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An Integral Part of Facilitating Mathematical Discussions: Follow-up Questioning

Abstract

This study explores the relationship between students’ perceptions and teachers’ discourse practices in mathematics classrooms. It reframes the sequence of Initiate-Response-Follow-up (IRF) with a renewed discourse structure that focuses on teachers’ follow-up actions including listening, thoughtful questioning, and effective talk moves. Specifically, the study analyzes how these follow-up actions were related to positive student perceptions about their teachers’ discourse practices around sustaining productive discussions in mathematics classrooms. Participants were secondary mathematics teachers (n = 57) and their students (n = 875) in U.S. schools. The study first considered the students’ perceptions of their teachers’ discourse practices, identifying which teachers were perceived by students to implement mathematics discussions. Next, the study identified and examined patterns of teacher practices in discussions—the teachers’ talk moves, duration, and frequency in asking follow-up questions. Findings indicate that the teachers identified by students as promoting mathematics discussion tended to ask follow-up questions that increased and sustained students’ participation in mathematics discussions. What this finding implies is that in asking follow-up questions, the teacher listened and responded to students’ ideas, and students felt heard. The study asserts that there is much potential for enhancing mathematics instruction by learning more about how teachers listen to and build on students’ responses.

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References

  1. Baxter, J. A., & Williams, S. (2010). Social and analytic scaffolding in middle school mathematics: Managing the dilemma of telling. Journal of Mathematics Teacher Education, 13(1), 7–26.

  2. Belo, N. A. H., van Driel, J. H., van Veen, K., & Verloop, N. (2014). Beyond the dichotomy of teacher- versus student-focused education: A survey study on physics teachers’ beliefs about the goals and pedagogy of physics education. Teaching and Teacher Education, 39, 89–101.

  3. Boaler, J., & Brodie, K. (2004). The importance, nature and impact of teacher questions. In D. E. McDougall & J. A. Ross (Eds.), Proceedings of the twenty-sixth annual meeting of the North American chapter of the international group for the psychology of mathematics education (Vol. 2, pp. 774–782). Toronto, Ontario: University of Toronto.

  4. Boston, M. D., & Smith, M. S. (2009). Transforming secondary mathematics teaching: Increasing the cognitive demands of instructional tasks used in teachers’ classrooms. Journal for Research in Mathematics Education, 40(2), 119–156.

  5. Cazden, C. B. (2001). Classroom discourse: The language of teaching and learning. Portsmouth, NH: Heinemann.

  6. Chapin, S. H., O’Connor, C., & Anderson, N. C. (2013). Classroom discussions in math: A teacher’s guide for using talk moves to support the common core and more. Sausalito, CA: Math Solutions.

  7. Chazan, D., & Ball, D. (1999). Beyond being told not to tell. For the Learning of Mathematics, 19(2), 2–10.

  8. Chin, C. (2007). Teacher questioning in science classrooms: Approaches that stimulate productive thinking. Journal of Research in Science Teaching, 44(6), 815–843.

  9. Choppin, J. M. (2007). Teacher-orchestrated classroom arguments. Mathematics Teacher, 10(4), 306–310.

  10. Cullen, R. (2002). Supportive teacher talk: The importance of the F-move. ELT Journal: English Language Teachers Journal, 56(2), 117–127.

  11. Davis, B. (1997). Listening for difference: An evolving conception of mathematics teaching. Journal for Research in Mathematics Education, 28(3), 355–376.

  12. Empson, S. B., & Jacobs, V. R. (2008). Learning to listen to children’s mathematics. In D. Tirosh & T. Woods (Eds.), International handbook of mathematics teacher education, Vol. II: Tools and processes in mathematics teacher education (pp. 257–281). Rotterdam, Netherlands: Sense Publishers.

  13. Engle, R. A. (2006). Framing interactions to foster generative learning: A situative account of transfer in a community of learners classroom. Journal of the Learning Sciences, 15(4), 451–498.

  14. Engle, R. A. (2011). The productive disciplinary engagement framework: Origins, key concepts and developments. In D. Y. Dai (Ed.), Design research on learning and thinking in educational settings: Enhancing intellectual growth and functioning (pp. 161–200). London: Taylor & Francis.

  15. Franke, M. L., & Kazemi, E. (2001). Teaching as learning within a community of practice: Characterizing generative growth. In T. Wood, B. C. Nelson, & J. Warfield (Eds.), Beyond classical pedagogy in elementary mathematics: The nature of facilitative teaching (pp. 47–74). Mahwah, NJ: Erlbaum.

