in the development of mathematics in Mozambique or elsewhere. Paulus Gerdes August 27, 2014 10 Mathematics Education in Mozambique Chapter 1 CHANGING MATHEMATICS EDUCATION IN MOZAMBIQUE 1 Educational Studies in Mathematics 12 (1981), 455-477 In this paper a brief description and analysis is given of mathematics education in different phases of the history of Mozambique, in the feudal and colonial times, during the National Liberation Struggle and after the Independence in 1975. The successes and problems that still have to be resolved of the post-independence period constitute the second part of the article, where particular attention has been given to teacher training and the first National Seminar on the Teaching of Mathematics. 0. INTRODUCTION Mathematics education in Mozambique is no exception to the evident but often forgotten ‘rule’, that — in the formulation of Howson 2 — “mathematical education does not take place in a vacuum.” In our view, the history of mathematical education in Mozambique can be understood as an integral part of the processes of change of society and of education in particular. To achieve such an understanding it is necessary, according to Neander3, to investigate the history of mathematics education at four interrelated levels: (1) economic development, (2) general political development, (3) development of mathematics, and (4) development of the educational system. It is not yet possible to analyse thoroughly these levels and their interdependencies in the concrete case of Mozambique, but we hope to bring forward sufficient elements of such an analysis to make understandable the first achievements and the outstanding problems of the post-independence period. 4 We begin this paper with a brief review of the history of education and mathematics education in Mozambique, focussing on 11 Paulus Gerdes changes in these important parameters of mathematics education: 5 for whom, by whom, with what objectives, curriculum, teaching