Abstract
Noticing is a skill that is not overtly observable yet is consequential to effective mathematics instruction. Researchers have found that prospective and practicing teachers can learn to notice, but little focus has been given to those who teach teachers to notice. The purpose of the study was to characterize mathematics teacher educators’ noticing and their ability to interpret students’ thinking and connect interpretations to evidence. Participants in the study included 16 mathematics teacher educators who took part in a course designed to support noticing. Results indicate the mathematics teacher educators noticed at varying degrees and improved their noticing and incidence of connections between interpretations and evidence. Findings indicated that 19% of participants had no shift in their noticing because they were at the highest level of noticing to begin with (Robust with Strong Evidence), which was considered advanced noticing. Twenty-five percent of the participants did not shift in their noticing at all and remained at Limited, which is considered an intermediate level of noticing. The remaining 56% of the participants improved their noticing. The results of the study reveal that at the end of the course a majority of the participants were able to connect interpretations with evidence. These findings are important because they describe mathematics teacher educators’ interpretations and evidence as they notice.
Similar content being viewed by others
References
Akkoc, H., & Alan, S. (2020). Important Events Noticed by Pre-Service Mathematics Teachers in a Technology-Enhanced Mathematics Lesson Video. In Society for Information Technology & Teacher Education International Conference (pp. 2069–2075). Association for the Advancement of Computing in Education (AACE).
Amador, J. (2016). Professional noticing practices of novice mathematics teacher educators. International Journal of Science and Mathematics Education, 14, 217–241.
Amador, J. (2020). Teacher leaders’ mathematical noticing: Eliciting and analyzing. InternationalJournal of Science and Mathematics Education, 18(2), 295–313.
Amador, J., Bragelman, J., & Castro Superfine, A. (in press). Prospective teachers’ noticing: A literature review of methodological approaches to support and analyze noticing. Teaching and Teacher Education.
Beattie, H. L., Ren L., Smith W. M., & Heaton R. M. (2017). Measuring elementary mathematics teachers’ noticing: Using child study as a vehicle. In: Schack E., Fisher M., Wilhelm J. (Eds.) Teacher Noticing: Bridging and Broadening Perspectives, Contexts, and Frameworks. Research in Mathematics Education. New York: Springer. https://doi.org/10.1007/978-3-319-46753-5_19.
Beswick, K., & Goos, M. (2018). Mathematics teacher educator knowledge: What do we know and where to from here? Journal of Mathematics Teacher Education, 21, 417–427. https://doi.org/10.1007/s10857-018-9416-4.
Castro Superfine, A., & Bragelman, J. (2018). Analyzing the impact of video representation complexity on preservice teacher noticing of children’s thinking. Eurasia Journal of Mathematics, Science and Technology Education, 14(11), 1–18. https://doi.org/10.29333/ejmste/99501.
Choy, B. (2016). Snapshots of mathematics teacher noticing during task design. Mathematics Education Research Journal, 28, 421–440.
Corbin, J., & Strauss, A. (2008). Basics of qualitative research: Techniques and procedures for developing grounded theory (3rd ed.). Thousand Oaks, CA: Sage Publications Inc.
Fernandez, C., Llinares, S., & Valls, J. (2012). Learning to notice students’ mathematical thinking through online discussions. ZDM – Mathematics Education, 44, 747–759.
Frank, K. A., Maroulis, S. J., Duong, M. Q., & Kelcey, B. M. (2013). What would it take to change an inference? Using Rubin’s causal model to interpret the robustness of causal inferences. Educational Evaluation and Policy Analysis, 35(4), 437–460.
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). London, England: Routlege.
Goodwin, C. (1994). Professional vision. American Anthropologist, 96(3), 606–633.
Helliwell, T. (2017). Mathematics teacher educator noticing: A methodology for researching my own learning. 1. Paper presented at BSRLM New Researcher’s Day and Day Conference.
Jacobs, V. R., Lamb, L. L. C., & Philipp, R. A. (2010). Professional noticing of children’s mathematical thinking. Journal for Research in Mathematics Education, 41(2), 169–202.
Jacobs, V. R., & Spangler, D. A. (2017). Research on core practices in K–12 mathematics teaching. In J. Cai (Ed.), Compendium for research in mathematics education (pp. 766–792). Reston, VA: National Council of Teachers of Mathematics.
