Skip to main content
Open Book Publishers

11. A critical conception of mathematics

Chapter of: Breaking Images: Iconoclastic Analyses of Mathematics and its Education(pp. 235–268)

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
Title11. A critical conception of mathematics
ContributorOle Skovsmose(author)
DOIhttps://doi.org/10.11647/obp.0407.11
Landing pagehttps://www.openbookpublishers.com/books/10.11647/obp.0407/chapters/10.11647/obp.0407.11
Licensehttps://creativecommons.org/licenses/by-nc/4.0/
CopyrightOle Skovsmose
PublisherOpen Book Publishers
Published on2024-12-11
Long abstractA critical conception of mathematics emerged through several routes: this chapter takes a closer look at three of them. First, we follow how the students’ movement, beginning in the late 1960s, inspired a critique of university studies in mathematics. This analysis turned into a critique of mathematical modelling, emphasising that it is an illusion that mathematics ensures objectivity and neutrality. It became recognised that, when brought into action, mathematics may have all kinds of technological, economic, and political impacts, including many of the most questionable kind. Second, we see how mathematics becomes recognised as a plurality of constructions. I show that mathematics is shaped through social, historical, cultural, and political – in short, human – processes, and that any uniform conception of mathematics is a deception, if not a falsification. Third, I illustrate how mathematics can be developed as a critical resource and become a means for identifying forms of economic and political oppression. Mathematics can play a part in the struggle for social justice.
Page rangepp. 235–268
Print length34 pages
LanguageEnglish (Original)
Contributors

Ole Skovsmose

(author)
https://orcid.org/0000-0002-1528-796X

Ole Skovsmose’s research has addressed landscapes of investigation, dialogue, students’ foreground, inclusive mathematics education, pedagogical imagination, mathematics in action, philosophy of mathematics education, and philosophy of mathematics. He has been professor at Aalborg University, Denmark, but is now associated to State University of São Paulo, Brazil. In 2024, he was awarded the Hans Freudenthal medal.

