Skip to main content
SpringerLink
Log in

Students and teachers mobilizing mathematical concepts through reciprocal noticing

  • Original Paper
  • Published:
ZDM – Mathematics Education Aims and scope Submit manuscript

Abstract

This article elaborates a theoretical, methodological, and analytical approach intended to highlight the materiality and reciprocity of noticing in mathematics classrooms. Drawing from highly resonant concepts from materialism and Indigenous Knowledges—two perspectives that researchers rarely bring into dialogue—this alternative approach explores the reciprocal, material, and more-than-human nature of noticing. By focusing on the role of movement in noticing, the approach discusses the indivisibility of sensing and making sense as students and teachers mobilize mathematical concepts. Applying this approach in a non-traditional analysis of two classroom episodes, the paper provides a discussion centered on what noticing looks like when humans are decentered, concepts are mobilized, and sensing meets making sense.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Abrahamson, D., & Sánchez-García, R. (2016). Learning is moving in new ways: The ecological dynamics of mathematics education. Journal of the Learning Sciences, 25, 203–239.

    Article  Google Scholar 

  • Alsawaie, O. N., & Alghazo, I. M. (2010). The effect of video-based approach on prospective teachers’ ability to analyze mathematics teaching. Journal of Mathematics Teacher Education, 13(3), 223–241.

    Article  Google Scholar 

  • Argüelles, J. (1987). The Mayan factor: Path beyond technology. Santa Fe: Bear & Company.

    Google Scholar 

  • Bakhtin, M. (1990). Author and hero in aesthetic activity (V. Liapunov, trans.). In M. Holquist & V. Liapunov (Eds.), Art and answerability: Early philosophical essays (pp. 4–256). Austin: University of Texas Press.

    Chapter  Google Scholar 

  • Ball, D. L. (1992). Magical hopes: Manipulatives and the reform of math education. American Educator, 16(2), 14–18.

    Google Scholar 

  • Barad, K. (2003). Posthumanist performativity: Towards an understanding of how matter comes to matter. Signs: Journal of Women in Culture and Society, 28(3), 801–831.

    Article  Google Scholar 

  • Barad, K. (2007). Meeting the universe halfway: Quantum physics and the entanglement of matter and meaning. Durham: Duke University Press.

    Book  Google Scholar 

  • Barad, K. (2010). Quantum entanglements and hauntological relations of inheritance: Dis/continuities, spacetime enfoldings, and justice-to-come. Derrida Today, 3(2), 240–268.

    Article  Google Scholar 

  • Barad, K. (2012). On touching: The inhuman that therefore I am. Differences: A Journal of Cultural Feminist Studies, 23(3), 206–223.

    Article  Google Scholar 

  • Barnhardt, R., & Kawagley, A. O. (2008). Indigenous Knowledge systems and Alaskan Native ways of knowing. Anthropology and Education Quarterly, 36(1), 8–23.

  • Bennett, J. (2010). Vibrant matter: A political ecology of things. Durham: Duke University Press.

    Book  Google Scholar 

  • Bodén, L., Lenz Taguchi, H., Moberg, E., & Taylor C. A. (2019). Relational materialism. In Oxford research encyclopedia of education. Oxford University Press. https://doi.org/10.1093/acrefore/9780190264093.013.789.

  • Boylan, M. (2017). Towards a mathematics education for ecological selves: Pedagogies for relational knowing and being. Philosophy of Mathematics Education Journal, 32, 1–15.

    Google Scholar 

  • Cajete, G. (2000). Native science: Natural laws of interdependence. Santa Fe: Clear Light Publishers.

    Google Scholar 

  • Châtelet, G. (2000). Figuring space: Philosophy, mathematics and physics (trans. Robert Shore and Muriel Zagha). Dordrecht: Kluwer Academic Publishers.

    Book  Google Scholar 

  • Choy, B. H. (2015). Snapshots of mathematics teacher noticing during task design. Mathematics Education Research Journal, 28, 421–440.

    Article  Google Scholar 

  • Colebrook, C. (2016). ‘A grandiose time of coexistence’: Stratigraphy of the Anthropocene. Deleuze Studies, 10(4), 440–454.

    Article  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 

  • de Araujo, Z., Amador, J., Estepa, A., Weston, T., Aming-Attai, R., & Kosko, K. W. (2015). Animating preservice teachers’ noticing. Mathematics Teacher Education and Development, 17(2), 25–44.

    Google Scholar 

  • de Freitas, E. (2016). Material encounters and media events: What kind of mathematics can a body do? Educational Studies in Mathematics, 91, 185–202.

    Article  Google Scholar 

  • de Freitas, E. (2017). Karen Barad’s quantum ontology and posthuman ethics: Rethinking the concept of relationality. Qualitative Inquiry, 23(9), 741–748.

    Article  Google Scholar 

  • de Freitas, E., & Sinclair, N. (2014). Mathematics and the body: Material entanglement in the classroom. New York: Cambridge University Press.

