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Texts of The POPULARIZATION OF MATHEMATICS AS INTERCULTURAL COMMUNICATION-AN EXPLORATORY STUDY Klara Kelecsenyi A Thesis in the Department of Mathematics and Statistics Presented in Partial Fulfillment of the Requirements For the Degree of Doctor of Philosophy (Mathematics) at Concordia University Montreal, Quebec, Canada September 2009 © Klara Kelecsenyi, 2009 Library and Archives Bibliotheque et 1*1 Canada Archives Canada Published Heritage Direction du Branch Patrimoine de I'edition 395 Wellington Street 395, rue Wellington Ottawa ON K1A 0N4 Ottawa ON K1A 0N4 Canada Canada Your file Votre reference ISBN: 978-0-494-63411-0 Our Trie Notre reference ISBN: 978-0-494-63411-0 NOTICE: AVIS: The author has granted a non­ L'auteur a accorde une licence non exclusive exclusive license allowing Library and permettant a la Bibliotheque et Archives Archives Canada to reproduce, Canada de reproduire, publier, archiver, publish, archive, preserve, conserve, sauvegarder, conserver, transmettre au public communicate to the public by par telecommunication ou par I'lntemet, preter, telecommunication or on the Internet, distribuer et vendre des theses partout dans le loan, distribute and sell theses monde, a des fins commerciales ou autres, sur worldwide, for commercial or non­ support microforme, papier, electronique et/ou commercial purposes, in microform, autres formats. paper, electronic and/or any other formats. The author retains copyright L'auteur conserve la propriete du droit d'auteur ownership and moral rights in this et des droits moraux qui protege cette these. Ni thesis. Neither the thesis nor la these ni des extraits substantiels de celle-ci substantial extracts from it may be ne doivent etre imprimes ou autrement printed or otherwise reproduced reproduits sans son autorisation. without the author's permission. In compliance with the Canadian Conformement a la loi canadienne sur la Privacy Act some supporting forms protection de la vie privee, quelques may have been removed from this formulaires secondaires ont ete enleves de thesis. cette these. While these forms may be included Bien que ces formulaires aient inclus dans in the document page count, their la pagination, il n'y aura aucun contenu removal does not represent any loss manquant. of content from the thesis. 1+1 Canada Ill ABSTRACT Popularization of mathematics as intercultural communication - An exploratory study Klara Kelecsenyi, Ph.D. Concordia University, 2009 Popularization of mathematics seems to have gained importance in the past decades. Besides the increasing number of popular books and lectures, there are national and international initiatives, usually supported by mathematical societies, to popularize mathematics. Despite this apparent attention towards it, studying popularization has not become an object of research; little is known about how popularizers choose the mathematical content of popularization, what means they use to communicate it, and how their audiences interpret popularized mathematics. This thesis presents a framework for studying popularization of mathematics and intends to investigate various questions related to the phenomenon, such as: - What are the institutional characteristics of popularization? - What are the characteristics of the mathematical content chosen to be popularized? - What are the means used by popularizers to communicate mathematical ideas? - Who are the popularizers and what do they think about popularization? - Who are the audience members of a popularization event? IV - How do audience members interpret popularization? The thesis presents methodological challenges of studying popularization and suggests some ideas on the methods that might be appropriate for further studies. Thus it intends to offer a first step for developing suitable means for studying popularization of mathematics. V ACKNOWLEDGMENTS First and foremost I would like to thank my supervisor, Professor Anna Sierpinska who constantly helped me throughout my doctoral studies. She was willing to decipher my messy thoughts and made sense of those I did not yet understand. Her wise guidance and advice (which it often took me a while to understand) made me ask a variety of questions about research and beyond. Thank you, Anna, for your dedication, support, and encouragement. I also wish to thank the lecturers and audience members who kindly agreed to participate in my study, and were willing to offer their time and share their views and comments with me. Finally, I would like to thank my family and friends for their constant support and encouragement during the years of my studies. vi CONTENTS List of Figures xvi Chapter 1. Introduction 1 Chapter 2. Building a framework for studying popularization of mathematics: Popularization as intercultural communication 6 2.1 Introduction 6 2.2 The tourist metaphor and its implications r 2.2.1 Popularization of mathematics is