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Conceptualising mathematics teacher noticing as a perception/action cycle

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Abstract

Most studies of mathematics teacher noticing employ information-processing-based models of noticing. While information processing has been used productively to research the cognitive requirements of noticing, critics have argued that these accounts conceptualise noticing as a relatively passive and mental act. This paper demonstrates how an alternative perception/action cycle model of noticing can draw attention to how teacher noticing is supported by active interaction with the classroom environment mid-lesson. Data from two primary mathematics lessons were gathered using a head-mounted camera technique. These data are analysed using the perception/action cycle model to demonstrate the model’s capacity to enable productive research. The model draws attention to aspects of teacher behaviour that support noticing that are given little weight when information processing informs analysis. By contrasting the noticing of one experienced and one beginning teacher, differences in the way that each teacher deployed their attention and looked for information mid-lesson can be ascertained. The experienced teacher took action that increased the likelihood that students would create mathematical representations that enabled perception of students’ mathematical thinking and deployed their attention so that they were more likely to be in the right place at the right time to notice. The perception/action cycle model draws attention to these under-researched aspects of mathematics teacher noticing.

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Access to data which contains images of children would require ethics clearance. Hence, an application to view the primary data of the study would need to be assessed by the relevant research ethics committee.

References

  • Acker, F. (2008). Head-mounted video cued recall in research: Is watching video from your own perspective a good way to jog your memory? (PhD). La Trobe University.

    Google Scholar 

  • Araujo, D., Davids, K., & Hristovski, R. (2006). The ecological dynamics of decision making in sport. Psychology of Sport and Exercise, 7(6), 653–676.

    Article  Google Scholar 

  • Atkinson, R. C., & Shiffrin, R. M. (1968). Human memory: A proposed system and its control processes. Psychology of Learning and Motivation, 2(4), 89–195.

    Article  Google Scholar 

  • Chemero, A. (2009). Radical embodied cognitive science. MIT.

    Book  Google Scholar 

  • Choy, B. H. (2016). Snapshots of mathematics teacher noticing during task design. Mathematics Education Research Journal, 28(3), 421–440.

    Article  Google Scholar 

  • Cobb, P. (2007). Putting philosophy to work: Coping with multiple theoretical perspectives. In F. K. Lester, Jr. (Ed.), Second handbook of research on mathematics teaching and learning (Vol. 1, pp. 3–38). Charlotte, NC: National Council of Teachers of Mathematics.

  • Cobb, P. (2011). Learning from distributed theories of intelligence. In E. Yackel, K. Gravemeijer, & A. Sfard (Eds.), A Journey in Mathematics Education Research: Insights from the Work of Paul Cobb. London: Springer.

  • Dindyal, J., Schack, E. O., Choy, B. H., & Sherin, M. G. (2021). Exploring the terrains of mathematics teacher noticing. ZDM.

  • Endsley, M. R. (1995). A taxonomy of situation awareness errors. Paper presented at the 21st Conference of the European Association for Aviation Psychology.

  • Endsley, M. R. (2012). Situation Awareness. In G. Salvendy (Ed.), Handbook of human factors and ergonomics (pp. 553–568). John Wiley & Sons.

    Chapter  Google Scholar 

  • Endsley, M. R., & Bolstad, C. A. (1994). Individual differences in pilot situation awareness. The International Journal of Aviation Psychology, 4(3), 241–264.

    Article  Google Scholar 

  • Endsley, M. R., & Rodgers, M. D. (1994). Situation awareness information requirements analysis for en route air traffic control. Paper presented at the Proceedings of the Human Factors and Ergonomics Society Annual Meeting.

  • Fisher, M. H., Thomas, J., Schack, E. O., Jong, C., & Tassell, J. (2018). Noticing numeracy now! Examining changes in preservice teachers’ noticing, knowledge, and attitudes. Mathematics Education Research Journal, 30(2), 209–232.

    Article  Google Scholar 

  • Galbraith, P. (2014). Custodians of quality: Mathematics education in Australasia where from? Where at? Where to? . Paper presented at the 37th annual conference of the Mathematics Education Research Group of Australiasia, Sydney.

  • Gibson, E. J. (1969). Principles of perceptual learning and development. Appleton-Century-Crofts.

    Google Scholar 

  • Gibson, J. J. (1972/2002). A theory of direct visual perception. In A. Noe & E. Thompson (Eds.), Vision and Mind: selected readings in the philosophy of perception (pp. 77–90). Cambridge, Mass: MIT Press. (Reprinted from: The psychology of knowing, pp. 215–240, by J. R. Royce and W. W. Rozenboom (eds), 1972, New York: Gordon & Breach).

  • Gibson, J. J. (1979). The ecological approach to visual perception. Houghton Mifflin Company.

    Google Scholar 

  • Goodwin, C. (2000). Practices of seeing, visual analysis: An ethnomethodological approach. In T. van Leeuwen & C. Jewitt (Eds.), Handbook of visual analysis (pp. 157–182). Sage.

