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Mathematical Science Communication a Study and a Case Study Mathematical Science Communication a Study and a Case Study beim Fachbereich Mathematik und Informatik der Freien Universit¨atBerlin eingereichte Dissertation zur Erlangung des Grades einer Doktorin der Naturwissenschaften (Dr. rer. nat.) vorgelegt von Diplom Mathematikerin (Dipl.-Math.) Anna Maria Hartkopf Berlin 2020 Anna Maria Hartkopf: Mathematical Science Communication Day of the thesis defense: September 23, 2020 Supervisor: Prof. G¨unter Ziegler Referees: Prof. G¨unter Ziegler Prof. Hans Peter Peters For my grandparents: Anni (née. Lankes) and Fritz Hartkopf, and Maria Schreiber (née. Bolten) Acknowledgements My biggest thanks go to my supervisor G¨unter M. Ziegler. He gave me the perfect combination of freedom to explore and support to realize my ideas. Hans Peter Peters patiently answered all my questions about the science of science communication. Thank you both very much. Many thanks are also owed to the Berlin Mathematical School and their mentoring program that led me to Heike Siebert, who supported my academic development in significant ways. I am grateful to the Collaborative Research Centre Discretization in Geometry and Dynamics which funded my position and the realization of the project. I would also like to thank my colleagues at AG Diskrete Geometry at Freie Universit¨atBerlin for their support. Pavle Blagojevi´cwas always a source of encouragement. Jean-Philippe Labb´e taught me coding in SAGE and to always look on the bright side. Moritz Firsching provided the code for the Koebe-Andreev-Thurston realization of the polyhedra. Elke Pose helped organize my funding and encouraged me in situations of doubt. Hannah Sch¨aferSj¨oberg, Sophia Elia and I shared an actual office and a virtual one during the pandemic. Having them by my side helped me through many decisions and obstacles. Without the Polytopia-Team, realizing the project would not have been possible; the team members and some of their many contributions follow. Max Pohlenz lent my scribbled wire- frames a professional design. Martin Skrodzki and Stefan Auerbach programmed the entire website from scratch and did an exceptional job at making it low-maintenance. The TikZ-artist Johanna Steinmeyer provided many pictures of wannabe and real polyhedra. Marie-Charlotte Brandenburg implemented the viewer, the Hamilton-game and the virtual-reality environment. She was on duty when Zeit-Online published an article about the project and approved of 800 polyhedra names within two days. Erin Henning is head of the social media department, and every week I looked forward to her laudation for the polyhedron of the week. She supported 7 the project by translating the website and the school materials and her enthusiastic work for workshops and events. Mara Kortenkamp is the latest addition to the team. Many thanks for the graphics on the descriptive statistics, the sitemap and the timeline. I would like to thank Thomas Vogt from Medienb¨uro der Deutschen Mathematiker Vereini- gung for his help with the press releases and for hosting the website on the server. Pauline Linke helped conceptualizing Polly's Journal and mastered the text processing program to give it an appealing design. Many thanks also go to the teachers and pupils who tested the school material: Stefan Korntreff, Gudrun Tisch and Anik´oRamshorn-Bircsak. Thanks to the kids in the MSG for just being awesome. Joseph Doolittle, Sophia Elia, Erin Henning, Katharina H¨oyng,Nevena Palic, and Paula Schiefer added readability to this thesis by proofreading it. Thank you all! Vielen Dank an Daniel, Moni und Peter. Contents Introduction 13 1 Mathematical Science Communication 17 1.1 Science Communication................................ 17 1.1.1 The Role of Education in Science Communication............. 19 1.1.2 Motivations of Science Communication.................... 20 1.1.3 Objectives for Science Communication.................... 20 1.1.3.1 Public Understanding of Science.................. 21 1.1.3.2 Scientific Literacy.......................... 22 1.1.3.3 Deficit Model............................. 24 1.1.3.4 Public Awareness of Science.................... 25 1.1.3.5 Trust { the New Variable in the Discourse............ 26 1.1.3.6 What about the Trust in Science in Germany?.......... 28 1.1.3.7 Skepticism as an Opportunity.................... 30 1.1.3.8 Untangling Science Journalism and Public Relations....... 30 1.2 Mathematical Science Communication........................ 32 1.2.1 Literature Review............................... 32 1.2.1.1 The Deficit Model { Presumed Dead yet Omnipresent...... 33 1.2.1.2 Formats of Mathematical Science Communication........ 37 1.2.1.3 Gender and Diversity........................ 38 1.2.1.4 Digression: The Image of Mathematics.............. 