References
  1. Alangui, W. (2010). Stone walls and water flows: Interrogating cultural practices and mathematics [Doctoral dissertation, University of Auckland, Auckland, New Zealand].
  2. Almeida, D. F., & Joseph, G. G. (2009). Kerala mathematics and its possible transmission to Europe. In P. Ernest, B. Greer, & B. Sriraman (Eds.), Critical issues in mathematics education (pp. 171–188). Information Age.
  3. Alrø, H., Ravn, O., & Valero, P. (Eds.). (2010). Critical mathematics education: Past, present, and future. Sense. https://doi.org/10.1163/9789460911644
  4. Andersson, A., & Barwell, R. (Eds.). (2021). Applying critical mathematics education. Brill. https://doi.org/10.1163/9789004465800
  5. Austin, J. L. (1962). How to do things with words. Oxford University Press.
  6. Avcı, B. (2019). Critical mathematics education: Can democratic mathematics education survive under neoliberal regime? Brill. https://doi.org/10.1163/9789004390232
  7. Barros, D. (2021). Lendo e escrevendo o mundo com a matemática em um movimento social: Discussões sobre representatividade e as lutas da comunidade LGBT+ [Reading and writing the world with mathematics in a social movement: Discussions on representation and the struggles of the LGBT+ community, Doctoral dissertation, São Paulo State University, Rio Claro, Brazil].
  8. Bartell, T. G. (Ed.). (2018). Towards equity and social justice in mathematics education. Springer. https://doi.org/10.1007/978-3-319-92907-1
  9. Barwell, R. (2013). The mathematical formatting of climate change: Critical mathematics education and post-normal science. Research in Mathematics Education, 15(1), 1–16. https://doi.org/10.1080/14794802.2012.756633
  10. Barwell, R., & Hauge, K. H. (2021). A critical mathematics education for climate change: A post-normal approach. In A. Andersson & R. Barwell (Eds.), Applying critical mathematics education (pp. 166–184). Brill. https://doi.org/10.1163/9789004465800_008
  11. Bernal, M. (1987). Black Athena: Afroasiatic roots of classical civilization, Volume 1: The fabrication of Ancient Greece, 1785–1985. Rutgers University Press.
  12. Booss-Bavnbek, B., & Høyrup, J. (Eds.). (2003). Mathematics and war. Birkhäuser.
  13. Britto, R. (2013). Educação matemática e democracia: Mídia e racismo [Mathematics education and democracy: Media and racism]. In Anais do VII Congresso Iberoamericano de Educação Matemática (pp. 3355–3362).
  14. Britto, R. (2022). Media and racism. In M. G. Penteado & O. Skovsmose (Eds.), Landscapes of investigation: Contributions to critical mathematics education (pp. 39–56). Open Book Publishers. https://doi.org/10.11647/OBP.0316.03
  15. Burton, L. (1995). Moving towards a feminist epistemology of mathematics. Educational Studies in Mathematics, 28(3), 275–291. https://doi.org/10.1007/BF01274177
  16. Coiffier, J, (2011). Fundamentals of numerical weather prediction. Cambridge University Press. https://doi.org/10.1017/CBO9780511734458
  17. Crutzen, P. J., & Stoermer, E. F. (2000). The ‘anthropocene’. Global Change Newsletter, 41(17), 17–18.
  18. D’Ambrosio, U. (1992). Ethnomathematics: A research programme on the history and philosophy of mathematics with pedagogical implications. Notices of the American Mathematics Society, 39, 1183–1185.
  19. D’Ambrosio, U. (2006). Ethnomathematics: Link between traditions and modernity. Sense. https://doi.org/10.1163/9789460911415
  20. Damerow, P., Elwitz, U., Keitel, C., & Zimmer, J. (1974). Elementarmathematik: Lernen für die Praxis [Elementary mathematics: Learning for practice]. Klett.
  21. Davis, J., & Jett, C. C. (2019). Critical race theory in mathematics education. Routledge.
  22. Ernest, P. (1998). Social constructivism as a philosophy of mathematics. State University of New York Press.
  23. Ernest, P., Sriraman, B., & Ernest, N. (Eds.). (2015). Critical mathematics education: Theory, praxis, and reality. Information Age.
  24. Frankenstein, M. (1983). Critical mathematics education: An application of Paulo Freire’s epistemology. Journal of Education, 165(4), 315–339. https://doi.org/10.1177/002205748316500403
  25. Frankenstein, M. (1989). Relearning mathematics: A different third R—radical maths. Free Association Books.
  26. Freire, P., & Macedo, D. (1987). Literacy: Reading the word and the world. Bergin & Garvey.
  27. Gerdes, P. (2008). Explorando poliedros do Nordeste de Moçambique [Exploring polyhedra from Northeast Mozambique]. In P. Palharas (Ed.), Etnomatemática: Um olhar sobre a diversidade cultural e a aprendizagem matemática (pp. 317–359). Edições Húmus.
  28. Gerdes, P. (2012). Otthava: Making baskets and doing geometry in the Makhuwa culture in the Northeast of Mozambique. Lulu.
