The Korea Society Of Educational Studies In Mathematics
[ Article ]
Journal of Educational Research in Mathematics - Vol. 30, No. 1, pp.153-175
ISSN: 2288-7733 (Print) 2288-8357 (Online)
Print publication date 28 Feb 2020
Received 10 Jan 2020 Revised 04 Feb 2020 Accepted 15 Feb 2020

Non-mathematical Discourse and Private Discourse in Mathematics Instruction

Cho, Jinwoo* ; Kim, Yeon**,
*Lecturer, Gyeongin National University of Education
**Professor, Silla University

Correspondence to: Professor, Silla University, South Korea,


The purpose of this study was to focus on non-mathematical discourse and private discourse as a way to identify the dynamics of interactions in mathematics instruction. The data for this study comprised a series of four lessons about the inverse function of a high school teacher. The findings report that mathematics instruction includes diverse kinds of discourse. Also, non-mathematical discourse and private discourse have their own roles and features and have combinations with mathematical discourse for the purposes of mathematics lessons. Based on results, the analysis of non-mathematical discourse and private discourse would contribute to expanding the understanding of mathematics instruction. This study discusses the roles of different kinds of discourses in mathematics instruction.


discourse in mathematics instruction, discourse analysis, mathematical discourse, non-mathematical Discourse, private discourse


