Abstract
This study aimed to investigate secondary mathematics teachers’ noticing of students’ mathematical thinking in the context of a professional development (PD) program utilizing modeling-based teacher investigations. The PD program was conducted with two groups of mathematics teachers from two public high schools. It included seven 1-month-long cycles, each consisting of an introductory meeting, the teachers’ classroom implementations of a model-eliciting activity (MEA), and a follow-up meeting focusing on the teachers’ collaborative investigation and discussion of students’ written work, including their strategies to solve the MEA. Findings suggested that participating in the PD program promoted the teachers’ noticing of students’ mathematical thinking, albeit differently, over time. We elaborated on the components of the PD program that might have influenced the teachers’ noticing of students’ mathematical thinking. Implications of the findings on teachers’ noticing for researchers, PD leaders, and teacher educators are discussed in terms of potential directions for future research and practice.
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Notes
In these implementations, students worked on the activity in groups of three or four, while the teacher circulated around the classroom. At least two researchers videotaped and took field notes with minimum interaction with students.
In Turkey, a teacher who first studied mathematics and then received teacher certification attends a higher number of mathematics courses than a teacher who studied mathematics education at the university. Thus, we assumed that a teacher with an undergraduate degree in mathematics might have more robust mathematical content knowledge.
“TRY” is an acronym for currency in Turkey.
Teacher 1 and Teacher 2 were the participants of the larger project but not involved in the current study.
We should note that students’ written work that Rana and Ayfer examined included more mathematically rich solutions than those examined by Kutay and Selda.
Kutay was absent from this meeting. Ayfer did not make any comment in the meeting as she expressed that (for some reason) she did not want to join the discussions. Thus, the meeting data for these two teachers were missing in the 5th MBTI.
References
Ball, D. L., & Cohen, D. K. (1999). Developing practice, developing practitioners: Toward a practice-based theory of professional education. In L. Darling-Hammond & G. Sykes (Eds.), Teaching as the learning profession: Handbook of policy and practice (pp. 3–32). Jossey-Bass Publishers.
Callejo, M. L., & Zapatera, A. (2017). Prospective primary teachers’ noticing of students’ understanding of pattern generalization. Journal of Mathematics Teacher Education, 20(4), 309–333. https://doi.org/10.1007/s10857-016-9343-1
Chamberlin, M. T. (2005). Teachers’ discussions of students’ thinking: Meeting the challenge of attending to students’ thinking. Journal of Mathematics Teacher Education, 8(2), 141–170. https://doi.org/10.1007/s10857-005-4770-4
Choy, B. H. (2016). Snapshots of mathematics teacher noticing during task design. Mathematics Education Research Journal, 28(3), 421–440. https://doi.org/10.1007/s13394-016-0173-3
Choy, B. H., & Dindyal, J. (2019). Productive teacher noticing: Implications for improving teaching. In T. L. Toh, B. Kaur, & E. G. Tay (Eds.), Mathematics education in Singapore (pp. 469–488). Springer. https://doi.org/10.1007/978-981-13-3573-0_20
Didis, M. G., Erbas, A. K., Cetinkaya, B., Cakiroglu, E., & Alacaci, C. (2016). Exploring prospective secondary mathematics teachers’ interpretation of student thinking through analysing students’ work in modelling. Mathematics Education Research Journal, 28(3), 349–378. https://doi.org/10.1007/s13394-016-0170-6
Doerr, H. M., & Lesh, R. (2003). A modeling perspective on teacher development. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 125–139). Lawrence Erlbaum.
Fernández, C., Llinares, S., & Valls, J. (2012). Learning to notice students’ mathematical thinking through on-line discussions. ZDM Mathematics Education, 44(6), 747–759. https://doi.org/10.1007/s11858-012-0425-y
Goldsmith, L. T., & Seago, N. (2011). Using classroom artifacts to focus teachers’ noticing: Affordances and opportunities. In M. G. Sherin, V. R. Jacobs, & R. A. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 169–187). Routledge.
