Further reading

  • Usiskin, Zalman. Conceptions of school algebra and uses of variables. In: Coxford, A. F.; Shulte, A. P. (eds.). The Ideas of Algebra, K–12. Reston: NCTM, 1988, pp. 8–19.
  • Küchemann, Dietmar. Algebra. In: Hart, K. M. (ed.). Children’s Understanding of Mathematics: 11–16. London: John Murray, 1981, pp. 102–119.
  • Clement, John; Lochhead, Jack; Monk, George S. Translation difficulties in learning mathematics. The American Mathematical Monthly, 88(4), 1981, pp. 286–290.
  • MacGregor, Mollie; Stacey, Kaye. Students’ understanding of algebraic notation: 11–15. Educational Studies in Mathematics, 33, 1997, pp. 1–19.
  • Philipp, Randolph A. The many uses of algebraic variables. The Mathematics Teacher, 85(7), 1992, pp. 557–561.
  • Kieran, Carolyn. The learning and teaching of school algebra. In: Grouws, D. A. (ed.). Handbook of Research on Mathematics Teaching and Learning. New York: Macmillan, 1992, pp. 390–419.
  • Kleiner, Israel. Evolution of the function concept: a brief survey. The College Mathematics Journal, 20(4), 1989, pp. 282–300.
  • Cajori, Florian. A History of Mathematical Notations. 2 vols. Chicago: Open Court, 1928–1929. On the cossic signs, the letters of Viète and Descartes, $f(x)$ and Herschel’s $\sin^{-1}$.
  • Heath, Thomas L. Diophantus of Alexandria: A Study in the History of Greek Algebra. Cambridge: Cambridge University Press, 1910.
  • Viète, François. In artem analyticem isagoge. Tours: Jamet Mettayer, 1591.
  • l’Hôpital, Guillaume de. Analyse des infiniment petits, pour l’intelligence des lignes courbes. Paris: Imprimerie Royale, 1696.

The older texts on functions on this site supplied the idea of the function as a sentence with a hole in it, used in chapter 1 and taken up again here.

Image sources

Image Source Licence
Cossic signs from Michael Stifel’s Arithmetica integra (1544) Wikimedia Commons public domain
Problem II.8 of Diophantus’s Arithmetica, Bachet’s edition (1621) Wikimedia Commons public domain
Title page of Viète’s In artem analyticem isagoge (1591), photo by Marcello Amadeo Wikimedia Commons CC BY-SA 4.0

The interactive figures (the roles of letters, the moving variable and the family of parabolas) were made for this book and work in all four languages of the site. The register of downloaded images, with the hash of each file, is in data/semiotica_imagens.json.

Chapter index · ← How to read a letter: a guide and a glossary · Chapter 4: equality, equivalence and proof →