Abstract
This analysis of the writing in a grade 7 mathematics textbook distinguishes between closed texts and open texts, which acknowledge multiple possibilities. I use tools that have recently been applied in mathematics contexts, focussing on grammatical features that include personal pronouns, modality, and types of imperatives, as well as on accompanying structural elements such as photographs and the number of possibilities presented. I extend this discussion to show how even texts that appear open can seduce readers into feeling dialogue while actually leading them down a narrow path. This phenomenon points to the normalizing power of curriculum. For this analysis and reflection, I draw on mathematics textbook material that I wrote. As a way of modelling an alternative to normalization, I identify myself as a self-critical author and thus invite readers to be critical of their reading and writing of mathematics texts.
Similar content being viewed by others
Notes
Eco (1979) theorizes the distinction between the intent of a work and the intent of its author.
There was significant discussion among the Bhutanese educators who commissioned this textbook series regarding the nature of these model student images: should they be cartoon-like caricatures or actual photographs? I do not understand sufficiently the cultural implications of their discussion and decision, but I have noted implications for the representation of humans as subjects of mathematics. A cartoon image is relatively generic and may reflect the penchant for generality in mathematics and the related obfuscation of human particularities. Dowling (1998) also noted distinctions between cartoon images and photographs in his analysis of mathematics textbooks; the intertextuality between such images and other texts read by students can position the students in various ways.
References
Bakhtin, M. (1975/1981). The dialogic imagination: Four essays. (M. Holquist, Ed.; C. Emerson & M. Holquist, trans). Austin, Texas: University of Texas Press.
Barnhart, R. (Ed.). (1988). The Barnhart dictionary of etymology. New York: H. W. Wilson.
Barthes, R. (1975). The pleasure of text. New York: Hill and Wang (Trans., R. Millar).
Barthes, R. (1978). A lover’s discourse. New York: Hill and Wang (Trans., R. Howard).
Barwell, R. (2011). Centripetal and centrifugal forces in multilingual mathematics classrooms. In M. Setati, T. Nkambule, & L. Goosen (Eds.), Proceedings of the ICMI Study 21 Mathematics and language diversity (pp. 1–9), Sào Paulo, Brazil.
Brown, T., Hanley, U., Darby, S., & Calder, N. (2007). Teachers’ conceptions of learning philosophies: Discussing context and contextualising discussion. Journal of Mathematics Teacher Education, 10, 183–200.
de Freitas, E., & Paton, J. (2009). (De)facing the self: Poststructural disruptions of the autoethnographic text. Qualitative Inquiry, 15(3), 483–498.
Derrida, J. (1976). Of grammatology. Delhi: Motilal Banarsidass.
Dowling, P. (1998). The sociology of mathematics education: Mathematical myths—pedagogic texts. London: Falmer.
Eco, U. (1979). The role of the reader. Bloomington, IN: University of Indiana Press.
Eco, U. (1994). Six walks in the fictional woods. Cambridge: Harvard University Press.
Ellsworth, E. (1997). Teaching positions: Difference, pedagogy, and the power of address. New York: Teachers College Press.
Fauvel, J. (1989). Platonic rhetoric in distance learning: How Robert Record taught the home learner. For the Learning of Mathematics, 9(1), 2–5.
Foucault, M. (1975/1977). Discipline and punish: The birth of the prison (trans. A. Sheridan). New York: Vintage.
Frankenstein, M. (1989). Relearning mathematics: A different third R—radical math(s). London: Free Association Books.
Gutstein, E., & Peterson, B. (Eds.). (2005). Rethinking mathematics: Teaching social justice by the numbers. Milwaukee: Rethinking Schools, Ltd.
Herbel-Eisenmann, B. (2009). Negotiating the “presence of the text”: How might teachers’ language choices influence the positioning of the textbook? In J. Remillard, B. Herbel-Eisenmann, & G. Lloyd (Eds.), Mathematics teachers at work: Connecting curriculum materials and classroom instruction (pp. 134–151). New York: Routledge.
Herbel-Eisenmann, B., & Wagner, D. (2007). A framework for uncovering the way a textbook may position the mathematics learner. For the Learning of Mathematics, 27(2), 8–14.
