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Mathematics Education in the Digital Era Alexei Volkov Viktor Freiman Editors Computations and Computing Devices in Mathematics Education Before the Advent of Electronic Calculators Computations and Computing Devices in Mathematics Education Before the Advent of Electronic Calculators MATHEMATICS EDUCATION IN THE DIGITAL ERA Volume 11 Series editors Dragana Martinovic, University of Windsor, ON, Canada Viktor Freiman, Université de Moncton, NB, Canada Editorial Board Marcelo Borba, State University of São Paulo, São Paulo, Brazil Rosa Maria Bottino, CNR – Istituto Tecnologie Didattiche, Genova, Italy Paul Drijvers, Utrecht University, Utrecht, The Netherlands Celia Hoyles, University of London, London, UK Zekeriya Karadag, Giresun Üniversitesi, Giresun, Turkey Stephen Lerman, London South Bank University, London, UK Richard Lesh, Indiana University, Bloomington, USA Allen Leung, Hong Kong Baptist University, Hong Kong Tom Lowrie, University of Canberra, Australia John Mason, Open University, UK Sergey Pozdnyakov, Saint-Petersburg State Electro Technical University, Saint-Petersburg, Russia Ornella Robutti, Università di Torino, Torino, Italy Anna Sfard, Michigan State University, USA & University of Haifa, Haifa, Israel Bharath Sriraman, University of Montana, Missoula, USA Anne Watson, University of Oxford, Oxford, UK More information about this series at http://www.springer.com/series/10170 Alexei Volkov Viktor Freiman (cid:129) Editors Computations and Computing Devices in Mathematics Education Before the Advent of Electronic Calculators 123 Editors AlexeiVolkov Viktor Freiman Centerfor General Education UniversitédeMoncton andInstitute of History Moncton, NB National TsingHua University Canada Hsinchu Taiwan ISSN 2211-8136 ISSN 2211-8144 (electronic) Mathematics Educationin the Digital Era ISBN978-3-319-73394-4 ISBN978-3-319-73396-8 (eBook) https://doi.org/10.1007/978-3-319-73396-8 LibraryofCongressControlNumber:2017962537 ©SpringerNatureSwitzerlandAG2018 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpart of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission orinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodologynowknownorhereafterdeveloped. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfrom therelevantprotectivelawsandregulationsandthereforefreeforgeneraluse. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authorsortheeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinor for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictionalclaimsinpublishedmapsandinstitutionalaffiliations. ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Contents Part I Introduction History of Computations, Computing Devices, and Mathematics Education from the Teaching and Learning Perspective: Looking for New Paths of Investigation . . . . . . . . . . . . . . . . . . . . . . . . . 3 Viktor Freiman and Alexei Volkov Part II Middle East, India, Greece, and Byzantine Empire in Antiquity and Middle Ages Computation in Early Mesopotamia. . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Duncan J. Melville Computational Techniques and Computational Aids in Ancient Mesopotamia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 Jens Høyrup Interpreting Tables of the Arithmetical Introduction of Nicomachus Through Pachymeres’ Treatment of Arithmetic: Preliminary Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 Athanasia Megremi and Jean Christianidis The So-Called “Dust Computations” in the Līlāvatī . . . . . . . . . . . . . . . . 95 Takanori Kusuba Reading Algorithms in Sanskrit: How to Relate Rule of Three, Choice of Unknown, and Linear Equation? . . . . . . . . . . . . . . . . . . . . . . 115 Charlotte-V. Pollet Part III Far East: China, Korea, Japan Chinese Counting Rods: Their History, Arithmetic Operations, and Didactic Repercussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 Alexei Volkov v vi Contents Interpreting Algorithms Written in Chinese and Attempting the Reconstitution of Tabular Setting: Some Elements of Comparative History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 Charlotte-V. Pollet Same Rods, Same Calculation? Contextualizing Computations in Early Eighteenth-Century Korea . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 Young Sook Oh The Education of Abacus Addition in China and Japan Prior to the Early 20th Century. