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Initiation-entry-focus-exit and participation: a framework for understanding teacher groupwork monitoring routines

Educational Studies in Mathematics volume 103, pages 251–272 (2020)Cite this article

Abstract

In this paper, we offer a framework for teacher monitoring routines—a consequential yet understudied aspect of instruction when teachers oversee students’ working together. Using a comparative case study design, we examine eight lessons of experienced secondary mathematics teachers, identifying common interactional routines that they take up with variation. We present a framework that illuminates the common moves teachers make while monitoring, including how they initiate conversations with students, their forms of conversational entry, the focus of their interactions, when and how they exit the interaction as well as the conversation’s overall participation pattern. We illustrate the framework through our focal cases, highlighting the instructional issues the different enactments engage. By breaking down the complex work of groupwork monitoring, this study informs both researchers and teachers in understanding the teachers’ role in supporting students’ collaborative mathematical sensemaking.

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References

  • Aguirre, J., Mayfield-Ingram, K., & Martin, D. (2013). The impact of identity in K-8 mathematics: rethinking equity-based practices. Reston, VA: The National Council of Teachers of Mathematics.

    Google Scholar 

  • Bakker, A. (2018). Design research in education: a practical guide for early career researchers. New York, NY: Routledge.

    Google Scholar 

  • Bakker, A., Smit, J., & Wegerif, R. (2015). Scaffolding and dialogic teaching in mathematics education: introduction and review. ZDM, 47(7), 1047–1065.

    Google Scholar 

  • Battey, D. (2013). “Good” mathematics teaching for students of color and those in poverty: the importance of relational interactions within instruction. Educational Studies in Mathematics, 82(1), 125–144.

    Google Scholar 

  • Carpenter, T. P., & Fennema, E. (1992). Cognitively guided instruction: building on the knowledge of students and teachers. International Journal of Educational Research, 17(5), 457–470.

    Google Scholar 

  • Cazden, C. (2001). Classroom discourse: the language of teaching and learning (2nd ed.). Portsmouth, NH: Heinemann.

    Google Scholar 

  • Cobb, P., Confrey, J., DiSessa, A., Lehrer, R., & Schauble, L. (2003). Design experiments in educational research. Educational Researcher, 32(1), 9–13.

    Article  Google Scholar 

  • Coburn, C. E., & Penuel, W. R. (2016). Research–practice partnerships in education: outcomes, dynamics, and open questions. Educational Researcher, 45(1), 48–54.

    Google Scholar 

  • Cohen, E. G., & Lotan, R. A. (2014). Designing groupwork: strategies for the heterogeneous classroom (3rd ed.). New York, NY: Teachers College Press.

    Google Scholar 

  • Ding, M., Li, X., Piccolo, D., & Kulm, G. (2007). Teacher interventions in cooperative-learning mathematics classes. The Journal of Educational Research, 100(3), 162–175.

    Google Scholar 

  • Engle, R. A., Langer-Osuna, J. M., & McKinney de Royston, M. (2014). Toward a model of influence in persuasive discussions: negotiating quality, authority, privilege, and access within a student-led argument. Journal of the Learning Sciences, 23(2), 245–268.

    Google Scholar 

  • Esmonde, I., & Langer-Osuna, J. M. (2013). Power in numbers: student participation in mathematical discussions in heterogeneous spaces. Journal for Research in Mathematics Education, 44(1), 288–315.

    Google Scholar 

  • Feldman, M. S., & Pentland, B. T. (2003). Reconceptualizing organizational routines as a source of flexibility and change. Administrative Science Quarterly, 48, 94–118.

    Google Scholar 

  • Franke, M. L., Kazemi, E., & Battey, D. (2007). Mathematics teaching and classroom practice. In F. K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 225–256). Charlotte, NC: Information Age Publishing.

    Google Scholar 

  • Goffman, E. (1955). On face-work: an analysis of ritual elements in social interaction. Psychiatry, 18(3), 213–231.

    Google Scholar 

  • González, N., Moll, L. C., & Amanti, C. (Eds.). (2006). Funds of knowledge: theorizing practices in households, communities, and classrooms. New York, NY: Routledge.

