Sociomathematical Norms and the Teacher’s Mathematical Belief: A Case Study from a Korean In-Service Elementary Teacher

Seon Mi Kang; Min Kyeong Kim

doi:10.12973/eurasia.2016.1308a

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Seon Mi Kang ¹, Min Kyeong Kim ¹ ^*

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¹ Ewha Womans University^* Corresponding Author

Abstract

Background:
The purpose of the present study is to analyze how the sociomathematical norm, or the process of promoting the understanding of mathematical concepts and principles through the interaction between teacher and students, is established in relation to the teacher’s mathematical beliefs in a fourth-grade mathematics class.

Material and methods:
13 sessions of Teacher K’s elementary mathematics class for a period of one year were observed and monitored by recording, and the students’ lesson activities sheets were collected after each class. Both the students and K were interviewed. The sociomathematical norm was modified and complemented, and coded into five components.

Results:
Teacher K highlighted both the view of ‘Mathematics as formal,’ which argues that mathematics requires logical thinking, and the view of ‘Mathematics as procedural,’ which claims that a mathematics problem allows for multiple solutions.

Conclusions:
A teacher’s mathematical belief is reflected in his or her decision making at every moment of a math class, and greatly influences teaching and learning, specifically, the instructions, objectives, content and methods involved in their classroom environment.

Keywords

elementary mathematics classroom
mathematical belief
mathematics classroom culture
sociomathematical norms

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, Volume 12, Issue 10, October 2016, 2733-2751

