Math Education and Learning

  • Marcel DanesiEmail author
Part of the Mathematics Education in the Digital Era book series (MEDE, volume 6)


Understanding contemporary patterns in math education and methods of pedagogy requires some knowledge of the history behind them. This chapter takes a rapid journey into the past, starting in antiquity and ending in the modern period with its emphasis on curriculum models of pedagogy. It also takes an initial glance at how math pedagogy can transcend traditional models via the incorporation of such topics as anecdotal math and the relation of math to language. The chapter concludes with an overview of math education in the Digital Age.


Mathematics Curriculum Ancient World Finish Line Curriculum Model Virtual Classroom 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Alexander, J. (2012). On the cognitive and semiotic structure of mathematics. In M. Bockarova, M. Danesi, & R. Núñez (Eds.), Semiotic and cognitive science essays on the nature of mathematics (pp. 1–34). Munich: Lincom Europa.Google Scholar
  2. Ambrose, R. C. (2002). Are we overemphasizing manipulatives in the primary grades to the detriment of girls? Teaching Children Mathematics, 9, 16–21.Google Scholar
  3. Ascher, M. (1991). Ethnomathematics: A multicultural view of mathematical ideas. Pacific Grove: Brooks/Cole.Google Scholar
  4. Bentham, J. (1988) [1780]. The principles of morals and legislation. New York: Prometheus.Google Scholar
  5. Berkeley, G. (2012) [1732]. Three dialogues between hylas and philonous. CreateSpace Independent Publishing Platform.Google Scholar
  6. Bishop, A. J., Clements, K., Keitel, C., Kilpatrick, J., & Leung, F. (1996). International handbook of mathematics education. New York: Springer.Google Scholar
  7. Bockarova, M., Danesi, M., & Núñez, R. (Eds.). (2012). Semiotic and cognitive science essays on the nature of mathematics. Munich: Lincom Europa.Google Scholar
  8. Bronowski, J. (1973). The ascent of man. Boston: Little, Brown, and Co.Google Scholar
  9. Chase, A. B. (1979). The Rhind mathematical papyrus: Free translation and commentary with selected photographs, transcriptions, transliterations and literal translations. Reston, VA: National Council of Teachers of Mathematics.Google Scholar
  10. Colyvan, M. (2013). Mating, dating, and mathematics: It’s all in the game. In M. Pitici (Ed.), The best writing in mathematics 2012 (pp. 262–271). Princeton: Princeton University Press.Google Scholar
  11. Danesi, M. (2002). The puzzle instinct: The meaning of puzzles in human life. Bloomington: Indiana University Press.Google Scholar
  12. Danesi, M. (2004). The liar paradox and the towers of hanoi: The ten greatest math puzzles of all time. Hoboken: John Wiley.Google Scholar
  13. Daniels, H. (Ed.). (1996). An introduction to Vygotsky. London: Routledge.Google Scholar
  14. Davis, B. (2015). Where mathematics curriculum comes from. In M. Bockarova, M. Danesi, D. Martinovic, & R. Núñez (Eds.), Mind in mathematics (pp. 3–18). Munich: Lincom Europa.Google Scholar
  15. Davydov, V. V., & Radzikhovskii, L. A. (1985). Vygotsky’s theory and the activity oriented approach in psychology. In J. V. Wertsch (Ed.), Culture, communication and cognition: vygotskian perspectives (pp. 59–69). Cambridge: Cambridge University Press.Google Scholar
  16. Dehaene, S. (1997). The number sense: How the mind creates mathematics. Oxford: Oxford University Press.Google Scholar
  17. Descartes, R. (1637). Essaies philosophiques. Leyden: L’imprimerie de Ian Maire.Google Scholar
  18. Descartes, R. (1641) [1986]. Meditations on first philosophy with selections from the objections and replies. Cambridge: Cambridge University Press.Google Scholar
  19. Devlin, K. (2011a). The man of numbers: Fibonacci’s arithmetic revolution. New York: Walker and Company.Google Scholar
  20. Devlin, K. (2011b). Mathematics education for a new era: Video games as a medium for learning. Boca Raton: CRC.CrossRefGoogle Scholar
  21. Dewey, J. (1961). Democracy and education. New York: Free Press.Google Scholar
  22. Diophantus (1982). Arithmetica: In the Arabic translation attributed to Qusta ibn Luqa. New York: Springer.Google Scholar
