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Exploring change in secondary mathematics teachers' noticing of argumentation through experiencing peer-assessment strategies

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Abstract

This study examines changes in secondary mathematics teachers' noticing of argumentation through experiencing a peer-assessment cycle. Sixty-one teachers participated in such a cycle comprised of (a) analyzing a written argumentation classroom situation (ACS) using a report format, (b) collaboratively assessing peers' ACS-reports using an ACS rubric format and providing feedback to peers, (c) receiving feedback from peers and individually refining the initial ACS-reports, and (d) reflecting on their experience. Analysis of teachers' initial and refined ACS-reports revealed changes in teachers’ noticing of various dimensions associated with argumentation. Analysis of teachers' written reflections and semi-structured interviews provided insights into the characteristics of the experience that supported or inhibited the change in their noticing of argumentation, from their perspective. The study provides evidence of the potential of the peer-assessment-cycle process for teachers' learning to notice key aspects of argumentation.

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  • 20 August 2023

    The original online version of this article was revised”: The position of tables and figures have been revised.

References

  • Asterhan, C. S. C., & Schwarz, B. B. (2016). Argumentation for learning: Well-trodden paths and unexplored territories. Educational Psychologist, 51(2), 164–187.

    Article  Google Scholar 

  • Ayalon, M. (2019). Exploring change in teachers’ attention to potential teaching situations of argumentation. Teaching and Teacher Education, 85, 190–203.

    Article  Google Scholar 

  • Ayalon, M., & Even, R. (2016). Factors shaping students’ opportunities to engage in argumentative activity. International Journal of Science and Mathematics Education, 14, 575–601.

    Article  Google Scholar 

  • Ayalon, M., & Hershkowitz, R. (2018). Mathematics teachers’ attention to potential classroom situations of argumentation. Journal of Mathematical Behavior., 49, 163–173.

    Article  Google Scholar 

  • Ayalon, M., & Nama, S. (First online). Secondary mathematics teachers’ envisioning of potential argumentation situations in the classroom. Research in Mathematics Education.

  • Ayalon, M. (under revision). Mathematics teachers’ noticing of argumentation: A framework for developing and investigating teachers’ proficiency in promoting argumentation in the mathematics classroom.

  • Ayalon, M., & Wilkie, K. J. (2020). Investigating peer-assessment strategies for mathematics pre-service teacher learning on formative assessment. Journal of Mathematics Teacher Education, 24(4), 399–426.

    Article  Google Scholar 

  • Ayalon, M., Wilkie, K., & Hajjar, K. (2022). Relating students’ emotions during argumentative discourse to their learning of real-life functional situations. Educational Studies in Mathematics, 6, 66.

    Google Scholar 

  • Ball, D. L., & Forzani, F. M. (2009). The work of teaching and the challenge for teacher education. Journal of Teacher Education, 60(5), 497–511.

    Article  Google Scholar 

  • Ball, D. L., & Bass, H. (2003). Making mathematics reasonable in school. In G. Martin (Ed.), Research compendium for the principles and standards for school mathematics (pp. 27–44). National Council of Teachers of Mathematics.

  • Barnhart, T., & van Es, E. A. (2015). Learning to analyze teaching: Developing pre-service science teachers’ abilities to notice, analyze and respond to student thinking. Teaching and Teacher Education, 45, 83–93.

    Article  Google Scholar 

  • Bas-Ader, S., Erbas, A. K., Cetinkaya, B., Alacaci, C., & Cakiroglu, E. (2021). Secondary mathematics teachers’ noticing of students’ mathematical thinking through modeling-based teacher investigations. Mathematics Education Research Journal, 66, 1–26.

    Google Scholar 

  • Bieda, K. N. (2010). Enacting proof-related tasks in middle school mathematics: Challenges and opportunities. Journal for Research in Mathematics Education, 41(4), 351–382.

    Article  Google Scholar 

  • Bieda, K. N., Ji, X., Drwencke, J., & Picard, A. (2014). Reasoning-and-proving opportunities in elementary mathematics textbooks. International Journal of Educational Research, 64, 71–80.