  29. Greer, B., Mukhopadhyay, S., Powell, A. B., & Nelson-Barber, S. (Eds.). (2009). Culturally responsive mathematics education. Routledge.
  30. Gutstein, E. (2006). Reading and writing the world with mathematics: Toward a pedagogy for social justice. Routledge.
  31. Gutstein, E. (2016). ‘Our issue, our people–Math as our weapon’: Critical mathematics in a Chicago neighborhood high school. Journal for Research in Mathematics Education, 47(5), 454–504. https://doi.org/10.5951/jresematheduc.47.5.0454
  32. Gutstein, E. (2018). The struggle is pedagogical: Learning to teach critical mathematics. In P. Ernest (Ed.), The philosophy of mathematics education today (pp. 131–143). Springer. https://doi.org/10.1007/978-3-319-77760-3_8
  33. Habermas, J. (1971). Knowledge and human interests. Beacon.
  34. Hardy, G. H. (1967). A mathematician’s apology. Cambridge University Press.
  35. Hawkins, A. J. (2019, May 15). Deadly Boeing crashes raise questions about airplane automation. The Verge. https://www.theverge.com/2019/3/15/18267365/boeing-737-max-8-crash-autopilot-automation
  36. Hood, K. (2017). The science of value: Economic expertise and the valuation of human life in US federal regulatory agencies. Social Studies of Science, 47(4), 441–456. https://doi.org/10.1177/0306312717693465
  37. Jensen A. A., Stentoft, D., & Ravn, O. (2019). Interdisciplinarity and problem-based learning in higher education: Research and perspectives form Aalborg University. Springer. https://doi.org/10.1007/978-3-030-18842-9
  38. Johnson, B. (2010). Algorithmic trading and DMA: An introduction to direct access trading strategies. Myeloma.
  39. Joseph, G. G. (2000). The crest of the peacock: The non-European roots of mathematics. Princeton University Press.
  40. Joseph, G. G. (Ed.). (2011). Kerala mathematics: History and its possible transmission to Europe. B. R. Publishing Corporation.
  41. Kaiser, G., & Rogers, P. (Eds.). (1995). Equity in mathematics education: Influences of feminism and culture. Falmer.
  42. Knijnik. G. (1996). Exclução e resistência: Educação matemática e legitimidade cultural [Exclusion and resistance: Mathematics education and cultural legitimacy]. Artes Médicas.
  43. Knijnik, G. (2012). Differentially positioned language games: Ethnomathematics from a philosophical perspective. Educational Studies in Mathematics, 80(1–2), 87–100. https://doi.org/10.1007/s10649-012-9396-8
  44. Knijnik, G. (2014). Juegos de lenguaje matemáticos de distintas formas de vida: Contribuciones de Wittgenstein y Foucault para pensar la educación matemática [Mathematical language games of different forms of life: Contributions by Wittgenstein and Foucault to thinking about mathematics education]. Educación Matemática, 25, 146–161.
  45. Knijnik, G. (2017). A ordem do discurso da matemática escolar e jogos de linguagem de outras formas de vida [The order of the discourse of school mathematics and language games of other forms of life]. Perspectivas da Educação Matemática, 10, 45–64.
  46. Kolmos, A., Fink, F. K., & Krogh, L. (Eds.). (2004). The Aalborg PBL model: Progress, diversity and challenges. Aalborg University Press.
  47. Martin, D. B. (2013). Race, racial projects, and mathematics education. Journal for Research in Mathematics Education, 44(1), 316–333. https://doi.org/10.5951/jresematheduc.44.1.0316
  48. Martin. D. B. (2019). Equity, inclusion, and antiblackness in mathematics education. Race Ethnicity and Education, 22(4), 459–478. https://doi.org/10.1080/13613324.2019.1592833
  49. Martin, D. B., & Gholson, M. (2012). On becoming and being a critical black scholar in mathematics education: The politics of race and identity. In O. Skovsmose & B. Greer (Eds.), Opening the cage: Critique and politics of mathematics education (pp. 203–222). Sense. https://doi.org/10.1007/978-94-6091-808-7_10
  50. McKenzie, D. (2007). Mathematics of climate change: A new discipline for an uncertain century. Mathematical Sciences Research Institute, Berkeley, California. http://library.msri.org/msri/MathClimate.pdf
  51. Monk, R. (1990). Ludwig Wittgenstein: The duty of genius. Jonathan Cape.
  52. Niss, M., & Hermann, K. (1982). Beskæftigelsesmodellen i SMEC III [The employment model in SMEC III]. Nyt Nordisk Forlag Arnold Busck.
  53. O’Neil, C. (2016). Weapons of math destruction: How big data increase inequality and threatens democracy. Broadway Books.
  54. Parra, A. I. S. (2018). Curupira’s walk: Prowling ethnomathematics theory through decoloniality. Aalborg Universitetsforlag.