https://doi.org/10.12973/eurasia.2016.1308a

Publication date: 25 Jul 2016

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Article Downloads: 4450

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References

Bowers J., Cobb P., & McClain, K. (1999). The evolution of mathematical practices: A case study. Cognition and Instruction, 17(1), 25~64.
Cho, J. (2001). Ethnography for research of mathematics teacher’s belief and classroom norm. Journal of Korea Society of Mathematics Education Series E: Communications of Mathematical Education, 12, 349-361.
Cobb, P., & Bauersfeld, H. (Eds.) (1995). The emergence of mathematical meaning: Interaction in classroom cultures. Mahwah, NJ: Lawrence Erlbaum Associates.
Cobb, P., & Bowers, J. (1999). Cognitive and situated learning perspectives in theory and practice. Educational Researcher, 28(2), 4-15.
Cobb, P., Stephan, M., McClain, K., & Gravemeiger, K. (2011). Participating in classroom mathematical practices. The Journey of the Learning Science, 10(1&2), 113-163.
Cobb, P., Wood, T., Yackel, E., & McNeal, B. (1992). Characteristics of classroom mathematics traditions: An international analysis. American Educational Research Journal, 29, 573- 604.
Cobb, P., Wood, T., Yackel, E., Nicholls, J., Wheatley, G., Trigatti, B., & Perlwitz, M. (1991). Assessment of a problem-centered second-grade mathematics project. Journal for Research in Mathematics Education, 22, 3-29.
Cobb, P., & Yackel, E. (1996). Constructivist, emergent, and sociocultural perspectives in the context of developmental research. Educational Psychologist, 31(3/4), 175-190.
Cobb, P., Yackel E., & Wood, T. (1991). Curriculum and teacher development: Psychological and anthropological perspectives. In E. Fennema, T. P. Carpenter & S. Lamon (Eds.), Integrating Research on Teaching and Learning Mathematics, (pp. 83-120). Albany, NY: SUNY Press.
Cobb, P., Yackel, E., & Wood, T. (2011). Young Children’s Emotional Acts While Engaged in Mathematical Problem Solving. In E.Yackel, K. Gravemeijer & A. Sfard (Eds.) A Journey in Mathematics Education Research (pp. 41-71). Dordrecht, the Netherlands: Springer Science & Business.
Creswell, J. W. (2012). Qualitative inquiry and research design: Choosing among the five traditions (3rd ed.). Thousand Oaks, CA: Sage.
Grigutsh, S., Raatz, U., & Törner, G. (1998). Einstellungen gegenüber Mathematics bei Mathematilehrern. (Mathematics teacher’s epistemological beliefs about the nature of mathematics). Journal für Mathematik-Didaktik (Journal of Mathematics Education), 19(1), 3-45.
Hiebert, J., & Wearne, D. (1993). Instructional tasks, classroom discourse, and students' learning in second- grade arithmetic. American Educational Research Journal, 30, 393- 425.
Hong. S. J., & Choi, C. W. (2009). Effects of communication oriented mathematics lessons on mathematical disposition and academic achievement. Journal of Elementary Mathematics Education in Korea, 13(2), 269-283.
Kamii, C., & Joseph, L. L. (2004). Young children continue to reinvent arithmetic: Implications of Piaget's theory. New York, NY: Teacher College Press.
Kim M. W. (2001). Relationship between the beliefs about mathematics and teaching-learning and teaching practices of a high school mathematics teacher. Unpublished doctoral dissertation, Korea National University of Education.
Kim, N. G. (2001). A consideration on the culture of mathematics classrooms. Education of Primary School Mathematics, 5(2), 163-172.
Kim, S. (2012). A study on the application of situated cognition theory in the mathematics education. Education of Primary School Mathematics, 15(1), 1-11.
Lampert, M. (1990). When the problem is not the question and the solution is not the answer: Mathematical knowing and teaching. American Educational Research Journal, 27(1), 29- 63.
Levenson. E., Tirosh D., & Tsamir, P. (2009). Students' perceived sociomathematical norms: The missing paradigm. The Journal of Mathematical Behavior, 28(2), 171-187.
Lodico, M. G., Spaulding, D. T., & Voegtle, K. H. (2010). Methods in educational research: From theory to practice (2nd ed.). San Francisco, CA: Jossey-Bass Wiley.
Lopez, L. M., & Allal, L. (2007). Sociomathematical norms and the regulation of problem solving in classroom microcultures. International Journal of Educational Research, 46(5), 252- 265.
McClain K., & Cobb, P. (2001). An analysis of development of sociomathematical norms in one first-grade classroom, Journal for Research in mathematics education, 32(3), 236-266.
Merriam, S. B. (2009). Qualitative research: A guide to design and implementation. San Francisco, CA: Jossey-Bass Wiley.
Mura, R. (1995). Images of mathematics held by university teachers of mathematical science. Educational Studies in Mathematics, 28(4), 385-399.
Nam, Y. J., & Song, Y. M. (2008). An analytic study of beliefs about mathematics and mathematics education of high school students. School Mathematics, 10(4), 649-669.
Nickson, M. (1994). The culture of the mathematics classroom: An unknown quantity? In D. Grouws (Ed.). Handbook of Research on Mathematics Teaching and Learning (pp. 101- 114). NY: Macmillan.
Pang, J. S. (2001a). A Study on the reform of mathematics education from the comparison of classroom culture. The Journal of Educational Research in Mathematics, 11(1), 11-35.
Pang, J. S. (2001b). Sociomathematical norms and the culture of the mathematics classroom. Journal of Educational Research in Mathematics, 11(2), 273-289.
Pang, J. S. (2006). Successes and difficulties in transforming elementary mathematics classrooms to student-centered instruction. Journal of Korea Society of Mathematics Education SeriesA: The Mathematical Education, 45(4), 457-479.
Park, S. S. (2004). Professional development for teachers of mathematics through community of mathematics teachers. Education of Primary School Mathematics, 8(1), 13-22.
Philipp, R. A. (2007). Mathematics teachers. Beliefs and A ect’. In: FK Lester, Jr.(ed.): Second Handbook of Research on Mathematics Teaching and Learning. Charlotte, NC: Information Age Publishing, 257-315.
Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19-28.
Song, K. H., & Yim, J. H. (2007). Establishing the culture of elementary mathematics classroom focused on the precise use of mathematical language. School Mathematics, 9(2). 181-196.
Tatsis, K., & Koeleza, E. (2008). Social and socio-mathematical norms in collaborative problemsolving. European Journal of Teacher Education, 31(1), 89-100.
Tatto, M. T., Ingvarson, L., Schwille, J., Peck, R., Senk, S. L., & Rowley, G. (2008). Teacher Education and Development Study in Mathematics (TEDS-M): Conceptual Framework - Policy, Practice, and Readiness to Teach Primary and Secondary Mathematics 2008.East Lansing, MI: Michigan State University, TEDS-M International Study Center.
Thompson, A. (1984). The relationship of teachers’ conceptions of mathematics and mathematics teaching to instructional practice. Educational Studies in Mathematics, 15, 105-127.
Voigt, J. (1996). Negotiation of mathematical meaning in classroom processes: Social interaction and learning mathematics. In L. P. Steffe, P. Nesher, P. Cobb, G. A. Goldin, & B. Greer (Eds.), Theories of mathematical learning (pp. 21-50). Mahwah, NJ: Lawrence Erlbaum Associates.
Wood, T., & Sellers, P. (1996). Assessment of a problem-centered mathematics program: Third grade. Journal for Research in Mathematics Education, 27(2). 337-353.
Yackel, E. (2001). Explanation, justification and argumentation in mathematics classrooms. In M. van den Heuvel-Panhuizen (Ed.), Proceedings of the 25th Conference of the International Group for the Psychology of Mathematics Education, Vol. 1 (pp. 9–24). Utrecht, Netherlands: Freudenthal Institute.
Yackel, E., & Cobb, P. (1996). Sociomathematical norm, argumentation, and autonomy in mathematics, Journal for Research in Mathematics Education, 27(4), 458-477.
Yackel, E., Rasmussen. C., & King, K. (2000). Social and sociomathematical norms in an advanced undergraduate Mathematics course. The Journal of Mathematical Behavior, 19(3), 275-287.

