Skip to main content
Log in

Awareness as an enactivist framework for the mathematical learning of teachers, mentors and institutions

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

A Correction to this article was published on 15 April 2024

This article has been updated

Abstract

This paper explores the learning of both individuals and organizations within the context of a 3-year professional development program for mathematics and science teachers in a middle school. We propose to extend the notion of awareness from individuals to autonomous systems as a means to study the learning of teachers, mentors, the school, and the organization that provided the program. We describe how the notions of structural determinism and co-evolution through structural coupling informed the enactment of the program, as well as how this perspective informed the design of research on teachers’ experiences of their deepening understanding of mathematics for teaching during this time. Then we elaborate on the levels of awareness developed by teachers, mentors, the school, and the organization as a result of the constant interactions and mutual influence along and beyond the program. Data consisted of post-interviews with eleven mathematics teachers, our own reflections, and the documents generated during the program.

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.

Similar content being viewed by others

Change history

References

  • Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: what makes it special? Journal of Teacher Education, 59(5), 389–407.

    Article  Google Scholar 

  • Brown, L., & Coles, A. (2011). Developing expertise: How enactivism re-frames mathematics teacher development. ZDM—The International Journal on Mathematics Education, 43(6–7), 861–873. doi:10.1007/s11858-011-0343-4.

    Article  Google Scholar 

  • Brown, L., & Coles, A. (2012). Developing “deliberate analysis” for learning mathematics and for mathematics teacher education: How the enactive approach to cognition frames reflection. Educational Studies in Mathematics, 80(1–2), 217–231.

    Article  Google Scholar 

  • Coles, A. (2015). On enactivism and language: towards a methodology for studying talk in mathematics classrooms. ZDM—The International Journal on Mathematics Education , 47(2) (this issue). doi:10.1007/s11858-014-0630-y.

  • Davis, B., & Renert, M. (2014). The math teachers know: Profound understanding of emergent mathematics. New York: Routledge.

    Google Scholar 

  • Davis, B., & Simmt, E. (2003). Understanding learning systems: Mathematics education and complexity science. Journal for Research in Mathematics Education, 34(2), 137–167.

    Article  Google Scholar 

  • Fernandez, C., & Yoshida, M. (2004). Lesson study: A Japanese approach to improving mathematics teaching and learning. Mahwah: Routledge.

    Google Scholar 

  • Fosnot, C., & Dolk, M. (2002). Young mathematicians at work: Constructing fractions, decimals and percents. Portsmouth: Heinemann.

    Google Scholar 

  • Galileo Educational Network Association (2014). Designing for deep mathematical understanding. http://galileo.org/designing-for-deep-math-understanding.pdf. Accessed 27 Nov 2014.

  • Gattegno, C. (1971). What we owe children: The subordination of teaching to learning. London: Routledge.

    Google Scholar 

  • Hewitt, D. (1999). Arbitrary and necessary part 1: A way of viewing the mathematics curriculum. For the Learning of Mathematics, 19(3), 2–51.

    Google Scholar 

  • Jaworski, B. (1999). What does it mean to promote development in teaching? A response to Ron Tzur’s paper: “Becoming a mathematics teacher educator: Conceptualising the terrain through self-reflective analysis”. In O. Zaslavsky (Ed.), Proceedings of the 23rd PME International Conference, Haifa, Israel, 1 (pp. 183–193).

  • Jaworski, B., & Wood, T. (Eds.). (2008). International handbook of mathematics teacher education: The mathematics teacher educator as a developing professional (Vol. 4). Rotterdam: Sense Publishers.

    Google Scholar 

  • Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press.

    Google Scholar 

  • Krainer, K. (1999). Promoting reflection and networking as an intervention strategy in professional development programs for mathematics teacher and mathematics teacher educators. In O. Zaslavsky (Ed.), Proceedings of the 23rd PME International Conference, Haifa, Israel, 1, 159–168.

  • Lerman, S., & Davis, B. (Eds.). (2009). Mathematical action & structures of noticing: Studies on John Mason’s contribution to mathematics education. Rotterdam: Sense Publishers.

    Google Scholar 

  • Lesh, R., & Harel, G. (2003). Problem solving, modeling, and local conceptual development. Mathematical Thinking and Learning, 5(2&3), 157–189.

    Article  Google Scholar 

  • Maheux, J., & Proulx, J. (2015). Doing|mathematics: Analysing data with/in an enactivist-inspired approach. ZDM—The International Journal on Mathematics Education, 47(2) (this issue). doi:10.1007/s11858-014-0642-7.

  • Marton, F. (1981). Phenomenography—Describing conceptions of the world around us. Instructional Science, 10, 177–200.

    Article  Google Scholar 

  • Marton, F., & Booth, S. (1997). Learning and awareness. Mahwah: Erlbaum.

    Google Scholar 

  • Mason, J. (1998). Enabling teachers to be real teachers: Necessary levels of awareness and structure of attention. Journal of Mathematics Teacher Education, 1(3), 243–267.

    Article  Google Scholar 

  • Mason, J. (2002). Researching your own practice: From noticing to reflection. London: Routledge.

