Educational Studies in Mathematics

, Volume 76, Issue 1, pp 49–63 | Cite as

Understanding mathematics textbooks through reader-oriented theory

Article

Abstract

Textbooks have the potential to be powerful tools to help students develop an understanding of mathematics. However, many students are unable to use their textbooks effectively as learning tools. This paper presents a framework that can be used to analyze factors that impact the ways students read textbooks. It adapts ideas from reader-oriented theory and applies them to the domain of mathematics textbooks. In reader-oriented theory, the reader is viewed as actively constructing meaning from a text through the reading process; this endeavor is shaped and constrained by the intentions of the author, the beliefs of the reader, and the qualities the text requires the reader to possess. This paper also discusses how reading mathematics textbooks is further constrained by the authority and closed structure of these textbooks. After describing the framework, the paper discusses recommendations for future avenues of research and pedagogy, highlighting the importance of teachers' roles in mediating their students' use of textbooks.

Keywords

Mathematics education Content area reading Reader-oriented theory Textbooks 

Notes

Acknowledgments

The authors wish to thank Kien Lim, the anonymous reviewers, and the editor for their comments on previous versions of this article.

References

  1. Ball, D. L., & Cohen, D. K. (1996). Reform by the book: What is—or might be—the role of curriculum materials in teacher learning and instructional reform? Educational Researcher, 25(9), 6–14.Google Scholar
  2. Bierhoff, H. (1996). A comparison of primary school textbooks in Britain, Germany, and Switzerland. Teaching Mathematics and Its Applications, 15(4), 141–160.CrossRefGoogle Scholar
  3. Bleich, D. (1994). Epistemological assumptions in the study of response. In J. P. Tompkins (Ed.), Reader-response criticism: From formalism to post-structuralism (pp. 134–163). Baltimore: Johns Hopkins University Press.Google Scholar
  4. Borasi, R., & Siegel, M. (1990). Reading to learn mathematics: New connections, new questions, new challenges. For the Learning of Mathematics, 10(3), 9–16.Google Scholar
  5. Borasi, R., Siegel, M., Fonzi, J., & Smith, C. F. (1998). Using transactional reading strategies to support sense-making and discussion in mathematics classrooms: An exploratory study. Journal for Research in Mathematics Education, 29(3), 275–305.CrossRefGoogle Scholar
  6. Carter, T. A., & Dean, E. O. (2006). Mathematics intervention for grades 5-11: Teaching mathematics, reading, or both? Reading Psychology, 27(2 & 3), 127–146.CrossRefGoogle Scholar
  7. Eco, U. (1979). The role of the reader: Explorations in the semiotics of texts. Bloomington, IN: Indiana University Press.Google Scholar
  8. Erlwanger, S. H. (1973). Benny's conception of rules and answers in IPI mathematics. Journal of Children's Mathematical Behavior, 1(2), 7–26.Google Scholar
  9. Fish, S. (1980). Is there a text in this class? The authority of interpretive communities. Cambridge, MA: Harvard University Press.Google Scholar
  10. Haggarty, L., & Pepin, B. (2002). An investigation of mathematics textbooks and their use in English, French, and German classrooms: Who get an opportunity to learn what? British Educational Research Journal, 28(4), 567–590.CrossRefGoogle Scholar
  11. Henderson, C., & Rosenthal, A. (2006). Reading questions: Encouraging students to read the text before coming to class. Journal of College Science Teaching, 35(7), 46–50.Google Scholar
  12. Herbel-Eisenmann, B. A. (2004). An examination of textbook “voice”: How might discursive choices undermine some goals of the reform? In D. E. McDougall & J. A. Ross (Eds.), Proceedings of the Twenty-sixth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 862–870) Toronto, ON.Google Scholar
  13. Holliday, W. G., Yore, L. D., & Alvermann, D. E. (1994). The reading-science-learning-writing connection: Breakthroughs, barriers, and promises. Journal of Research in Science Teaching, 31, 877–893.CrossRefGoogle Scholar
  14. Hughes-Hallett, D., McCallum, W. G., Gleason, A. M., Osgood, B. G., Flath, D. E., Quinney, D., et al. (2009). Calculus: Single variable (5th ed.). Hoboken: Wiley.Google Scholar
  15. K-12 Mathematics Curriculum Center. (2005). The changing mathematics curriculum: An annotated bibliography. Newton, MA: Education Development Center.Google Scholar
  16. Kang, W., & Kilpatrick, J. (1992). Didactic transposition in mathematics textbooks. For the Learning of Mathematics, 12(1), 2–7.Google Scholar
  17. Konior, J. (1993). Research into the construction of mathematical texts. Educational Studies in Mathematics, 24(3), 251–256.CrossRefGoogle Scholar
  18. Kucan, L., & Beck, I. (1997). Thinking aloud and reading comprehension: Inquiry, instruction, and social interaction. Review of Educational Research, 67(3), 271–299.Google Scholar
