Calculation algorithms are fated to be supplanted, and the art of using them replaced by different sets of skills, and eventually: machines. Yet, using and creating algorithms is still mathematically relevant and in fact contributes to the evolution of mathematics itself. In school and everyday life, however, calculating is often seen as a mindless, boring activity. Algorithms are indeed designed to require as less thinking as possible. I suggest that taking a playful attitude towards algorithms in school is essential so that they can be appreciated in full. Playing with algorithms allow them to really become objects of interest, and be offered as one particular way of experiencing mathematics.
This is a preview of subscription content, access via your institution.
He actually dedicated 20 years of his life computing a total of 707 digits without noticing the mistake he made in the 528th digit.
Another powerful example concerns the inferiority of the prime counting function versus the logarithmic integral. A large number of confirming observations were made before the first counterexamples were identified, hence the interest in continuing calculations.
Abdeljaouad, M. 2005. Les arithmétiques arabes: 9e-15e siècles. Tunis: Ibn Zeidoun.
Abdeljaouad, M., and J. Oaks. 2012. De la découverte d’al-Lubâb fî sharh ‘a’mâl al-hisâb d’al-Hawârî al-Misrâtî. Actes du 11e Colloque Maghrébin sur l’Histoire des mathématiques Arabes, Alger-Kooba: École Normale Supérieure.
Askey, R. 1995. Cube root algorithms. Mathematics in School 24 (2): 42–43.
Babbage, C. 1864/2011. Passages from the Life of a Philosopher. Cambridge: Cambridge University Press.
Ballheim, C. 1999. How our readers feel about calculators. In Mathematics education dialogues, ed. Z. Usiskin, 4–5. Reston, VA: NCTM.
Baroody, A.J., and A. Dowker (eds.). 2003. The development of arithmetic concepts and skills: Constructive adaptive expertise. Mahwah, NJ: Lawrence Erlbaum Associates.
Borwein, J., and D. Bailey. 2003. Mathematics by experiment: plausible reasoning in the 21st century. Natick, MA: A K Peters.
Borwein, J., D. Bailey, and R. Girgensohn. 2004. Experimentation in mathematics: computational paths to discovery. Natick, MA: A K Peters.
Bretherton, I. 1984. Symbolic play: The development of social understanding. New York: Academic Press.
Butlen, D., and M. Peizard. 2000. Calcul mental et résolution de problèmes numériques au début du collège. Repères IREM 41: 5–24.
Carpenter, T.P. 1986. Conceptual knowledge as a foundation for procedural knowledge. In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics, 113–132. Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
Cerquetti-Aberkane, F., and A. Rodriguez. 2002. Faire des mathématiques avec des images et des manuscrits historiques du cours moyen au collège. Champigny-sur-Marne, France: CRDP de l’académie de Créteil.
Chabert, J.-L. (dir.), E. Barbin, M. Guillemot, A. Michel-Pajus, J. Borowczyk, A. Djebbar, J.-C. Martzloff. 1994. Histoire d’algorithmes: du caillou à la puce. Paris: Belin.
Chaitin, G.J. 2004. Thoughts on the Riemann hypothesis. The Mathematical Intelligencer 26 (1): 4–7.
Châtelet, G. 2000. Figuring space: Philosophy, mathematics, and physics. Dordrecht & Boston: Kluwer.
Daston, L. 1994. Enlightenment calculations. Critical Inquiry 21 (1): 182–202.
Davis, B. 1996. Teaching mathematics: Toward a sound alternative. New York: Garland Publishing Inc.
Davis, P.J. 1972. Fidelity in mathematical discourse: Is one and one really two? American Mathematical Monthly, 252–263.
Davis, P.J. 2006. Mathematics & common sense: A case of creative tension. Natick, MA: A K Peters/Boca Raton, FL: CRS Press.
de Prony, G.R. 1824. Notice sur les grandes tables logarithmiques et trigonometriques: adaptées au nouveau système métrique décimal. Paris: Didot.
Djebbar, A. 1997. Matériaux pour l’étude des problèmes récréatifs de la tradition mathématique arabe (IXe-XVe siècles). Nantes: Université d’été de Nantes.
Dowek, G. 2007. Les métamorphoses du calcul: une étonnante histoire de mathématiques. Paris: Le Pommier.
Eisner, E.W. 1990. The role of art and play in children’s cognitive development. In Children’s play and learning: Perspectives and policy implications, ed. E. Klugman and S. Smilansky, 43–56. New York: Teachers College Press.
Emmer, M. 1998. The mathematics of war. ZDM 30 (3): 74–77.
Ernest, P. 1994. Mathematics, education, and philosophy: An international perspective. London & Washington, D.C.: The Falmer Press.