    Book  Google Scholar 

  • 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). New York: Routledge.

    Google Scholar 

  • Mason, J., Burton, L., & Stacey, K. (2010). Thinking mathematically (2nd ed.). London: Prentice Hall.

    Google Scholar 

  • Maturana, H. R., & Varela, F. J. (1998). The tree of knowledge: The biological roots of human understanding. Boston: Shambhala.

    Google Scholar 

  • Metz, M., Preciado-Babb, A. P., & Marcotte, C. (2014). Designing for deep mathematical understanding: reflections on the design and implementation of a framework for teachers In A. P. Preciado-Babb, A. Solares Rojas, & K. Francis (Eds.), What, how and why: An international conversation on mathematics teacher learning. Mexico City: Universidad Pedagógica Nacional (in press).

  • Metz, M., & Simmt, E. (2015). Researching mathematical experience from the perspective of an empathic second-person observer. ZDM—The International Journal on Mathematics Education, 47(2) (this issue). doi:10.1007/s11858-014-0621-z.

  • Meyer, D. (2014). dy/dan: Less helpful. http://blog.mrmeyer.com. Accessed 27 Nov 2014.

  • Preciado-Babb, A. P., Metz, M., & Marcotte, C. (2013). A phenomenological study of teachers’ professional learning and their understanding of mathematics-for-teaching. In A. P. Preciado-Babb, A. Solares Rojas, I. T. Sandoval Cáceres, & C. Butto Zarzar (Eds.), Proceedings of the First Meeting between the National Pedagogic University and the Faculty of Education of the University of Calgary (pp. 79–84). Calgary: Faculty of Education of the University of Calgary. http://dspace.ucalgary.ca/handle/1880/49736. Accessed 27 Nov 2014.

  • Reid, D. (2002). Conjectures and refutations in grade 5 mathematics. Journal for Research in Mathematics Education, 33(1), 5–29.

    Article  Google Scholar 

  • Reid, D., & Mgombelo, J. (2015). Survey of key concepts in enactivist theory and methodology. ZDM—The International Journal on Mathematics Education, 47(2) (this issue). doi:10.1007/s11858-014-0634-7.

  • Rowland, T., Turner, F., & Thwaites, A. (2014). Research into teacher knowledge: a stimulus for development in mathematics teacher education practice. ZDM—The International Journal on Mathematics Education, 46(2), 317–328. doi:10.1007/s11858-013-0564-9.

    Article  Google Scholar 

  • Sakonidis, C., & Potari, D. (2014). Mathematics teacher educators’/researchers’ collaboration with teachers as a context for professional learning. ZDM—The International Journal on Mathematics Education, 46(2), 293–304. doi:10.1007/s11858-014-0569-z.

    Article  Google Scholar 

  • Steinbring, H. (1998). Elements of epistemological knowledge for mathematics teachers. Journal of Mathematics Teacher Education, 1(2), 157–189.

    Article  Google Scholar 

  • Steinbring, H. (2015). Mathematical interaction shaped by communication, epistemological constraints and enactivism. ZDM—The International Journal on Mathematics Education, 47(2) (this issue). doi:10.1007/s11858-014-0629-4.

  • Thompson, E., & Stapleton, M. (2009). Making sense of sense-making: Reflections on enactive and extended mind theories. Topoi, 28, 23–30.

    Article  Google Scholar 

  • Towers, J., Martin, L. C., & Heater, B. (2013). Teaching and learning mathematics in the collective. The Journal of Mathematical Behavior, 32(3), 424–433. doi:10.1016/j.jmathb.2013.04.005.

    Article  Google Scholar 

  • Varela, F. J. (1999). Ethical know-how: Action, wisdom, and cognition. Stanford: Stanford University Press.

    Google Scholar 

  • Varela, F., & Shear, J. (1999). The view from within: First person approaches to the study of consciousness. Bowling Green: Imprint Academic.

    Google Scholar 

  • Varela, F. J., Thompson, E., & Rosh, E. (1991). The embodied mind: Cognitive science and human experience. Cambridge: The MIT Press.

    Book  Google Scholar 

  • Zaslavsky, O., & Leikin, R. (1999). Interviewing the training of mathematics teacher-educators and the professional development of mathematics teachers. In O. Zaslavsky (Ed.), Proceedings of the 23rd PME International Conference, Haifa, Israel, 1, 141–158.

  • Zazkis, R., Sinclair, N., & Liljedahl, P. (2009). Lesson play: a vehicle for multiple shifts of attention in teaching. In B. Davis & S. Lerman (Eds.), Mathematical action & structures of noticing: Studies on John Mason’s contribution to mathematics education (pp. 165–177). Rotterdam: Sense Publishers.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Armando Paulino Preciado Babb.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Preciado Babb, A.P., Metz, M. & Marcotte, C. Awareness as an enactivist framework for the mathematical learning of teachers, mentors and institutions. ZDM Mathematics Education 47, 257–268 (2015). https://doi.org/10.1007/s11858-014-0657-0

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11858-014-0657-0

Keywords

Navigation