How did mathematics teachers work four thousand years ago? Curricula and syllabuses in Mesopotamia

Surprising as it may seem, education in Mesopotamia is remarkably well documented. The reason for this abundance of sources is the nature of the writing support that was used in the Ancient Near East, namely, the clay, an indestructible material that has survived from antiquity to the present day. School exercises, including mathematics exercises, have been found by the tens of thousands during archaeological excavation in Iraq, Syria and Iran. One can detect how masters worked through careful analysis of exercises for beginners and sets of problems for advanced students. The work of masters left traces on these documents, which allow us to partly reconstruct the organization of teaching. In this paper, I focus on didactical structures conveyed by sets of texts from diverse levels of education. I show the diversity of these structures, and try to grasp the mathematical notions conveyed by them. For that, I rely on homogeneous sets of documents produced by communities of students or masters quite well identified. I consider two sets of texts from Nippur, and a set of texts found in a Southern city, perhaps Larsa.

Michalowski, P. (2012). Literacy, Schooling and the Transmission of Knowledge in Early Mesopotamian Culture. In W. S. van Egmond & W. H. van Soldt (Eds.), Theory and Practice of Knowledge Transfer. Studies in School Education in the Ancient Near East and Beyond(pp. 39-57). Leiden: PIHANS

Proust, C. (2012). Teachers' writings and students' 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). New York: Springer.

Proust, C. (2014). Does a Master always Write for his Students? Some Evidence from Old Babylonian Scribal Schools. In A. Bernard and C. Proust (Eds.), Scientific Sources and Teaching Contexts throughout History: Problems and Perspectives (Boston Studies in the Philosophy of Science) (pp. 69-94). New York: Springer.

Proust, C. (2015 (issued 2017)). La chanson des mathématiques dans l’Edubba. In M. C. Bustamante (Ed.), Scientific Writings and Orality (Archives Internationales d’Histoire des Sciences Vol. 65/2) (pp. 19-49). Brepols,

Veldhuis, N. (1997). Elementary Education at Nippur, The Lists of Trees and Wooden Objects, Ph. D. dissertation, University of Groningen.

Comment les professeursde mathématiques travaillaient-ils il y a quatre mille ans? Cursus etprogressions en Mésopotamie

Aussi surprenant que cela puisse paraître, l'éducation en Mésopotamie est remarquablement bien documentée. La raison de cette abondance de sources est la nature du support d'écriture qui avait été utilisé dans le Proche-Orient ancien, à savoir l'argile, un matériau indestructible qui a survécu depuis l'antiquité jusqu'à nos jours. Des exercices scolaires, y compris des exercices de mathématiques, ont été découverts par dizaines de milliers lors des fouilles archéologiques en Irak, en Syrie et en Iran. On peut percevoir comment les maîtres travaillaient grâce à une analyse minutieuse des exercices destinés aux écoliers débutants et des séries de problèmes destinées aux étudiants avancés. Le travail des maîtres a laissé des traces dans ces documents, ce qui nous permet de reconstruire en partie l'organisation de l'enseignement. Dans cet article, je m'intéresse principalement aux structures didactiques telles qu'on peut les percevoir dans des ensembles de textes scolaires de différents niveaux. Je montre la diversité de ces structures et j'essaye de saisir les notions mathématiques qu'elles véhiculent. Pour cela, je me base sur des ensembles homogènes de documents produits par des communautés d'étudiants ou de maîtres relativement bien identifiés. Je considère deux séries de textes de Nippur, et un ensemble de textes trouvés dans une ville du sud, peut-être Larsa.

Michalowski, P. (2012). Literacy, Schooling and the Transmission of Knowledge in Early Mesopotamian Culture. In W. S. van Egmond & W. H. van Soldt (Eds.), Theory and Practice of Knowledge Transfer. Studies in School Education in the Ancient Near East and Beyond(pp. 39-57). Leiden: PIHANS.

Proust, C. (2012). Teachers' writings and students' 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). New York: Springer.

Proust, C. (2014). Does a Master always Write for his Students? Some Evidence from Old Babylonian Scribal Schools. In A. Bernard and C. Proust (Eds.), Scientific Sources and Teaching Contexts throughout History: Problems and Perspectives (Boston Studies in the Philosophy of Science) (pp. 69-94). New York: Springer.

Proust, C. (2015 (issued 2017)). La chanson des mathématiques dans l’Edubba. In M. C. Bustamante (Ed.), Scientific Writings and Orality (Archives Internationales d’Histoire des Sciences Vol. 65/2) (pp. 19-49). Brepols.

Veldhuis, N. (1997). Elementary Education at Nippur, The Lists of Trees and Wooden Objects, Ph. D. dissertation, University of Groningen.