    Article  Google Scholar 

  • Biza, I., Nardi, E., & Zhachariades, T. (2007). Using tasks to explore teacher knowledge in situation-specific contexts. Journal of Mathematics Teacher Education, 10, 301–309.

    Article  Google Scholar 

  • Black, P., & Wiliam, D. (2009). Developing the theory of formative assessment. Educational Assessment, Evaluation and Accountability, 21(1), 5–31.

    Article  Google Scholar 

  • Black, P., Harrison, C., Lee, C., Marshal, B., & Wiliam, D. (2003). Assessment for learning: Putting it into practice. Open University Press.

    Google Scholar 

  • Borko, H., Jacobs, J. K., Eiteljorg, E., & Pittman, M. E. (2008). Video as a tool for fostering productive discussions in mathematics professional development. Teaching and Teacher Education, 24(2), 417–436.

    Article  Google Scholar 

  • Borko, H., Koellner, K., Jacobs, J., & Seago, N. (2011). Using video representations of teaching in practice based professional development programs. ZDM Mathematics Education, 43(1), 175–187.

    Article  Google Scholar 

  • Brown, G. T. L., & Harris, L. R. (2013). Student self-assessment. In J. H. McMillan (Ed.), The Sage handbook of research on classroom assessment (pp. 367–393). Sage.

    Chapter  Google Scholar 

  • Chazan, D. (1993). High school geometry students’ justification for their views of empirical evidence and mathematical proof. Educational Studies in Mathematics, 24(4), 359–387.

    Article  Google Scholar 

  • Chazan, D., Herbst, P., & Clark, L. (2016). Research on the teaching of mathematics: A call to theorize the role of society and schooling in mathematics. In D. Gitomer & C. Bell (Eds.), Handbook of research on teaching (5th ed., pp. 1039–1097). AERA.

    Chapter  Google Scholar 

  • Cohen, J. (1988). Statistical power analysis Jbr the behavioral (pp. 18–74). Lawrence Erlbaum.

  • Common Core State Standards Initiative (CCSSI). (2010). Common Core State Standards for Mathematics. Retrieved from http://corestandards.org/asserts/CCSSI_Math%20Standards.pdf

  • Conner, A., Singletary, L. M., Smith, R. C., Wagner, P. A., & Francisco, R. T. (2014). Teacher support for collective argumentation: A framework for examining how teachers support students’ engagement in mathematical activities. Educational Studies in Mathematics, 86, 401–429.

    Article  Google Scholar 

  • Creswell, J. W. (2007). Qualitative inquiry and research design: Choosing among five approaches (2nd ed.). Sage.

    Google Scholar 

  • Davis, P. J., & Hersh, R. (1981). The mathematical experience. Birkhäuser.

    Google Scholar 

  • Felton, M., Garcia-Mila, M., & Gilabert, S. (2009). Deliberation versus dispute: The impact of argumentative discourse goals on learning and reasoning in the science classroom. Informal Logic, 29, 417–446.

    Article  Google Scholar 

  • Francisco, J. M., & Maher, C. A. (2005). Conditions for promoting reasoning in problem solving: Insights from a longitudinal study. Journal of Mathematical Behavior, 24, 361–372.

    Article  Google Scholar 

  • Francisco, N. P., & Maher, C. (2011). Teachers attending to students’ mathematical reasoning: Lessons from an after-school research program. Journal of Mathematics Teacher Education, 14, 49–66.

    Article  Google Scholar 

  • González, G., & Skultety, L. (2018). Teacher learning in a combined professional development intervention. Teaching and Teacher Education, 71, 341–354.

    Article  Google Scholar 

  • Hanrahan, S. J., & Isaacs, G. (2001). Assessing self-and peer-assessment: The students’ views. Higher Education Research & Development, 20(1), 53–70.

    Article  Google Scholar 

  • Hattie, J., & Timperley, H. (2007). The power of feedback. Review of Educational Research, 77, 81–112.

    Article  Google Scholar 

  • Huberman, M. (1995). Networks that alter teaching: Conceptualizations, exchanges and experiments. Teachers and Teaching, 1(2), 193–211.

