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

Description

This volume traces back the history of interaction between the “computational” or “algorithmic” aspects of elementary mathematics and mathematics education throughout ages. More specifically, the examples of mathematical practices analyzed by the historians of mathematics and mathematics education who authored the chapters in the present collection show that the development (and, in some cases, decline) of counting devices and related computational practices needs to be considered within a particular context to which they arguably belonged, namely, the context of mathematics instruction; in their contributions the authors also explore the role that the instruments played in formation of didactical approaches in various mathematical traditions, stretching from Ancient Mesopotamia to the 20th century Europe and North America. Front Matter ....Pages i-viii Front Matter ....Pages 1-1 History of Computations, Computing Devices, and Mathematics Education from the Teaching and Learning Perspective: Looking for New Paths of Investigation (Viktor Freiman, Alexei Volkov)....Pages 3-21 Front Matter ....Pages 23-23 Computation in Early Mesopotamia (Duncan J. Melville)....Pages 25-47 Computational Techniques and Computational Aids in Ancient Mesopotamia (Jens Høyrup)....Pages 49-63 Interpreting Tables of the Arithmetical Introduction of Nicomachus Through Pachymeres’ Treatment of Arithmetic: Preliminary Observations (Athanasia Megremi, Jean Christianidis)....Pages 65-93 The So-Called “Dust Computations” in the Līlāvatī (Takanori Kusuba)....Pages 95-113 Reading Algorithms in Sanskrit: How to Relate Rule of Three, Choice of Unknown, and Linear Equation? (Charlotte-V. Pollet)....Pages 115-133 Front Matter ....Pages 133-133 Chinese Counting Rods: Their History, Arithmetic Operations, and Didactic Repercussions (Alexei Volkov)....Pages 137-188 Interpreting Algorithms Written in Chinese and Attempting the Reconstitution of Tabular Setting: Some Elements of Comparative History (Charlotte-V. Pollet)....Pages 189-214 Same Rods, Same Calculation? Contextualizing Computations in Early Eighteenth-Century Korea (Young Sook Oh)....Pages 215-241 The Education of Abacus Addition in China and Japan Prior to the Early 20th Century (Yifu Chen)....Pages 243-264 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) (Marion Cousin)....Pages 265-295 Front Matter ....Pages 295-295 Counting Devices in Russia (Alexei Volkov)....Pages 299-338 A Short History of Computing Devices from Schickard to de Colmar: Emergence and Evolution of Ingenious Ideas and Technologies as Precursors of Modern Computer Technology (Viktor Freiman, Xavier Robichaud)....Pages 339-364 Computation Devices in Nineteenth-Century Mathematics Instruction in Europe (Gert Schubring)....Pages 365-384 Toward a History of the Teaching of Calculation in Russia (Alexander Karp)....Pages 385-405 Front Matter ....Pages 407-407 The Unsettling Playfulness of Computing (Jean-François Maheux)....Pages 409-431 Calculating Aids in Mathematics Education Before the Advent of Electronic Calculators: Didactical and Technological Prospects (Dragana Martinovic)....Pages 433-458 Back Matter ....Pages 459-471