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Teacher moves for supporting student reasoning

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Abstract

Teachers play a critical role in supporting students’ mathematical engagement. There is evidence that meaningful student engagement occurs more often in student-centered classrooms, in which the teacher and the students mutually share mathematical authority. However, teacher-centered instruction continues to dominate classroom discourse, and teachers struggle to effectively support student inquiry. This paper presents a framework of teacher moves specific to inquiry-oriented instruction, the Teacher Moves for Supporting Student Reasoning (TMSSR) framework. Based on the analysis of four instructors’ implementations of a middle grades (ages 12–14) research-based unit on ratio and linear functions, the TMSSR framework organizes pedagogical moves into four categories, eliciting, responding, facilitating, and extending, and then places individual moves within each category on a continuum according to their potential for supporting student reasoning. In this manner, the TMSSR framework characterizes how multiple teacher moves can work together to foster an inquiry-oriented environment. We detail the framework with data examples and then present a classroom episode exemplifying the framework’s operation.

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References

  • Australian Curriculum, Assessment and Reporting Authority (ACARA). (2015). Australian Curriculum: Mathematics. Retrieved from http://www.australiancurriculum.edu.au/Mathematics/.

  • Ball, D. L., & Bass, H. (2003). Making mathematics reasonable in school. In J. Kilpatrick, W. G. Martin, & D. Schifter (Eds.), A research companion to principles and standards for school mathematics (pp. 27–44). Reston: National Council of Teachers of Mathematics.

    Google Scholar 

  • Bauersfeld, H. (1980). Hidden dimensions in the so-called reality of a mathematics classroom. Educational Studies in Mathematics, 11, 23–41.

    Article  Google Scholar 

  • Brousseau, G. (1997). In N. Balacheff, M. Cooper, R. Sutherland, & V. Warfield (Eds.), Theory of didactical situations in mathematics: Didactique des mathematiques, 1970–1990. Dordrecht: Kluwer Academic Publishers.

    Google Scholar 

  • Cady, J., Meier, S. L., & Lubinski, C. A. (2006). The mathematical tale of two teachers: A longitudinal study relating mathematics instructional practices to level of intellectual development. Mathematics Education Research Journal, 18(1), 3–26.

    Article  Google Scholar 

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

    Google Scholar 

  • Cengiz, N., Kline, K., & Grant, T. J. (2011). Extending students’ mathematical thinking during whole-group discussions. Journal of Mathematics Teacher Education, 14, 355–374.

    Article  Google Scholar 

  • Cobb, P., & Steffe, L. P. (1983). The constructivist researcher as teacher and model builder. Journal for Research in Mathematics Education, 28, 258–277.

    Article  Google Scholar 

  • Cuban, L. (1993). The lure of curricular reform and its pitiful history. Phi Delta Kappan, 75(2), 182–185.

    Google Scholar 

  • Driscoll, M. (1999). Fostering algebraic thinking: A guide for teachers, grades 6–10. Newton: Education Development Center, Inc..

    Google Scholar 

  • Ellis, A. B. (2007). Connections between generalizing and justifying: Students’ reasoning with linear relationships. Journal for Research in Mathematics Education, 38(3), 194–229.

    Google Scholar 

  • Ellis, A. B., Ozgur, Z., Kulow, T., Williams, C. C., & Amidon, J. (2015). Quantifying exponential growth: Three conceptual shifts in creating multiplicative rates of change. The Journal of Mathematical Behavior, 39, 135–155.

    Article  Google Scholar 

  • Ellis, A. B., Ozgur, Z., Kulow, T., Dogan, M. F., & Amidon, J. (2016). An exponential growth learning trajectory: Students’ emerging understanding exponential growth through covariation. Mathematical Thinking and Learning, 18(3), 151–181.

    Article  Google Scholar 

  • Engeström, Y. (1987). Learning by expanding. Helsinki: Orienta-konsultit.

    Google Scholar 

  • Engeström, Y. (1999). Activity theory and individual and social transformation. In Y. Engestrom, R. Miettinen, & R. Punamaki (Eds.), Perspective on activity theory (pp. 19–38). New York: Cambridge University Press.

    Chapter  Google Scholar 

  • Evans, S., & Dawson, C. (2017). Orchestrating productive whole class discussions: The role of designed student responses. Mathematics Teacher Education and Development, 19(2), 159–179.