organized action 7 2.2.2 Admission to a popularization of mathematics event is non-selective 8 2.2.3 Participation in a popularization of mathematics event is not compulsory 8 2.2.4 Popularization of mathematics attempts to make mathematics appear attractive to the visitors 9 2.2.5 Mathematics is a culture 9 2.2.6 The visited mathematical culture must be somewhat "exotic" for the audience to warrant organizing a popularization of mathematics event to show it 11 2.2.7 Popularization of mathematics involves communication between two cultures, but not enculturation in or acculturation to a foreign culture 12 vii 2.2.8 There are different models of communication between popularizers and the audience in popularization of mathematics 14 2.2.9 Popularization of mathematics has a political agenda 20 2.2.10 Popularization of mathematics faces several important challenges: problems of communicability and translation 22 2.3 A framework for studying popularization of mathematics 28 Chapter 3. Institutional environments of popularization of mathematics 32 3.1 Introduction 32 3.2 A notion of institution 32 3.3 To what extent is popularization of mathematics institutionalized? 36 3.4 Position of popularization of mathematics in international conferences 41 3.4.1 Popularization of mathematics in ICMs 41 3.4.2 Popularization of mathematics in conferences on mathematics education 45 3.5 The "rules of the game" in popularization of mathematics 46 3.6 The institutional environments of the "Medial Representation" lecture and the "Escher" lecture 51 3.6.1 The institutional environment of the "Medial representation" lecture 51 viii 3.6.2 The institutional environment of the "Escher" lecture 53 3.6.3 General remarks about the institutional contexts of the lecture series 54 3.7 Conclusions 55 Chapter 4. The popularized mathematics 57 4.1 Introduction 57 4.2 Attempts at categorizing the mathematical content of popularization 61 4.3 Investigating one recurrent topic in popularization: The proof of the irrationality of the square root of two 68 4.3.1 Proof of irrationality of V2~ in Constance Reid's "From zero to infinity" 68 4.3.2 Proof of irrationality of V2 in Ian Stewart's "Letters to a young mathematician" 69 4.3.3 Proof of irrationality of V2 in Phillip J. Davis and Reuben Hersh, "The Mathematical Experience" 70 4.3.4 Proof of irrationality of V2~ in Roger Penrose's "The Road to Reality. A Complete Guide to the Laws of the Universe" 71 4.3.5 Conjectures about reasons for including the proof of irrationality of V^ in a popular book 73 4.4 The mathematical content of two popular lectures 76 ix 4.4.1 The mathematical content of the first lecture: Medial representations 77 4.4.2 The mathematical content of the second lecture: the mathematics of Escher's "Print Gallery" lithograph 81 4.4.3 Comparison of the mathematical content of the two lectures 83 4.5 Conclusions 83 Chapter 5. Analyzing the means that popularizers use to communicate their message 85 5.1 Introduction 85 5.2 The Duval-Jakobson framework for studying mathematical texts 89 5.3 Interpretation of the Duval-Jakobson framework in the context of popularization of mathematics 93 5.3.1 The meta-discursive functions 93 5.3.2 The discursive functions 100 5.3.3 The non-discursive functions 107 5.4 Comparing the mathematical discourse in a research paper and an expository article 110 5.4.1 Choice of the papers 110 5.4.2 Some general remarks about the two papers to be compared 112 X 5.4.3 Comparing the role of metadiscursive functions of language in the two papers 113 5.4.4 Comparing the role of non-discursive functions of language in the two papers 114 5.4.5 Comparing the role of discursive functions of language in the two papers 115 5.4.6 Some additional remarks on the use of communicative functions of language in the two papers 118 5.5 Comparing two popular lectures from the point of view of the means used to convey the message 120 5.5.1 The "Medial representation" lecture 120 5.5.2 The "Escher" lecture 126 5.5.3 Comparing the two lectures 129 5.6 Conclusions 131 Chapter 6. Popularizers and their views of mathematics and popularization 133 6.1 Introduction 133 6.2 A "family portrait" of popularizers based on nine interviews 134 6.2.1 Backgrounds and professions 134 6.2.2 Views on the goals of popularization of mathematics ... 136 xi 6.2.3 Popularizers' views on the conditions of success of popularization 139 6.3 Individual portraits of two popularizers, with their lectures in the background 142 6.3.1 The lecturers' backgrounds 143 6.3.2 The choice of the topic of the lecture 144 6.3.3 Lecturers' expectations about the audience's understanding of the lectures 146 6.3.4 Popularizers' beliefs about effective means of communicating mathematics in their lectures 150 6.3.5 Comparison of the lecturers' views 154 6.4 Conclusions 155 Chapter 7. Analysis of interviews with members of the audience of popular lectures.
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