Skip to main content
Open Book Publishers

2. Why and how people develop mathematics

Chapter of: Breaking Images: Iconoclastic Analyses of Mathematics and its Education(pp. 25–60)

Export Metadata

  • ONIX 3.1
  • ONIX 3.0
    • Thoth
    • Project MUSE
      Cannot generate record: No BIC or BISAC subject code
    • OAPEN
    • JSTOR
      Cannot generate record: No BISAC subject code
    • Google Books
      Cannot generate record: No BIC, BISAC or LCC subject code
    • OverDrive
      Cannot generate record: No priced EPUB or PDF URL
  • ONIX 2.1
  • CSV
  • JSON
  • OCLC KBART
  • BibTeX
  • CrossRef DOI deposit
    Cannot generate record: This work does not have any ISBNs
  • MARC 21 Record
    Cannot generate record: MARC records are not available for chapters
  • MARC 21 Markup
    Cannot generate record: MARC records are not available for chapters
  • MARC 21 XML
    Cannot generate record: MARC records are not available for chapters
Metadata
Title2. Why and how people develop mathematics
ContributorBrian Greer(author)
DOIhttps://doi.org/10.11647/obp.0407.02
Landing pagehttps://www.openbookpublishers.com/books/10.11647/obp.0407/chapters/10.11647/obp.0407.02
Licensehttps://creativecommons.org/licenses/by-nc/4.0/
CopyrightBrian Greer
PublisherOpen Book Publishers
Published on2024-12-11
Long abstractThe development of mathematics by humans has a long and unfinished history. In this, necessarily highly selective, overview, the discussion is framed in terms of the environments – physical, cultural, socio-political, specialised – within which people, including those designated as ‘mathematicians’ do what is called ‘mathematics’ in all its many forms. These forms include the traditional divide between ‘ pure’ and ‘ applied’. A distinction is drawn between internal and external processes driving the development, and within internal drivers between those of creation and those of systematisation. The links between this chapter and Chapter 13 are stressed throughout.
Page rangepp. 25–60
Print length36 pages
LanguageEnglish (Original)
Contributors

Brian Greer

(author)
https://orcid.org/0009-0007-5230-1904

Brian Greer began his research on mathematical cognition, before shifting his interest to school mathematics. That evolved to reflect a characterization of mathematics as a human activity embedded in historical, cultural, social and political – in short, human – contexts.