  23. Duin, A. H., Baer, L. L., & Starke-Meyerring, D. (2001). Educause leadership strategies: Partnership in the learning marketspace. New York: Wiley.Google Scholar
  24. Ellis, M. W., & Berry, R. Q. (2005). The paradigm shift in mathematics education: Explanations and implications of reforming conceptions of teaching and learning. The Mathematics Educator, 15(1), 7–17.Google Scholar
  25. Elwes, R. (2014). Mathematics 1001. Buffalo: Firefly.Google Scholar
  26. Fauvel, J. (Ed.). (2002). History in mathematics education. New York: Springer.Google Scholar
  27. Gillings, R. J. (1961). Think-of-a-number: problems 28 and 29 of the Rhind mathematical papyrus. The Mathematics Teacher, 54, 97–102.Google Scholar
  28. Gillings, R. J. (1962). Problems 1 to 6 of the Rhind mathematical papyrus. The Mathematics Teacher, 55, 61–65.Google Scholar
  29. Gillings, R. J. (1972). Mathematics in the time of the pharaohs. Cambridge, Mass.: MIT Press.Google Scholar
  30. Gobbi, A. (2012). Ipotesi glottodidattica 2.0. Journal of e-Learning and Knowledge Society, 8, 47–56.Google Scholar
  31. Hartimo, M. (Ed.). (2010). Phenomenology and mathematics. New York: Springer.Google Scholar
  32. Hartsell, T., & Yuen, S. (2006). Video streaming in online learning. AACE Journal, 14, 31–43.Google Scholar
  33. Hegel, G. W. F. (1807). Phaenomenologie des geistes. Leipzig: Teubner.Google Scholar
  34. Hilbert, D. (1931). Die grundlagen der elementaren zahlentheorie. Mathematische Annalen, 104, 485–494.CrossRefGoogle Scholar
  35. Howson, A. G. (ed.) (1973). Developments in mathematical education: Proceedings of the second international congress on mathematical education. Cambridge: Cambridge University Press.Google Scholar
  36. Hume, D. (1902) [1749]. An enquiry concerning human understanding. Oxford: Clarendon.Google Scholar
  37. Johnson, G. (2013). Useful invention or absolute truth: What is math? In G. Kolata & P. Hoffman (Eds.), The New York Times book of mathematics (pp. 3–8). New York: Sterling.Google Scholar
  38. Karp, A., & Schubring, G. (Eds.). (2014). Handbook on the history of mathematics education. New York: Springer.Google Scholar
  39. Kasner, E., & Newman, J. (1940). Mathematics and the imagination. New York: Simon and Schuster.Google Scholar
  40. James, W. (1890). The principles of psychology. New York: Dover.CrossRefGoogle Scholar
  41. Lakoff, G., & Núñez, R. (2000). Where mathematics comes from: How the embodied mind brings mathematics into being. New York: Basic Books.Google Scholar
  42. Leibniz, G. W. (1690 [1923]). De arte combinatoria. Berlin: Akademie Verlag.Google Scholar
  43. Li, Y., & Shiran, D. (1987). Chinese mathematics: A concise history. New York: Oxford University Press.Google Scholar
  44. Locke, J. (1975) [1690]. An essay concerning human understanding, ed. by P. H. Nidditch. Oxford: Clarendon Press.Google Scholar
  45. Martinovic, D. (2013). Gesturing and “cursoring” in online multimedia calculus lectures. In M. Bockarova, M. Danesi, & R. Núñez (Eds.), Semiotic and cognitive science essays on the nature of mathematics (pp. 117–134). Munich: Lincom Europa.Google Scholar
  46. Martinovic, D. (2015). Digital technologies and mathematical minds. In M. Bockarova, M. Danesi, D. Martinovic, & R. Núñez (Eds.), Mind in mathematics (pp. 105–114). Munich: Lincom Europa.Google Scholar
  47. Menghini, M., Furinghetti, F., Giacardi, L., & Arzarello, F. (Eds.). (2008). The first century of the International Commission on Mathematical Instruction (1908–2008): Reflecting and shaping the world of mathematics education. Rome: Istituto della Enciclopedia Italiana.Google Scholar
  48. Michelich, V. (2002). Streaming media to enhance teaching and improve learning. The Technology Source.Google Scholar
  49. Mighton, J. (2015). All things being equal: Using evidence based approaches to close the achievement gap in math. In M. Bockarova, M. Danesi, D. Martinovic, & R. Núñez (Eds.), Mind in mathematics (pp. 100–104). Munich: Lincom Europa.Google Scholar
  50. Mills, J. S. (2002) [1859] On liberty. New York: Dover.Google Scholar