    Article  Google Scholar 

  • Israel Ministry of Education. (2019). Mathematics Curriculum for Grades 7–9. Retrieved from http://meyda.education.gov.il/files/Mazkirut_Pedagogit/matematika/mavo.pdf (in Hebrew)

  • Jacobs, J., Hiebert, J., Givvin, K., Hollingsworth, H., Garnier, H., & Wearne, D. (2006). Does eighth-grade mathematics teaching in the United States align with the NCTM Standards? Results from the TIMSS 1999 video studies. Journal for Research in Mathematics Education, 37(1), 5–32.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Jiménez-Aleixandre, M. P., & Erduran, S. (2008). Argumentation in science education: An overview. In S. Erduran & M. P. Jiménez-Aleixandre (Eds.), Argumentation in science education: Perspectives from classroom-based research (pp. 3–28). Springer.

    Google Scholar 

  • Kennedy, M. (2016). Parsing the practice of teaching. Journal of Teacher Education, 67(1), 6–17.

    Article  Google Scholar 

  • Knuth, E. J., & Sutherland, J. (2004). Student understanding of generality. In D. E. McDougall & J. A. Ross (Eds.), Proceedings of the 26th annual meeting of the North American chapter of the international group for the psychology of mathematics education (vol. 2, pp. 561–567). OISE/UT.

  • König, J., Santagata, R., Scheiner, T., Adleff, A.-K., Yang, X., & Kaiser, G. (2022). Teacher noticing: A systematic literature review on conceptualizations, research designs, and findings on learning to notice. Educational Research Review, 66, 100453.

    Article  Google Scholar 

  • Kosko, K. W., Rougee, A., & Herbst, P. (2014). What actions do teachers envision when asked to facilitate mathematical argumentation in the classroom? Mathematics Education Research Journal, 26, 459–476.

    Article  Google Scholar 

  • Krummheuer, G. (2007). Argumentation and participation in the primary mathematics classroom. Two episodes and related theoretical abductions. Journal of Mathematical Behavior, 26(1), 60–82.

    Article  Google Scholar 

  • Lave, J. (1996). Teaching, as learning, in practice. Mind, Culture and Activity, 3(3), 149–164.

    Article  Google Scholar 

  • Lincoln, Y. S. (1995). Emerging criteria for quality in qualitative and interpretive research. Qualitative Inquiry, 1(3), 275–289.

    Article  Google Scholar 

  • Martino, A. M., & Maher, C. A. (1999). Teacher questioning to promote justification and generalization in mathematics: What research practice has taught us. The Journal of Mathematical Behavior, 18(1), 53–78.

    Article  Google Scholar 

  • McNeill, K. L., & Pimentel, D. S. (2010). Scientific discourse in three urban classrooms: The role of the teacher in engaging high school students in argumentation. Science Education, 94(2), 203–229.

    Google Scholar 

  • Melhuish, K., Thanheiser, E., & Fagan, J. (2019). The student discourse observation tool: Supporting teachers in noticing justifying and generalizing. Mathematics Teacher Educator, 7(2), 57–74.

    Article  Google Scholar 

  • Melhuish, K., Thanheiser, E., & Guyot, L. (2020). Elementary school teachers’ noticing of essential mathematical reasoning forms: Justification and generalization. Journal of Mathematics Teacher Education, 23, 35–67.

    Article  Google Scholar 

  • Meschede, N., Fiebranz, A., Möller, K., & Stefensky, M. (2017). Teachers’ professional vision, pedagogical content knowledge and beliefs: On its relation and differences between pre-service and in-service teachers. Teaching and Teacher Education, 66, 158–170.

    Article  Google Scholar 

  • Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook. Sage.

  • Mitchell, R. N., & Marin, K. A. (2015). Examining the use of a structured analysis framework to support prospective teacher noticing. Journal of Mathematics Teacher Education, 18(6), 551–575.

    Article  Google Scholar 

  • Mueller, M., Yankelewitz, D., & Maher, C. (2012). A framework for analyzing the collaborative construction of arguments and its interplay with agency. Educational Studies in Mathematics, 80, 369–387.