References
  1. Asperó, D., & Schindler, R. (2021). Martin’s Maximum++ implies Woodin’s Pmax axiom (∗). Annals of Mathematics, 193(3), 793–835. https://doi.org/10.4007/annals.2021.193.3.3
  2. Atiyah, M. (2007). Bourbaki, A Secret Society of Mathematicians and The Artist and the Mathematician [Book review]. Notices of the American Mathematical Society, 54(9), 1150–1152.
  3. Aubin, D. (1997). The withering immortality of Nicolas Bourbaki: A cultural connector at the confluence of mathematics, structuralism, and the Oulipo in France. Science in Context, 10(2), 297–342. https://doi.org/10.1017/S0269889700002660
  4. Bishop, A. J. (1988). Mathematical enculturation: A cultural perspective on mathematics education. Kluwer. https://doi.org/10.1007/978-94-009-2657-8
  5. Bishop, A. J. (1990). Western mathematics: The secret weapon of cultural imperialism. Race & Class, 32(2), 51–65. https://doi.org/10.1177/030639689003200204
  6. Boas, F. (1955). Primitive art. Dover. (Original work published 1927)
  7. Bourbaki, N. (1950). The architecture of mathematics. American Mathematical Monthly, 57(4), 221–232.
  8. Cajori, F. (1993). A history of mathematical notations. Dover. (Original work published 1928–1929)
  9. Corry, L. (2009). Writing the ultimate mathematics textbook: Nicholas Bourbaki’s Éléments de Mathématique. In E. Robson & J. Steadall (Eds.), Oxford handbook of history of mathematics (pp. 565–588). Oxford University Press.
  10. Cullen, C. (2009). People and numbers in early imperial China. In E. Robson & J. Steadall (Eds.), Oxford handbook of history of mathematics (pp. 591–618). Oxford University Press.
  11. De Morgan, A. (1910). Study and difficulties of mathematics. University of Chicago Press. (Original work published 1831)
  12. Devlin, K. (2014). The most common misconception about probability? In E. J. Chernoff & B. Sriraman (Eds.), Probabilistic thinking: Presenting plural perspectives (pp. ix–xiii). Springer.
  13. Dieudonné, J. A. (1970). The work of Nicholas Bourbaki. American Mathematical Monthly, 77, 134–145.
  14. Fischbein, E. (1987). Intuition in science and mathematics: An educational approach. Reidel.
  15. Fisher, D. (2021). Global understanding of complex systems problems can start in pre-college education. In F. K. S. Leung, G. A. Stillman, G. Kaiser, & K. L. Wong (Eds.), Mathematical modeling education in East and West. Springer. https://doi.org/10.1007/978-3-030-66996-6_3
  16. Freudenthal, H. (1973). Mathematics as an educational task. Reidel.
  17. Freudenthal, H. (1991). Revisiting mathematics education. Kluwer.
  18. Greer, B. (1992). Multiplication and division as models of situations. In D. Grouws (Ed.), Handbook of research on mathematics education (pp. 276–295). Macmillan.
  19. Greer, B. (2021). Learning from history: Jens Høyrup on mathematics, education, and society. In D. Kollosche (Ed.), Exploring new ways to connect: Proceedings of the Eleventh International Mathematics Education and Society Conference (Vol. 2, pp. 487–496). Tredition. https://doi.org/10.5281/zenodo.5414119
  20. Greer, B., & Harel, G. (1998). The role of isomorphisms in mathematical cognition. Journal of Mathematical Behavior, 17(1), 5–24. https://doi.org/10.1016/S0732-3123(99)80058-3
  21. Hacking, I. (1990). The taming of chance. Cambridge University Press. https://doi.org/10.1017/CBO9780511819766
  22. Hacking, I. (2014). Why is there philosophy of mathematics at all? Cambridge University Press. https://doi.org/10.1017/CBO9781107279346
  23. Harouni, H. (2015). Toward a political economy of mathematics education. Harvard Educational Review, 85(1), 50-74. https://doi.org/10.17763/haer.85.1.2q580625188983p6
  24. Heinzmann, G., & Petitot, J. (2020). The functional role of structure in Bourbaki. In E. H. Reck & G. Schiemer (Eds.), The prehistory of mathematical structuralism (pp. 187–214). Oxford University Press. https://doi.org/10.1093/oso/9780190641221.003.0008
  25. Hersh, R., & John-Steiner, V. (2011). Loving and hating mathematics. Princeton University Press.
  26. Høyrup, J. (1994). In measure, number, and weight. State University of New York Press.
  27. Høyrup, J. (1995). The art of knowing: An essay on epistemology in practice [Lecture notes]. https://ojs.ruc.dk/index.php/fil1/article/view/1947
  28. Høyrup, J. (2013). Algebra in cuneiform [Preprint]. Max Planck Institute for the History of Science. https://www.mpiwg-berlin.mpg.de/Preprints/P452.PDF
  29. Høyrup, J. (2019). Selected essays on pre- and early modern mathematical practice. Springer. https://doi.org/10.1007/978-3-030-19258-7