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 Yifu Chen Teaching Computation in 19th-Century Japan: The Transition from Individual Coaching on Traditional Devices at the End of the Edo Period (1600–1868) to Lectures on Western Mathematics During the Meiji Period (1868–1912) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 Marion Cousin Part IV Early Modern Europe and Russia Counting Devices in Russia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299 Alexei Volkov AShortHistoryofComputingDevicesfromSchickard todeColmar: Emergence and Evolution of Ingenious Ideas and Technologies as Precursors of Modern Computer Technology. . . . . . . . . . . . . . . . . . . . . 339 Viktor Freiman and Xavier Robichaud Computation Devices in Nineteenth-Century Mathematics Instruction in Europe. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365 Gert Schubring Toward a History of the Teaching of Calculation in Russia. . . . . . . . . . 385 Alexander Karp Part V Conclusion The Unsettling Playfulness of Computing. . . . . . . . . . . . . . . . . . . . . . . . 409 Jean-François Maheux Calculating Aids in Mathematics Education Before the Advent of Electronic Calculators: Didactical and Technological Prospects. . . . . . . 433 Dragana Martinovic Index of Technical Terms.... ..... .... .... .... .... .... ..... .... 459 Index of Individuals .... .... ..... .... .... .... .... .... ..... .... 463 Index of Primary Materials .. ..... .... .... .... .... .... ..... .... 469 Editors and Contributors About the Editors Alexei Volkov is a professor of the Center for General Education and of the Graduate Institute of History of the National Tsing Hua University (Hsinchu, Taiwan).Hisresearchfocusesonthehistoryofmathematicsandmathematicsedu- cation in East and Southeast Asia. He has published a number of papers and book chaptersonthesetopics,including“Didacticaldimensionsofmathematicalproblems: ‘weighted distribution’ in a Vietnamese mathematical treatise”, in Alain Bernard and Christine Proust (eds.), Scientific Sources and Teaching Contexts Throughout History:ProblemsandPerspectives,Dordrechtetc:Springer,2014,pp.247–272and “Argumentation for state examinations: demonstration in traditional Chinese and Vietnamese mathematics”, in Karine Chemla (ed.), The History of Mathematical ProofinAncientTraditions,CambridgeUniversityPress,2012,pp.509–551. ViktorFreiman isaFullProfessorofMathematicsEducationattheUniversitéde Moncton,Canada.Hiswork,besidesthehistoryofmathematicseducation,focuses ontheuseofdigitaltechnologyinteachingandlearning,interdisciplinarylearning, computationalthinking,designthinking,creativity,mathematical problem-solving, andgiftedness.Since2014,heisdirectorofCompeTI.CA(CompétencesenTICen Atlantique) partnership network, studying a lifelong development of digital com- petences.Heisco-editoroftheSpringerBookSeriesMathematicsEducationinthe Digital Era. Contributors Yifu Chen Independent Scholar, Kaohsiung, Taiwan Jean Christianidis Department of History and Philosophy of Science, National and Kapodistrian University of Athens, Athens, Greece; Centre Alexandre Koyré, Paris, France vii viii EditorsandContributors Marion Cousin Institut d’Asie Orientale, École normale supérieure de Lyon, Lyon, France Viktor Freiman Université de Moncton, Moncton, NB, Canada JensHøyrup RoskildeUniversity,Roskilde,Denmark;InstitutefortheHistoryof Natural Sciences, Chinese Academy of Sciences, Beijing, China; Max-Planck-Institut Für Wissenschaftsgeschichte, Berlin, Germany Alexander Karp Teachers College, Columbia University, New York, NY, USA Takanori Kusuba History and Philosophy of Science, Osaka University of Economics, Osaka, Japan Jean-FrançoisMaheux UniversitéduQuébecàMontréal,Montréal,QC,Canada Dragana Martinovic University of Windsor, Windsor, ON, Canada Athanasia Megremi Department of History and Philosophy of Science, National and Kapodistrian University of Athens, Athens, Greece Duncan J. Melville St. Lawrence University, Canton, NY, USA Young Sook Oh Program of History and Philosophy of Science, Seoul National University, Seoul, South Korea Charlotte-V. Pollet Center for General Education, National Chiao-Tung University, Hsinchu, Taiwan Xavier Robichaud Université de Moncton, Shippagan, NB, Canada Gert Schubring Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil Alexei Volkov National Tsing-Hua University, Hsinchu, Taiwan Part I Introduction
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