Herbel-Eisenmann, B., & Wagner, D. (2010). Appraising lexical bundles in mathematics classroom discourse: Obligation and choice. Educational Studies in Mathematics, 75(1), 43–63.
Herbel-Eisenmann, B., Wagner, D., & Cortes, V. (2010). Lexical bundle analysis in mathematics classroom discourse: The significance of stance. Educational Studies in Mathematics, 75(1), 23–42.
Lacan, J. (1966/2002). Ecrits: A selection (Trans. B. Fink). New York: Norton.
Love, E., & Pimm, D. (1996). ‘This is so’: A text on texts. In A. Bishop et al. (Eds.), International handbook of mathematics education: Part one (pp. 371–409). Dordrecht: Kluwer.
Martin, J., & White, P. (2005). The language of evaluation: Appraisal in English. New York: Palgrave.
Mesa, V. & Chang, P. (2008). Instructors’ language in two undergraduate mathematics classrooms. Proceedings of the 32nd Conference of the International Group for the Psychology of Mathematics Education held jointly with the 30th Conference of PME-NA, Morelia, Mexico, vol. 3, pp. 367–374.
Morgan, C. (1998). Writing mathematically: The discourse of investigation. London: Falmer.
Pimm, D. (2009). Part III commentary: Who knows best? Tales of ordination, subordination, and insubordination. In J. Remillard, B. Herbel-Eisenmann, & G. Lloyd (Eds.), Mathematics teachers at work: Connecting curriculum materials and classroom instruction (pp. 190–196). New York: Routledge.
Rotman, B. (1988). Toward a semiotics of mathematics. Semiotica, 72(1/2), 1–35.
Rowland, T. (2000). The pragmatics of mathematics education: Vagueness in mathematical discourse. New York: Falmer.
Small, M., Connelly, R., Sterenberg, G., & Wagner, D. (2008). Teacher’s guide to understanding mathematics: Textbook for Class VII. Thimpu: Curriculum and Professional Support Division, Department of School Education.
Small, M., Connelly, R., Hamilton, D., Sterenberg, G., & Wagner, D. (2008). Understanding mathematics: Textbook for Class VII. Thimpu: Curriculum and Professional Support Division, Department of School Education.
Stocker, D. (2006). Maththatmatters: A teacher resource linking math and social justice. Toronto: Canadian Centre for Policy Alternatives.
van Langenhove, L., & Harré, R. (1999). Introducing positioning theory. In R. Harré & L. van Lagenhove (Eds.), Positioning theory: Moral contexts of intentional action (pp. 14–31). Oxford: Blackwell.
Wagner, D. (2010). The seductive queen—mathematics textbook protagonist. In U. Gellert, E. Jablonka & C. Morgan (Eds.) (2010). Proceedings of the Sixth International Mathematics Education and Society Conference (pp. 438–448), Berlin, Germany.
Wagner, D. (2011). Mathematics and a nonkilling worldview. In J. Pim (Ed.), Engineering nonkilling: Scientific responsibility and the advancement of killing-free societies (pp. 105–116). Honolulu: Center for Global Nonkilling.
Wagner, D., & Herbel-Eisenmann, B. (2008). ‘Just don’t:’ The suppression and invitation of dialogue in the mathematics classroom. Educational Studies in Mathematics, 67(2), 143–157.
Weiss, M. (2010). Opening the closed text: The poetics of representations of teaching. ZDM Mathematics Education, 43, 17–27.
White, P. (2003). Beyond modality and hedging: A dialogic view of the language of intersubjective stance. Text, 23(2), 259–284.
Wollen, P. (1982). Readings and writings. London: Verso.
Author information
Authors and Affiliations
Corresponding author
Additional information
This article is an elaboration on a paper published in the Proceedings of the Sixth International Mathematics Education and Society Conference (Wagner, 2010).
Rights and permissions
About this article
Cite this article
Wagner, D. Opening mathematics texts: resisting the seduction. Educ Stud Math 80, 153–169 (2012). https://doi.org/10.1007/s10649-011-9372-8
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10649-011-9372-8