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Margherita Piazzolla Beloch in the Italian Mathematics Education Tradition

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Faces of Geometry

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 172))

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Abstract

The paper focuses on Margherita Beloch’s (1879–1976, married Piazzolla) approach to mathematical education, with particular attention to the education of prospective highschool teachers, which continued the approach by Federigo Enriques, as presented in his Questioni riguardanti le matematiche elementari (final edition, 1924–1927) written in collaboration with several university colleagues and highschool teachers. The educational role of classical geometrical matters regarding constructions was vindicated by her, from a personal approach including her attention to technology and applications, in her Lezioni di Matematica Complementare (1953).

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Notes

  1. 1.

    The interest of studying Beloch’s cultural profile was reported to Laura Tedeschini Lalli by Mario Fiorentini (born in 1918), professor at the University of Ferrara, who played an important role in Italian geometry in the 1960s and 1970s.

  2. 2.

    References to Margherita Beloch can be found in the website Scienza a due voci [4] and in Strikland [5, pp. 33–36]. A first interpretative profile, albeit short, is presented in [6, pp 3–5].

  3. 3.

    During her career she wrote letters to the Ministry of Education to ask to be transferred in another university, such as Rome or Naples, in order to be closer to her family and to have more favourable work conditions (the letters are preserved in the Italian National State Archive, see [7]).

  4. 4.

    She became member of the PNF (National Fascist Party) in 1926 (see [7]).

  5. 5.

    Report on Margherita Piazzola Beloch’s scientific and didactical activity during the years 1927–1930, in occasion of her confirmation in the role of full professor, December 6, 1930, written by F. Calzolari, Dean of the Faculty of Science, Ferrara University, my translation (document preserved in [7]).

  6. 6.

    Mathesis, the Italian Society of Mathematical and Physical Sciences, was born in 1895 on the initiative of secondary school teachers, to improve and enhance the teaching of mathematics in schools of all levels, see [10].

  7. 7.

    Alfred Bray Kempe (1849–1922), James Joseph Sylvester (1814–1897), Christoph Scheiner (1573–1650).

  8. 8.

    With Valerio Talamanca, I have discussed her contribution in [19]. See also Michael Friedman essay [20, pp. 318–340]. Beloch contributions went unnoticed for many years, until the interest on this subject was rekindled by the First International Meeting of Origami Science and Technology, held in Ferrara in December 1989, and organized by the Italian Center for Diffusion of Origami (Bologna), with Humyaki Huzita as main promoter; Luigi Pepe opened the conference with a remembrance of Beloch, and the Proceedings begin with the reprint of some pages from LMC on paper folding and her publications on solvability of any geometrical problem of 3rd degree by paper folding.

  9. 9.

    Fröbel’s educational geometrical activities are part of a group of nineteenth century contributions trying to transform the rote learning of written arithmetic by the introduction of intuitive geometry (solid objects, linear drawing, and so on), see [22].

  10. 10.

    Fold seven was announced by Koshiro Hatori in 2002, but it had been already mentioned by Jacques Justine in the Proceedings of the First International Meeting of Origami Science and Technology in Ferrara in 1989 [25, see note 5].

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Acknowledgements

The author thanks Laura Tedeschini Lalli for first proposing to her and Valerio Talamanca to study the mathematical treatment of paper folding, and then for inviting her to submit an article on Margherita Beloch for Faces of Geometry. She thanks Ana Millán Gasca for discussions about the historical framework and the connections with the work of Federigo Enriques, and Tommaso Dell’Era for precious hints about archive research. She also thanks Valerio Talamanca for further discussions about the resolution of third degree problems via paper folding.

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  1. Department of Architecture, Roma Tre University, Rome, Italy

    Paola Magrone

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  1. Dipartimento di Matematica, Politecnico di Milano, Milan, Italy

    Paola Magnaghi-Delfino

  2. Università degli Studi eCampus, Novedrate, Italy

    Giampiero Mele

  3. Dipartimento di Matematica, Politecnico di Milano, Milan, Italy

    Tullia Norando

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Magrone, P. (2021). Margherita Piazzolla Beloch in the Italian Mathematics Education Tradition. In: Magnaghi-Delfino, P., Mele, G., Norando, T. (eds) Faces of Geometry. Lecture Notes in Networks and Systems, vol 172. Springer, Cham. https://doi.org/10.1007/978-3-030-63702-6_16

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