An investigation of pedagogical techniques in Descartes' La géométrie

Abstract

Much research has been conducted about the philosophy and mathematical writings of René Descartes, but that which focuses on pedagogy does so in a holistic manner. The present study uses a systematic approach to identify pedagogical techniques within each sentence of Descartes' La géométrie. Next, the study provides an analysis of La géométrie based on the techniques identified, their frequencies, and patterns of use within the text. The results of this analysis indicate that Descartes placed a high value on the use of demonstration, particularly in conjunction with deductive reasoning and multiple representations; that Descartes believed his method of approaching mathematical problems was superior to other methods; and that Descartes was in fact concerned with whether his readers understood his ideas or not.

Acknowledgements

I am extremely grateful to Dr Kathleen M Clark of Florida State University for her assistance and guidance in the preparation of this article.

Notes

¹ ‘I have also omitted here the demonstration of most of my statements, because they seem to me so easy that if you take the trouble to examine them systematically the demonstrations will present themselves to you and it will be of much more value to you to learn them in that way than by reading them’ (1637/1954, 192).