    Google Scholar 

  • Greeno, J. G. (1998). The situativity of knowing, learning, and research. American Psychologist, 53(1), 5–26.

    Google Scholar 

  • Henningsen, M., & Stein, M. K. (1997). Mathematical tasks and student cognition: classroom-based factors that support and inhibit high-level mathematical thinking and reasoning. Journal for Research in Mathematics Education, 28, 524–549.

    Google Scholar 

  • Horn, I. S. (2012). Strength in numbers: collaborative learning in secondary mathematics. Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Horn, I. S. (2017). Motivated: designing math classrooms where students want to join in. Portsmouth, NH: Heinemann.

    Google Scholar 

  • Horn, I. S. (2020). Supporting the development of pedagogical judgment: connecting instruction to contexts through classroom video with experienced mathematics teachers. In G. M. Lloyd (Ed.), International handbook of mathematics teacher education (vol. 3, pp. 289–310). Leiden: Brill.

    Google Scholar 

  • Horn, I. S., & Kane, B. D. (2015). Opportunities for professional learning in mathematics teacher workgroup conversations: relationships to instructional expertise. Journal of the Learning Sciences, 24(3), 373–418.

    Google Scholar 

  • Horn, I. S., & Kane, B. D. (2019). What we mean when we talk about teaching: The limits of professional language and possibilities for professionalizing discourse in teachers’ conversations. Teachers College Record, 121(6), 1–34.

  • Horn, I. S., & Little, J. W. (2010). Attending to problems of practice: routines and resources for professional learning in teachers’ workplace interactions. American Educational Research Journal, 47(1), 181–217.

    Google Scholar 

  • Howe, C., Hennessy, S., Mercer, N., Vrikki, M., & Wheatley, L. (2019). Teacher–student dialogue during classroom teaching: does it really impact on student outcomes? Journal of the Learning Sciences, 1–51. https://doi.org/10.1080/10508406.2019.1573730

  • Jordan, B., & Henderson, A. (1995). Interaction analysis: foundations and practice. The Journal of the Learning Sciences, 4(1), 39–103.

    Google Scholar 

  • Kendon, A. (1990). Conducting interaction: Patterns of behavior in focused encounters. Cambridge, England: Cambridge University Press.

  • Kennedy, M. M. (2005). Inside teaching: How classroom life undermines reform. Cambridge, MA: Harvard University Press.

  • Kumashiro, K. K. (2001). “Posts” perspectives on anti-oppressive education in social studies, English, mathematics, and science classrooms. Educational Researcher, 30(3), 3–12.

    Google Scholar 

  • Lampert, M., Boerst, T. A., & Graziani, F. (2011). Organizational resources in the service of school-wide ambitious teaching practice. Teachers College Record, 113(7), 1361–1400.

    Google Scholar 

  • Langer-Osuna, J. M. (2011). How Brianna became bossy and Kofi came out smart: understanding the trajectories of identity and engagement for two group leaders in a project-based mathematics classroom. Canadian Journal of Science, Mathematics and Technology Education, 11(3), 207–225.

    Google Scholar 

  • Langer-Osuna, J. M. (2016). The social construction of authority among peers and its implications for collaborative mathematics problem solving. Mathematical Thinking and Learning, 18(2), 107–124.

    Google Scholar 

  • Lave, J., & Wenger, E. (1991). Situated learning: legitimate peripheral participation. Cambridge: Cambridge University Press.

    Google Scholar 

  • Lavie, I., Steiner, A., & Sfard, A. (2019). Routines we live by: from ritual to exploration. Educational Studies in Mathematics, 101(2), 153–176.

    Google Scholar 

  • Leander, K. M. (2002). Silencing in classroom interaction: Producing and relating social spaces. Discourse Processes, 34(2), 193–235.

  • Lefstein, A., & Snell, J. (2013). Better than best practice: developing teaching and learning through dialogue. New York, NY: Routledge.

    Google Scholar 

  • Liljedahl, P. (2019). Conditions for supporting problem solving: vertical non-permanent surfaces. In P. Liljedahl & M. Santos-Trigo (Eds.), Mathematical problem solving (pp. 289–310). Cham: Springer.

    Google Scholar 

  • Lincoln, Y. S., & Guba, E. G. (1985). Naturalistic inquiry. Newberry Park, CA: Sage.