    Book  Google Scholar 

  • de Freitas, E., & Sinclair, N. (2018). The quantum mind: Alternative ways of reasoning with uncertainty. Canadian Journal f Science, Mathematics, and Technology Education, 18(3), 271–283.

    Article  Google Scholar 

  • Deleuze, G. (1995). Difference and repetition. New York: Columbia University Press.

    Google Scholar 

  • Dominguez, H. (2019). Theorizing reciprocal noticing with non-dominant students in mathematics. Educational Studies in Mathematics, 102(1), 75–89.

    Article  Google Scholar 

  • Eagleton, T. (1990). The significance of theory. Cambridge: Basil Blackwell.

    Google Scholar 

  • Estapa, A., Pinnow, R. J., & Chval, K. B. (2016). Supporting novice teachers as they learn to teach English language learners. The New Educator, 12(1), 85–104.

    Article  Google Scholar 

  • Ferguson, A. A. (2000). Bad boys: Public schools in the making of black masculinity. Ann Arbor: University of Michigan Press.

    Book  Google Scholar 

  • Fernandes, A. (2012). Mathematics preservice teachers learning about English language learners through task-based interviews and noticing. Mathematics Teacher Educator, 1(1), 10–22.

    Article  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.

    Article  Google Scholar 

  • Foucault, M. (1979). Discipline and punish: The birth of the prison. New York: Vintage Books.

    Google Scholar 

  • Goodwin, C. (1994). Professional vision. American Anthropologist, 96(3), 606–633.

    Article  Google Scholar 

  • Grosz, E. (2005). Time travels: Feminism, nature, power. Durham: Duke University Press.

    Book  Google Scholar 

  • Guattari, F. (1992). Chaosmose. Paris: Galilée.

    Google Scholar 

  • Gutiérrez, R. (2017). Living mathematx: Towards a vision for the future. Philosophy of Mathematics Education Journal, 32, 1–34.

    Google Scholar 

  • Hand, V. (2012). Seeing culture and power in mathematical learning: Toward a model of equitable instruction. Educational Studies in Mathematics, 80, 233–247.

    Article  Google Scholar 

  • Hatcher, A., Bartlett, C., Marshall, A., & Marshall, M. (2009). Two-eyed seeing in the classroom environment: Concepts, approaches, and challenges. Canadian Journal of Science, mathematics and technology education, 9(3), 141–153.

    Article  Google Scholar 

  • Hoban, G. F. (2002). Teacher learning for educational change. Buckingham: Open University Press.

    Google Scholar 

  • Ingold, T. (2011). Being alive: essays on movement, knowledge and description. London: Routledge.

    Book  Google Scholar 

  • Ingold, T. (2013). Making: Anthropology, archaeology, art and architecture. London: Routledge.

    Book  Google Scholar 

  • Jacobs, V. R., Lamb, L. L., & Philipp, R. A. (2010). Professional noticing of children’s mathematical thinking. Journal for Research in Mathematics Education, 41, 169–202.

    Article  Google Scholar 

  • Jilk, L. M. (2016). Supporting teacher noticing of students’ mathematical strengths. Mathematics Teacher Educator, 4(2), 188–199.

    Article  Google Scholar 

  • Lakoff, G., & Núñez, R. E. (2000). Where mathematics comes from: How the embodied mind brings mathematics into being. New York: Basic Books.

    Google Scholar 

  • Little Bear, L. (2000). Jagged worldviews colliding. In M. Battiste (Ed.), Reclaiming indigenous voice and vision (pp. 77–85). Vancouver: UBC Press.

    Google Scholar 

  • Lobato, J., Hohensee, C., & Rhodehamel, B. (2013). Students’ mathematical noticing. Journal for Research in Mathematics Education, 44(5), 809–850.

    Article  Google Scholar 

  • Louie, N. L. (2018). Culture and ideology in mathematics teacher noticing. Educational Studies in Mathematics, 97, 55–69.

    Article  Google Scholar 

  • Manning, E. (2007). Politics of touch: Sense, movement, sovereignty. Minneapolis: University of Minnesota Press.

    Google Scholar 

  • Marshall, Y., & Alberti, B. (2014). A matter of difference: Karen Barad, ontology and archaeological bodies. Cambridge Archaeological Journal, 24(1), 19–36.

    Article  Google Scholar 

  • Martin, K. A. (1998). Becoming a gendered body: Practices of preschools. American Sociological Review, 63, 494–511.

    Article  Google Scholar 

  • Martínez Parédez, D. (1964). Hunab Ku: Síntesis del pensamiento filosófico Maya. Distrito Federal, México, Editorial Orión.

  • 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: The discipline of noticing. London: Routledge Falmer.

    Book  Google Scholar 

  • Mason, J. (2009). Teaching as disciplined enquiry. Teachers and Teaching: Theory and Practice, 15(2), 2005–2223.

    Article  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). Cham: Springer.

