Characterizing mathematical discourse according to teacher and student interactions: The core of mathematical discourse
Sedef Çelik Demirci 1 * , Adnan Baki 2
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1 Artvin Çoruh University, Faculty of Education, Türkiye
2 Trabzon University, Fatih Faculty of Education, Türkiye
* Corresponding Author


The discussion on the development of mathematical discourse plays a key role in the determination of the in-classroom interactions in mathematics learning and instruction. The present study aims to present a theoretical framework for the nature of mathematical discourse that addresses the teacher and student interaction in the classroom. Previous studies attempted to discuss the theoretical structure in mathematical discourse with the embedded theory approach. The findings revealed the core of mathematical discourse that reflected the structure of mathematical discourse based on open, axial and selective codes determined based on the embedded theory approach. The external structure of this core reflects the types of in-classroom interaction, while the internal structure reflects the development of the mathematical discourse. The external structure included four types of interaction: teacher, teacher-class, teacher-student, and student-student. The internal structure includes mathematical discourse movements associated with three stages: motivation, explanation of mathematical ideas, and achievement of mathematical ideas. The external structure of mathematical discourse core revealed the general state of in-classroom interaction core, and the internal structure revealed the specific mathematical discourse based on the mathematical content. It could be suggested that the discourse movements in the mathematical discourse core determined in the present study would provide guidelines for mathematical communications. The study also includes recommendations for future studies on the employment of this general and specific theoretical mathematical discourse framework.