Ernest, P. 2014. Certainty in mathematics: Is there a problem? Philosophy of Mathematics Education Journal 28: 1–22.
Franklin, J. 1987. Non-deductive logic in mathematics. British Journal for the Philosophy of Science 38 (1): 1–18.
Furinghetti, F. 1993. Images of mathematics outside the community of mathematicians: Evidence and explanations. For the Learning of Mathematics 13 (2): 33–38.
Ginsburg, H.P. 2006. Mathematical play and playful mathematics: A guide for early education. In Play = Learning: How play motivates and enhances children’s cognitive and social-emotional growth, ed. D. Singer et al., 145–165. Oxford: Oxford University Press.
Grier, D.A. 2013. When computers were human. Princeton, NJ: Princeton University Press.
Hart, K.M. (ed.). 1981. Children’s understanding of mathematics. London: John Murray.
Hilton, P. 1980. Math anxiety: Some suggested causes and cures: Part 2. Two-Year College Mathematics Journal 11 (4): 246–251.
Heege, H.T. 1983. The multiplication algorithm: An integrated approach. For the Learning of Mathematics 3 (3): 29–34.
Holton, D., A. Ahmed, H. Williams, and C. Hill. 2001. On the importance of mathematical play. International Journal of Mathematical Education in Science and Technology 32 (3): 401–415.
Huszár, K., and M. Rolínek. 2014. Playful Math—An introduction to mathematical games. Sommer campus am IST Austria. Online at: https://repository.ist.ac.at/312/1/Playful_Math.pdf.
Jankvist, U.T. 2007. Empirical research in the field of using history in mathematics education. Nordic Studies in Mathematics Education 12 (3): 83–105.
Kant, I. 1934/1781. Critique of Pure Reason. London: Macmillan.
Katz, V.J. (Ed.). 2000. Using history to teach mathematics: An international perspective. Washington, D.C.: The Mathematical Association of America.
Kilpatrick, J., J. Swafford, and B. Findell. 2001. The strands of mathematical proficiency. In J. Kilpatrick, J. Swafford, and B. Findell. (eds.), Adding it up: Helping children learn mathematics (pp. 115–155). Washington, D.C.: National Academies Press.
Kitcher, P., and W. Aspray (Eds.). 1988. History and philosophy of modern mathematics. Minneapolis: University of Minnesota.
Klein, J. 1992. Greek mathematical thought and the origin of algebra. New York, NY: Dover Publications.
Kline, M. 1982. Mathematics: The loss of certainty. New York, NY: Oxford University Press.
Körner, T.W. 1996. The pleasures of counting. Cambridge: Cambridge University Press.
Lakatos, I. 1976. Proofs and refutations: The logic of mathematical discovery. Cambridge etc.: Cambridge University Press.
Leontiev [Leontyev], A.N. 1979. The problem of activity in psychology. In The concept of activity in Soviet psychology, ed. J.V. Wertsch, 37–71. Armonk, NY: Sharpe.
Lerman, S. 1990. Alternative perspectives of the nature of mathematics and their influence on the teaching of mathematics. British Educational Research Journal 16 (1): 53–61.
Madell, R. 1985. Childrens’ natural processes. Arithmetic Teacher 32: 20–22.
Maheux, J.F. 2010. How do we know? An epistemological journey in the day-to-day, moment to-moment, of researching teaching and learning in mathematics education. Doctoral thesis, Victoria, BC: University of Victoria.
Maheux, J.F. 2011. Epistemological issues to educational use of technology: The case of calculators in elementary mathematics. In L. Gómez Chova, D. Martí Belenguer, A. López Martínez (Eds.), 3rd International Conference on Education and New Learning Technologies, July 4th-6th, 2011. EDULEARN11 Proceedings CD. Barcelona, Spain: International Association of Technology, Education and Development, 495–505.
Maheux, J.F., and J. Proulx. 2018. Mathematics education (research) liberated from teaching and learning: Towards (the future of) doing mathematics. The Mathematics Enthusiast 15 (1): 78–99.
McIntosh, A., B.J. Reys, and R.E. Reys. 1992. A proposed framework for examining basic number sense. For the Learning of Mathematics 12: 2–8.
Morley, A. 1932. Teaching and learning algorithms. For the Learning of Mathematics 2 (2): 50–51.
Netz, R. 2009. Ludic proof: Greek mathematics and the Alexandrian aesthetic. Cambridge: Cambridge University Press.
Neyland, J. 2001. An ethical critique of technocratic mathematics education: Towards an ethical philosophy of mathematics education. Doctoral dissertation, Victoria University of Wellington.