How to cite this article

APA

Kang, S. M., & Kim, M. K. (2016). Sociomathematical Norms and the Teacher’s Mathematical Belief: A Case Study from a Korean In-Service Elementary Teacher. Eurasia Journal of Mathematics, Science and Technology Education, 12(10), 2733-2751. https://doi.org/10.12973/eurasia.2016.1308a

Vancouver

Kang SM, Kim MK. Sociomathematical Norms and the Teacher’s Mathematical Belief: A Case Study from a Korean In-Service Elementary Teacher. EURASIA J Math Sci Tech Ed. 2016;12(10):2733-51. https://doi.org/10.12973/eurasia.2016.1308a

AMA

Kang SM, Kim MK. Sociomathematical Norms and the Teacher’s Mathematical Belief: A Case Study from a Korean In-Service Elementary Teacher. EURASIA J Math Sci Tech Ed. 2016;12(10), 2733-2751. https://doi.org/10.12973/eurasia.2016.1308a

Chicago

Kang, Seon Mi, and Min Kyeong Kim. "Sociomathematical Norms and the Teacher’s Mathematical Belief: A Case Study from a Korean In-Service Elementary Teacher". Eurasia Journal of Mathematics, Science and Technology Education 2016 12 no. 10 (2016): 2733-2751. https://doi.org/10.12973/eurasia.2016.1308a

Harvard

Kang, S. M., and Kim, M. K. (2016). Sociomathematical Norms and the Teacher’s Mathematical Belief: A Case Study from a Korean In-Service Elementary Teacher. Eurasia Journal of Mathematics, Science and Technology Education, 12(10), pp. 2733-2751. https://doi.org/10.12973/eurasia.2016.1308a

MLA

Kang, Seon Mi et al. "Sociomathematical Norms and the Teacher’s Mathematical Belief: A Case Study from a Korean In-Service Elementary Teacher". Eurasia Journal of Mathematics, Science and Technology Education, vol. 12, no. 10, 2016, pp. 2733-2751. https://doi.org/10.12973/eurasia.2016.1308a