    Article  Google Scholar 

  • Mueller, M., Yankelewitz, D., & Maher, C. (2014). Teachers promoting student mathematical reasoning. Investigations in Mathematics Learning, 7(2), 1–20.

    Article  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 

  • Reinholz, D. (2016). The assessment cycle: A model for learning through peer assessment. Assessment & Evaluation in Higher Education, 41(2), 301–315.

    Article  Google Scholar 

  • Rotem, S. H., & Ayalon, M. (2023). Changes in noticing multiple dimensions in classroom situations among pre-service mathematics teachers. Teaching and Teacher Education, 121, 103932.

    Article  Google Scholar 

  • Sadler, D. R. (1998). Formative assessment: Revisiting the territory. Assessment in Education: Principles, Policy & Practice, 5(1), 77–84.

    Google Scholar 

  • Santagata, R. (2011). From teacher noticing to a framework for analyzing and improving classroom lessons. In M. Sherin, V. Jacobs, & P. Randy (Eds.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 152–168). Routledge.

  • Santagata, R., Zannoni, C., & Stigler, J. W. (2007). The role of lesson analysis in pre-service teacher education: An empirical investigation of teacher learning from a virtual video-based field experience. Journal of Mathematics Teacher Education, 10(2), 123–140.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Scheiner, T. (2021). Towards a more comprehensive model of teacher noticing. ZDM-Mathematics Education, 53(1), 85–94.

    Article  Google Scholar 

  • Scherrer, J., & Stein, M. K. (2013). Effects of a coding intervention on what teachers learn to notice during whole-group discussion. Journal of Mathematics Teacher Education, 16(2), 105–124.

    Article  Google Scholar 

  • Schoenfeld, A. (2011). Noticing matters. A lot. Now what? In M. G. Sherin, V. R. Jacobs, & R. A. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers’ eyes. Routledge.

  • Schwarz, B. B., & Baker, M. J. (2017). Dialogue: Argumentation and education: History, theory and practice. Cambridge University Press.

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

    Article  Google Scholar 

  • Sherin, M. G., Jacobs, V. R., & Philipp, R. (2011a). Mathematics teacher noticing: Seeing through teachers’ eyes. Routledge.

    Book  Google Scholar 

  • Sherin, M. G., Russ, R. S., & Colestock, A. A. (2011b). Accessing mathematics teachers’ in-the-moment noticing. In M. G. Sherin, V. R. Jacobs, & R. A. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 79–94). Routledge.

    Chapter  Google Scholar 

  • Shulman, L. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14.

    Article  Google Scholar 

  • Slakmon, B., & Schwarz, B. B. (2019). Deliberative emotional talk. International Journal of Computer Supported Collaborative Learning, 14(2), 185–217.

    Article  Google Scholar 

  • Smith, H., Cooper, A., & Lancaster, L. (2002). Improving the quality of undergraduate peer assessment: A case for student and staff development. Innovations in Education and Teaching International, 39, 71–81.

    Article  Google Scholar 

  • Solar, H., Ortiz, A., Deulofeu, J., & Ulloa, R. (2020). Teacher support for argumentation and the incorporation of contingencies in mathematics classrooms. International Journal of Mathematical Education in Science and Technology, 52(7), 977–1005.

    Article  Google Scholar 

  • Sriraman, B., & Umland, K. (2020). Argumentation in mathematics education. In S. Lerman (Ed.), Encyclopedia of Mathematics Education (pp. 63–66). Springer.

    Chapter  Google Scholar 

  • Staples, M. (2014). Supporting student justification in middle school mathematics classrooms: Teachers' work to create a context for justification. CRME Publications 4. Retrieved from: http://digitalcommons.uconn.edu/merg_docs/4

  • Staples, M. E., Bartlo, J., & Thanheiser, E. (2012). Justification as a teaching and learning practice: Its (potential) multifaceted role in middle grades mathematics classrooms. The Journal of Mathematical Behavior, 31, 447–462.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Staples, M., & Conner, A. (2022). Introduction: Conceptualizing argumentation, justification, and proof in mathematics education. In Conceptions and consequences of mathematical argumentation, justification, and proof (pp. 1–10). Springer.‏

  • Staples, M., & Newton, J. (2016). Teachers’ contextualization of argumentation in the mathematics classroom. Theory into Practice, 55(4), 294–301.