  55. Palhares. P. (Ed.). (2008). Etnomatemática: Um olhar sobre a diversidade cultural e a aprendizagem matemática [Ethnomathematics: A look at cultural diversity and mathematical learning]. Edições Húmus.
  56. Raju, C. K. (2007). Cultural foundations of mathematics: The nature of mathematical proof and the transmission of the calculus from India to Europe in the 16th c. CE. PearsonLongman.
  57. Raju, C. K. (2012). Euclid and Jesus: How and why the church changed mathematics and Christianity across two religious wars. Multiversity and Citizens International.
  58. Restivo, S. (1992). Mathematics in society and history. Kluwer. https://doi.org/10.1007/978-94-011-2944-2
  59. Restivo, S., Bendegem, J. P. van, & Fischer, R. (Eds.). (1993). Math worlds: Philosophical and social studies of mathematics and mathematics education. State University of New York Press.
  60. Rio violence: Police killings reach record high in 2019. (2020, January 23). BBC News. https://www.bbc.com/news/world-latin-america-51220364
  61. Rosa, M., D’Ambrosio, U., Orey, D. C., Shirley, L., Alangui, W. V., Palhares, P., & Gavarrete, M. E. (Eds.). (2016). Current and future perspectives of ethnomathematics as a program. Springer. https://doi.org/10.1007/978-3-319-30120-4
  62. Rosa, M., & Orey, D. (2016). State of the art in Ethnomathematics. In M. Rosa, U. D’Ambrosio, D. C. Orey, L. Shirley, W. V. Alangui, P. Palhares & M. E. Gavarrete (Eds.), Current and future perspectives of ethnomathematics as a program. Springer. https://doi.org/10.1007/978-3-319-30120-4_3
  63. Said, E. (1979). Orientalism. Vintage Books.
  64. Searle, J. (1969). Speech acts. Cambridge University Press. https://doi.org/10.1017/CBO9781139173438
  65. Silva, G. H. G., & Skovsmose, O. (2019). Affirmative actions in terms of special rights: Confronting structural violence in Brazilian higher education. Power and Education, 11(2), 204–220. https://doi.org/10.1177/1757743819837682
  66. Skovsmose, O. (2004). Mathematics in action: A challenge for social theorising. Philosophy of Mathematics Education Journal, 18.
  67. Skovsmose, O. (2005). Travelling through education: Uncertainty, mathematics, responsibility. Sense. https://doi.org/10.1163/9789087903626
  68. Skovsmose, O. (2011). An invitation to critical mathematics education. Sense. https://doi.org/10.1007/978-94-6091-442-3
  69. Skovsmose, O. (2012). Mathematics as discourse. Boletim em Educação Matemática, 26(43), 1–18.
  70. Skovsmose, O. (2014). Critique as uncertainty. Information Age.
  71. Skovsmose, O. (2015). (Ethno)mathematics as discourse. In C. Bergsten & B. Sriraman (Eds.), Refractions of mathematics education: Festschrift for Eva Jablonka (pp. 155–172). Information Age.
  72. Skovsmose (2021). Mathematics and crises. Educational Studies in Mathematics, 108(12), 369–383. https://doi.org/10.1007/s10649-021-10037-0
  73. Skovsmose, O. (2023). Critical mathematics education. Springer.
  74. Skovsmose, O., & Greer, B. (Eds.). (2012). Opening the cage: Critique and politics of mathematics education. Sense. https://doi.org/10.1007/978-94-6091-808-7
  75. Torfing, J. (1999). New theories of discourse: Laclau, Mouffe, and Žižek. Wiley-Blackwell.
  76. Turing, A. M. (1937). On computable numbers, with an application to the Entscheidungsproblem. Proceeding of the London Mathematical Society, s2–42(1), 230–265. https://doi.org/10.1112/plms/s2-42.1.230
  77. Vithal, R., Christiansen, I. M., & Skovsmose, O. (1995). Project work in university mathematics education: A Danish experience: Aalborg University. Educational Studies in Mathematics, 29(2), 199–223. https://doi.org/10.1007/BF01274213
  78. Volk, D. (1975). Plädoyer für einen problemorientierten Mathematikunterricht in emanzipatorischer Absicht [Plea for problem-oriented mathematics education with an emancipatory intention]. In M. Ewers (Ed.), Naturwissenschaftliche Didaktik zwischen Kritik und Konstruktion (pp. 203–234). Belz.
  79. Volk, D. (Ed.). (1979). Kritische Stichwörter zum Mathematikunterricht [Critical keywords on mathematics education]. Fink.
  80. Wager, A. A., & Stinson, D. W. (Eds.). (2012). Teaching mathematics for social justice: Conversations with mathematics educators. National Council of Mathematics Teachers.
  81. Warner, T. T. (2011). Numerical weather and climate prediction. Cambridge University Press. https://doi.org/10.1017/CBO9780511763243
  82. Wittgenstein, L. (1978). Remarks on the foundations of mathematics. Blackwell.
  83. Wittgenstein, L. (1989). Wittgenstein’s lectures on the foundations of mathematics: Cambridge, 1939. University of Chicago Press.
  84. Wittgenstein, L. (1997). Philosophical investigations. Blackwell.
  85. Wittgenstein, L. (2002). Tractatus logico-philosophicus. Routledge and Kegan Paul.