    Google Scholar 

  • Gray, W. D. (2006). The emerging rapprochement between cognitive and ecological analyses. In A. Kirlik (Ed.), Adaptive perspectives on human-technology interaction: Methods and modfiles for cognitive engineering and human-computer interaction (pp. 230–246). Oxford University Press.

    Google Scholar 

  • IEA. (2014). Definition and domains of ergonomics. Retrieved from http://www.iea.cc/whats/index.html

  • Jacobs, V. R. (2017). Complexities in measuring teacher noticing: Commentary. In E. O. Schack, M. H. Fisher, & J. A. Wilhelm (Eds.), Teacher Noticing: Bridging and Broadening Perspectives, Contexts, and Frameworks (pp. 273–279): Springer.

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

  • Jacobs, V. R., Lamb, L. L. C., Philipp, R. A., & Schappelle, B. P. (2011). Deciding how to respond on the basis of children’s understandings. In M. G. Sherin, V. R. Jacobs, & R. A. Philipp (Eds.), Mathematics teacher noticing: Seeing through the eyes of the teacher (pp. 97–116). Routledge.

    Google Scholar 

  • Jacobs, V. R., Philipp, R. A., & Sherin, M. G. (2020). Noticing of mathematics teachers. In S. Lerman (Ed.), Encyclopedia of Mathematics Education (pp. 639–641): Springer International Publishing.

  • 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): National Council of Teachers of Mathematics.

  • James, W. (1890). The principles of psychology. H. Holt.

    Google Scholar 

  • Jazby, D. (2014). Do teachers make decisions like firefighters? Applying naturalistic decision-making methods to teacher in-class decision making in mathematics. In J. Anderson, M. Cavanagh, & A. Prescott (Eds.), Proceedings of the 37th annual conference of the Mathematics Education Research Group of Australasia (pp. 303-310). Sydney: MERGA.

  • Jazby, D. (2016). An ecological analysis of mathematics teachers’ noticing. In B. White, M. Chinnappan, & S. Trenholm (Eds.), Proceedings of the 39th conference of the mathematics education research group of Australasia (pp. 358-365). Adelaide: MERGA.

  • Jazby, D. (2019). Teaching 'on the fly': Investigating the mid-lesson adaptive behaviour of primary mathematics teachers. (PhD), University of Melbourne, Melbourne. Retrieved from http://hdl.handle.net/11343/225143

  • Jones, D. G. (2000). Subjective measures of situation awareness. In M. R. Endsley & D. J. Garland (Eds.), Situation awareness analysis and measurement (pp. 113–128). Lawrence Erlbaum Associates.

    Google Scholar 

  • Kaiser, G., Blömeke, S., Koenig, J., Busse, A., Doehrmann, M., & Hoth, J. (2017). Professional competencies of (prospective) mathematics teachers—Cognitive versus situated approaches. Educational Studies in Mathematics, 94(2), 161–182.

    Article  Google Scholar 

  • Kirlik, A. (1995). Requirements for psychological models to support design: Toward ecological task analysis. In J. Flach, P. Hancock, J. Caird, & K. J. Vicente (Eds.), Global perspectives on the ecology of human-machine systems (pp. 68–120). Lawrence Erlbaum.

    Google Scholar 

  • Kirlik, A. (1998). The ecological expert: Acting to create information to guide action. In Fourth Annual Symposium on Human Interaction with Complex Systems (pp. 15–27). Dayton, OH: IEEE.

  • Klein, G. (1993). A recognition-primed decision (RPD) model of rapid decision making. In G. Klein, J. Orasanu, R. Calderwood, & C. Zsambok (Eds.), Decision making in action: Models and methods (pp. 138–147). Ablex Publishing.

    Google Scholar 

  • König, J., Blömeke, S., Klein, P., Suhl, U., Busse, A., & Kaiser, G. (2014). Is teachers’ general pedagogical knowledge a premise for noticing and interpreting classroom situations? A video-based assessment approach. Teaching and Teacher Education, 38, 76–88.

    Article  Google Scholar 

  • Lakatos, I. (1970). Falsification and the methodology of scientific research programmes. In I. Lakatos & A. Musgrave (Eds.), Criticism and the growth of knowledge (pp. 91–195). Cambridge University Press.

    Chapter  Google Scholar 

  • Lipshitz, R., Klein, G., Orasanu, J., & Salas, E. (2001). Taking stock of naturalistic decision making. Journal of Behavioral Decision Making, 14(5), 331–352.

    Article  Google Scholar 

  • Mason, J. (2002). The discipline of noticing: Researching your own practice. RoutledgeFalmer.

    Book  Google Scholar 

  • Mason, J. (2017). Probing beneath the surface of experience. In E. O. Schack, M. H. Fisher, & J. A. Wilhelm (Eds.), Teacher noticing: Bridging and broadening perspectives, contexts, and frameworks (pp. 1–17): Springer.