  51. Munzert, A. W. (1991). Test your IQ. New York: Prentice-Hall.Google Scholar
  52. Musser, G. L., Burger, W. F., & Peterson, B. E. (2006). Mathematics for elementary teachers: A contemporary approach. Hoboken: John Wiley.Google Scholar
  53. Nielsen, M. (2012). Reinventing discovery: The new era of networked science. Princeton: Princeton University Press.Google Scholar
  54. Nietzsche, F. (1999) [1883]. Thus spake Zarathustra. New York: Dover.Google Scholar
  55. Olivastro, D. (1993). Ancient puzzles: Classic brainteasers and other timeless mathematical games of the last 10 centuries. New York: Bantam.Google Scholar
  56. Peano, G. (1973). Selected works of Giuseppe Peano, H. Kennedy, ed. and trans. London: Allen and Unwin.Google Scholar
  57. Polya, G. (1957). How to solve it. New York: Doubleday.Google Scholar
  58. Posamentier, A. S., & Lehmann, I. (2007). The (fabulous) Fibonacci numbers. New York: Prometheus.Google Scholar
  59. Raju, C. K. (2007). Cultural foundations of mathematics. Delhi: Pearson Longman.Google Scholar
  60. Rowlett, P. (2013). The unplanned impact of mathematics. In M. Pitici (Ed.), The best writing in mathematics 2012 (pp. 21–29). Princeton: Princeton University Press.Google Scholar
  61. Russell, B., & Whitehead, A. N. (1913). Principia mathematica. Cambridge: Cambridge University Press.Google Scholar
  62. Sartre, J.-P. (1993) [1943]. Being and nothingness. New York: Washington Square Press.Google Scholar
  63. Schneider, H. (1965). Solving math word problems. Woodland Hills, California: Word/Fraction Math Aid Co.Google Scholar
  64. Selin, H. (2000). Mathematics across cultures. Dordrecht: Kluwer.CrossRefGoogle Scholar
  65. Selvin, S. (1975). A problem in probability (letter to the editor). American Statistician, 29, 67.CrossRefGoogle Scholar
  66. Sinclair, N. (2008). The history of geometry curriculum in the United States. Charlotte, NC: Information Age Publishing.Google Scholar
  67. Spinoza, B. de (2005) [1677]. Ethics. Harmondsworth: Penguin.Google Scholar
  68. Stanic, G., & Kilpatrick, J. (Eds.). (2003). A history of school mathematics. Reston, VA: National Council of Teachers of Mathematics.Google Scholar
  69. Stein, K. (2013). Penn GSE study shows MOOCs have relatively few active users, with only a few persisting to course end (
  70. Stilborne, L. & MacGibbon, P. (2001). Video/Video conferencing in support of distance education. Retrieved from
  71. Strohmeier, J., & Westbrook, P. (1999). Divine harmony: The life and teachings of Pythagoras. Berkeley, CA: Berkeley Hills Books.Google Scholar
  72. Swetz, F. J. & Kao, T. I. (1977). Was Pythagoras Chinese? An examination of right-triangle theory in ancient China. University Park: Pennsylvania State University Press.Google Scholar
  73. Turing, A. (1936). On computable numbers with an application to the entscheidungs problem. Proceedings of the London Mathematical Society, 42, 230–265.Google Scholar
  74. Van Hiele, Pierre M. (1984). The child’s thought and geometry. In David Fuys, Dorothy Geddes, and Rosamond Tischler (eds.), English translations of selected writings of Dina van Hiele-Geldof and P. M. van Hiele, pp. 243-252. Brooklyn: Brooklyn College of Education.Google Scholar
  75. von Neumann, J., & Morgenstern, O. (1944). The theory of games and economic behavior. Princeton: Princeton University Press.Google Scholar
  76. Vygotsky, L. S. (1962). Thought and language. Cambridge, Mass.: MIT Press.CrossRefGoogle Scholar
  77. Vygotsky, L. S. (1978). Mind in society. Cambridge, MA: Cambridge University Press.Google Scholar
  78. Weigel, M. (2014). MOOCs and online learning: research roundup. Retrieved from
  79. Yancey, A. V., Thompson, C. S., & Yancey, J. S. (1989). Children must learn to draw diagrams. Arithmetic Teacher, 36, 15–19.Google Scholar
  80. Zemsky, R. (2014). With a MOOC MOOC here and a MOOC MOOC there, here a MOOC, there a MOOC, everywhere a MOOC MOOC. Journal of General Education, 53, 237–243.CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Victoria CollegeUniversity of TorontoTorontoCanada

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