  19. Link, H. (1976). Rezeptionsforschung: Eine einführung in methoden und probleme [Reception Research: An introduction to methods and problems]. Stuttgart: Kohlhammer.Google Scholar
  20. Lithner, J. (2003). Students' mathematical reasoning in university textbook exercises. Educational Studies in Mathematics, 52, 29–55.CrossRefGoogle Scholar
  21. Love, E., & Pimm, D. (1996). ‘This is so’: A text on texts. In A. Bishops, K. Clements, C. Keitel, J. Kilpatrick, & C. Laborde (Eds.), International handbook of mathematics education (pp. 371–409). Boston: Kluwer Academic Publishing.Google Scholar
  22. Marbach-Ad, G., & Sokolove, P. (2000). Undergraduate biology students learn to ask higher level questions? Journal of Research in Science Teaching, 37(8), 854–870.CrossRefGoogle Scholar
  23. McNamara, D. S., Kintsch, E., Songer, N. B., & Kintsch, W. (1996). Are good texts always better? Interactions of text coherence, background knowledge, and levels of understanding in learning from text. Cognition and Instruction, 14(1), 1–43.CrossRefGoogle Scholar
  24. Morgan, C. (1996). “The language of mathematics”: Towards a critical analysis of mathematics texts. For the Learning of Mathematics, 16(3), 2–10.Google Scholar
  25. Neth, A., & Voigt, J. (1991). Lebensweltliche inszenierungen. Die aushandlung schulmathematischer bedeutungen an sachaufgaben [Real-world Role Plays: The negotiation of school-related mathematical meanings through assigned tasks]. In H. Maier & J. Voigt (Eds.), Interpretative Unterrichtsforschung [Interpretative Pedagogy Research] (pp. 79–116). Köln: Aulis.Google Scholar
  26. Österholm, M. (2006). Characterizing reading comprehension of mathematical texts. Educational Studies in Mathematics, 63(3), 325–346.CrossRefGoogle Scholar
  27. Otte, M. (1983). Textual strategies. For the Learning of Mathematics, 3(3), 15–28.Google Scholar
  28. Raman, M. (2002). Coordinating informal and formal aspects of mathematics: Student behavior and textbook messages. Journal of Mathematical Behavior, 21(2), 135–150.CrossRefGoogle Scholar
  29. Reys, B. J., Reys, R. E., & Chavez, O. (2004). Why mathematics textbooks matter. Educational Leadership, 5(61), 61–66.Google Scholar
  30. Rezat, S. (2006). The structures of German mathematics textbooks. Zentralblatt für Didaktik der Mathematik, 38(6), 482–487.CrossRefGoogle Scholar
  31. Rosenblatt, L. (1938). Literature as exploration. New York: Appleton-Century.Google Scholar
  32. Rosenblatt, L. (1985). Viewpoints: Transaction versus interaction—a terminological rescue operation. Research in the Teaching of English, 19(1), 96–107.Google Scholar
  33. Rotman, B. (2006). Toward a semiotics of mathematics. In R. Hersh (Ed.), Unconventional essays on the nature of mathematics (pp. 97–127). New York: Springer.CrossRefGoogle Scholar
  34. Schraw, G., & Bruning, R. (1999). How implicit models of reading affect motivation to read and reading engagement. Scientific Studies of Reading, 3(3), 281–302.CrossRefGoogle Scholar
  35. Siegel, M., Borasi, R., & Smith, C. (1989). A critical review of reading in mathematics instruction: The need for a new synthesis. Unpublished manuscript. Rochester, NY: University of Rochester. Retrieved June 25, 2008, from ERIC database (ED301863).Google Scholar
  36. Smith, F. (2004). Understanding reading: A psycholinguistic analysis of reading and learning to read (6th ed.). Mahwah, NJ: Lawrence Erlbaum Associates.Google Scholar
  37. Stewart, J. (2007). Calculus (6th ed.). New York: Brooks-Cole.Google Scholar
  38. Stickles, P., & Stickles, J. (2008). Using reading assignments in teaching calculus. Mathematics and Computer Education, 42(1), 6–10.Google Scholar
  39. Voigt, J. (1994). Negotiation of mathematical meaning and learning mathematics. Educational Studies in Mathematics, 26(2/3), 275–298.CrossRefGoogle Scholar
  40. Wandersee, J. (1988). Ways students read texts. Journal of Research in Science Teaching, 25(1), 69–84.CrossRefGoogle Scholar
  41. Weber, K., Brophy, A., & Lin, K. (2008). Learning advanced mathematical concepts by reading text. Paper presented at Conference on Research in Undergraduate Mathematics Education, San Diego, CA. Retrieved August 7, 2008, from http://cresmet.asu.edu/crume2008/Proceedings/Weber%20LONG.pdf.
  42. Weinberg, A. (2010). The implied reader in calculus textbooks. Proceedings of the 32nd Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (in press).Google Scholar
  43. Weinberg, A., Wiesner, E., Benesh, B., & Boester, T. (2010). Undergraduate students' self-reported use of mathematics textbooks. Problems, Resources, and Issues in Mathematics Undergraduate Studies (in press).Google Scholar
  44. Wilson, W. D. (1981). Readers in texts. PMLA, 96(5), 848–863.CrossRefGoogle Scholar
  45. Wolff, E. (1971). Der intendierte leser [The Intended Reader]. Poetica, 4, 140–146.Google Scholar
  46. Yore, L. D. (2000). Enhancing science literacy for all students with embedded reading instruction and writing-to-learn activities. Journal of Deaf Studies and Deaf Education, 5(1), 105–112.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Ithaca CollegeIthacaUSA

Personalised recommendations