    Google Scholar 

  • Forman, E. A., McCormick, D. E., & Donato, R. (1998). Learning what counts as a mathematical explanation. Linguistics and Education, 9(4), 313–339.

    Article  Google Scholar 

  • Frailvillig, J. L., Murphy, L. A., & Fuson, K. C. (1999). Advancing children’s mathematical thinking in everyday mathematics classrooms. Journal for Research in Mathematics Education, 30(2), 148–170.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Frey, N., & Fisher, D. (2010). Identifying instructional moves during guided learning. The Reading Teacher, 64(2), 84–95.

    Article  Google Scholar 

  • Glaser, B. G., & Strauss, A. L. (1967). The discovery of grounded theory: Strategies for qualitative research. Chicago: Aldine.

    Google Scholar 

  • Graesser, A. C., & Person, N. K. (1994). Question asking during tutoring. American Educational Research Journal, 31, 104–137.

    Article  Google Scholar 

  • Harry, B., Surges, K. M., & Klingner, J. K. (2005). Mapping the process: An exemplar of process and challenge in grounded theory analysis. Educational Researcher, 34(2), 3–13.

    Article  Google Scholar 

  • Herbel-Eisenmann, B., Drake, C., & Cirillo, M. (2009). “Muddying the clear waters”: Teachers’ take-up of the linguistic idea of revoicing. Teaching and Teacher Education, 25, 268–277.

    Article  Google Scholar 

  • Herbel-Eisenmann, B. A., Steele, M. D., & Cirillo, M. (2013). (Developing) teacher discourse moves: A framework for professional development. Mathematics Teacher Educator, 1(2), 181–196.

    Article  Google Scholar 

  • Herbert, S. (2014). A framework for teachers’ knowledge of mathematical reasoning. In J. Anderson, M. Cavanagh, & A. Prescott (Eds.), Curriculum in focus: Research guided practice (Proceedings of the 36th annual conference of the Mathematics Education Research Group of Australasia) (pp. 702–705). Sydney: MERGA.

    Google Scholar 

  • Hufferd-Ackles, K., Fuson, K. C., & Sherin, M. G. (2004). Describing levels and components of a math-talk learning community. Journal for Research in Mathematics Education, 35(2), 81–116.

    Article  Google Scholar 

  • Hunter, R. (2008). Facilitating communities of mathematical inquiry. In M. Goos, R. Brown, & K. Makar (Eds.). Navigating currents and charting directions (Proceedings of the 31st annual conference of the Mathematics Education Research Group of Australasia, Vol. 1, pp. 31–39). Brisbane: MERGA.

  • Hunter, R. (2012). Coming to ‘know’ mathematics through being scaffolded to ‘talk and do’ mathematics. International Journal for Mathematics Teaching and Learning, 13. Retrieved from http://www.cimt.org.uk/journal/hunter2.pdf.

  • Hunter, R., Hunter, J., Jorgensen, R., & Choy, B. H. (2016). Innovative and powerful pedagogical practices in mathematics education. In K. Makar et al. (Eds.), Research in mathematics education in Australasia 2012–2015 (pp. 213–234). Singapore: Springer Science+Business Media.

    Chapter  Google Scholar 

  • Jeannotte, D., & Kieran, C. (2017). A conceptual model of mathematical reasoning for school mathematics. Educational Studies in Mathematics, 96(1), 1–12.

    Article  Google Scholar 

  • Knuth, E., & Peressini, D. (2001). A theoretical framework for examining discourse in mathematics classrooms. Focus on Learning Problems in Mathematics, 23(2), 5–22.

    Google Scholar 

  • Krussel, L., Edwards, B., & Springer, G. T. (2004). The teacher discourse moves: A framework for analyzing discourse in mathematics classrooms. School Science and Mathematics, 104(7), 307–312.

    Article  Google Scholar 

  • Lampert, M., & Cobb, P. (2003). Communication and language. In J. Kilpatrick, W. G. Martin, & D. Schifter (Eds.), A research companion to principles and standards for school mathematics (pp. 237–249). Reston: National Council of Teachers of Mathematics.

