Abstract
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 is as much an aspect of culture as it is a collection of algorithms.
Carl Boyer (1906–1976)
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References
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.
Ambrose, R. C. (2002). Are we overemphasizing manipulatives in the primary grades to the detriment of girls? Teaching Children Mathematics, 9, 16–21.
Ascher, M. (1991). Ethnomathematics: A multicultural view of mathematical ideas. Pacific Grove: Brooks/Cole.
Bentham, J. (1988) [1780]. The principles of morals and legislation. New York: Prometheus.
Berkeley, G. (2012) [1732]. Three dialogues between hylas and philonous. CreateSpace Independent Publishing Platform.
Bishop, A. J., Clements, K., Keitel, C., Kilpatrick, J., & Leung, F. (1996). International handbook of mathematics education. New York: Springer.
Bockarova, M., Danesi, M., & Núñez, R. (Eds.). (2012). Semiotic and cognitive science essays on the nature of mathematics. Munich: Lincom Europa.
Bronowski, J. (1973). The ascent of man. Boston: Little, Brown, and Co.
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.
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.
Danesi, M. (2002). The puzzle instinct: The meaning of puzzles in human life. Bloomington: Indiana University Press.
Danesi, M. (2004). The liar paradox and the towers of hanoi: The ten greatest math puzzles of all time. Hoboken: John Wiley.
Daniels, H. (Ed.). (1996). An introduction to Vygotsky. London: Routledge.
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.
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.
Dehaene, S. (1997). The number sense: How the mind creates mathematics. Oxford: Oxford University Press.
Descartes, R. (1637). Essaies philosophiques. Leyden: L’imprimerie de Ian Maire.
Descartes, R. (1641) [1986]. Meditations on first philosophy with selections from the objections and replies. Cambridge: Cambridge University Press.
Devlin, K. (2011a). The man of numbers: Fibonacci’s arithmetic revolution. New York: Walker and Company.
Devlin, K. (2011b). Mathematics education for a new era: Video games as a medium for learning. Boca Raton: CRC.
Dewey, J. (1961). Democracy and education. New York: Free Press.
Diophantus (1982). Arithmetica: In the Arabic translation attributed to Qusta ibn Luqa. New York: Springer.
Duin, A. H., Baer, L. L., & Starke-Meyerring, D. (2001). Educause leadership strategies: Partnership in the learning marketspace. New York: Wiley.
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.
Elwes, R. (2014). Mathematics 1001. Buffalo: Firefly.
Fauvel, J. (Ed.). (2002). History in mathematics education. New York: Springer.
Gillings, R. J. (1961). Think-of-a-number: problems 28 and 29 of the Rhind mathematical papyrus. The Mathematics Teacher, 54, 97–102.
Gillings, R. J. (1962). Problems 1 to 6 of the Rhind mathematical papyrus. The Mathematics Teacher, 55, 61–65.
Gillings, R. J. (1972). Mathematics in the time of the pharaohs. Cambridge, Mass.: MIT Press.
Gobbi, A. (2012). Ipotesi glottodidattica 2.0. Journal of e-Learning and Knowledge Society, 8, 47–56.
Hartimo, M. (Ed.). (2010). Phenomenology and mathematics. New York: Springer.
Hartsell, T., & Yuen, S. (2006). Video streaming in online learning. AACE Journal, 14, 31–43.
Hegel, G. W. F. (1807). Phaenomenologie des geistes. Leipzig: Teubner.
Hilbert, D. (1931). Die grundlagen der elementaren zahlentheorie. Mathematische Annalen, 104, 485–494.
Howson, A. G. (ed.) (1973). Developments in mathematical education: Proceedings of the second international congress on mathematical education. Cambridge: Cambridge University Press.
Hume, D. (1902) [1749]. An enquiry concerning human understanding. Oxford: Clarendon.
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.
Karp, A., & Schubring, G. (Eds.). (2014). Handbook on the history of mathematics education. New York: Springer.
Kasner, E., & Newman, J. (1940). Mathematics and the imagination. New York: Simon and Schuster.
James, W. (1890). The principles of psychology. New York: Dover.
Lakoff, G., & Núñez, R. (2000). Where mathematics comes from: How the embodied mind brings mathematics into being. New York: Basic Books.