  • Miller, K. F. (2011). Situation awareness in teaching: What educators can learn from video-based research in other feilds. In M. G. Sherin, V. R. Jacobs, & R. A. Philipp (Eds.), Mathematics Teacher Noticing: Seeing Through Teachers' Eyes (pp. 51–65). New York: NY: Routledge.

  • Moors, A., & De Houwer, J. (2007). What is automaticity? An analysis of its component features and their interrelations. In J. A. Bargh (Ed.), Social psychology and the unconscious: The automaticity of higher mental processes (pp. 11–50). Psychology Press.

    Google Scholar 

  • Omodei, M. M., & McLennan, J. (1994). Studying complex decision making in natural settings: Using a head-mounted video camera to study competitive orienteering. Perceptual and Motor Skills, 79, 1411–1425.

    Article  Google Scholar 

  • Omodei, M. M., McLennan, J., & Wearing, A. J. (2005). How expertise is applied in real-world dynamic environments: Head-mounted video and cued recall as a methodology for studying routines in decision making. In T. Betsch & S. Haberstroh (Eds.), The routines of decision making (pp. 271–288). Lawrence Erlbaum.

    Google Scholar 

  • Omodei, M. M., Wearing, A. J., & McLennan, J. (1997). Head-mounted video recording: A methodology for studying naturalistic decision making. In R. Flin, E. Salas, M. Strub, & L. Martin (Eds.), Decision making under stress: Emerging themes and aplications (pp. 137–146). Ashgate.

    Google Scholar 

  • Randel, J. M., Pugh, H. L., & Reed, S. K. (1996). Differences in expert and novice situation awareness in naturalistic decision making. International Journal of Human-Computer Studies, 45(5), 579–597. https://doi.org/10.1006/ijhc.1996.0068

    Article  Google Scholar 

  • Salmon, P. M., Stanton, N. A., Walker, G. H., Baber, C., Jenkins, D. P., McMaster, R., & Young, M. S. (2008). What really is going on? Review of situation awareness models for individuals and teams. Theoretical Issues in Ergonomics Science, 9(4), 297–323. https://doi.org/10.1080/14639220701561775

    Article  Google Scholar 

  • Schack, E. O., Fisher, M. H., & Wilhelm, J. A. (2017). Teacher noticing: Bridging and broadening perspectives, contexts, and frameworks: Springer.

  • Scheiner, T. (2016). Teacher noticing: Enlightening or blinding? ZDM, 48(1), 227–238. https://doi.org/10.1007/s11858-016-0771-2

    Article  Google Scholar 

  • Scheiner, T. (2020). Towards a more comprehensive model of teacher noticing. ZDM. https://doi.org/10.1007/s11858-020-01202-5

    Article  Google Scholar 

  • Schoenfeld, A. H. (2011). Noticing matters. A lot. What now? In M. G. Sherin, V. R. Jacobs, & R. A. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers' eyes. New York: Routledge.

  • Sherin, B., & Star, J. R. (2011). Reflections on the study of teacher noticing. In M. G. Sherin, V. R. Jacobs, & R. A. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 66–78). Routledge.

    Chapter  Google Scholar 

  • Smith, K., & Hancock, P. (1995). Situation awareness is adaptive, externally directed consciousness. Human Factors: THe Journal of the Human Factors and Ergonomics Society, 37(1), 137–148.

    Article  Google Scholar 

  • Stahnke, R., Schueler, S., & Roesken-Winter, B. (2016). Teachers’ perception, interpretation, and decision-making: A systematic review of empirical mathematics education research. ZDM, 48(1–2), 1–27.

    Article  Google Scholar 

  • Uhlarik, J., & Comerford, D. A. (2002). A review of situation awareness literature relevant to pilot surveillance functions. Federal Aviation Adminstration, US Department of Transportation.

    Google Scholar 

  • Yang, X., Kaiser, G., König, J., & Blömeke, S. (2019). Professional noticing of mathematics teachers: A comparative study between Germany and China. International Journal of Science and Mathematics Education, 17(5), 943–963.

    Article  Google Scholar 

  • Yang, X., Kaiser, G., König, J., & Blömeke, S. (2020). Relationship between Chinese mathematics teachers’ knowledge and their professional noticing. International Journal of Science and Mathematics Education. https://doi.org/10.1007/s10763-020-10089-3

    Article  Google Scholar 

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The researcher received financial support via the Science of Learning Research Centre (SLRC), an ARC-funded organisation, as a student member.

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  1. RMIT University, Melbourne, Australia

    Dan Jazby

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  1. Dan Jazby
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Correspondence to Dan Jazby.

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Jazby, D. Conceptualising mathematics teacher noticing as a perception/action cycle. Math Ed Res J 35 (Suppl 1), 133–155 (2023). https://doi.org/10.1007/s13394-021-00392-9

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