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
DOI: https://doi.org/10.29275/jerm.2020.02.30.1.153

Non-mathematical Discourse and Private Discourse in Mathematics Instruction

Cho, Jinwoo* ; Kim, Yeon**,
*Lecturer, Gyeongin National University of Education jinwoo1987@hanmail.net
**Professor, Silla University yeonkim10@silla.ac.kr

Correspondence to: Professor, Silla University, South Korea, yeonkim10@silla.ac.kr

Abstract

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.

Keywords:

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

References

  • 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.. [https://doi.org/10.1086/461730]
  • 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.. [https://doi.org/10.3102/0013189X07312896]
  • Ball, D. L. & Forzani, F. (2009). The work of teaching and the challenge for teacher education. Journal of Teacher Education, 60(5), 497-511.. [https://doi.org/10.1177/0022487109348479]
  • 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.. [https://doi.org/10.1177/0022487108324554]
  • 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.. [https://doi.org/10.1007/s10649-009-9202-4]
  • Barwell, R. (2016). Formal and informal mathematical discourses: Bakhtin and Vygotsky, dialogue and dialectic. Educational Studies in Mathematics, 92(3), 331-345.. [https://doi.org/10.1007/s10649-015-9641-z]
  • 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.. [https://doi.org/10.3102/01623737025002119]
  • Cohen, D. K. (2011). Teaching and its predicaments. Cambridge, MA: Harvard University Press. . [https://doi.org/10.4159/harvard.9780674062788]
  • 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.. [https://doi.org/10.1007/978-94-009-1465-0_30]
  • 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.. [https://doi.org/10.5951/jresematheduc.44.1.0037]
  • 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.. [https://doi.org/10.1177/0022487111428328]
  • 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.. [https://doi.org/10.3102/00028312042002371]
  • 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. . [https://doi.org/10.1080/07370000802177235]
  • 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.. [https://doi.org/10.1007/s10649-015-9625-z]
  • 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.. [https://doi.org/10.15718/discog.2014.21.1.105]
  • 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.. [https://doi.org/10.1007/s10649-015-9618-y]
  • 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. . [https://doi.org/10.1177/0022487112473837]
  • Langer-Osuna, J. (2018). Productive disruptions: Rethinking the role of off-task interactions in collaborative mathematics learning. Education Sciences, 8(2), 87.. [https://doi.org/10.3390/educsci8020087]
  • Lave, J., & Wenger, E. (1991). Situated learning: Legitimate peripheral participation. Cambridge: Cambridge university press.. [https://doi.org/10.1017/CBO9780511815355]
  • Llewellyn, A. (2016). Problematising the pursuit of progress in mathematics education. Educational Studies in Mathematics, 92(3), 299-314.. [https://doi.org/10.1007/s10649-015-9645-8]
  • Miles, M. B., Huberman, A. M. & Saldaña, J. (2014). Qualitative data analysis: a methods sourcebook. Thousand Oaks, CA: SAGE. http://mirlyn.lib.umich.edu/Record/012444368.
  • 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. . [https://doi.org/10.3102/0002831217695217]
  • 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.. [https://doi.org/10.5951/jresematheduc.42.2.0167]
  • Searle, J. R. (1969). Speech acts: An essay in the philosophy of language (Vol. 626). Cambridge: Cambridge university press.. [https://doi.org/10.1017/CBO9781139173438]
  • Sfard, A. (1998). On two metaphors for learning and the dangers of choosing just one. Educational researcher, 27(2), 4-13.. [https://doi.org/10.3102/0013189X027002004]
  • 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.. [https://doi.org/10.1023/A:1014097416157]
  • 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.. [https://doi.org/10.1207/S15327884MCA0801_04]
  • Sfard, A. (2008). Thinking as communicating: Human development, the growth of discourses, and mathematizing. Cambridge: Cambridge University Press.. [https://doi.org/10.1017/CBO9780511499944]
  • 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.. [https://doi.org/10.1007/s10649-012-9398-6]
  • Vygotsky, L. S. (1980). Mind in society: The development of higher psychological processes. Harvard university press.. [https://doi.org/10.2307/j.ctvjf9vz4]
  • 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.. [https://doi.org/10.3102/0034654308320292]
  • Wenger, E. (1998). Communities of practice: Learning, meaning and identity. Cambridge, UK: Cambridge University Press. [https://doi.org/10.1017/CBO9780511803932]
  • 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.. [https://doi.org/10.2307/749877]
  • Yin, R. K. (2003). Case study research: Design and methods. Thousand Oaks, CA: Sage Publications..