  • Arzarello, F. (1998). The role of natural language in prealgebraic and algebraic thinking. In H. Steinbring, M. Bussi, & A. Sierpinska (Eds.), Language and communication in the mathematics classroom (pp. 249-261). Reston, VA: National Council of Teachers of Mathematics. .
  • Austin, J. L. (1962). How to do things with words. Cambridge: Havard University Press. .
  • Ball, D. L. (1993). With an eye on the mathematical horizon: Dilemmas of teaching elementary school mathematics. The Elementary School Journal, 93(4), 373-397.. []
  • Ball, D. L. & Bass, H. (2003). Toward a practice-based theory of mathematical knowledge for teaching. In: Davis, B.Simmt, E., eds. Proceedings of the 2002 annual meeting of the Canadian Mathematics Association Study Group. Edmonton, AB: CMESG/GDEDM, pp. 3-14..
  • Ball, D. L. & Forzani, F. (2007). What makes education research “educational”?. Educational Research 36(9), 529-540.. []
  • Ball, D. L. & Forzani, F. (2009). The work of teaching and the challenge for teacher education. Journal of Teacher Education, 60(5), 497-511.. []
  • Ball, D. L., Thames, M. H. & Phelps, G. (2008). Content knowledge for teaching: What makes it special?. Journal of Teacher Education, 59(5), 389-407.. []
  • Bakhtin, M. M. (1981). The dialogic imagination: Four essays. (Ed., M. Holquist; Trans, C. Emerson & M. Holquist). Austin, TX: University of Texas Press..
  • Bakhtin, M. M. (1986). Speech genres and other late essays. (Eds & Trs., W. McGee, C. Emerson, & M. Holoquist), Austin, TX: University of Texas Press..
  • Barwell, R. (2009). Researchers’ descriptions and the construction of mathematical thinking. Educational Studies in Mathematics, 72(2), 255-269.. []
  • Barwell, R. (2016). Formal and informal mathematical discourses: Bakhtin and Vygotsky, dialogue and dialectic. Educational Studies in Mathematics, 92(3), 331-345.. []
  • Brousseau, G. (1997). Theory of didactical situations in mathematics. Dordrecht, The Netherlands: Kluwer Academic Publishers..
  • Chapman, A. (1993). Language and learning in school mathematics: A social semiotic perspective. Issues in educational research, 3(1), 35-46..
  • Cohen, D. K., Raudenbush, S. W. & Ball, D. L. (2003). Resources, instruction, and research. Educational Evaluation and Policy Analysis 25(2), 119-142.. []
  • Cohen, D. K. (2011). Teaching and its predicaments. Cambridge, MA: Harvard University Press. . []
  • Ellerton, N. F., & Clarkson, P. C. (1996). Language factors in mathematics teaching and learning. In International handbook of mathematics education (pp. 987-1033). Springer, Dordrecht.. []
  • Erickson, F. (1986). Qualitative methods in research on teaching. In: M. C. Wittrock, ed. Handbook of research on teaching. New York: Macmillan, pp. 119-161..
  • Freudenthal, H. (1978). Weeding and sowing: Preface to a science of mathematical education. Dordrecht, The Netherlands: Reidel..
  • Gutiérrez, R. (2013). The sociopolitical turn in mathematics education. Journal for Research in Mathematics Education, 44(1), 37-68.. []
  • Halliday, M. (1978). Language as social semiotic. Arnold: London..
  • Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K. C., Wearne, D., Murray, H., Olivier, A. & Human, P. (1997). Making sense: Teaching and learning mathematics with understanding. Portsmouth, NH: Heinemann..
  • Hiebert, J. & Morris, A. K. (2012). Teaching, rather than teachers, as a path toward improving classroom instruction. Journal of Teacher Education, 63(2), 92-102.. []
  • Hill, H. C., Rowan, B. & Ball, D. L. (2005). Effects of teachers' mathematical knowledge for teaching on student achievement. American Educational Research Journal 42: 371-406.. []
  • Hill, H. C., Blunk, M. L., Charalambous, C. Y., Lewis, J. M., Phelps, G. C., Sleep, L. & Ball, D. L. (2008). Mathematical knowledge for teaching and the mathematical quality of instruction: An exploratory study. Cognition and Instruction, 26(4), 430-511. . []
  • Hwang, S. W., Kang, B. G., Kim, Y. R., Yun, G., Kim, S. Y., Song, M. H., Lee, S. W., Do, J., Lee, M-H., Park, H. J., Park, J. H. (2014). Calculus 2. Seoul: Sinsago..
  • Ing, M., Webb, N. M., Franke, M. L., Turrou, A. C., Wong, J., Shin, N., & Fernandez, C. H. (2015). Student participation in elementary mathematics classrooms: the missing link between teacher practices and student achievement?. Educational Studies in Mathematics, 90(3), 341-356.. []
  • Jeon, J. (2014). A study on key words analysis of the public and private discourse in Korean spoken language. Discourse and Cognition, 21(1), 105-126.. []
  • Kazak, S., Wegerif, R., & Fujita, T. (2015). The importance of dialogic processes to conceptual development in mathematics. Educational Studies in Mathematics, 90(2), 105-120.. []
  • Kim, N. H., Na, G. S., Park, K. M., Lee, K. H., Chung, Y. O., & Hong, J. G. (2006). Mathematics Curriculum and Textbook Research. Seoul: Kyung-Mun-SA.
  • Lampert, M. (2001). Teaching problems and the problems in teaching. New Haven, CT: Yale University Press..
  • Lampert, M., Franke, M. L., Kazemi, E., Ghousseini, H., Turrou, A. C., Beasley, H., Cunard, A. & Crowe, K. (2013). Keeping it complex: Using rehearsals to support novice teacher learning of ambitious teaching. Journal of Teacher Education, 64(3), 226-243. . []
  • Langer-Osuna, J. (2018). Productive disruptions: Rethinking the role of off-task interactions in collaborative mathematics learning. Education Sciences, 8(2), 87.. []
  • Lave, J., & Wenger, E. (1991). Situated learning: Legitimate peripheral participation. Cambridge: Cambridge university press.. []
  • Llewellyn, A. (2016). Problematising the pursuit of progress in mathematics education. Educational Studies in Mathematics, 92(3), 299-314.. []
  • Miles, M. B., Huberman, A. M. & Saldaña, J. (2014). Qualitative data analysis: a methods sourcebook. Thousand Oaks, CA: SAGE.
  • Ministry of Education (2015). Mathematics Curriculum. Notification of the Ministry of Education No. 2015-74. [Vol 8]. Seoul: Author. .
  • Morris, A. K., Hiebert, J. & Spitzer, S. (2009). Mathematical knowledge for teaching in planning and evaluating instruction: What can preservice teachers learn?. Journal for Research in Mathematics Education 40(5), 491-529..
  • Morris, A. K., & Hiebert, J. (2017). Effects of Teacher Preparation Courses: Do Graduates Use What They Learned to Plan Mathematics Lessons? American Educational Research Journal, 54(3), 524-567. . []
  • NCTM(2007). 학교수학을 위한 원리와 규준, (류희찬 외 5인, 역). 서울: 경문사. (영어 원작은 1998년 출판).
  • Noh, D. K. (1996). Korean spoken language and written language. Goyang: Kookhak..
  • Pimm, D. (1987). Speaking mathematically: Communication in mathematics classrooms. London, UK: Routledge..
  • 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.. []
  • Searle, J. R. (1969). Speech acts: An essay in the philosophy of language (Vol. 626). Cambridge: Cambridge university press.. []
  • Sfard, A. (1998). On two metaphors for learning and the dangers of choosing just one. Educational researcher, 27(2), 4-13.. []
  • Sfard, A. (2001). There is more to discourse than meets the ears: Looking at thinking as communicating to learn more about mathematical learning. Educational studies in mathematics, 46(1-3), 13-57.. []
  • Sfard, A., & Kieran, C. (2001). Cognition as communication: Rethinking learning-by-talking through multi-faceted analysis of students' mathematical interactions. Mind, Culture, and Activity, 8(1), 42-76.. []
  • Sfard, A. (2008). Thinking as communicating: Human development, the growth of discourses, and mathematizing. Cambridge: Cambridge University Press.. []
  • Sfard, A., Nesher, P., Streefland, L., Cobb, P., & Mason, J. (1998). Learning mathematics through conversation: Is it as good as they say?. For the learning of mathematics, 18(1), 41-51..
  • Seo, S. K. & Kim, H. J. (2005). On some Practical Conditions for Developing Spoken Language Corpus. Language Facts and Perspectives, 16, 5-29. .
  • Simon, M. A. (2009). Amidst multiple theories of learning in mathematics education. Journal for Research in Mathematics Education, 40(5), 477-490..
  • Stigler, J. W. & Hiebert, J. (1999). The teaching gap: Best ideas from the world's teachers for improving education in the classroom. New York: Free Press..
  • Temple, C., & Doerr, H. M. (2012). Developing fluency in the mathematical register through conversation in a tenth-grade classroom. Educational Studies in Mathematics, 81(3), 287-306.. []
  • Vygotsky, L. S. (1980). Mind in society: The development of higher psychological processes. Harvard university press.. []
  • 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.. []
  • Wenger, E. (1998). Communities of practice: Learning, meaning and identity. Cambridge, UK: Cambridge University Press. []
  • Wertsch, J. (2014). 보이스 오브 마인드: 매개된 행위에 대한 사회문화적 접근, (박동섭 역). 서울: 학이시습. (영어초판은 1991년 출판). .
  • Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for research in mathematics education, 27(4), 458-477.. []
  • Yin, R. K. (2003). Case study research: Design and methods. Thousand Oaks, CA: Sage Publications..