    Google Scholar 

  • Lampert, M., Franke, M. L., Kazemi, E., Ghousseini, H., Turrou, A. C., Beasley, H., et al. (2013). Keeping it complex: Using rehearsals to support novice teacher learning of ambitions teaching. Journal of Teacher Education, 64(3), 226–243.

    Article  Google Scholar 

  • Lannin, J., Ellis, A. B., & Elliott, R. (2011). Essential understandings project: Mathematical reasoning (gr. K – 8). Reston: National Council of the Teachers of Mathematics.

    Google Scholar 

  • Larsson, M., & Ryve, A. (2012). Balancing on the edge of competency-oriented versus procedural-oriented practices: Orchestrating whole-class discussions of complex mathematical problems. Mathematics Education Research Journal, 24(4), 447–465.

    Article  Google Scholar 

  • Leach, G., Hunter, R., & Hunter, J. (2014). Teachers repositioning culturally diverse students as doers and thinkers of mathematics. In J. Anderson, M. Cavanagh, & A. Prescott (Eds.), Proceedings of the 37th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 381–388). Sydney: MERGA.

    Google Scholar 

  • Leatham, K. R., Peterson, B. E., Stockero, S. L., & Van Zoest, L. R. (2015). Conceptualizing mathematically significant pedagogical opportunities to build on student thinking. Journal for Research in Mathematics Education, 46(1), 88–124.

    Article  Google Scholar 

  • Leikin, R., & Dinur, S. (2007). Teacher flexibility in mathematical discussion. Journal of Mathematical Behavior, 18(3), 328–247.

    Article  Google Scholar 

  • Leikin, R., & Rosa, S. (2006). Learning through teaching: A case study on the development of a mathematics teacher’s proficiency in managing an inquiry-based classroom. Mathematics Education Research Journal, 18(3), 44–68.

    Article  Google Scholar 

  • Lobato, J., Clarke, D., & Ellis, A. B. (2005). Initiating and eliciting in teaching: A reformulation of telling. Journal for Research in Mathematics Education, 36(2), 101–136.

    Google Scholar 

  • Mata-Pereira, J., & da Ponte, J. P. (2017). Enhancing students’ mathematical reasoning in the classroom: Teacher actions facilitating generalization and justification. Educational Studies in Mathematics, 96(2), 169–186.

    Article  Google Scholar 

  • Nardi, B. A. (1996). Studying context: A comparison of activity theory, situated action models, and distributed cognition. In B. A. Nardi (Ed.), Context and consciousness: Activity theory and human-computer interaction. Cambridge: MIT Press.

    Google Scholar 

  • Nathan, M., & Knuth, E. (2003). A study of whole classroom mathematical discourse and teacher change. Cognition and Instruction, 21(2), 175–207.

    Article  Google Scholar 

  • Reiten, L., Ozgur, Z., & Ellis, A. B. (2015). Students engaging in mathematical practices: As the gears turn. Wisconsin Teacher of Mathematics, 68(1), 7–11.

    Google Scholar 

  • Rittenhouse, P. S. (1998). The teachers’ role in mathematical conversation: Stepping in and out. In M. Lampert & M. Blunk (Eds.), Talking mathematics in school: Studies of teaching and learning (pp. 163–189). Cambridge: Cambridge University Press.

    Chapter  Google Scholar 

  • Russell, S. J. (1999). Mathematical reasoning in the elementary grades. In L. V. Stiff & R. R. Curcio (Eds.), Developing Mathematical Reasoning in Grades K-12, 1999 yearbook (pp. 1–12). Reston: National Council of Teachers of Mathematics.

    Google Scholar 

  • Saldaña, J. (2009). The coding manual for qualitative researchers. Los Angeles: SAGE.

    Google Scholar 

  • Simon, M., Saldanha, L., McClintock, E., Akar, G., Watanabe, T., & Zembat, I. (2010). A developing approach to studying students’ learning through their mathematical activity. Cognition and Instruction, 28(1), 70–112.

    Article  Google Scholar 

  • Smith, M., & Stein, M. K. (2011). Five practices for orchestrating productive mathematics discussions. Reston: NCTM.

