Skip to main content
Log in

Opening the closed text: the poetics of representations of teaching

  • Original Article
  • Published:
ZDM Aims and scope Submit manuscript

Abstract

I provide an analysis of the uses of representations of teaching by embedding such representations within Umberto Eco’s theory of the open work, in which literary works are understood not as carriers of a string of meanings, controlled by the author (“closed works”), but rather as fields of meaning. I contend that the well-established tradition of using representations of teaching for pedagogical purposes corresponds to the use of closed works. In contrast, their use for research purposes corresponds to the use of open works. I develop these considerations through an analysis of several representations of teaching, and show how features of these representations work variously to either open or close the work. I also provide anecdotal evidence that viewers of such “open works” may fall victim to a version of the so-called “intentional fallacy.” I discuss the implications of this for the integrity of the research enterprise.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2

Similar content being viewed by others

Notes

  1. These videos may be accessed online through Pearson’s “My Education Lab” service (http://www.myeducationlab.com).

  2. All names used in this paper are pseudonyms.

  3. Moderator, Researcher, «Staff 1» and «Staff 2» are all members of the ThEMaT research project. Their names have been elided in the transcript.

References

  • Eco, U. (1979). The role of the reader: Explorations in the semiotics of texts. Bloomington: Indiana University Press.

    Google Scholar 

  • Eco, U. (1989). The open work. Cambridge: Harvard University Press.

    Google Scholar 

  • Eco, U. (1994). The limits of interpretation. Bloomington: Indiana University Press.

    Google Scholar 

  • Hall, R. (2000). Videorecording as theory. In A. Kelly & R. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 647–664). Mahwah, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Herbst, P., & Chazan, D. (2003a). Exploring the practical rationality of mathematics teaching through conversations about videotaped episodes: the case of engaging students in proving. For the Learning of Mathematics, 23(1), 2–14.

    Google Scholar 

  • Herbst, P., & Chazan, D. (2003b). ThEMaT: Thought Experiments in Mathematics Teaching. Proposal to the National Science Foundation, Education and Human Resources Directorate, Division of Elementary, Secondary, and Informal Education, Teachers’ Professional Continuum Program.

  • Herbst, P., & Chazan, D. (2006). Producing a viable story of geometry instruction: What kind of representation calls forth teachers’ practical rationality? In S. Alatorre, et al. (Eds.), Proceedings of the 28th PME-NA conference (Vol. 2, pp. 213–220). Mérida, México: UPN.

  • Herbst, P., & Miyakawa, T. (2008). When, how, and why prove theorems? A methodology for studying the perspective of geometry teachers. Zentralblatt für Didaktik der Mathematik, 40(3), 469–486.

    Article  Google Scholar 

  • Herbst, P., Nachlieli, T., & Chazan, D. (2009). Studying the practical rationality of mathematics teaching: What goes into “installing” a theorem in Geometry? Cognition and Instruction (accepted).

  • Sfard, A. (1998). On two metaphors for learning and the dangers of choosing just one. Educational Researcher, 27(2), 4–13.

    Google Scholar 

  • Van de Walle, J., Karp, K., & Bay-Williams, J. (2010). Elementary and middle school mathematics: Teaching developmentally. Boston: Allyn & Bacon.

    Google Scholar 

  • Weiss, M., & Herbst, P. (2007, April). Every single little proof they do, you could call it a theorem: Translation between abstract concepts and concrete objects in the Geometry classroom. Paper presented at the annual meeting of the American Educational Research Association, Chicago, IL.

  • Weiss, M., & Herbst, P. (2010, April). Geometry teachers’ mathematical sensibility: The role of theory-building and problem-solving in the secondary geometry course. Paper presented at the annual meeting of the American Educational Research Association, San Diego, CA.

  • Wiggins, G., & McTighe, J. (2005). Understanding by Design. Alexandria, VA: Association for Supervision and Curriculum Development.

  • Wimsatt, W. K., & Beardsley, M. C. (1946/1999). The intentional fallacy. In N. Warburton (Ed.), Philosophy: Basic readings (pp. 480–492). New York: Routledge.

Download references

Acknowledgments

I am grateful to Patricio Herbst, director of the research project ThEMaT (“Thought Experiments in Mathematics Teaching”, NSF grant ESI-0353285) for permission to use ThEMaT animations and research data in this paper.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Michael Kevin Weiss.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Weiss, M.K. Opening the closed text: the poetics of representations of teaching. ZDM Mathematics Education 43, 17–27 (2011). https://doi.org/10.1007/s11858-010-0281-6

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11858-010-0281-6

Keywords

Navigation