Abstract
This chapter concerns the exploration of the history of mathematics with emphasis on its potential for secondary school teachers’ education. From an example coming from the history of mathematics (Ptolemy’s Almagest), we emphasize how history can provide inaugural understandings in mathematics that could foster didactic and pedagogical reflections of pre-service and in-service teachers. Firstly, we present the example coming from the history of mathematics in the Greco-Roman world, with the concern to situate the mathematical works in its intellectual ambiance. From a hermeneutico-phenomenological stance, we describe different ways-of-being and ways-of-doing mathematics appearing from the example that underpins the inaugural understandings that can be found in Ptolemy’s work. This leads to some element of a didactic and pedagogical reflection around teaching and learning trigonometry. Finally, we open the discussion about how the exploration of these inaugural understandings can be an opportunity to discuss and to reflect on major theorization and conceptualization in mathematics education such as embodied or situated cognition or historico-cultural perspectives.
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Notes
- 1.
Let’s mention that, already in the second half of the nineteenth century, mathematicians like Felix Klein and Augustus De Morgan, and historians like Paul Tannery and Gino Loria, were showing an active interest in the role of the history of mathematics in education already (see Barbin et al., 2020). Furthermore, we can go back even to Proclus to whom the history of mathematics could help pointing out and discussing the first discovers of a given result, having in mind educational goals (see Fried, 2014).
- 2.
A Gadamerian concept which refers to the process in which a hypothesis is put up related to what the student is confronted, tested against the source by confronting it with other parts of the text, modified, tested again and so on, and so on.
- 3.
We cannot read neither the Greek, nor the Arabic, nor the Latin. The document of work, which is our, is the French translation of the abbot Halma, at the beginning of the nineteenth century, from a Greek copy of the Middle Ages (Delambre, 1988). It exists Greek and Arabic copies of the Almagest from the end of the Middle Ages.
- 4.
Let’s mention that the word “trigonometry” as never been used by the mathematician from antiquity. The word will appear with Regiomontanus, mathematician of the Renaissance who will translate Ptolemy’s Almagest (Charbonneau, 2002).
- 5.
The use of degree for measuring the angle was already done by the Mesopotamian astronomers, the Greek astronomers will continue to subdivide the circle in 360 degrees and used the sexagesimal numeration for their calculations. It is not the case for mathematicians like Euclid or Archimedes (Charbonneau, 2002).
- 6.
This excerpt does not show all parts of Ptolemy’s table. After the arc column and the chord column, there is a third column labelled “sixtieths”. Numbers in this column gives the average number of sixtieths of a unit that must be added to a given chord each time the angle increases by one minute of arc.
- 7.
Let’s mention that the words sinus come from the translation of jaïb, which is the Arabic word for cavity or hollow. The word jaïb is related phonetically to jiva, which is the word for chord in Sanskrit.
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Guillemette, D. (2023). The Exploration of Inaugural Understandings in the History of Mathematics and Its Potential for Didactic and Pedagogical Reflection. In: Romero Sanchez, S., Serradó Bayés, A., Appelbaum, P., Aldon, G. (eds) The Role of the History of Mathematics in the Teaching/Learning Process. Advances in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-031-29900-1_1
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