    Google Scholar 

  • Lotan, R. A. (2003). Group-worthy tasks. Educational Leadership, 60(6), 72–75.

    Google Scholar 

  • Louie, N. L. (2017). The culture of exclusion in mathematics education and its persistence in equity-oriented teaching. Journal for Research in Mathematics Education, 48(5), 488–519.

    Google Scholar 

  • Mercer, N., & Sams, C. (2006). Teaching children how to use language to solve maths problems. Language and Education, 20(6), 507–528.

    Google Scholar 

  • Moschkovich, J. (2007). Using two languages when learning mathematics. Educational Studies in Mathematics, 64(2), 121–144.

    Google Scholar 

  • NCTM (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.

  • Paris, D. (2012). Culturally sustaining pedagogy: a needed change in stance, terminology, and practice. Educational Researcher, 41(3), 93–97.

    Google Scholar 

  • Schoenfeld, A., Dosalmas, A., Fink, H., Sayavedra, A., Tran, K., Weltman, A., … Zuniga-Ruiz, S. (2019). Teaching for robust understanding with lesson study. In R. Huang, A. Takahashi, & J. P. da Ponte (Eds.), Theory and practice of lesson study in mathematics (pp. 135–159). Cham: Springer.

    Google Scholar 

  • Shah, N., & Lewis, C. M. (2019). Amplifying and attenuating inequity in collaborative learning: toward an analytical framework. Cognition and Instruction, 37(4), 423–452.

    Google Scholar 

  • Smith, M., & Sherin, M. G. (2019). The 5 practices in practice: successfully orchestrating mathematical discussion in your middle school classroom. Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Smith, M. S., Bill, V., & Hughes, E. K. (2007). Thinking through a lesson: the key to successfully implementing high-level tasks. Mathematics Teaching in the Middle School, 14(3).

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

    Google Scholar 

  • Stein, M. K., Grover, B. W., & Henningsen, M. (1996). Building student capacity for mathematical thinking and reasoning: an analysis of mathematical tasks used in reform classrooms. American Educational Research Journal, 33(2), 455–488.

    Google Scholar 

  • Strauss, A., & Corbin, J. (1998). Basics of qualitative research: procedures and techniques for developing grounded theory. Thousand Oaks, CA: Sage.

    Google Scholar 

  • Webb, N. M., Franke, M. L., De, T., Chan, A. G., Freund, D., Shein, P., & Melkonian, D. K. (2009). ‘Explain to your partner’: teachers' instructional practices and students' dialogue in small groups. Cambridge Journal of Education, 39(1), 49–70.

    Google Scholar 

  • Wegerif, R., Fujita, T., Doney, J., Linares, J. P., Richards, A., & Van Rhyn, C. (2017). Developing and trialing a measure of group thinking. Learning and Instruction, 48, 40–50.

    Google Scholar 

  • Yin, R. K. (2017). Case study research and applications: design and methods. Thousand Oaks, CA: Sage.

    Google Scholar 

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Acknowledgments

We are thankful to the participating teachers, as well as Nicole Louie and Anna Sfard who gave helpful feedback on earlier stages of work, Avital Ashtar for her help with the graphic representations, and the SIGMa research team: Patricia Buenrostro, Grace Chen, Brette Garner, Mariah Harmon, Lara Jasien, Samantha Marshall, Elizabeth Metts, Jessica Moses, Katherine Schneeberger McGugan, and Chi Xiao. Feedback from the three anonymous reviewers strengthened the final manuscript. This material is based upon work supported by the National Science Foundation under grant #DRL-1620920. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation or other collaborators.

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  1. Peabody College, Vanderbilt University, Nashville, TN, USA

    Nadav Ehrenfeld & Ilana S. Horn

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  1. Nadav Ehrenfeld
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Correspondence to Nadav Ehrenfeld.

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Nadav Ehrenfeld and Ilana S. Horn contributed equally to this paper.

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Ehrenfeld, N., Horn, I.S. Initiation-entry-focus-exit and participation: a framework for understanding teacher groupwork monitoring routines. Educ Stud Math 103, 251–272 (2020). https://doi.org/10.1007/s10649-020-09939-2

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