    Article  Google Scholar 

  • Star, J. R., Lynch, K., & Perova, N. (2011). Using video to improve preservice mathematics teachers’ abilities to attend to classroom features. In M. G. Sherin, V. R. Jacobs, & R. A. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 117–133). Routledge.

    Google Scholar 

  • Stein, N. L., & Albro, E. R. (2001). The origins and nature of arguments: Studies in conflict understanding, emotion, and negotiation. Discourse Processes, 32(2–3), 113–133.

    Article  Google Scholar 

  • Stockero, S. L., Rupnow, R. L., & Pascoe, A. E. (2017). Learning to notice important student mathematical thinking in complex classroom interactions. Teaching and Teacher Education, 63, 384–395.

    Article  Google Scholar 

  • Swan, M., & Burkhardt, H. (2012). Designing assessment of performance in mathematics. Educational Designer: Journal of the International Society for Design and Development in Education, 2(5), 1–41.

    Google Scholar 

  • Topping, K. J. (1998). Peer assessment between students in colleges and universities. Review of Educational Research, 68, 249–276.

    Article  Google Scholar 

  • Topping, K. J. (2010). Peers as a source of formative assessment. In H. Andrade & G. J. Cizek (Eds.), Handbook of formative assessment (pp. 61–74). Routledge.

    Google Scholar 

  • Topping, K. J., & Ehly, S. (Eds.). (1998). Peer-assisted learning. Erlbaum.

    Google Scholar 

  • van Eemeren, F. H., & Grootendorst, R. (2004). A systematic theory of argumentation. Cambridge University Press.

    Google Scholar 

  • van Es, E. A. (2011). A framework for learning to notice student thinking. In M. G. Sherin, V. Jacobs, & R. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 134–151). Routledge.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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, 165–187.

    Article  Google Scholar 

  • Weber, K., Maher, C., Powell, A., & Lee, H. (2008). Learning opportunities from group discussions: Warrants become the objects of debate. Educational Studies in Mathematics, 68(3), 247–261.

    Article  Google Scholar 

  • Yackel, E. (2002). What we can learn from analysing the teacher’s role in collective argumentation. Journal of Mathematical Behavior, 21(4), 423–440.

    Article  Google Scholar 

  • Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation and autonomy in mathematics. Journal for Research in Mathematics Education, 27(4), 458–477.

    Article  Google Scholar 

  • Yang, M., Badger, R., & Yu, Z. (2006). A comparative study of peer and teacher feedback in a Chinese EFL writing class. Journal of Second Language Writing, 15, 179–200.

    Article  Google Scholar 

  • Yang, X., König, J., & Kaiser, G. (2021). Growth of professional noticing of mathematics teachers: A comparative study of Chinese teachers noticing with different teaching experiences. ZDM–Mathematics Education, 53, 29–42.

    Article  Google Scholar 

  • Zevenbergen, R. (2001). Peer assessment of student constructed posters: Assessment alternatives in preservice mathematics education. Journal of Mathematics Teacher Education, 4, 95–113.

    Article  Google Scholar 

  • Zhuang, Y., & Conner, A. (2022). Secondary mathematics teachers’ use of students’ incorrect answers in supporting collective argumentation. Mathematical Thinking and Learning, 26, 1–24.

    Article  Google Scholar 

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  1. University of Haifa, Haifa, Israel

    Samaher Nama & Michal Ayalon

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“The original online version of this article was revised”: The position of tables and figures have been revised.

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Nama, S., Ayalon, M. Exploring change in secondary mathematics teachers' noticing of argumentation through experiencing peer-assessment strategies. J Math Teacher Educ (2023). https://doi.org/10.1007/s10857-023-09586-3

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