Abstract
The aim of this paper is to gain a better understanding of the role and scope of historical knowledge in work on using history of mathematics in education. This work can come from three types of actors, namely, teachers, teacher trainers, and educational researchers. The texts written by these actors show that their objectives and practices can be different, as is the historical knowledge they deploy. We can read writings of teachers who seek to ‘give meaning’ to school knowledge, by integrating original texts into their teaching progression. We also can read writings of educational researchers who prepare ‘history capsules’ for teachers, which can be introduced into teaching from time to time. To carry out this research, I focus on analyzing the complex relationships between the following three poles: objectives, pedagogical practices, and historical knowledge. To this end, I use the notion of ideal types introduced and developed by the sociologist Max Weber. Section 1 is devoted to the construction of ideal types corresponding to my aim. Based on these ideal types, in Sect. 2, I elaborate on the role and scope of historical knowledge in concrete situations where the history of mathematics is used; specifically, on the one hand during the reading of original texts in an educational context, and on the other hand, in the particular context of teachers education. Some further comments are made in the third and last section.
Similar content being viewed by others
Notes
Italics are in Weber’s text.
The group consists of six teachers in high schools (A. Boyé, A. Bureau, C. Guillet, M.-L. Moureau, C. Nizan-Picard and I. Voillequin) and myself.
Translation from French is mine.
References
Barbin, É. (Ed.). (1988). Pour une perspective historique dans l’enseignement des mathématiques. IREM de Lyon.
Barbin, É. (1991). The reading of original texts. Why and how to introduce a historical perspective. For the Learning of Mathematics, 11(2), 12–14.
Barbin, É. (1997). Histoire et enseignement des mathématiques: Pourquoi? comment? Bulletin De L’association Mathématique Du Québec, XXXVII(1), 20–25.
Barbin, É. (2019). Faire des mathématiques avec l’histoire au lycée. Ellipses.
Barbin, É., Jabœuf, F., Lalande, F., & Nouazé, Y. (Eds.). (1995). Proceedings of ESU1 History and Epistemology in Mathematics Education. IREM de Montpellier.
Barbin, É., Kronfellner, M., & Tzanakis, C. (Eds.). (2011). Proceedings of ESU6 history and epistemology in mathematics education. Technische Universität Wien.
Barnett, J., Lodder, J., Pengelley, D., Pivkina, I., & Ranjan, I. (2011). Designing student projects for teaching and learning discrete mathematics and computer science via primary historical sources. In C. Tzanakis & V. Katz (Eds.), Recent developments on introducing a historical dimension in Mathematics Education (pp. 187–198). Mathematical Association of America.
Biggs, N. L., Lloyd, E. K., & Wilson, R. J. (1998). Graph theory 1736–1936. Clarendon Press.
Boyé, A. (2000). Point math. Classe de seconde. Hatier.
Brousseau, G. (1998). Théorie des situations didactiques. La Pensée Sauvage Éditions.
Caveing, M. (1982). La constitution du type mathématique de l’idéalité dans la pensée grecque, thèse de l’université de Paris X, t. Université de Lille III.
Chevalarias, N. (2019). Some elements on the training in history of mathematics for teachers in France. In É. Barbin, U. T. Jankvist, T. Hoff Kjeldsen, B. Smestad, & C. Tzanakis (Eds.), Proceedings of ESU8 History and Epistemology in Mathematics Education (pp. 291–300). Oslo Metropolitan University.
Diophante. (1926). Les six livres arithmétiques et le Livre des nombres polygones. Desclée de Brouwer et Cie. Ver Eecke P. (Trans.).
Euclid. (1956). The thirteen books of Euclid’s Elements. Dover publications. Heath T. L. (Trans.).
Euler, L. (1736). Solutio problematis ad geometriam situs pertinentis. In Novi commentarii acadademiae scientarium imperialis petropolitanque, VIII, pp. 128–140.
Fauvel, J. (Ed.). (1990). The IREM papers. History in the mathematics classroom. The Mathematical Association.
Fauvel, J., & Van Maanen, J. (2002). History in mathematics education. Kluwer Academic Publishers.
