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Listening to learn: investigating how teacher leaders elicit and attend to students’ mathematical thinking in clinical interviews

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Abstract

Eliciting and attending to students’ thinking is an important component of teaching mathematics for understanding. Clinical interview protocols have shown the potential to support teachers in developing these skills. However, less is known about how to support teacher leaders’ knowledge and development of these skills. Given that teacher leaders provide opportunities to foster teachers’ knowledge of these ideas, more needs to be known about teacher leaders’ abilities and knowledge in this area, and how clinical interviews might support teacher leaders’ pedagogical knowledge. This study explored the nuances in understanding the ways in which teacher leaders elicited and attended to student thinking when conducting clinical interviews. Findings show that while the majority of teacher leaders who engaged in conducting clinical interviews asked probing questions and engaged in observational thinking, they also faced challenges in moving toward responsive listening, particularly when students struggled with providing justification for a task.

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References

  • Amador, J. (2016). Professional noticing practices of novice mathematics teacher educators. International Journal of Science and Mathematics Education, 14(1), 217–241.

    Article  Google Scholar 

  • Amador, J. M. (2020). Teacher leaders’ mathematical noticing: Eliciting and analyzing. International Journal of Science and Mathematics Education, 18(2), 295–313.

    Article  Google Scholar 

  • Amador, J., & Weiland, I. (2015). What preservice teachers and knowledgeable others professionally notice during lesson study. The Teacher Educator, 50(2), 109–126.

    Article  Google Scholar 

  • Ambrose, R. (2004). Initiating change in prospective elementary school teachers’ orientations to mathematics teaching by building on beliefs. Journal of Mathematics Teacher Education, 7(2), 91–119.

    Article  Google Scholar 

  • Ball, D. L., & Bass, H. (2000). Interweaving content and pedagogy in teaching and learning to teach: Knowing and using mathematics. Multiple Perspectives on the Teaching and Learning of Mathematics, 4, 83–104.

    Google Scholar 

  • Ball, D. L., Lubienski, S. T., & Mewborn, D. S. (2001). Research on teaching mathematics: The unsolved problem of teachers’ mathematical knowledge. Handbook of Research on Teaching, 4, 433–456.

    Google Scholar 

  • Bengo, P. (2016). Secondary mathematics coaching: The components of effective mathematics coaching and implications. Teaching and Teacher Education, 60, 88–96.

    Article  Google Scholar 

  • Bennett, C., Amador, J., & Avila, C. (2015). Framing professional conversations with teachers: Developing administrators’ professional noticing of students’ mathematical thinking. NCSM Journal of Mathematics Education Leadership, 16(2), 14–26.

    Google Scholar 

  • Borko, H., Koellner, K., & Jacobs, J. (2014). Examining novice teacher leaders’ facilitation of mathematics professional development. The Journal of Mathematical Behavior, 33, 149–167.

    Article  Google Scholar 

  • Brodie, K. (2011). Working with learners’ mathematical thinking: Towards a language of description for changing pedagogy. Teaching and Teacher Education, 27(1), 174–186.

    Article  Google Scholar 

  • Buschman, L. (2001). Research, reflection, practice: december 2001: Using student interviews to guide classroom instruction: An action research project. Teaching Children Mathematics, 8(4), 222–227.

    Article  Google Scholar 

  • Carpenter, T. P., Fennema, E., & Franke, M. L. (1996). Cognitively guided instruction: A knowledge base for reform in primary mathematics instruction. The Elementary School Journal, 97(1), 3–20.

    Article  Google Scholar 

  • Carpenter, T. P., Fennema, E., Franke, M. L., Levi, L., & Empson, S. B. (2000). Cognitively Guided Instruction: A Research-Based Teacher Professional Development Program for Elementary School Mathematics. Research Report.

  • Choppin, J. (2011). The impact of professional noticing on teachers’ adaptations of challenging tasks. Mathematical Thinking and Learning, 13(3), 175–197.

    Article  Google Scholar 

  • Chval, K. B., Arbaugh, F., Lannin, J. K., Van Garderen, D., Cummings, L., Estapa, A. T., & Huey, M. E. (2010). The transition from experienced teacher to mathematics coach: Establishing a new identity. The Elementary School Journal, 111(1), 191–216.