Goodwin, C. (1994). Professional vision. American Anthropologist, 96(3), 606–633. https://www.jstor.org/stable/682303
González, G., & Vargas, G. E. (2020). Teacher noticing and reasoning about student thinking in classrooms as a result of participating in a combined professional development intervention. Mathematics Teacher Education and Development, 22(1), 5–32. https://mted.merga.net.au/index.php/mted/article/view/449
Gronow, M., Mulligan, J., & Cavanagh, M. (2020). Teachers’ understanding and use of mathematical structure. Mathematics Education Research Journal. https://doi.org/10.1007/s13394-020-00342-x
Guner, P., & Akyuz, D. (2020). Noticing students’ mathematical thinking within the context of lesson study. Journal of Teacher Education, 71(5), 568–583. https://doi.org/10.1177/0022487119892964
Ivars, P., Fernández, C., Llinares, S., & Choy, B. H. (2018). Enhancing noticing: Using a hypothetical learning trajectory to improve pre-service primary teachers’ professional discourse. Eurasia Journal of Mathematics, Science and Technology Education, 14(11), Article em1599. https://doi.org/10.29333/ejmste/93421
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. https://doi.org/10.1007/s11858-015-0717-0
Jacobs, V. R., Lamb, L. C., & Philipp, R. A. (2010). Professional noticing of children’s mathematical thinking. Journal for Research in Mathematics Education, 41(2), 169–202. http://www.jstor.org/stable/20720130
Jacobs, V. R., & Spangler, D. A. (2018). Research on core practices in K-12 mathematics teaching. In J. Cai (Ed.), Compendium for research in mathematics education (pp. 766−792). National Council of Teachers of Mathematics.
LaRochelle, R., Nickerson, S. D., Lamb, L. C., Hawthorne, C., Philipp, R. A., & Ross, D. L. (2019). Secondary practising teachers’ professional noticing of students’ thinking about pattern generalisation. Mathematics Teacher Education and Development, 21(1), 4–27. https://mted.merga.net.au/index.php/mted/article/view/563
Lee, M. Y. (2019). The development of elementary pre-service teachers’ professional noticing of students’ thinking through adapted lesson study. Asia-Pacific Journal of Teacher Education, 47(4), 383–398. https://doi.org/10.1080/1359866X.2019.1607253
Lesh, R., & Doerr, H. M. (2003). Foundations of a models and modeling perspective on mathematics teaching, learning, and problem solving. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models and modelling perspectives on mathematics problem solving, learning, and teaching (pp. 3−33). Lawrence Erlbaum.
Lesh, R., Hoover, M., Hole, B., Kelly, A., & Post, T. (2000). Principles for developing thought-revealing activities for students and teachers. In R. Lesh & A. Kelly (Eds.), Handbook of research design in mathematics and science education (pp. 591–645). Lawrence Erlbaum.
Lesseig, K., Casey, S., Monson, D., Krupa, E. E., & Huey, M. (2016). Developing an interview module to support secondary PSTs’ noticing of student thinking. Mathematics Teacher Educator, 5(1), 29–46. https://doi.org/10.5951/mathteaceduc.5.1.0029
Mason, J. (2011). Noticing: Roots and branches. In M. G. Sherin, V. R. Jacobs, & R. A. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 35–50). Routledge.
Miles, M., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook (2nd ed.). Sage.
National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematics success for all.
Nickerson, S., Lamb, L., & LaRochelle, R. (2017). Challenges in measuring secondary mathematics teachers’ professional noticing of students’ mathematical thinking. In E. O. Schack, M. H. Fisher, & J. A. Wilhelm (Eds.), Teacher noticing: Bridging and broadening perspectives, contexts, and frameworks (pp. 381–398). Springer.