  • Abele, A. (1998). Reasoning process and quality of reasoning. In F. Seeger., J. Voigt & U. Waschescio (Eds.), The culture of the mathematics classroom (pp. 127–157). Cambridge University Press.
  • Adler, J., & Ronda, E. (2015). A framework for describing mathematics discourse in instruction and interpreting differences in teaching. African Journal of Research in Mathematics, Science and Technology Education, 19(3), 237-254.
  • Baki, A., & Celik, S. (2019). Analysis of teacher-class discussion during problem-solving processes. In A. Baki, B. Güven & M. Güler (Eds), Proceedings of 4th International Turkish Computer & Mathematics Education Symposium (pp. 141-147). Türkbilmat Eğitim Hizmetleri.
  • Ballard, D. (2017). Discourse in math-Don’t just talk about it. Consortium on Reaching Excellence in Education. Retrieved March 3, 2021, from https://www. content/uploads/2017/08/discourse-inmath-whitepaper.pdf.
  • Bennett, C. (2014). Creating cultures of participation to promote mathematical discourse. Middle School Journal, 46(2), 20–25.
  • Blanke, B. L. (2009). Understanding mathematical discourse in the elementary classroom: A case study [Unpublished doctoral dissertation]. Oregon State University.
  • Bozkurt, A., Kılıç Kırcalı, P., & Özmantar, M. F. (2017). An investigation of the question types in mathematics instruction of middle school classrooms. Yildiz Journal of Educational Research, 2(1), 26-54.
  • Brendefur, J., & Frykholm, J. (2000). Promoting mathematical communication in the classroom: Two preservice teachers' conceptions and practices. Journal of Mathematics TeacherEducation, 3(2), 125-153.
  • Cazden, C. (2001). Classroom discourse: The language of learning and teaching. Portsmouth: Heinemann.
  • Ceron, J. (2019). Using ıntentional talk and talk moves to facilitate mathematical discourse. [Unpublished master’s thesis]. California State University.
  • Chapin, S. H., O’Connor, C., & Anderson, N. C. (2003). Classroom discussions: Using math talk to help students learn. Math Solutions Publications.
  • Charmaz, K. (2006). Constructing grounded theory: A practical guide through qualitative analysis. Sage.
  • Christensen, L. B., Johnson, B., Turner, L. A., & Christensen, L. B. (2011). Research methods, design, and analysis. Pearson.
  • Demirbağ, M. (2017). The effects of authoritative and dialogic discourses on
pre-service science teachers’ argument development. Journal of Uludag University Faculty of Education 30(1), 321-340.
  • Drageset, O. G. (2015). Student and teacher interventions: A framework for analysing mathematical discourse in the classroom.Journal of Mathematics Teacher Education, 18(3), 253-272.
  • DuCloux, K. K. (2020). Facilitating mathematical discourse in online learning environments. In P. Wachira & J.Keengwe (Eds.), Handbook of Research on Online Pedagogical Models for Mathematics Teacher Education (pp. 245-256). IGI Global.
  • Durksen, T. L., Way, J., Bobis, J., Anderson, J., Skilling, K., & Martin, A. J. (2017). Motivation and engagement in mathematics: A qualitative framework for teacher-student interactions. Mathematics Education Research Journal, 29, 163–181.
  • Erath, K., Prediger, S., Quasthoff, U., & Heller, V. (2018). Discourse competence as important part of academic language proficiency in mathematics classrooms: the case of explaining to learn and learning to explain. Educational Studies in Mathematics, 99(2), 161-179.
  • Hale, C. C., Nanni, A., & Hooper, D. (2018). Conversation analysis in language teacher education: an approach for reflection through action research. Hacettepe University Journal of Education (HUJE), 33 (Special Issue), 54-71.
  • Hufferd-Ackles, K., Fuson, K., & Sherin, M. (2004). Describing levels and components of a math-talk learning community. Journal for Research in Mathematics Education, 35, 81–116.
  • Johnson, D. W. (1981). Student-student interaction: The neglected variable in education. Educational researcher, 10(1), 5-10.
  • Kalathil, R. R. (2004). Investigating the structure of discourse for reform-based mathematics classrooms [Unpublished doctoral dissertation]. Northwestern University.
  • Kazemi, E., & Hintz, A. (2014). Intentional talk: How to structure and lead productive mathematical discussions. Stenhouse Publishers.
  • Kim, D. J. & Lim, W. (2017). The relative interdependency of colloquial and mathematical discourses regarding the notion and calculations of limit: An evidence-based cross-cultural study. International Journal of Science and Mathematics Education, 16(8), 1561-1579.
  • Knuth, E., & Peressini, D. (2001). Unpacking the nature of discourse in mathematics classrooms. Mathematics Teaching in the Middle School, 6(5), 320-325.
  • Larsson, M. (2015). Orchestrating mathematical whole-class discussions in the problem-solving classroom: Theorizing challenges and support for teachers [Unpublished doctoral dissertation]. Mälardalen University.
  • Legesse, M., Luneta, K., & Ejigu, T. (2020). Analyzing the effects of mathematical discourse-based instruction on eleventh-grade students’ procedural and conceptual understanding of probability and statistics. Studies in Educational Evaluation, 67(2020) 100918.
  • Lemke, J. L. (1990). Talking science: Language, learning, and values. Ablex Lessons.
  • Matson, C. L. H. (2010). Talking about mathematics: prompting discussion among community college students in algebra tutoring [Unpublished master’s thesis]. Amsterdam University.
  • Mercer, N. (1995). The guided construction of knowledge: Talk amongst teachers and learners. Multilingual matters.
  • Miles, B., M., & Huberman, A., M. (1994). Qualitative data analysis (21 Ed.). Sage Publication.
  • Morgan, C., Craig, T., Schuette, M. and Wagner, D. (2014). Language and communication in mathematics education: An overview of research in the field. ZDM –The International Journal on Mathematics Education-, 46(6), 843-853. 0624-9
  • Mortimer, E., & Scott, P. (2003). Meaning making in secondary science classrooms. Open University Press.
  • Muto-Humprey, K. (2010). Discourse analysis through interpersonal meaning.
  • Nathan, M. J. & Knuth, E. J. (2003). A study of whole classroom mathematical discourse and teacher change. Cognition and Instruction, 21(2), 175-207.
  • National Council of Teachers of Mathematics [NCTM]. (2000). Principles and standarts for school mathematics: An overview. NCTM.
  • Neuman, W. L. (2013). Social research methods: Qualitative and quantitative approaches. Pearson education.
  • Piccolo, D. L., Harbaugh, A. P., Carter, T. A., Capraro, M. M., & Capraro, R. M. (2008). Quality of instruction: Examining discourse in middle school mathematics instruction. Journal of Advanced Academics, 19(3), 376-410.
  • Pirie, S. E. B., & Schwarzenberger, R. L. E. (1988). Mathematical discussion and mathematical understanding. Educational Studies in mathematics, 19(4), 459-470.
  • Richards, J. (1991). Mathematical discussions. In E. von Glasersfeld (Ed.), Radical constructivism in mathematics education (pp. 13-51). The Netherlands: Kluwer.
  • Ryve, A. (2011). Discourse research in mathematics education: A critical evaluation of 108 journal articles. Journal for Research in Mathematics Education, 42(2), 167-199.
  • Saban, A., & Ersoy, A. (2016). Eğitimde nitel araştırma desenleri [Qualitative research patterns in education]. Anı Press.
  • Sabbagh, S.A. (2014). The discourse levels used by mathematics teachers to promote students’ understanding and thinking for the high school in Jordan. International Proceedings of Economics Development and Research, 78(15), 74-79.
  • Sfard, A. (2000). On reform movement and the limits of mathematical discourse. Mathematical thinking and learning, 2(3), 157-189.
  • Sfard, A. (2012). Introduction: Developing mathematical discourse some insights from communicational research. International Journal of Educational Research, 51(52), 1-9.
  • Shilo, A., & Kramarski, B. (2019). Mathematical-metacognitive discourse: how can it be developed among teachers and their students? Empirical evidence from a videotaped lesson and two case studies. ZDM Mathematics Education, 51(4), 1-16. 01016-6
  • Shortino-Buck, M. M. (2017). Mathematical discourse in elementary classrooms [Unpublished doctoral dissertation] University of Portland.
  • Tanışlı, D. (2016). Satır aralarını okuma sanatı: Söylem çözümlemesi ve matematik eğitimi. [The art of reading between the lines: Discourse analysis and mathematics education]. In E. Bingölbali, S. Arslan ve Ö.İ., Zembat (Eds.), Theories in mathematics education (s. 901-915). PegemA.
  • Ticar, M. A. J., Luna, C. A., & Tan, R. G. (2020). Argumentative discourse-centered classroom to hone students’ mathematical comprehension and confidence. American Journal of Educational Research, 8(5), 304-308.
  • Viseu, F., & Oliveira, I. B. (2012). Open-ended tasks in the promotion of classroom communication in mathematics. International Electronic Journal of Elementary Education, 4(2), 287-300.
  • Vui, T. (2007, December). Enhancing classroom communication to develop students‟ mathematical thinking. In Proceeding of APEC-TSUKUBA International Conference III, Innovation of Classroom Teaching and Learning through Lesson Study, Focusing on Mathematical Communication (pp.1-10) Tokyo and Kanazawa, Japan.
  • 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(3), 516-551.
  • Yang, E. F., Chang, B., Cheng, H. N., & Chan, T. W. (2016). Improving pupils’ mathematical communication abilities through computer-supported reciprocal peer tutoring. Journal of Educational Technology & Society, 19(3), 157-169.


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