    Article  Google Scholar 

  • Coles, A. (2013). Using video for professional development: The role of the discussion facilitator. Journal of Mathematics Teacher Education, 16(3), 165–184.

    Article  Google Scholar 

  • Crespo, S. (2000). Seeing more than right and wrong answers: Prospective teachers’ interpretations of students’ mathematical work. Journal of Mathematics Teacher Education, 3(2), 155–181.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Dunphy, E. (2010). Exploring young children’s (mathematical) thinking: Preservice teachers reflect on the use of the one-to-one interview. International Journal of Early Years Education, 18(4), 331–347.

    Article  Google Scholar 

  • Ellemor-Collins, D. L., & Wright, R. J. (2008). Assessing student thinking about arithmetic: Videotaped interviews. Teaching Children Mathematics, 15(2), 106–111.

    Article  Google Scholar 

  • Empson, S. B., & Jacobs, V. R. (2008). Learning to listen to children’s mathematics. In International Handbook of Mathematics Teacher Education: Volume 2 (pp. 257-281). Brill Sense.

  • Fennema, E., Carpenter, T. P., Franke, M. L., Levi, L., Jacobs, V. R., & Empson, S. B. (1996). A longitudinal study of learning to use children’s thinking in mathematics instruction. Journal for Research in Mathematics Education, 27(4), 403–434.

    Article  Google Scholar 

  • Fernández, C., Llinares, S., & Valls, J. (2012). Learning to notice students’ mathematical thinking through on-line discussions. ZDM Mathematics Education, 44(6), 747–759.

    Article  Google Scholar 

  • Fraivillig, 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., Carpenter, T. P., Levi, L., & Fennema, E. (2001). Capturing teachers’ generative change: A follow-up study of professional development in mathematics. American Educational Research Journal, 38(3), 653–689.

    Article  Google Scholar 

  • Gallucci, C., Van Lare, M. D., Yoon, I. H., & Boatright, B. (2010). Instructional coaching: Building theory about the role and organizational support for professional learning. American Educational Research Journal, 47(4), 919–963.

    Article  Google Scholar 

  • Gamoran Sherin, M., & Van Es, E. A. (2009). Effects of video club participation on teachers’ professional vision. Journal of Teacher Education, 60(1), 20–37.

    Article  Google Scholar 

  • Gavin, H. (2008). Understanding research methods and statistics in psychology. Understanding Research Methods and Statistics in Psychology, 1-424.

  • Gibbons, L. K., & Cobb, P. (2016). Content-focused coaching: Five key practices. The Elementary School Journal, 117(2), 237–260.

    Article  Google Scholar 

  • Ginsburg, H. P., Klein, A., & Starkey, P. (1998). The Development of Children's Mathematical Thinking: Connecting Research with Practice.

  • Ginsburg, H. P., & Seo, K.-H. (1999). Mathematics in children’s thinking. Mathematical Thinking and Learning, 1(2), 113–129.

    Article  Google Scholar 

  • Grossman, P., Hammerness, K., & McDonald, M. (2009). Redefining teaching, re-imagining teacher education. Teachers and Teaching: Theory and Practice, 15(2), 273–289.

    Article  Google Scholar 

  • Hammer, D., Goldberg, F., & Fargason, S. (2012). Responsive teaching and the beginnings of energy in a third grade classroom. Review of Science, Mathematics and ICT Education, 6(1), 51–72.

    Google Scholar 

  • Heng, M. A., & Sudarshan, A. (2013). “Bigger number means you plus!”—Teachers learning to use clinical interviews to understand students’ mathematical thinking. Educational Studies in Mathematics, 83(3), 471–485.

    Article  Google Scholar 

  • Huang, R., & Li, Y. (2012). What matters most: A comparison of expert and novice teachers’ noticing of mathematics classroom events. School Science and Mathematics, 112(7), 420–432.

    Article  Google Scholar 

  • Hunting, R. P. (1997). Clinical interview methods in mathematics education research and practice. The Journal of Mathematical Behavior, 16(2), 145–165.

    Article  Google Scholar 

  • Jackson, K., Cobb, P., Wilson, J., Webster, M., Dunlap, C., & Appelgate, M. (2015). Investigating the development of mathematics leaders’ capacity to support teachers’ learning on a large scale. ZDM, 47(1), 93–104.