Leibniz, G. W. (1690 [1923]). De arte combinatoria. Berlin: Akademie Verlag.
Li, Y., & Shiran, D. (1987). Chinese mathematics: A concise history. New York: Oxford University Press.
Locke, J. (1975) [1690]. An essay concerning human understanding, ed. by P. H. Nidditch. Oxford: Clarendon Press.
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.
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.
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.
Michelich, V. (2002). Streaming media to enhance teaching and improve learning. The Technology Source.
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.
Mills, J. S. (2002) [1859] On liberty. New York: Dover.
Munzert, A. W. (1991). Test your IQ. New York: Prentice-Hall.
Musser, G. L., Burger, W. F., & Peterson, B. E. (2006). Mathematics for elementary teachers: A contemporary approach. Hoboken: John Wiley.
Nielsen, M. (2012). Reinventing discovery: The new era of networked science. Princeton: Princeton University Press.
Nietzsche, F. (1999) [1883]. Thus spake Zarathustra. New York: Dover.
Olivastro, D. (1993). Ancient puzzles: Classic brainteasers and other timeless mathematical games of the last 10 centuries. New York: Bantam.
Peano, G. (1973). Selected works of Giuseppe Peano, H. Kennedy, ed. and trans. London: Allen and Unwin.
Polya, G. (1957). How to solve it. New York: Doubleday.
Posamentier, A. S., & Lehmann, I. (2007). The (fabulous) Fibonacci numbers. New York: Prometheus.
Raju, C. K. (2007). Cultural foundations of mathematics. Delhi: Pearson Longman.
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.
Russell, B., & Whitehead, A. N. (1913). Principia mathematica. Cambridge: Cambridge University Press.
Sartre, J.-P. (1993) [1943]. Being and nothingness. New York: Washington Square Press.
Schneider, H. (1965). Solving math word problems. Woodland Hills, California: Word/Fraction Math Aid Co.
Selin, H. (2000). Mathematics across cultures. Dordrecht: Kluwer.
Selvin, S. (1975). A problem in probability (letter to the editor). American Statistician, 29, 67.
Sinclair, N. (2008). The history of geometry curriculum in the United States. Charlotte, NC: Information Age Publishing.
Spinoza, B. de (2005) [1677]. Ethics. Harmondsworth: Penguin.
Stanic, G., & Kilpatrick, J. (Eds.). (2003). A history of school mathematics. Reston, VA: National Council of Teachers of Mathematics.
Stein, K. (2013). Penn GSE study shows MOOCs have relatively few active users, with only a few persisting to course end (http://www.gse.upenn.edu/pressroom/press-releases/2013/12/penn-gse-study-shows-moocs-have-relatively-few-active-users-only-few-persisti).
Stilborne, L. & MacGibbon, P. (2001). Video/Video conferencing in support of distance education. Retrieved from http://www.col.org/Knowledge/ks_videoconferencing.htm.
Strohmeier, J., & Westbrook, P. (1999). Divine harmony: The life and teachings of Pythagoras. Berkeley, CA: Berkeley Hills Books.
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.
Turing, A. (1936). On computable numbers with an application to the entscheidungs problem. Proceedings of the London Mathematical Society, 42, 230–265.
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.
von Neumann, J., & Morgenstern, O. (1944). The theory of games and economic behavior. Princeton: Princeton University Press.
Vygotsky, L. S. (1962). Thought and language. Cambridge, Mass.: MIT Press.
Vygotsky, L. S. (1978). Mind in society. Cambridge, MA: Cambridge University Press.
Weigel, M. (2014). MOOCs and online learning: research roundup. Retrieved from http://journalistsresource.org/studies/society/education/moocs-onlinelearning-research-roundup
Yancey, A. V., Thompson, C. S., & Yancey, J. S. (1989). Children must learn to draw diagrams. Arithmetic Teacher, 36, 15–19.
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.
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Danesi, M. (2016). Math Education and Learning. In: Learning and Teaching Mathematics in The Global Village. Mathematics Education in the Digital Era, vol 6. Springer, Cham. https://doi.org/10.1007/978-3-319-32280-3_1
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