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

Alexei Volkov is Professor of the Center for General Education of the National Tsing-Hua University (Hsinchu, Taiwan). He received his PhD degree in history of mathematics from the Institute for History of Science and Technology of the Soviet (Russian) Academy of Sciences in 1989, and since then has been working on the history of mathematics, history of mathematics education and history of science in East and Southeast Asia, in particular, in pre-modern China and Vietnam.    Viktor Freiman, Ph. D. in teaching computer science is Full Professor at the Université de Moncton, Canada. His main research interests, besides the history of mathematics education, focuses on innovations in teaching and learning, STEAM-education, mathematical giftedness, problem solving, virtual learning communities, as well as digital literacy. He is director of the CompéTICA Partnership Network, funded by the Social Sciences and Humanities Research Council of Canada (2014-2017) to investigate digital competence development in the life-long perspective. He is also co-editor of the book Series Mathematics Education in the Digital Era (since 2014).

“This volume will be received by those learning and teaching undergraduate mathematics and mathematics education … it could serve as a useful starting point for a class lecture, a history of mathematics paper, or a senior thesis.” (Peggy Kidwell, MAA Reviews, April 06, 2019)

• Introduction, by A. Volkov and V. Freiman.- Part 1. Middle East and Greece in Antiquity and Middle Ages.- Chapter 1. “Computation in Early Mesopotamia,” by Duncan Melville.- Chapter 2. “Computations in Ancient Mesopotamian Mathematics: from Ur III to the Seleucid period”, by Jens Hoyrup.- Chapter 3. “Computation Techniques in Ancient Greek Sources,” by Fabio Acerbi.- Chapter 4. “Procedural aspects in Nicomachus’ Arithmetic introduction and its transmission to Byzantine higher education,” by Jean Christianidis and Athanasia Megremi.- Part 2: Oriental traditions.- Chapter 5. “Counting instruments and computations in traditional Chinese mathematics: didactical aspects,” by Alexei Volkov.- Chapter 6. “Dust computations in the Lilavati,” by Takanori Kusuba.- Chapter 7. “The role of the prescription of division in the algorithmic approach for setting up tabular algebraic equations in medieval China and India: a comparison,” by Charlotte-V. Pollet.- Chapter 8. “Same Rods, Same Calculation? Contextualizing Computations in Eighteenth-Century Korea,” by Oh Young-Sook.- Chapter 9. “On the History of Exercises in the Computations Performed with the Abacus in China and Japan,” by Chen Yi-Fu.- Chapter 10. “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),” by Marion Cousin.- Part 3. Early modern Europe and Russia.- Chapter 11. “Computation Devices in 19th Century Mathematics Instruction in Europe,” by Gert Schubring.- Chapter 12. “Teaching computation in Russia,” by Alexander Karp.- Chapter 13. “Computational devices in 19-20 century schools – evolution from tool of calculation to the tool of teaching and learning,” by Viktor Freiman.- Part 4. Theoretical approaches and concluding remarks.- Chapter 14. “The unsettling pleasure of computing,” by Jean-François Maheux.- Chapter 15. “Transition to electronic devices:technological affordances and didactical perspective,” by Nathalie Sinclair.- Chapter 16. “Concluding remarks,” by Viktor Freiman and Alexei Volkov.