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Desire of teachers and realities in textbooks: dealing with history of mathematics in the new French curriculum and its impact on teacher training

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Abstract

Many international studies focus empirically on integrating the history of mathematics in mathematics education. Over the last 2 decades, some studies also revealed theoretical elements concerning the implementation of learning sessions and/or their didactical analysis and effectiveness. This paper has the aim of complementing these empirical studies with a more systematic approach in the French context. Defended for decades within the IREM (Institut de recherche sur l’enseignement des mathématiques), the history of mathematics is now officially introduced in the French curriculum. Nevertheless, is it really sufficient for teachers to change their habits by implementing the history of mathematics in their practices? To answer this question, I first present an unpublished survey with secondary school mathematics teachers (pupils from 10- to 18 years old) about the introduction of the history of mathematics in their classes. This survey allows the comparison of teachers’ desires (‘history of mathematics in potentiality’) and realities in classrooms (‘history of mathematics in actuality’). Then I focus on French mathematics textbooks (for pupils from 15- to 18 years old) in order to question their effectiveness as tools for the introduction of a historical perspective. I describe the historical/mathematical tasks available in these textbooks focusing on their reference to Fibonacci. Finally, I present a proposition to implement the history of mathematics in mathematics education starting from the textbooks, aiming to help mathematics teachers to redesign the tasks of their textbooks so as to be more relevant.

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Notes

  1. In this study, I did not address the classroom use of mathematics textbooks and its impact. Numerous international studies showed how teachers and students use (or do not use) textbooks, as well as how they are used in class. See, e.g., the international comparative study by Pepin and Haggarty (2001) or more recent surveys (Fan et al., 2013, 2018; Schubring & Fan, 2018).

  2. In the following, I do not differentiate the results of the survey between middle and high schools, except in the case where a clear difference between the two is observed. I then mention it explicitly.

  3. In France, a teaching sequence takes about 2 weeks and is generally devoted to a mathematical theme, including an activity, a lesson, exercises, and assessments.

  4. The question I asked was: “Have you already set up a reading of ancient texts with your pupils?”.

  5. Jankvist (2009a, 2009b) identified three different approaches to including history: illumination approaches (the teaching and learning of mathematics is supplemented by succinct historical information such as names, biographical information, or narratives stories), modules approaches (instructional units devoted to history, and quite often, based on case studies, original sources), and history-based approaches (in which mathematical concepts and results are presented in the order of their historical appearance, and HM is used to structure courses, though not necessarily explicitly). In the following, I use this terminology.

  6. I keep here the main idea advocated by Tzanakis et al. (2000), namely, “in a genetic approach, the emphasis is less on how to use theories, methods and concepts, and more why they provide an answer to specific mathematical problems and questions, without however disregarding the ‘technical’ role of mathematical knowledge” (p. 209).

  7. In the following, I focus only on the Liber Abbaci even though I could obviously have mentioned other of Fibonacci’s works, and in particular his important Practica Geometriae for the numerous geometric problems (Hughes, 2008; Moyon, 2017). I cite Fibonacci (2020) as reference to the Latin edition of the Liber Abbaci (with this spelling, except in references and citations where I kept the original spelling), Sigler (2002) as reference to the English translation, and Moyon (2016) as reference to the French translation (only excerpts).

  8. Tzanakis et al., (2000, pp. 214–215) proposed another categorization for what they call “historical snippets” in textbooks according to their format and their content. This categorization is really interesting as a first approach, for example, when it is necessary to analyze textbooks in pre-service teacher training.

  9. It would be the case for any other name of a mathematician to whom a mathematical result (theorem, proof, or reasoning) or a mathematical object has been attributed.

  10. Jankvist, Clark, and Mosvold (2020) present a similar enterprise with a chapter in a textbook for mathematics teacher education used history in relation to the concept of function. Schorcht (2018a, p. 272) clarified his procedure to redesign tasks.

  11. The methodological remarks of Chemla (2021) about textual anachronism in the HM are particularly relevant to the work on Fibonacci’s texts.

  12. A folio of an original manuscript (Biblioteca Nazionale di Firenze, Codice magliabechiano Conv. Soppr. C 1, 2616, fol. 124r.) is available on Wikipedia showing the excerpt on the Rabbit problem. https://fr.wikipedia.org/wiki/Leonardo_Fibonacci#/media/Fichier:Liber_abbaci_magliab_f124r.jpg.

  13. We could stop the mathematical activity here. Then I would be in a task of the acting past type (remain in the past, historical information, mathematical acting), of which there are very few according to Fig. 1.

  14. Fried et al. (2016, p. 216) present hermeneutics as the “art or the science of interpreting texts”. Following basic guidelines, this procedure is based on the systematic distinction between the author and the reader of a text. It considers both the historical perspective and the modern conception of a mathematical topic. From this tension, a deeper understanding of both the mathematics itself and the HM result (Barnett et al., 2014, p. 23).

  15. Scientific knowledge and practices are time-dependent: they have a historical origin and developed through history. Even if we can only observe—indirectly—the effects of the past thanks to primary sources (manuscripts for example), it is necessary to identify them as being part of history (and not only as an anecdote, a legend, or a myth). See, for example, Barbin’s work on the historicity of evidence and demonstration (as cited in Guitart, 2018).

  16. The relation between the Eye of Horus and fractions must be questioned. In particular, Ritter (2003) argued that “the ‘Horus-eye fractions’ were, in their origin at least, neither fractions nor associated with the Eye of Horus (p. 297)”.

  17. An explanation of the text was made by Dunton and Grimm (1966). It is useful for modern readers who do not know medieval Latin.

  18. See, in particular, the notions of circularity, condescension and recapitulation developed by Herreman (2018).

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    Marc Moyon

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Appendix

Appendix

See Table 13.

Table 13 List of French high school mathematics textbooks (rows in white background: textbooks edited before the 2019 curriculum reform; rows in grey background: textbooks edited after the 2019 reform)
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Moyon, M. Desire of teachers and realities in textbooks: dealing with history of mathematics in the new French curriculum and its impact on teacher training. ZDM Mathematics Education 54, 1613–1630 (2022). https://doi.org/10.1007/s11858-022-01427-6

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