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.

Offers an in-depth investigation of the history of techniques of computations and of the use of computing devices in mathematics

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.