Neyland, J. 2004. Toward a postmodern ethics of mathematics education. In Mathematics education within the postmodern, ed. M. Walshaw, 55–73. Greenwich, CT: Information Age Publishing.
Neyland, J. 2010. Rediscovering the spirit of education after scientific management. Rotterdam & Boston & Taipei: Sense Publishers.
Ormell, C. 1992. New thinking about the nature of mathematics. Geelong, Vic.: Deakin University, Centre for Studies in Mathematics, Science and Environmental Education.
Pitri, E. 2001. The role of artistic play in problem solving. Art Education 54 (3): 46–51.
Plunkett, S. 1979. Decomposition and all that rot. Mathematics in Schools 8 (3): 2–5.
Proulx, J., and M. Beisiegel. 2009. Mathematical curiosities about division of integers. The Mathematics Enthusiast 6 (3): 411–422.
Rabardel, P. 1995. Les hommes et les technologies; approche cognitive des instruments contemporains. Paris: Armand Colin.
Rashed, R. 1997. Histoire des sciences arabes, Paris: Seuil.
Russel, B. 1967. The Autobiography of Bertrand Russell: 1872–1914 (volume 1). London: George Allen & Unwin Ltd.
Ruthven, K. 2009. Towards a calculator-aware number curriculum. Mediterranean Journal of Mathematics Education 8 (1): 111–124.
Sewell, B. 1981. Use of mathematics by adults in daily life. Leicester: Advisory Council for Adult and Continuing Education.
Shapiro, S. 2000. Thinking about mathematics. Oxford: Oxford University Press.
Shechtman, N., and J. Knudsen. 2009. Bringing out the playful side of mathematics: Using methods from improvisational theater in professional development for urban middle school math teachers. Play and Performance: Play and Culture Studies 11: 105–134.
Thompson, A.G. 1984. The relationship of teachers’ conceptions of mathematics and mathematics teaching to instructional practice. Educational Studies in Mathematics 15 (2): 105–127.
Thompson, I. 1994. Young children’s idiosyncratic written algorithms for addition. Educational Studies in Mathematics 26 (4): 323–345.
Tucker, K. 2014. Mathematics through play in the early years. London: SAGE.
Tymoczko, T. 1998. New directions in the philosophy of mathematics. Princeton, NJ: Princeton University Press.
Tzanakis, C., A. Arcavi, C.C. de Sa, M. Isoda, C.K. Lit, M. Niss, et al. 2002. Integrating history of mathematics in the classroom: An analytic survey. In History in mathematics education: The ICMI Study, eds. J. Fauvel and J. Van Maanen, 201–240. New York etc.: Kluwer Academic Publishers.
Van Oers, B. 2010. Emergent mathematical thinking in the context of play. Educational Studies in Mathematics 74 (1): 23–37.
Vygotsky, L.S. 1966. Igra i ee rol’ v umstvennom razvitii rebenka (Play and its role in the mental development of the child; in Russian). Voprosy psikhologii, 12(6), 62–76. [English translation by N. Veresov and M. Barrs is published in 2016 in International Research in Early Childhood Education 7 (2): 3–25 and available online at https://files.eric.ed.gov/fulltext/EJ1138861.pdf.]
Weeks, C. 2008. Interview with Evelyne Barbin. HPM Newsletter 67: 1–4.
Whitton, S. 1998. The playful ways of mathematicians’ work. In Play from birth to twelve and beyond: Contexts, perspectives, and meanings, ed. D.P Fromberg and D. Bergen, 473–481. New York and London: Garland Publishing.
Wiener, N. 1915. Is mathematical certainty absolute? The Journal of Philosophy, Psychology and Scientific Methods, 568–574.
Wilkes, M.V. 1956. Automatic digital computers. New York: Wiley.
Young-Loveridge, J., M. Taylor, S. Sharma, and N. Hāwera. 2006. Students’ perspectives on the nature of mathematics. In P. Grootenboer, R. Zevenbergen & M. Chinnappan (Eds.), Identities, Cultures and Learning Spaces. (Proceedings of the 29th Annual Conference of the Mathematics Education Research Group of Australasia). Adelaide, SA: MERGA, vol. 2, pp. 583–590. Available online at https://researchcommons.waikato.ac.nz/handle/10289/2129.
Editors and Affiliations
Rights and permissions
© 2018 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Maheux, JF. (2018). The Unsettling Playfulness of Computing. In: Volkov, A., Freiman, V. (eds) Computations and Computing Devices in Mathematics Education Before the Advent of Electronic Calculators. Mathematics Education in the Digital Era, vol 11. Springer, Cham. https://doi.org/10.1007/978-3-319-73396-8_16
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-73394-4
Online ISBN: 978-3-319-73396-8
eBook Packages: EducationEducation (R0)