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Rethinking critical mathematics: a comparative analysis of critical, reform, and traditional geometry instructional texts

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Abstract

This paper presents findings from a comparative analysis of three similar secondary geometry texts, one critical unit, one standards-based reform unit, and one specialist chapter. I developed the critical unit as I took the tenets of critical mathematics (CM) and substantiated them in printed curricular materials in which to teach as part of a larger study. The reform and specialist texts were both sections from commercially available textbooks. The primary goal of the textual analysis was to examine how the incorporation of critical or political themes into the required secondary mathematics curriculum transformed this curriculum. Key findings were that the CM text exchanged political for mathematical content and sent class-based messages about students’ academic potential. I conclude by arguing that the CM agenda proposed by advocates in the USA is problematic in terms of promoting equity in mathematics education.

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Notes

  1. A complete copy of the CM text is provided in the dissertation of Brantlinger (2007) available by request to the author.

References

  • Au, W., Bigelow, B., & Karp, S. (Eds.). (1994). Rethinking our classrooms (vol. 1). Milwaukee: Rethinking Schools.

    Google Scholar 

  • Brantlinger, A. (2005). The geometry of inequality. Rethinking Schools, 19(3), 53–55.

    Google Scholar 

  • Brantlinger, A. (2007) Geometries of inequality: Teaching and researching critical mathematics in a low-income urban high school (unpublished doctoral dissertation). Northwestern University, Evanston, IL

  • Brantlinger, A. (2010). A view from the other side: Practitioner research on critical mathematics pedagogy in an urban high school. In K. Scott & W. Blanchett (Eds.), Research in urban educational settings: Lessons learned and implications for future practice. Charlotte: Information Age Publishing.

    Google Scholar 

  • Brantlinger, A. (2011). Critical mathematics in a secondary setting: Promise and problems. In B. Atweh, M. Graven, W. Secada, & P. Valero (Eds.), Mapping equity and quality in mathematics education. Dordrecht: Springer.

    Google Scholar 

  • Delpit, L. (1986). Skills and other dilemmas of a progressive black educator. Harvard Educational Review, 56, 379–385.

    Google Scholar 

  • Dowling, P. (1998). The sociology of mathematics education: Mathematical myths/pedagogic texts. London: Falmer Press.

    Google Scholar 

  • Ernest, P. (1998). Social constructivism as a philosophy of mathematics. Albany: State University of New York Press.

    Google Scholar 

  • Fendel, D., Resek, D., Alper, L., & Fraser, S. (1998a). Interactive mathematics program (IMP): Integrated high school mathematics. Emeryville: Key Curriculum Press.

    Google Scholar 

  • Fendel, D., Resek, D., Alper, L., & Fraser, S. (1998b). “Do Bees Build it Best?” Teacher’s guide. Emeryville: Key Curriculum Press.

    Google Scholar 

  • Frankenstein, M. (1983). Critical mathematics education: An application of Paulo Freire’s epistemology. Boston University Journal of Education, 165(4), 315–339.

    Google Scholar 

  • Frankenstein, M. (1989). Relearning mathematics: A different third R—radical maths. London: Free Association Books.

    Google Scholar 

  • Freire, P. (1971). Pedagogy of the oppressed (M. B. Ramos, Trans.). New York: Seabury.

    Google Scholar 

  • Gutiérrez, R. (2002). Enabling the practice of mathematics teachers in context: Towards a new equity research agenda. Mathematical Thinking and Learning, 4(2–3), 145–187.

    Article  Google Scholar 

  • Gutstein, E. (2003). Teaching and learning mathematics for social justice in an urban, Latino school. Journal for Research in Mathematics Education, 34(1), 37–73.

    Article  Google Scholar 

  • Gutstein, E. (2006). Reading and writing the world with mathematics: Toward a pedagogy for social justice. New York: Routledge.

    Google Scholar 

  • Gutstein, E., & Peterson, B. (Eds.). (2005). Rethinking mathematics: Teaching social justice by the numbers. Milwaukee: Rethinking Schools.

    Google Scholar 

  • Herbst, P. (2006). Teaching geometry with problems: Negotiating instructional situations and mathematical tasks. Journal for Research in Mathematics Education, 37(4), 313–347.

    Google Scholar 

  • Lave, J. (1988). Cognition in practice: Mind, mathematics, and culture in everyday life. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston: National Council of Teachers of Mathematics.

    Google Scholar 

  • Nemirovsky, R. (1996). A functional approach to algebra: Two issues that emerge. In N. Bednarz, C. Kieran, & L. Lee (Eds.), Approaches to algebra: Perspectives for research and teaching (pp. 295–313). Dordrecht: Kluwer Academic Publishers.

    Google Scholar 

  • Powell, A. B. & Brantlinger, A. (2008). A pluralistic view of critical mathematics. Proceedings of The Fifth International Conference on Mathematics Education and Society. Albufeira, Portugal.

  • Presmeg, N. (1998). Metaphoric and metonymic signification in mathematics. Journal of Mathematical Behavior, 17(1), 25–32.

    Article  Google Scholar 

  • Rhoad, R., Milauskas, G., & Whipple, R. (1991). Geometry for enjoyment and challenge. Geneva: McDougal Littell.

    Google Scholar 

  • Sells, L. W. (1978). Mathematics: A critical filter. Science Teacher, 45, 28–29.

    Google Scholar 

  • Skovsmose, O. (1985). Mathematical education versus critical education. Educational Studies in Mathematics, 16(4), 337–354.

    Article  Google Scholar 

  • Skovsmose, O. (1994). Towards a philosophy of critical mathematical education. Dordrecht: Kluwer.

    Google Scholar 

  • Tate, W. F. (1995). Returning to the root: A culturally relevant approach to mathematics pedagogy. Theory into Practice, 34, 166–173.

    Article  Google Scholar 

  • Turner, E., & Font Strawhun, B. T. (2005). With math, it’s like you have more defense. In E. Gutstein & B. Peterson (Eds.), Rethinking mathematics. Milwaukee: Rethinking Schools.

    Google Scholar 

  • Williams, J., & Joseph, G. G. (1993). Statistics and inequality: A global perspective. In D. Newlson, G. G. Joseph, & J. Williams (Eds.), Multicultural mathematics: Teaching mathematics from a global perspective (pp. 175–204). New York: Oxford University Press.

    Google Scholar 

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Correspondence to Andrew Brantlinger.

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This article is a revision of work presented in my 2007 dissertation co-chaired by Professors Carol D. Lee and Miriam G. Sherin at Northwestern University. Jim Spillane and Eric Gutstein were the third and fourth members of the committee. Arthur B. Powell at Rutgers University at Newark, Dan Chazan at the University of Maryland, and Laurel Cooley of Brooklyn College provided helpful feedback on drafts. I am also indebted to three anonymous reviewers and the editor of Educational Studies in Mathematics for their feedback.

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Brantlinger, A. Rethinking critical mathematics: a comparative analysis of critical, reform, and traditional geometry instructional texts. Educ Stud Math 78, 395–411 (2011). https://doi.org/10.1007/s10649-011-9331-4

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