  16. Franke, M. L., Webb, N. M., Chan, A. G., Ing, M., Freund, D., & Battey, D. (2009). Teacher questioning to elicit students’ mathematical thinking in elementary school classrooms. Journal of Teacher Education, 60(4), 380–392.

  17. Gasser, L., Grütter, J., Buholzer, A., & Wettstein, A. (2018). Emotionally supportive classroom interactions and students’ perceptions of their teachers as caring and just. Learning and Instruction, 54, 82–92.

  18. Gilson, C. M. (2014). Middle school teachers’ listening orientations during individualized conferences with struggling, average, and high-ability readers. Doctoral Dissertations. University of Connecticut, Storrs, CT. Retrieved December 2, 2017 from http://digitalcommons.uconn.edu/dissertations/392/.

  19. Harkness, S. S., & Wachenheim, K. (2008). Using listening journals in math methods. The Teacher Educator, 43, 59–71.

  20. Hellermann, J. (2005). Syntactic and prosodic practices for cohesion in series of three-part sequences in classroom talk. Research on Language and Social Interaction, 38(1), 105–130.

  21. 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.

  22. Hintz, A., & Tyson, K. (2015). Complex listening: Supporting students to listen as mathematical sense-makers. Mathematical thinking and learning, 17, 296–326.

  23. Hintz, A. , Tyson, K. , English, A. R. (2018). Actualizing the rights of the learner: The role of pedagogical listening. Democracy and education, 26(2), Article 8. Retrieved October 21, 2018 from https://democracyeducationjournal.org/home/vol26/iss2/8.

  24. Horn, I. S. (2008). Accountable argumentation as a participation structure to support mathematical learning through disagreement. In A. Schoenfeld (Ed.), A study of teaching: Multiple lenses, multiple views (pp. 97–126) Journal for Research in Mathematics Education monograph series. Reston, VA: National Council of Teachers of Mathematics.

  25. Hufferd-Ackles, K., Fuson, K., & Sherin, M. G. (2004). Describing levels and components of a math-talk learning community. Journal for Research in Mathematics Education, 35, 81–116.

  26. Imm, K., & Stylianou, D. A. (2012). Talking mathematically: An analysis of discourse communities. The Journal of Mathematical Behavior, 31(1), 130–148.

  27. Jacobs, V. R., & Empson, S. B. (2016). Responding to children’s mathematical thinking in the moment: An emerging framework of teaching moves. ZDM Mathematics Education, 48(1–2), 185–197.

  28. Jansen, A. (2012). Developing productive dispositions during small-group work in two sixth-grade mathematics classrooms: Teachers’ facilitation efforts and students’ self-reported benefits. Middle Grades Research Journal, 7(1), 37–56.

  29. Jefferson, G. (2004). Glossary of transcript symbols with an introduction. In G. Lerner (Ed.), Conversation analysis: Studies from the first generation (pp. 130–131). Amsterdam/Philadelphia, PA: John Benjamins Publishing Company.

  30. Kazemi, E., & Stipek, D. (2009). Promoting conceptual thinking in four upper-elementary mathematics classrooms. Journal of Education, 189(1–2), 123–137.

  31. Kim, H. (2019). Teacher learning opportunities provided by implementing formative assessment lessons :Becoming responsive to student mathematical thinking. International journal of science and mathematics education, 17(2), 341–363.

  32. Lave, J., & Wenger, E. (1991). Situated learning: Legitimate peripheral participation. Cambridge, England: Cambridge University Press.

  33. Lee, Y. A. (2007). Third turn position in teacher talk: Contingency and the work of teaching. Journal of Pragmatics, 39, 1204–1230.

  34. Lloyd, M. H., Kolodziej, N. J., & Brashears, K. M. (2016). Classroom discourse: An essential component in building a classroom community. School Community, 26, 291–304.

  35. Mehan, H. (1979). Learning lessons: Social organization in the classroom. Cambridge, MA: Harvard University Press.

  36. Mercer, N., & Dawes, L. (2014). The study of talk between teachers and students, from the 1970s until the 2010s. Oxford Review of Education, 40(4), 430–445.

  37. Middleton, J. A., & Jansen, A. (2011). Motivation matters and interest counts: Fostering engagement in mathematics. Reston, VA: National Council of Teachers of Mathematics.