    Article  Google Scholar 

  • Jacobs, V. R., & Ambrose, R. C. (2008). Making the most of story problems. Teaching Children Mathematics, 15(5), 260–266.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Jacobs, V. R., Franke, M. L., Carpenter, T. P., Levi, L., & Battey, D. (2007). Professional development focused on children’s algebraic reasoning in elementary school. Journal for Research in Mathematics Education, 38(3), 258–288.

    Google Scholar 

  • Jacobs, V. R., Lamb, L. L., & Philipp, R. A. (2010). Professional noticing of children’s mathematical thinking. Journal for Research in Mathematics Education, 41(2), 169–202.

    Article  Google Scholar 

  • Jilk, L. M. (2016). Supporting teacher noticing of students’ mathematical strengths. Mathematics Teacher Educator, 4(2), 188–199.

    Article  Google Scholar 

  • Kazemi, E., & Franke, M. L. (2004). Teacher learning in mathematics: Using student work to promote collective inquiry. Journal of Mathematics Teacher Education, 7(3), 203–235.

    Article  Google Scholar 

  • Lampert, M. (2001). Teaching problems and the problems of teaching. Yale University Press.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Lee, M. Y., & Choy, B. H. (2017). Mathematical teacher noticing: The key to learning from lesson study (pp. 121–140). Teacher noticing: Bridging and broadening perspectives, contexts, and frameworks.

    Google Scholar 

  • McDonough, A., Clarke, B., & Clarke, D. M. (2002). Understanding, assessing and developing children’s mathematical thinking: The power of a one-to-one interview for preservice teachers in providing insights into appropriate pedagogical practices. International Journal of Educational Research, 37(2), 211–226.

    Article  Google Scholar 

  • Obara, S. (2010). Mathematics coaching: A new kind of professional development. Teacher Development, 14(2), 241–251.

    Article  Google Scholar 

  • Sherin, M. G. (2002). When teaching becomes learning. Cognition and Instruction, 20(2), 119–150.

    Article  Google Scholar 

  • Sherin, M. G., & Han, S. Y. (2004). Teacher learning in the context of a video club. Teaching and Teacher Education, 20(2), 163–183.

    Article  Google Scholar 

  • Sherin, M. G., & van Es, E. A. (2009). Effects of video club participation on teachers’ professional vision. Journal of Teacher Education, 60(1), 20–37.

    Article  Google Scholar 

  • Star, J. R., & Strickland, S. K. (2008). Learning to observe: Using video to improve preservice mathematics teachers’ ability to notice. Journal of Mathematics Teacher Education, 11(2), 107–125.

    Article  Google Scholar 

  • Steinberg, R. M., Empson, S. B., & Carpenter, T. P. (2004). Inquiry into children’s mathematical thinking as a means to teacher change. Journal of Mathematics Teacher Education, 7(3), 237–267.

    Article  Google Scholar 

  • Van Es, E. A. (2011). A framework for learning to notice student thinking. In Mathematics teacher noticing (pp. 164-181). Routledge.

  • van Es, E. A., Cashen, M., Barnhart, T., & Auger, A. (2017). Learning to notice mathematics instruction: Using video to develop preservice teachers’ vision of ambitious pedagogy. Cognition and Instruction, 35(3), 165–187.

    Article  Google Scholar 

  • Wager, A. A. (2014). Noticing children’s participation: Insights into teacher positionality toward equitable mathematics pedagogy. Journal for Research in Mathematics Education, 45(3), 312–350.

    Article  Google Scholar 

  • Walkoe, J. (2015). Exploring teacher noticing of student algebraic thinking in a video club. Journal of Mathematics Teacher Education, 18(6), 523–550.

    Article  Google Scholar 

  • Weiland, I. S., Hudson, R. A., & Amador, J. M. (2014). Preservice formative assessment interviews: The development of competent questioning. International Journal of Science and Mathematics Education, 12(2), 329–352.

    Article  Google Scholar 

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Correspondence to Nicora Placa.

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Placa, N. Listening to learn: investigating how teacher leaders elicit and attend to students’ mathematical thinking in clinical interviews. J Math Teacher Educ (2023). https://doi.org/10.1007/s10857-023-09614-2

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