Sánchez-Matamoros, G., Fernández, C., & Llinares, S. (2015). Developing pre-service teachers’ noticing of students’ understanding of the derivative concept. International Journal of Science and Mathematics Education, 13(6), 1305–1329. https://doi.org/10.1007/s10763-014-9544-y
Schack, E. O., Fisher, M. H., Thomas, J. N., Eisenhardt, S., Tassel, J., & Yoder, M. (2013). Prospective elementary school teachers’ professional noticing of children’s early numeracy. Journal of Mathematics Teacher Education, 16(5), 379–397. https://doi.org/10.1007/s10857-013-9240-9
Schack, E. O., Fisher, M. H., & Wilhelm, J. A. (Eds.). (2017). Teacher noticing: Bridging and broadening perspectives, contexts, and frameworks. Springer. https://doi.org/10.1007/978-3-319-46753-5
Scheiner, T. (2021). Towards a more comprehensive model of teacher noticing. ZDM Mathematics Education, 53(1), 85–94. https://doi.org/10.1007/s11858-020-01202-5
Schorr, R. Y., & Lesh, R. (2003). A modeling approach for providing teacher development. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 141–157). Lawrence Erlbaum.
Sherin, M. G., & Han, S. Y. (2004). Teacher learning in the context of a video club. Teaching and Teacher Education, 20(2), 163–183. https://doi.org/10.1016/j.tate.2003.08.001
Sherin, M. G., Jacobs, V. R., & Philipp, R. A. (2011). Situating the study of teacher noticing. In M. G. Sherin, V. R. Jacobs, & R. A. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 3–13). Routledge.
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. https://doi.org/10.1177/0022487108328155
Simpson, A., & Haltiwanger, L. (2017). “This is the first time I’ve done this”: Exploring secondary prospective mathematics teachers’ noticing of students’ mathematical thinking. Journal of Mathematics Teacher Education, 20(4), 335–355. https://doi.org/10.1007/s10857-016-9352-0
Smith, M. S. (2001). Practice-based professional development for teachers of mathematics. National Council of Teachers of Mathematics.
Stockero, S. L., Rupnow, R. L., & Pascoe, A. E. (2017). Learning to notice important students’ mathematical thinking in complex classroom interactions. Teaching and Teacher Education, 63, 384–395. https://doi.org/10.1016/j.tate.2017.01.006
van Es, E. A. (2011). A framework for learning to notice student thinking. In M. G. Sherin, V. R. Jacobs, & R. A. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 134–151). Routledge.
van Es, E. A., & Sherin, M. G. (2008). Mathematics teachers’ “learning to notice” in the context of a video club. Teaching and Teacher Education, 24(2), 244–276. https://doi.org/10.1016/j.tate.2006.11.005
Walkoe, J. (2015). Exploring teacher noticing of student algebraic thinking in a video club. Journal of Mathematics Teacher Education, 18(6), 523–550. https://doi.org/10.1007/s10857-014-9289-0
Zawojewski, J., Chamberlin, M. T., Hjalmarson, M. A., & Lewis, C. (2008). Developing design studies in mathematics education professional development. In A. E. Kelly, R. A. Lesh, & J. Y. Baek (Eds.), Handbook of design research methods in education: Innovations in science, technology, engineering, and mathematics learning and teaching (pp. 219–245). Routledge.
Acknowledgements
The research reported here is based on the first author’s PhD Dissertation completed at the Middle East Technical University under the supervision of the second and the third authors. We thank Dr. Engin Ader for his support and valuable comments on an earlier version of this article.
Funding
This research was partly supported by The Scientific and Technological Research Council of Turkey (TÜBİTAK) under grant number 110K250. The opinions expressed do not necessarily reflect the views of the TÜBİTAK.
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Bas-Ader, S., Erbas, A.K., Cetinkaya, B. et al. Secondary mathematics teachers’ noticing of students’ mathematical thinking through modeling-based teacher investigations. Math Ed Res J 35 (Suppl 1), 81–106 (2023). https://doi.org/10.1007/s13394-021-00389-4
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DOI: https://doi.org/10.1007/s13394-021-00389-4