Further reading

  • Seron, Xavier; Fayol, Michel. Number transcoding in children: a functional analysis. British Journal of Developmental Psychology, 12, 1994, pp. 281–300.
  • Miura, Irene T.; Kim, Chungsoon C.; Chang, Chih-Mei; Okamoto, Yukari. Effects of language characteristics on children’s cognitive representation of number: cross-national comparisons. Child Development, 59, 1988, pp. 1445–1450.
  • Skemp, Richard R. Relational understanding and instrumental understanding. Mathematics Teaching, 77, 1976, pp. 20–26.
  • Gray, Eddie M.; Tall, David O. Duality, ambiguity, and flexibility: a “proceptual” view of simple arithmetic. Journal for Research in Mathematics Education, 25(2), 1994, pp. 116–140.
  • Halliday, Michael A. K. Language as Social Semiotic. London: Edward Arnold, 1978. The chapter on the mathematics register.
  • Pimm, David. Speaking Mathematically: Communication in Mathematics Classrooms. London: Routledge & Kegan Paul, 1987.
  • Baruk, Stella. L’âge du capitaine: de l’erreur en mathématiques. Paris: Seuil, 1985.
  • Brousseau, Guy. Théorie des situations didactiques. Grenoble: La Pensée Sauvage, 1998.
  • Pólya, George. How to Solve It. Princeton: Princeton University Press, 1945.
  • Matz, Marilyn. Towards a process model for high school algebra errors. In: Sleeman, D.; Brown, J. S. (eds.). Intelligent Tutoring Systems. London: Academic Press, 1982, pp. 25–50.
  • Gray, Jeremy J. A commentary on Gauss’s mathematical diary, 1796–1814, with an English translation. Expositiones Mathematicae, 2, 1984, pp. 97–130.
  • Berndt, Bruce C. Ramanujan’s Notebooks, parts I to V. New York: Springer, 1985–1998.
  • Kanigel, Robert. The Man Who Knew Infinity: A Life of the Genius Ramanujan. New York: Scribner, 1991.
  • Halmos, Paul R. How to write mathematics. L’Enseignement Mathématique, 16, 1970, pp. 123–152.
  • Knuth, Donald E.; Larrabee, Tracy; Roberts, Paul M. Mathematical Writing. Washington: Mathematical Association of America, 1989.
  • Nemeth, Abraham. The Nemeth Braille Code for Mathematics and Science Notation. Louisville: American Printing House for the Blind, 1972.

Image sources

Image Source Licence
The Ishango bone Wikimedia Commons CC BY-SA 4.0, Joeykentin
Mental Arithmetic, by Nikolai Bogdanov-Belsky (1895) Wikimedia Commons public domain
First entry in Gauss’s diary (1796) Wikimedia Commons public domain
The “ΕΥΡΗΚΑ” in Gauss’s diary (1796) Wikimedia Commons public domain
A page from Ramanujan’s notebooks Wikimedia Commons public domain
The cubarithm in Recherches et inventions (1926) Wikimedia Commons public domain

The interactive figures (numbers written as spoken, the false rules and Gauss’s eureka) work in all four languages of the site. The record of the downloaded images, with the hash of each file, is in data/semiotica_imagens.json.

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