39 1.2.2 Conceptualizing the Objectives of Mathematical Science Communication 41 1.2.2.1 Mathematical Citizen Science.................... 45 1.3 What's Next for Mathematical Science Communication?.............. 49 2 POLYTOPIA { Adopt a Polyhedron 51 2.1 Motivation, Objectives and Methods......................... 51 2.1.1 Motivation................................... 51 2.1.2 Objectives.................................... 52 2.1.3 Methods..................................... 53 2.1.4 Classification.................................. 54 2.2 Execution of the Project................................ 57 2.2.1 Website..................................... 57 2.2.1.1 Webdesign.............................. 58 2.2.1.2 Implementation........................... 60 2.2.1.3 Content................................ 62 2.2.2 Timeline..................................... 64 2.3 Results of the Project................................. 66 2.3.1 Defining Success................................ 66 2.3.2 User Numbers................................. 66 2.3.3 User Survey................................... 68 2.3.3.1 Demographical Data......................... 69 2.3.3.2 Self-Claimed Interest and Skill................... 70 2.3.3.3 Did you Learn Something New about Math here?........ 73 2.3.3.4 Pathways to the Project....................... 73 2.3.3.5 How would you Rate this Page?.................. 75 2.4 Conclusion....................................... 76 3 Mathematics Education 77 3.1 Bridging Formal and Informal Learning....................... 77 3.2 Didactical Concepts behind the School Materials.................. 80 3.2.1 Project Teaching in the Math Class..................... 80 3.2.2 Inquiry Based Learning............................ 81 3.2.3 Dialogical Learning............................... 84 3.2.4 EIS-Principle.................................. 85 3.3 School Material..................................... 87 3.3.1 Class Set.................................... 87 3.3.2 Finding Research Questions.......................... 88 3.3.3 Polly's Journal................................. 89 3.3.4 Discovery Cards................................ 91 3.3.5 Project Teaching as the Backdrop for all Materials............. 91 3.4 Linking Points to the Curriculum { Competencies and Central Themes...... 93 3.4.1 Primary Education............................... 93 3.4.2 Secondary Education.............................. 95 3.5 Applying Didactical Principles into the Project Design............... 96 4 Mathematics 97 4.1 \Adopting a What?": On the Term Polyhedron ................... 97 4.2 Genealogy of the Term Polyhedron .......................... 98 4.3 Defining the Term Polyhedron ............................. 105 4.3.1 Convex 3-Polytope............................... 105 4.3.2 Vertices, Edges and Faces of Polyhedra................... 107 4.3.3 Combinatorial Equivalence Classes...................... 107 4.3.4 Steinitz' Theorem............................... 108 4.3.5 Koebe-Andreev-Thurston Generalization of Steinitz' Theorem...... 109 4.3.6 Putting it into Practice............................ 110 4.3.6.1 Visualization Files.......................... 111 4.3.6.2 Edge Unfoldings and Crafting Sheets............... 111 4.4 D¨urer'sConjecture................................... 115 4.4.1 D¨urerInvents the Edge Unfolding...................... 115 4.4.2 Shephard's Problem.............................. 116 4.4.3 Gr¨unbaum's Questions............................. 117 4.4.4 Computational Experiments.......................... 119 4.4.4.1 Random Unfoldings { Schevon................... 119 4.4.4.2 Attempts to Characterize the Simple Cut Tree { Fukuda.... 120 4.4.4.3 Systematic Approach { Schlickenrieder.............. 120 4.4.4.4 Finding more Counterexamples { Lucier.............. 121 4.4.5 Theoretical Work................................ 122 4.4.5.1 First Steps { DiBiase........................ 122 4.4.5.2 Combinatorial Result { Ghomi................... 122 4.4.6 Related Problems................................ 123 4.4.6.1 Non-convex Polyhedra........................ 123 4.4.6.2 General Unfolding.......................... 124 4.4.6.3 Pseudo-Edge Unfolding by Ghomi and Barvinok......... 126 4.4.6.4 The Inverted Problem: Is a Polygon a Net of a Polyhedron?.. 126 4.4.6.5 Higher Dimensions.......................... 128 Conclusion 129 Bibliography 133 Appendix 147 Glossary............................................ 150 Data Protection....................................... 161 Survey............................................. 166 School Material........................................ 169 Class Set........................................ 169 Class Set { Front Page................................. 171 Research Questions................................... 172 Class Set { Teachers' Manual............................
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