Heath, T. (1910). Diophantus of Alexandria. A sudy in the history of Greek Algebra. Cambridge University Press.
Høyrup, J. (1995). Les quatre côtés et l’aire. In É. Barbin, F. Jabœuf, F. Lalande, & Y. Nouazé (Eds.), Proceedings of ESU1 history and epistemology in mathematics education (pp. 507–531). IREM de Montpellier.
Hyksova, M. (2011). Geometric probability applications through historical excursion. In É. Barbin, M. Kronfellner, & C. Tzanakis (Eds.), Proceedings of ESU6 history and epistemology in mathematics education (pp. 211–222). Technische Universität Wien.
Jankvist, U. T. (2012). History, application, and philosophy of mathematics in mathematics education: Accessing and assessing students’ overview and judgment. In 12th International Congress on Mathematical Education (pp. 1–21).
Kool, M. (1995). Using historical arithmetic books in teaching mathematics to low-attainers. In É. Barbin, F. Jabœuf, F. Lalande, & Y. Nouazé (Eds.), Proceedings of ESU1 history and epistemology in mathematics education (pp. 227–240). IREM de Montpellier.
Morey, B., & de Faria, P. C. (2011). The teaching of mathematics mediated by the history of mathematics. In É. Barbin, M. Kronfellner, & C. Tzanakis (Eds.), Proceedings of ESU6 history and epistemology in mathematics education (pp. 223–233). Technische Universität Wien.
Morin, É. (2019). On the importance of the relationship to knowledge in science education. Cultural Studies of Science Education, 14, 621–625.
Pouliot, C., Bader, B., & Therriault, G. (2010). The notion of the relationship to knowledge: A theoretical tool for research in science education. International Journal of Environmental & Science Education, 5(3), 239–264.
Radford, L., & Guérette, G. (1996). Quadratic equations: Reinventing the formula. A teaching sequence based on the historical development of algebra. In M. J. Lagarto & E. Veloso (Eds.), Historia e Educaçao Mathematica. Proceedings, II (pp. 301–308). Departimento de Matematics da Universidad do Minho.
Rashed, R., & Houzel, C. (2013). Les ‘Arithmétiques’ de Diophante. De Gruyter.
Siu, M.-K. (2006). No, I don’t use history of mathematics in my class, Why? In F. Furinghetti, S. Kaijser, & C. Tzanakis (Eds.), Proceedings HPM 2004 and ESU4 (pp. 268–277). Uppsala University.
Vallhonesta, F. R., Massa Esteve, M. R., Guevara Cansanova, I., Puig-Pla, C., & Roca-Rosell, A. (2015). P, Teaching training in the history of mathematics. In É. Barbin, U. T. Jankvist, & T. Kjeldsen (Eds.), Proceedings of ESU7 history and epistemology in mathematics education (pp. 113–128). Danish School of Education.
Van Brummelen, G. (1995). Using ancient astronomy to teach trigonometry. A case study. In É. Barbin, F. Jabœuf, F. Lalande, & Y. Nouazé (Eds.), Proceedings of ESU1 history and epistemology in mathematics education (pp. 276–281). IREM de Montpellier.
Vicentini, C., Chevalarias, N., Clark, K. M., & Roelens, M. (2019). History, epistemology and teaching mathematics. In É. Barbin, U. T. Jankvist, T. Hoff Kjeldsen, B. Smestad, & C. Tzanakis (Eds.), Proceedings of ESU8 history and epistemology in mathematics education (pp. 205–219). Oslo Metropolitan University.
Vitrac, B. (2005). Peut-on parler d’algèbre dans les mathématiques grecques anciennes ? (pp. 1–44). Mirror of Heritage.
Weber, M. (1949). On the methodology of the social sciences. The Free Press. Shils, E. A. & Finch, H. A. (Trans.).
Acknowledgements
I thank David Pengelley for his assistance in the use of the English language in my paper. I also thank the three reviewers of the paper for their remarks and comments.
Funding
This research was supported by Université de Nantes.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Barbin, É. On the role and scope of historical knowledge in using the history of mathematics in education. ZDM Mathematics Education 54, 1597–1611 (2022). https://doi.org/10.1007/s11858-022-01410-1
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11858-022-01410-1