# Sociomathematical and mathematical norms related to definition in pre-service primary teachers’ discourse

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## Abstract

This study is part of a wider research program, which seeks to investigate the existence (or not) of relationships between sociomathematical and mathematical norms at different academic levels. Here, we consider the norms that arise in the interaction between primary student teachers when they solve a mathematical task related to the mathematical definition. We hypothesize that in the colloquial mathematical discourse between these students coexist two types of discourse as follows: sociomathematical and mathematical, each one with its specific norms. This coexistence can originate commognitive conflicts. We have been able to identify different commognitive conflicts that arose from the simultaneous existence of sociomathematical norms and mathematical norms linked to defining, approaching their generation.

## Keywords

Sociomathematical norms Mathematical norms Commognitive conflicts## Notes

### Acknowledgments

The research reported here was financially supported by the Ministry of Science and Innovation (Spain) through a grant corresponding to the project no. PSI2008-02289.

An earlier version of this paper was presented as a Research Report at the 35th International Conference on the Psychology of Mathematics Education (PME) in Ankara, Turkey, July 2011.

## References

- Biddle, B. J., & Thomas, E. J. (1966). Prescriptions. In B. J. Biddle & E. J. Thomas (Eds.),
*Role theory: Concepts and research*(pp. 103–104). NY: Wiley and Sons, Inc.Google Scholar - Borasi, R. (1991).
*Learning mathematics through inquiry*. Portsmouth: Heinemann Educational Books, Ins.Google Scholar - García, M., Sánchez, V., & Escudero, I. (2007). Learning through reflection in mathematics teacher education.
*Educational Studies in Mathematics, 64*(1), 1–17.CrossRefGoogle Scholar - Gorgorió, N., & Planas, N. (2005). Social representations as mediators of mathematical learning in multiethnic classrooms.
*European Journal of Psychology of Education, XX*, 91–104.CrossRefGoogle Scholar - Harel, G., Selden, A., & Selden, J. (2006). Advanced mathematical thinking. In A. Gutierrez & P. Boero (Eds.),
*Handbook of research on the psychology of mathematics education*(pp. 147–172). Rotterdam: Sense Publishers.Google Scholar - Herbel-Eisenmann, B. (2003). Examining “norms” in mathematics education literature: Refining the lens.
*Paper presented at NCTM Research Pre*-*Session Symposium*:*The role of beliefs*,*values and norms in mathematics classroom*:*A conceptualization of theoretical lenses*. San Antonio, TX, USA.Google Scholar - Hershkowitz, R., & Schwarz, B. (1999). The emergent perspective in rich learning environments: Some roles of tools and activities in the construction of sociomathematical norms.
*Educational Studies in Mathematics, 39*, 149–166.CrossRefGoogle Scholar - Kieran, C., Forman, E., & Sfard, A. (2001). Bridging the individual and the social: discursive approaches to research in mathematics education. A PME special issue.
*Educational Studies in Mathematics, 46*, 1–3.CrossRefGoogle Scholar - Lave, J., & Wenger, E. (1991).
*Situated learning. Legitimate peripheral participation*. New York: Cambridge University Press.CrossRefGoogle Scholar - Morgan, C. (2005). What is a definition for in school mathematics? In M. Bosch (Ed.),
*European Research in Mathematics Education IV: Proceedings of the Fourth Congress of the European Society for Research in Mathematics Education*. Sant Feliu de Guíxols: FUNDEMI IQS—Universitat Ramon Llull.Google Scholar - Ouvrier-Buffet, C. (2006). Exploring mathematical definition construction processes.
*Educational Studies in Mathematics, 63*(3), 259–282.CrossRefGoogle Scholar - Sánchez, V., García, M., Escudero, I., Gavilan, J. M., Trigueros, R., & Sánchez-Matamoros, G. (2008). Una aproximación a las matemáticas en el bachillerato. ¿Qué se pretende que aprendan los alumnos? [An approach to mathematics in 16-18 year old students. What is intended for students to learn?]
*Enseñanza de las Ciencias, 26*(2), 267–276.Google Scholar - Sfard, A. (2001). There is more to discourse that meets the ears: Looking at thinking as communicating to learn more about mathematical learning.
*Educational Studies in Mathematics, 46*(1–3), 13–57.CrossRefGoogle Scholar - Sfard, A. (2006). Participationist discourse on mathematics learning. In J. Maasz & W. Schlöglmann (Eds.),
*New Mathematics Education Research and Practice*(pp. 153–170). Rotterdam: Sense Publishers.Google Scholar - Sfard, A. (2007). When the rules of discourse change, but nobody tells you: Making sense of mathematics learning from commognitive standpoint.
*Journal of Learning Sciences, 16*(4), 567–615.CrossRefGoogle Scholar - Sfard, A. (2008).
*Thinking as communicating*:*Human development*,*the growth of discourses and mathematizing*. Cambridge University PressGoogle Scholar - Sfard, A. (2012). Introduction: Developing mathematical discourse. Some insights from communicational research.
*International Journal of Educational Research, 51–52*, 1–9.CrossRefGoogle Scholar - Sinclair, N., & Moss, J. (2012). The more it changes, the more it becomes the same: The development of the routine of shape identification in dynamic geometry environment.
*International Journal of Educational Research, 51–52*, 28–44.Google Scholar - Tatsis, K., & Koleza, E. (2008). Social and sociomathematical norms in collaborative problem solving.
*European Journal of Teacher Education, 31*(1), 89–100.CrossRefGoogle Scholar - Wells, G. (1999).
*Dialogic inquiry*:*Towards a sociocultural practice and theory of education*. Cambridge University Press.Google Scholar - Van Dormolen, J., & Zaslavsky, O. (2003). The many facets of a definition: The case of periodicity.
*Journal of Mathematical Behavior, 22*, 91–106.CrossRefGoogle Scholar - Yackel, E. (2000). Creating a mathematics classroom environment that fosters the development of mathematical argumentation.
*Paper prepared for Working Group 1*:*Mathematics education in Pre and Primary School*.*Ninth International Congress of Mathematical Education*. Tokyo/Makuhari, Japan.Google Scholar - Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics.
*Journal for Research in Mathematics Education, 27*(4), 390–408.CrossRefGoogle Scholar - Zaslavsky, O., & Shir, K. (2005). Students’ conceptions of a mathematical definition.
*Journal for Research in Mathematics Education, 36*(4), 317–347.Google Scholar