Kaiser, G., Busse, A., Hoth, J., König, J., & Blömeke, S. (2015). About the complexities of video-based assessments: Theoretical and methodological approaches to overcoming shortcomings of research on teachers’ competence. International Journal of Science and Mathematics Education, 13(3), 369–387.
Kilic, S. D. (2019). Pre-service teachers’ noticing of 7th grade students’ errors and misconceptions about the subject of equations. Sakarya University Journal of Education, 9(1), 184–207.
Krupa E. E., Huey M., Lesseig K., Casey S., & Monson D. (2017) Investigating secondary preservice teacher noticing of students’ mathematical thinking. In E. Schack, M. Fisher M., J. Wilhelm (Eds.) Teacher Noticing: Bridging and Broadening Perspectives, Contexts, and Frameworks. Research in Mathematics Education. (pp. 49–72). New York: Springer.
Landis, J. R., & Koch, G. G. (1977). The measurement of observer agreement for categorical data. Biometrics, 33, 159–174.
Lester, F. (2010). Teaching and learning mathematics: Translating research for secondary school teachers. Reston, VA: NCTM.
Mason, J. (2002). Researching your own practice: From noticing to reflection. London, England: Routledge Falmer.
Mason, J. (2011). Noticing: Roots and branches. In M. G. Sherin, V. R. Jacobs, & R. A. Philipp (Eds.), Mathematics teacher noticing: Seeing though teachers’ eyes (pp. 35–50). New York: Routledge.
McHugh, M. (2012). Interrater reliability: the kappa statistic. Biochem Med (Zagreb), 22(3), 276–282.
Mitchell, R., & Marin, K. (2015). Examining the use of a structured analysis framework to support prospective teacher noticing. Journal of Mathematics Teacher Education, 18(6), 551–575.
Roth McDuffie, A., Foote, M. Q., Drake, C., Turner, E., Aguirre, J., Bartell, T. G., & Bolson, C. (2014). Use of video analysis to support prospective K-8 teachers’ noticing of equitable practices. Mathematics Teacher Educator, 2(2), 108–140.
Schack, E. O., Fisher, M. H., Thomas, J. N., Eisenhardt, S., Tassell, J., & Yoder, M. (2013). Prospective elementary school teachers’ professional noticing of children’s early numeracy. Journal of Mathematics Teacher Education, 16, 379–397.
Sherin, M. G., & Han, S. Y. (2004). Teacher learning in the context of a video club. Teaching and Teacher Education, 20(2), 163–183.
Sherin, M. G., Jacobs, V. R., & Philipp, R. A. (Eds.). (2011). Mathematics teacher noticing: Seeing through teachers’ eyes. New York: Taylor and Francis.
Sherin, M. G., & van Es, E. A. (2005). Using video to support teachers’ ability to notice classroom interactions. Journal of Technology and Teacher Education, 13, 475–491.
Sherin, M. G., & van Es, E. A. (2009). Effects of video club participation on teachers’ professional vision. Journal of Teacher Education, 60, 20–37.
Sherin, M. G., Jacobs, V. R., & Philipp, R. A. (Eds.). (2011). Mathematics teacher noticing: Seeing through teachers’ eyes. New York: Taylor and Francis.
Smith, M. S., & Stein, M. K. (1998). Selecting and creating mathematical tasks: From research to practice. Mathematics Teaching in the Middle School, 3(5), 344–350.
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, 107–125.
National Council of Teachers of Mathematics (NCTM). (2014). Principles to actions: Ensuring mathematical success for all. Reston: National Council of Teachers of Mathematics. NGSS Lead States. 2013. Next Generation Science Standards: For States, By States. Washington, DC: The National Academies Press.
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). New York: 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 & Instruction, 35(3), 165–187.
van Es, E. A., & Sherin, M. G. (2002). Learning to notice: Scaffolding new teachers’ interpretations of classroom interactions. Journal of Technology and Teacher Education, 10(4), 571–597.
van Es, E. A., & Sherin, M. G. (2006). How different video club designs support teachers in “learning to notice.” Journal of Computing in Teacher Education, 22, 125–135.
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.
Walkoe, J. (2015). Exploring teacher noticing of student algebraic thinking in a video club. Journal of Mathematics Teacher Education, 18(6), 523–550.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Amador, J.M. Mathematics teacher educator noticing: examining interpretations and evidence of students’ thinking. J Math Teacher Educ 25, 163–189 (2022). https://doi.org/10.1007/s10857-020-09483-z
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10857-020-09483-z