Advertisement

The Development of Mathematics Practices in the Mesopotamian Scribal Schools

Tablets and tokens, lists and tables, wedges and digits, a complex system of artefacts for doing and learning mathematics, 2000 years BCE
  • Luc Trouche
Chapter
Part of the Mathematics Education Library book series (MELI, volume 110)

Abstract

This chapter proposes a view on a particular moment in the development of mathematics and the learning of mathematics, 2000 bce in Mesopotamia: a particular moment regarding the medium, with the development of writing and of systems of signs; particular regarding the development of mathematics, with the development of a sexagesimal positional numerical system and of associated algorithms; particular regarding the places dedicated to learning, with the development of scribal schools; and, last but not least, particular regarding the ‘supports’, with the use of clay tablets ‘still alive’ today. It aims to evidence the complex system of artefacts supporting mathematical practices, and mathematics teaching and learning in scribal schools.

Keywords

Memory Usage Mathematics Practice Literary Text Regular Number Final Digit 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Artigue, M. (2005). L’intelligence du calcul. Actes de l’Université d’été “Le calcul sous toutes ses formes”. Ministère de l’éducation nationale, France (Internet link to be added).Google Scholar
  2. Bachelard, G. (1934). La formation de l’esprit scientifique. Contribution à une psychanalyse de la connaissance objective (Vol. 5). Paris: Librairie philosophique J. Vrin, 1967.Google Scholar
  3. Bachimont, B. (2010). Le numérique comme support de la connaissance: entre matérialisation et interprétation. In G. Gueudet & L. Trouche (Eds.), Ressources vives. Le travail documentaire des professeurs en mathématiques (pp. 75–90). Rennes: PUR.Google Scholar
  4. Bednarz, N., & Janvier, B. (1984). La numération (première partie). Les difficultés suscitées par son apprentissage. Grand N, 33, 5–31. Retrieved from http://www-irem.ujf-grenoble.fr/revues/revue_n/fic/33/33n1.pdf.
  5. Charpin, D. (2002). Esquisse d’une diplomatique des documents mésopotamiens Bibliothèque de l’École des chartes, 160, 487–511. Retrieved from http://www.persee.fr/web/revues/home/prescript/article/bec_0373-6237_2002_num_160_2_451101#.
  6. Goody, J. (1977). The domestication of the savage mind. Cambridge: Cambridge University Press.Google Scholar
  7. ETCSL. The electronic text corpus of sumerian literature. Oxford University. Retrieved August 2014, from http://etcsl.orinst.ox.ac.uk/cgi-bin/etcsl.cgi?text=t.2.5.5.2&display=Crit&charenc=gcirc&lineid=t2552.p2#t2552.p2.
  8. Gueudet, G., Pepin, B., & Trouche, L. (Eds.). (2012). From text to ‘lived’ resources: Mathematics curriculum materials and teacher development. New York: Springer.Google Scholar
  9. Hébert, E. (Dir.). (2004). Instruments scientifiques à travers l’histoire. Actes du colloque Les instruments scientifiques dans le patrimoine: quelles mathématiques? Rouen les 6, 7 et 8 avril 2001. Paris: EllipsesGoogle Scholar
  10. Kramer, S. N. (1949). Schooldays: A sumerian composition relating to the education of a scribe. Journal of the American Oriental Society, 69(4), 199–215.CrossRefGoogle Scholar
  11. Høyrup, J. (2002). Lengths, widths, surfaces. A portrait of old Babylonian algebra and its kin (Studies and sources in the history of mathematics and physical sciences). Berlin: Springer.CrossRefGoogle Scholar
  12. Lavoie, P. (1994). Contribution à une histoire des mathématiques scolaires au Québec: l'arithmétique dans les écoles primaires (1800-1920). thèse de doctorat, Faculté des sciences de l’éducation, Université de Laval, Québec.Google Scholar