  30. Høyrup, J. (2020). From Hesiod to Saussure, from Hippocrates to Jevons: An introduction to the history of scientific thought between Iran and the Atlantic [Preprint]. Max Planck Institute for the History of Science.
  31. Huffman, C. (2018). Pythagoras. In E. N. Zalta (Ed.), The Stanford Encyclopedia of Philosophy (Winter 2018 Edition). https://plato.stanford.edu/archives/win2018/entries/pythagoras
  32. Kantor, J.-M. (2011). Bourbaki’s structures and structuralism. The Mathematical Intelligencer, 33(1). https://doi.org/10.1007/s00283-010-9173-4
  33. Kaput, J. J. (1992). Technology and mathematics education. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 515–556). Macmillan.
  34. Kaput, J. (1994). Democratizing access to calculus: New routes to old roots. In: A. H. Schoenfeld (Ed.), Mathematical thinking and problem solving (pp. 77–156). Lawrence Erlbaum Associates.
  35. Kaput, J. J. (1998) Representations, inscriptions, descriptions and learning: A kaleidoscope of windows. Journal of Mathematical Behavior, 17(2), 283–301. https://doi.org/10.1016/S0364-0213(99)80062-7
  36. Kaput, J. J., & Schaffer, D. W. (2002). On the development of human representational competence from an evolutionary point of view. In K. Gravemeijer, R. Lehrer, B. van Oers, & L. Verschaffel (Eds.), Symbolizing, modelling and tool use in mathematics (pp. 277-293). Kluwer. https://doi.org/10.1007/978-94-017-3194-2_17
  37. Lakoff, G., & Núñez, R. E. (2000). Where mathematics comes from: How the embodied mind brings mathematics into being. Basic Books.
  38. Latour, B. (2008). The Netz-works of Greek deductions. Social Studies of Science, 38, 441–449.
  39. Mandelbrot, B. B. (2002). Mathematics and society in the 20th century. In M. L. Frame & B. B. Mandelbrot (Eds.), Fractals, graphics, and mathematics education (pp. 29–32). Mathematical Association of America.
  40. Mashaal, M. (2006). Bourbaki: A secret society of mathematicians. American Mathematical Society.
  41. Moritz, R. E. (1958). On mathematics: A collection of witty, profound, amusing passages about mathematics and mathematicians. Dover.
  42. Mukhopadhyay, S. (2009). The decorative impulse: Ethnomathematics and Tlingit basketry. ZDM Mathematics Education, 41, 117–130. https://doi.org/10.1007/s11858-008-0151-7
  43. National Mathematics Advisory Panel (2008). Foundations for success: The final report of the National Mathematics Advisory Panel. US Department of Education. https://files.eric.ed.gov/fulltext/ED500486.pdf
  44. Nails, D., & Monoson, S. (2022). Socrates. In E. N. Zalta (Ed.), The Stanford Encyclopedia of Philosophy (Summer 2022 Edition). https://plato.stanford.edu/archives/sum2022/entries/socrates/
  45. Netz, R. (2003). The shaping of deduction in Greek mathematics: A study in cognitive history. Cambridge University Press. https://doi.org/10.1017/CBO9780511543296
  46. Newman, J. R. (Ed.). (1956). The world of mathematics. Simon and Schuster.
  47. Núñez, R. (2000). Mathematical idea analysis: What embodied cognitive science can say about the human nature of mathematics. In T. Nakahara & M. Koyama (Eds.), Proceedings of the 24th Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 3–22). IGPME.
  48. Parshall, K. H. (2009). The internationalization of mathematics in a world of nations, 1800–1960. In E. Robson & J. Steadall (Eds.), Oxford handbook of history of mathematics (pp. 85–104). Oxford University Press.
  49. Runde, V. (2003). Why I don’t like ‘pure’ mathematics. Pi in the Sky, 7, 30–31. https://arxiv.org/abs/math/0310152
  50. Thom, R. (1971). ‘Modern’ mathematics: An educational and philosophical error? American Scientist, 59(6), 695–699.
  51. Thurstone, W. P. (1994). On proof and progress in mathematics. Bulletin of the American Mathematical Society, 30, 161–177.
  52. Urton, G. (1997). The social life of numbers: A Quechua ontology of numbers and philosophy of arithmetic. University of Texas Press.
  53. Urton, G. (2009). Mathematics and authority: A case study in Old and New World accounting. In E. Robson & J. Steadall (Eds.), Oxford handbook of history of mathematics (pp. 27–55). Oxford University Press.
  54. Verhulst, F. (2012). Mathematics is the art of giving the same name to different things: An interview with Henri Poincaré. Niew Archief voor Wiskunde, 13(5), 154–158.
  55. Wigner, E. (1960). The unreasonable effectiveness of mathematics in the natural sciences. Communications in Pure and Applied Mathematics, 13, 1–14.