Computations and Computing Devices in Mathematics Education Before the Advent of Electronic Calculators

464 Pages·2018·14.63 MB·English

by  Alexei Volkov

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
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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