# Univocal and dialogic discourse in secondary mathematics classrooms: the case of attending to precision

- 518 Downloads
- 2 Citations

## Abstract

Univocal discourse, characterized by its function of conveying information from one person to another, is common in mathematics classrooms but dialogic teaching aims at students coming to participate in dialogic discourse, that is, discourse functioning to generate new meaning within a community. Many mathematical practices are directed at the development and refinement of new mathematical ideas, and many mathematics educators call for collaborative sense making, so there is potential for mutual support between dialogic discourse and such practices as attending to precision. Drawing on data from five secondary mathematics classrooms, this study focused on instances of attending to precision in whole-class settings. We coded these instances based on the degree to which the discourse was univocal or dialogic. We found that the instances were predominantly univocal but that these univocal instances varied with regard to whose ideas were being transmitted—the teacher’s or a student’s. Dialogic instances were rare but we share examples in which the co-construction of meaning through discourse involved attending to precision in ways that were qualitatively different than the univocal instances. The study provides illustrations of dialogic interactions and discusses the balance between univocal and dialogic discourse that is sought within dialogic teaching. It also contributes to the field an initial analytic framework for and examples of attending to precision in secondary classrooms. We discuss implications with regard to students’ roles in secondary mathematics classroom discourse.

## Keywords

Classroom discourse Communication Attending to precision Dialogic discourse## Notes

### Acknowledgments

This study was supported by the University of Missouri Research Council and the University of Missouri System Research Board. We thank the participating teachers and students who made this work possible.

