Skip to main content

Advertisement

Log in

Prospective mathematics teachers’ development of noticing in an online teacher education program

  • Original Article
  • Published:
ZDM Aims and scope Submit manuscript

Abstract

In this study we aimed to characterize the development of prospective mathematics teachers’ noticing in an online teacher education program. Prospective teachers wrote narratives about their own teaching during their traineeship period at schools, and shared them with their colleagues and with the university tutor in an online forum. A narrative is a description of a teaching–learning situation that incorporates reasons about what has happened during the teaching, and justifications of plausible future teaching actions. We analyzed changes in the prospective teachers’ narratives by scrutinizing how prospective teachers identify Mathematically Significant Pedagogical Opportunities to Build on Student Thinking (MOSTs) and in which ways they take advantage of them. Additionally, we analyzed whether these changes could be related to the feedback provided in the online forum. The findings indicate changes in how prospective teachers notice their practice, evidenced by the manner in which the MOSTs are taken advantage of, and by the reasons given for their actions. These findings suggest that sharing narratives in online forums and receiving feedback from their colleagues and from the university tutor help prospective teachers to enhance the skill of noticing, leading to changes in their practice. This research provides new knowledge about how online contexts in teacher education programs promote opportunities for collaborative learning, noticing development, and changes in teachers’ practices.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  • Amador, J. (2019). Noticing as a tool to analyze mathematics instruction and learning. In S. Llinares & O. Chapman (Eds.), International handbook of mathematics teacher education: Tools and processes in mathematics teacher education. Rotterdam: Sense Publishers.

    Google Scholar 

  • Borba, M. C., Askar, P., Engelbrecht, J., Gadanidis, G., Llinares, S., & Aguilar, M. S. (2016). Blended learning, e-learning and mobile learning in mathematics education. ZDM Mathematics Education, 48(5), 589–610.

    Google Scholar 

  • Borba, M. C., Chiari, A. S. S., & Almeida, H. R. F. L. (2018). Interactions in virtual learning environments: New roles for digital technology. Educational Studies in Mathematics, 98(3), 269–286.

    Google Scholar 

  • Borba, M. C., Clarkson, P., & Gadanidis, G. (2013). Learning with the use of the Internet. In M. A. K. Clements, A. Bishop, C. Keite-Kreidt, J. Kilpatrick, & F. K. Leung (Eds.), Third international handbook of mathematics education (pp. 691–720). London: Springer.

    Google Scholar 

  • Borba, M. C., & Llinares, S. (2012). Online mathematics teacher education: Overview of an emergent field of research. ZDM The International Journal on Mathematics Education, 44(6), 697–704.

    Google Scholar 

  • Buhagiar, M. (2013). Mathematics student teachers’ views on tutor feedback during teaching practice. European Journal of Teacher Education, 36(1), 55–67.

    Google Scholar 

  • Cavanagh, M., & McMaster, H. (2015). A professional experience learning community for secondary mathematics: Developing pre-service teachers’ reflective practice. Mathematics Education Research Journal, 27(4), 471–490.

    Google Scholar 

  • Chapman, O. (2008). Narratives in mathematics teacher education. In D. Tirosh & T. Wood (Eds.), International handbook of mathematics teacher education: Tools and processes in mathematics teacher education (pp. 15–38). Rotterdam: Sense Publishers.

    Google Scholar 

  • Clay, E., Silverman, J., & Fisher, D. (2012). Unpacking online asyncronous collaboration in mathematics teacher education. ZDM Mathematics Education, 44, 761–773.

    Google Scholar 

  • Coll, C., Rochera, M. J., & de Gispert, I. (2014). Supporting online collaboration learning in small groups: Teacher feedback on learning content, academic task and social participation. Computers and Education, 75, 53–64.

    Google Scholar 

  • Doyle, W., & Cater, K. (2003). Narrative and learning to teach: Implications for teacher-education curriculum. Journal of Curriculum Studies, 35(2), 129–137.

    Google Scholar 

  • Fenstermacher, G., & Richardson, V. (1993). The elicitation and reconstruction of practical arguments in teaching. Journal of Curriculum Studies, 25(2), 101–114.

    Google Scholar 

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

    Google Scholar 

  • Fernández, C., Sánchez-Matamoros, G., Valls, J., & Callejo, M. L. (2018). Noticing students’ mathematical thinking: Characterization, development and contexts. Avances de Investigación en Educación Matemática, 13, 39–61.

    Google Scholar 

  • Hattie, J., & Timperley, H. (2007). The power of feedback. Review of Educational Research, 77(1), 81–112.

    Google Scholar 

  • Huisman, B., Saab, N., van den Broek, P., & van Driel, J. (2019). The impact of formative peer feedback on higher education students’ academic writing: A meta-analysis. Assessment and Evaluation in Higher Education, 44(6), 863–880.