    Google Scholar 

  • Speer, N. M. (2008). Connecting beliefs and practices: A fine-grained analysis of a college mathematics teacher’s collections of beliefs and their relationship to his instructional practices. Cognition and Instruction, 26(2), 218–267.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Steen, L. (1999). Twenty questions about mathematical reasoning. In L. V. Stiff (Ed.), Developing mathematical reasoning in grades K-12. (1999 Yearbook (pp. 270–285). Reston: NCTM.

    Google Scholar 

  • Steffe, L. P., & Thompson, P. W. (2000). Teaching experiment methodology: Underlying principles and essential elements. In A. Kelly & R. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 267–306). Mahwah: Lawrence Erlbaum Associates.

    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.

    Article  Google Scholar 

  • Strauss, A. (1987). Qualitative analysis for social scientists. New York: Cambridge University Press.

    Book  Google Scholar 

  • Strauss, A., & Corbin, J. (1990). Basics of qualitative research: Grounded theory procedures and techniques. Newbury Park: Sage.

    Google Scholar 

  • Sullivan, P., Aulert, A., Lehmann, A., Hislop, B., Shepherd, O., & Stubbs, A. (2013). Classroom culture, challenging mathematical tasks and student persistence. In V. Steinle, L. Ball, & C. Bardini (Eds.), Mathematics education: Yesterday, today and tomorrow (Proceedings of the 36th annual conference of the Mathematics Education Research Group of Australasia) (pp. 618–625). Melbourne: MERGA.

    Google Scholar 

  • Towers, J., & Prouex, J. (2013). An enactivist perspective on teaching mathematics: Reconceptualising and expanding teaching actions. Mathematics Teacher Education and Development, 15(1), 5–28.

    Google Scholar 

  • Truxaw, M. P., & DeFranco, T. (2008). Mapping mathematics classroom discourse and its implications for models of teaching. Journal for Research in Mathematics Education, 39(5), 489–525.

    Google Scholar 

  • Voigt, J. (1995). Thematic patterns of interaction and sociomathematical norms. In P. Cobb & H. Bauersfeld (Eds.), The emergence of mathematical meaning: Interaction in classroom cultures (pp. 165–201). Hillsdale: Lawrence Erlbaum Associates.

    Google Scholar 

  • Webb, N., & Palincsar, A. S. (1996). Group processes in the classroom. In D. Berlmer & R. Calfee (Eds.), Handbook of educational psychology (pp. 841–873). New York: Simon & Schuster Macmillan.

    Google Scholar 

  • Wertsch, J., & Toma, C. (1995). Discourse and learning in the classroom: A sociocultural approach. In L. Steffe & J. Gale (Eds.), Constructivism in education (pp. 159–174). Hillsdale: Lawrence Erlbaum.

    Google Scholar 

  • Wood, T. (1994). Patterns of interaction and the culture of mathematics classrooms. In S. Lerman (Ed.), The culture of the mathematics classroom (pp. 149–168). Dordrecht: Kluwer Academic Publishers.

    Google Scholar 

  • Wood, T. (1998). Alternative patterns of communication in mathematics classes: Funneling or focusing? In H. Steinbring, M. Bartolini Bussi, & A. Sierpinska (Eds.), Language and communication in the mathematics classroom (pp. 167–178). Reston: National Council of Teachers of Mathematics.

    Google Scholar 

  • Yackel, E., & Hanna, G. (2003). Reasoning and proof. In J. Kilpatrick, W. G. Martin, & D. Schifter (Eds.), A research companion to principles and standards for school mathematics (pp. 227–236). Reston: National Council of Teachers of Mathematics.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics and Science Education, University of Georgia, 105 Aderhold Hall, 110 Carlton Street, Athens, GA, 30602, USA

    Amy Ellis

  2. Department of Mathematics and Science Education, Dokuz Eylül University, Uğur Mumcu Cad. 135 Sk. No:5, 35150, Buca, İzmir, Turkey

    Zekiye Özgür

  3. School of Mathematical Sciences, University of Northern Colorado, 501 20th Street, Campus Box 122, Greeley, CO, 80639, USA

    Lindsay Reiten

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  1. Amy Ellis
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  2. Zekiye Özgür
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Correspondence to Amy Ellis.

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Ellis, A., Özgür, Z. & Reiten, L. Teacher moves for supporting student reasoning. Math Ed Res J 31, 107–132 (2019). https://doi.org/10.1007/s13394-018-0246-6

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