## References

- Akkus, R., & Hand, B. (2011). Examining teachers’ struggles as they attempt to implement dialogical interaction as part of promoting mathematical reasoning within their classrooms.
*International Journal for Science and Mathematics Education,**9*, 975–998.CrossRefGoogle Scholar - Alexander, R. J. (2005).
*Towards dialogic teaching: Rethinking classroom talk*. Cambridge: Dialogos.Google Scholar - Azzouni, J. (2009). Why do informal proofs conform to formal norms?
*Foundations of Science,**14*, 9–26.CrossRefGoogle Scholar - Bakhtin, M. (1986).
*Speech genres and other late essays*. Austin: University of Texas.Google Scholar - Barwell, R., & Kaiser, G. (2005). Mathematics education in culturally diverse classrooms.
*ZDM,**37*, 61–63.CrossRefGoogle Scholar - Cazden, C. B. (1986). Classroom discourse. In M. C. Wittrock (Ed.),
*Handbook of research on teaching*(pp. 432–463). New York: Macmillan.Google Scholar - Cirillo, M., Steele, M. D., Otten, S., Herbel-Eisenmann, B. A., McAneny, K., & Riser, J. Q. (2014). Teacher discourse moves: Supporting productive and powerful discourse. In K. Karp (Ed.),
*Using research to improve instruction*(pp. 141–149). Reston: National Council of Teachers of Mathematics.Google Scholar - Clarke, D. (2006). Using international research to contest prevalent oppositional dichotomies.
*ZDM,**38*, 376–387.CrossRefGoogle Scholar - Dimmel, J. K., & Herbst, P. G. (2015). The semiotic structure of geometry diagrams: How textbook diagrams convey meanings.
*Journal for Research in Mathematics Education,**46*, 147–195.CrossRefGoogle Scholar - Engle, R., & Conant, F. (2002). Guiding principles for fostering productive disciplinary engagement: Explaining emerging argument in a community of learners classroom.
*Cognition and Instruction,**20*, 399–483.CrossRefGoogle Scholar - Fennell, F., Kobett, B., & Wray, J. (2013).
*Using look for’s to consider the Common Core State Standards*.*Paper presented at the annual meeting of the Association of Mathematics Teacher Education*, Orlando, FL.Google Scholar - Herbel-Eisenmann, B., Johnson, K. R., Otten, S., Cirillo, M., & Steele, M. D. (2014). Mapping talk about the mathematics register in a secondary mathematics teacher study group.
*Journal of Mathematical Behavior,*. doi: 10.1016/j.jmathb.2014.09.003.Google Scholar - Herbel-Eisenmann, B. A., & Otten, S. (2011). Mapping mathematics in classroom discourse.
*Journal for Research in Mathematics Education,**42*, 451–485.Google Scholar - Hill, H. C., Charalambous, C. Y., & Kraft, M. A. (2012). When rater reliability is not enough: Teacher observation systems and a case for the generalizability study.
*Educational Researcher,**41*, 56–64.CrossRefGoogle Scholar - Kazak, S., Wegerif, R., & Fujita, T. (2015). The importance of dialogic processes to conceptual development in mathematics.
*Educational Studies in Mathematics,*. doi: 10.1007/s10649-015-9618-y.Google Scholar - Kieran, C. (2007). Learning and teaching of algebra at the middle school through college levels: Building meaning for symbols and their manipulation. In F. K. Lester Jr (Ed.),
*Second handbook of research on mathematics teaching and learning*(pp. 707–762). Charlotte: Information Age Publishing.Google Scholar - Koestler, C., Felton, M. D., Bieda, K. N., & Otten, S. (2013).
*Connecting the NCTM process standards and the CCSSM practices*. Reston: National Council of Teachers of Mathematics.Google Scholar - Lakatos, I. (1976).
*Proofs and refutations: The logic of mathematical discovery*. Cambridge: Cambridge University Press.CrossRefGoogle Scholar - Lobato, J., Clarke, D., & Ellis, A. B. (2005). Initiating and eliciting in teaching: A reformulation of telling.
*Journal for Research in Mathematics Education,**36*, 101–136.Google Scholar - Lundin, M. (2008). Meaning making of precision and procedures in school science.
*Canadian Journal of Science, Mathematics, and Technology Education,**8*, 25–34.CrossRefGoogle Scholar - Mahavier, W. S., & Mahavier, W. T. (2008). Calculus: The importance of precise notation.
*PRIMUS,**18*, 349–360.CrossRefGoogle Scholar - Mehan, H. (1979). “What time is it, Denise?”: Asking known information questions in classroom discourse.
*Theory into Practice,**18*, 285–294.CrossRefGoogle Scholar - Mercer, N., & Howe, C. (2012). Explaining the dialogic processes of teaching and learning: The value and potential of sociocultural theory.
*Learning, Culture and Social Interaction,**1*, 12–21.CrossRefGoogle Scholar - Mortimer, E. F., & Scott, P. H. (2003).
*Meaning making in secondary science classrooms*. Maidenhead: Open University Press.Google Scholar - Nardi, E. (2011). Driving noticing yet ‘risking precision’: University mathematicians’ pedagogical perspectives on verbalisation in mathematics.
*Proceedings of the 7th Conference on European Research in Mathematics Education*. Rzeszow, Poland: European Research in Mathematics Education.Google Scholar - National Governors Association Center for Best Practices, & Council of Chief State School Officers. (2010).
*Common Core State Standards for Mathematics*. Washington, DC: Author.Google Scholar - Nystrand, M., Wu, L., Gamorgan, A., Zeiser, S., & Long, D. (2003). Questions in time: Investigating the structure and dynamics of unfolding classroom discourse.
*Discourse Processes,**35*, 135–198.CrossRefGoogle Scholar - Otten, S., Engledowl, C., & Spain, V. (2014). Teachers’ developing talk about the mathematical practice of attending to precision. In S. Oesterle, C. Nicol, P. Liljedahl & D. Allan (Eds.),
*Proceedings of the 38th conference of the International Group for the Psychology of Mathematics Education and the 36th conference of the North American Chapter*(Vol. 6, p. 191). Vancouver: PME.Google Scholar - Otten, S., & Soria, V. M. (2014). Relationships between students’ learning and their participation during enactment of middle school algebra tasks.
*ZDM - The International Journal on Mathematics Education,**46*, 815–827.CrossRefGoogle Scholar - Peressini, D. D., & Knuth, E. J. (1998). Why are you talking when you could be listening? The role of discourse and reflection in the professional development of a secondary mathematics teacher.
*Teaching and Teacher Education,**14*, 107–125.CrossRefGoogle Scholar - Pimm, D. (1987).
*Speaking mathematically: Communication in mathematics classrooms*. New York: Routledge.Google Scholar - Scott, P. H., Mortimer, E. F., & Aguiar, O. G. (2006). The tension between authoritative and dialogic discourse: A fundamental characteristic of meaning making interactions in high school science lessons.
*Science Education,**90*, 605–631.CrossRefGoogle Scholar - Staples, M., & Colonis, M. M. (2007). Making the most of mathematical discussions.
*Mathematics Teacher,**101*, 257–261.Google Scholar - Stigler, J. W., & Hiebert, J. (1999).
*The teaching gap: Best ideas from the world’s teachers for improving education in the classroom*. New York: Simon and Schuster.Google Scholar - Tarr, J. E., Grouws, D. A., Chavez, O., & Soria, V. M. (2013). The effects of content organization and curriculum implementation on students’ mathematics learning in second-year high school courses.
*Journal for Research in Mathematics Education,**44*, 683–729.CrossRefGoogle Scholar - Truxaw, M. P., & DeFranco, T. C. (2008). Mapping mathematics classroom discourse and its implications for models of teaching.
*Journal for Research in Mathematics Education,**39*, 489–525.Google Scholar - Vygotsky, L. (1978).
*Mind in society: The development of higher psychological processes*. Cambridge: Harvard University Press.Google Scholar - Walshaw, M., & Anthony, G. (2008). The teacher’s role in classroom discourse: A review of recent research into mathematics classrooms.
*Review of Educational Research,**78*, 516–551.CrossRefGoogle Scholar - Wegerif, R. (2006). Dialogic education: What is it and why do we need it?
*Education Review,**19*(2), 58–66.Google Scholar - Zandieh, M., & Rasmussen, C. (2010). Defining as a mathematical activity: A framework for characterizing progress from informal to more formal ways of reasoning.
*Journal of Mathematical Behavior,**29*, 57–75.CrossRefGoogle Scholar