    Google Scholar 

  • Ivars, P., & Fernández, C. (2018). The role of writing narratives in developing pre-service elementary teachers’ noticing. In G. J. Stylianides & K. Hino (Eds.), Research advances in the mathematical education of pre-service elementary teachers, ICME-13 Monographs (pp. 245–259). London: Springer.

    Google Scholar 

  • Leatham, K., Peterson, B., Stokero, Sh, & Van Zoest, L. (2015). Conceptualizaing mathematically significant pedagogical opportunities to build on student thinking. Journal for Research in Mathematics Education, 46(1), 88–124.

    Google Scholar 

  • Llinares, S., & Valls, J. (2009). The building of preservice primary teachers’ knowledge of mathematics teaching: Interaction and online video case studies. Instructional Science, 37(3), 247–271.

    Google Scholar 

  • Llinares, S., & Valls, J. (2010). Prospective primary mathematics teachers’ learning from on-line discussions in a virtual-based environment. Journal of Mathematics Teacher Education, 13(2), 177–196.

    Google Scholar 

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

    Google Scholar 

  • Narciss, S. (2013). Designing and evaluating tutorial feedback strategies for digital learning environments on the basis of the Interactive Tutorial Feedback Model. Digital Education Review, 23(1), 7–26.

    Google Scholar 

  • Philpott, C. (2014). Socioculturally situated narratives as co-authors of student teachers’ learning from experience. Teaching Education, 25(4), 391–409.

    Google Scholar 

  • Polkinghorne, D. E. (1988). Narrative knowing and the human sciences. Albany: Suny Press.

    Google Scholar 

  • Ponte, J. P., et al. (2009). Tools and settings supporting mathematics teaches’ learning in and from practice. In R. Even & D. L. Ball (Eds.), The professional education and development of teachers of mathematics. The 15th ICMI study (pp. 185–209). New York: Springer.

    Google Scholar 

  • Pulvermacher, Y., & Lefstein, A. (2016). Narrative representations of practice: What and how can student teachers learn from them? Teaching and Teacher Education, 55, 255–266.

    Google Scholar 

  • Rohads, K., Radu, J., & Weber, K. (2011). The teacher internship experiences of prospective high school mathematics teachers. International Journal of Science and Mathematics Education, 9, 999–1022.

    Google Scholar 

  • Rowland, T., & Zazkis, R. (2013). Contingency in mathematics classroom: Opportunities taken and opportunities missed. Canadian Journal of Science, Mathematics and Technology Education, 13(2), 137–153.

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  • Silverman, J. (2012). Exploring the relationships between teachers prominence in online collaboration and the development of mathematical content knowledge for teaching. Journal of Technology and Teacher Education, 20(1), 47–69.

    Google Scholar 

  • Stockero, S. L., & Van Zoest, L. R. (2013). Characterizing pivotal teaching moments in beginning mathematics teachers’ practice. Journal of Mathematics Teacher Education, 16(2), 125–147.

    Google Scholar 

  • Teuscher, D., Leatham, K., & Peterson, B. E. (2017). From a framework to a lens: Learning to notice student mathematical thinking. In E. O. Schack, et al. (Eds.), Teacher noticing: Bringing and broadening perspectives, contexts, and frameworks (pp. 31–48). London: Springer.

    Google Scholar 

  • Van der Pol, J., van der Berg, B. A. M., Admiraal, W. F., & Simons, P. R. J. (2008). The nature, reception, and use of online peer feedback in higher education. Computers and Education, 51(4), 1804–1817.

    Google Scholar 

  • Wang, Z., Gong, Sh, Xu, S., & Hu, X. (2019). Elaborated feedback and learning: Examining cognitive and motivational influences. Computers and Education, 136(1), 130–140.

    Google Scholar 

  • Wells, G. (1999). Dialogic inquiry: Towards a sociocultural practice and theory of education. Cambridge: Cambridge University Press.

    Google Scholar 

  • Yang, S. (2016). Conceptualizing effective feedback practice through an online community of inquiry. Computers and Education, 94, 162–177.

    Google Scholar 

  • Zhu, Q., & Carless, D. (2018). Dialogue within peer feedback processes: Clarification and negotiation of meaning. Higher Education Research and Development, 37(4), 883–897.

    Google Scholar 

Download references

Acknowledgements

This research was supported by the project EDU2017-87411-R from the Ministerio of Economia, Industria y Competitividad (Spain), by the project PROMETEO2017-135 from Conselleria de Educación, Investigación, Cultura y Deporte de la Generalitat Valenciana (Spain) and by the grant UCPI-IN6-007-2017 of the Universidad Estatal a Distancia (UNED) de Costa Rica.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ceneida Fernández.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fernández, C., Llinares, S. & Rojas, Y. Prospective mathematics teachers’ development of noticing in an online teacher education program. ZDM Mathematics Education 52, 959–972 (2020). https://doi.org/10.1007/s11858-020-01149-7

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11858-020-01149-7

Keywords

Navigation