  38. Moschkovich, J. (2003). What counts as mathematical discourse? In N. A. Pateman, B. J. Dougherty, & J. Zilliox (Eds.), Proceedings of the 2003 joint meeting of Psychology of Mathematics Education and Psychology of Mathematics Education-North American chapter (Vol. 3, pp. 325–331). Honolulu, HI: University of Hawaii.

  39. Moschkovich, J. N. (2007). Examining mathematical discourse practices. For the Learning of Mathematics, 27(1), 24–30.

  40. National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematics success for all. Reston, VA: Author.

  41. Ryve, A. (2011). Discourse research in mathematics education: A critical evaluation of 108 journal articles. Journal for Research in Mathematics Education, 42(2), 167–198.

  42. Sherin, M. G. (2002). A balancing act: Developing a discourse community in a mathematics classroom. Journal of Mathematics Teacher Education, 5, 205–233.

  43. Sherin, M. G., Mendez, E. P., & Louis, D. A. (2000). Talking about math talk. In M. Burke (Ed.), Learning mathematics for a new century: 2000 yearbook of the NCTM (pp. 188–196). Reston, VA: National Council of Teachers of Mathematics.

  44. Sinclair, J. M., & Coulthard, R. M. (1975). Towards an analysis of discourse: The English used by teachers and pupils. London, England: Oxford University Press.

  45. Smith, M. S., & Stein, M. K. (2011). 5 practices for orchestrating productive mathematics discussions. Reston, VA: National Council of Teachers of Mathematics.

  46. Sohmer, R., Michaels, S., O'Connor, M. C., & Resnick, L. B. (2009). Guided construction of knowledge in the classroom: The troika of well structured talk, tasks, and tools. In B. Schwarz & T. Dreyfus (Eds.), Advances in learning and instruction (pp. 105–129).London, England: Elsevier.

  47. Staples, M. (2007). Supporting whole-class collaborative inquiry in a secondary mathematics classroom. Cognition and Instruction, 25(2–3), 161–217.

  48. Stein, C. A. (2007). Let’s talk. Promoting mathematical discourse in the classroom. Mathematics Teacher, 101(4), 285–289.

  49. Stein, M. K., Engle, R., Smith, M. S., & Hughes, E. K. (2008). Orchestrating productive mathematical discussions: Five practices for helping teachers move beyond show and tell. Mathematical Thinking and Learning, 10(4), 313–340.

  50. Tainio, L., & Laine, A. (2015). Emotion work and affective stance in the mathematics classroom: The case of IRE sequences in Finnish classroom interaction. Educational Studies in Mathematics, 89(1), 67–87.

  51. Tschannen-Moran, M., Bankole, R. A., Mitchell, R. M., & Moore, D. M. (2013). Student academic optimism: A confirmatory factor analysis. Journal of Educational Administration, 51(2), 150–175.

  52. Wallach, T., & Even, R. (2005). Hearing students: The complexity of understanding what they are saying, showing, and doing. Journal of Mathematics Teacher Education, 8, 393–417.

  53. Wells, G. (1993). Reevaluating the IRF sequence: A proposal for the articulation of theories of activity and discourse for the analysis of teaching and learning in the classroom. Linguistics and Education, 5, 1–38.

  54. Wells, G. (1999). Dialogic inquiry: Towards a sociocultural practice and theory of education. New York, NY: Cambridge University Press.

  55. Willey, C., Gatza, A., & Flessner, C. (2017). Mathematics discourse communities: Language ideologies and urban mathematics teaching with Latinas/os. Journal of Cases in Educational Leadership, 20(1), 34–48. https://doi.org/10.1177/1555458916687600.

  56. Wood, D. (1992). Teaching talk. In K. Norman (Ed.), Thinking voices: The work of the national oracy project (pp.203–214). London, England: Hodder and Stoughton for the National Curriculum Council.

  57. Wood, T. (1999). Creating a context for argument in mathematics class. Journal of Research in Mathematics Education, 30(2), 171–191.

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Correspondence to Hee-Jeong Kim.

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Lim, W., Lee, J., Tyson, K. et al. An Integral Part of Facilitating Mathematical Discussions: Follow-up Questioning. Int J of Sci and Math Educ 18, 377–398 (2020). https://doi.org/10.1007/s10763-019-09966-3

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Keywords

  • Mathematical discourse
  • Listening
  • Follow-up actions
  • Talk moves