  13. Lieberman, S. J. (1980). On clay pebbles, hollow clays balls, and writing: A Sumerian view. American Journal of Archaeology, 84, 339–58.CrossRefGoogle Scholar
  14. MacGinnis, J., Willis Monroe, M., Wicke, D., & Matney, T. (2014). Artefacts of cognition: The use of clay tokens in a neo-Assyrian Provincial Administration. Cambridge Archaeological Journal, 24, 289–306. doi: 10.1017/S0959774314000432.CrossRefGoogle Scholar
  15. Mariotti, M. A., & Maracci, M. (2012). Resources for the teacher from a semiotic mediation perspective. In G. Gueudet, B. Pepin, & L. Trouche (Eds.), From text to ‘lived’ resources: Mathematics curriculum materials and teacher development (pp. 59–75). Dordrecht: Springer.Google Scholar
  16. Maschietto, M., & Soury-Lavergne, S. (2013). Designing a duo of material and digital artifacts: The pascaline and Cabri Elem e-books in primary school mathematics. ZDM, The International Journal on Mathematics Education, 45(7), 959–971.CrossRefGoogle Scholar
  17. Neugebauer, O., & Sachs, A. J. (1984). Mathematical and metrological texts. Journal of Cuneiform Studies, 36, 243–51.CrossRefGoogle Scholar
  18. Proust, C. (2000). Multiplication babylonienne: la part non écrite du calcul. Revue D’histoire des Mathématiques, 6, 293–303.Google Scholar
  19. Proust, C. (2007). Tablettes mathématiques de Nippur (Varia Anatolica Vol. XVIII). Istanbul: IFEA, De Boccard.Google Scholar
  20. Proust, C. (2012a). Master’ writings and student’s writings: School material in mesopotamia. In G. Gueudet, B. Pepin, & L. Trouche (Eds.), From text to ‘lived’ resources: Mathematics curriculum materials and teacher development (pp. 161–179). Dordrecht: Springer.Google Scholar
  21. Proust, C. (2012b). Interpretation of reverse algorithms in several mesopotamian texts. In K. Chemla (Ed.), The history of mathematical proof in ancient tradition (pp. 384–422). Cambridge: Cambridge University Press.Google Scholar
  22. Robson, E. (2000). Mathematical cuneiform tablets in Philadelphia. Part 1: Problems and calculations. SCIAMVS, 1, 11–48.Google Scholar
  23. Sachs, A. J. (1947). Babylonian mathematical texts I. Journal of Cuneiform Studies, 1, 219–40.CrossRefGoogle Scholar
  24. Schmandt-Besserat, D. (2009). Tokens and writing: The cognitive development. SCRIPTA, 1, 145–154. The Hunmin Jeongeum Society.Google Scholar
  25. Trouche, L. (2000). La parabole du gaucher et de la casserole à bec verseur, éléments de méthode pour une étude des processus d’apprentissage dans un environnement de calculatrices complexes. Educational Studies in Mathematics, 41(3), 239–264.CrossRefGoogle Scholar
  26. Trouche, L. (2005). Des artefacts aux instruments: Une approche pour guider et intégrer les usages des outils de calcul dans l’enseignement des mathématiques. Actes de l’Université d’été “Le calcul sous toutes ses formes”. Ministère de l’éducation nationale, France. Retrieved from https://www.academia.edu/2744338/Trouche_L._2005_Des_artefacts_aux_instruments_une_approche_pour_guider_et_integrer_les_usages_des_outils_de_calcul_dans_lenseignement_des_mathematiques
  27. Trouche, L., & Drijvers, P. (2010). Handheld technology for mathematics education: Flashback into the future. ZDM–The International Journal on Mathematics Education, 42(7), 667–681.CrossRefGoogle Scholar
  28. Veldhuis, N. C. (1997). Elementary education at Nippur. The lists of trees and wooden objects. PhD Rijksuniversiteit Groningen. Retrieved from http://dissertations.ub.rug.nl/faculties/arts/1997/n.c.veldhuis/.

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Luc Trouche
    • 1
  1. 1.Institut Français de l’EducationEcole Normale Supérieure de LyonLyonFrance

Personalised recommendations