    Google Scholar 

  • McDuffie, A. R., Foote, M. Q., Bolson, C., Turner, E., Aguirre, J. A., Bartell, T. G., et al. (2014). Using video analysis to support prospective K-8 teachers’ noticing of students’ multiple mathematical knowledge bases. Journal of Mathematics Teacher Education, 17, 245–270.

    Article  Google Scholar 

  • McLaren, P. (1986). Schooling as a ritual performance: Towards a political economy of educational symbols and gestures. London: Routledge and Kegan Paul.

    Google Scholar 

  • Mikulan, P., & Sinclair, N. (2017). Thinking mathematics pedagogy stratigraphically in the Anthropocene. Philosophy of Mathematics Education Journal, 32, 1–13.

    Google Scholar 

  • Mikulan, P., & Sinclair, N. (2019). Stratigraphy as a method for studying the different modes of existence arising in the mathematical classroom. ZDM, 51, 239–249.

    Article  Google Scholar 

  • Moyer, P. (2001). Are we having fun yet? How teachers use manipulatives to teach mathematics. Educational Studies in Mathematics, 47, 175–197.

    Article  Google Scholar 

  • Mt. Pleasant, J. . (2016). Food yields and nutrient analysis of the Three Sisters: A Haudenosaunee cropping system. Ethnobiology Letters, 7(1), 87–98.

    Article  Google Scholar 

  • Neal, L. I., McCray, A. D., Webb-Johnson, G., & Bridgest, S. T. (2003). The effects of African American movement styles on teachers’ perceptions and reactions. Journal of Special Education, 37(1), 49–57.

    Article  Google Scholar 

  • Pais, A. (2012). A critical approach to equity. In O. Skovsmose & B. Greer (Eds.), Opening the cage: Critique of mathematics education (pp. 49–91). Rotterdam: Sense Publishers.

    Chapter  Google Scholar 

  • Palmer, A. (2011). “How many sums can I do”? Performative strategies and diffractive thinking as methodological tools for rethinking mathematical subjectivity. Reconceptualizing Educational Research Methodology, 1(1), 3–18.

    Google Scholar 

  • Peirce, C. S. (1992). Reasoning and the logic of things. Cambridge: Harvard University Press.

    Google Scholar 

  • Piaget, J. (1928). Judgment and reasoning in the child. New York: Harcourt Brace.

    Google Scholar 

  • Radford, L. (2008). Connecting theories in mathematics education: Challenges and possibilities. ZDM - The International Journal on Mathematics Education, 40, 317–327.

    Article  Google Scholar 

  • Radford, L. (2009). Why do gestures matter? Sensuous cognition and the palpability of mathematical meanings. Educational Studies in Mathematics, 70(3), 111–126.

    Article  Google Scholar 

  • Rancière, J. (2004). The politics of aesthetics: The distribution of the sensible. New York: Continuum.

    Google Scholar 

  • Roth, W. M. (2011). Geometry as objective science in elementary school classrooms: Mathematics in the flesh. New York: Routledge.

    Book  Google Scholar 

  • Roth, W. M. (2015). Excess of graphical thinking: Movement, mathematics and flow. For the Learning of Mathematics, 35(1), 2–7.

    Google Scholar 

  • Roth, W. M. (2016). Growing-making mathematics: A dynamic perspective on people, materials, and movement in classrooms. Educational Studies in Mathematics, 93, 87–103.

    Article  Google Scholar 

  • Santagata, R., & Guarino, J. (2011). Using video to teach future teachers to learn from teaching. ZDM - The International Journal on Mathematics Education, 43, 133–145.

    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 

  • Serres, M. (2011). Variations on the body (trans. Randolph Burks). Minneapolis: Univocal.

    Google Scholar 

  • Sheets-Johnstone, M. (2011). The primacy of movement. Amsterdam: John Benjamins.

    Book  Google Scholar 

  • Sherin, M. G., Jacobs, V. R., & Philipp, R. (2011). Situating the study of teacher noticing. In M. G. Sherin, V. R. Jacobs, & R. A. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 3–13). New York: Routledge.

    Chapter  Google Scholar 

  • Skovsmose, O. (2005). Travelling through education: Uncertainty, mathematics, responsibility. Rotterdam: Sense Publishers.

    Book  Google Scholar 

  • Skovsmose, O., & Greer, B. (2012). Opening the cage? Critical agency in the face of uncertainty. In O. Skovsmose & B. Greer (Eds.), Opening the cage: Critique of mathematics education (pp. 369–386). Rotterdam: Sense Publishers.

    Chapter  Google Scholar 

  • Valsiner, J. (1987). Culture and the development of children’s action: A theory of human development. New York: Wiley.

    Google Scholar 

  • 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.

    Google Scholar 

  • van Es, E. A., Hand, V., & Mercado, J. (2017). Making visible the relationship between teachers’ noticing for equity and equitable teaching practice. In E. O. Schack, M. Fisher, & J. Wilhelm (Eds.), Teacher noticing: Bridging and broadening perspectives, contexts, and frameworks (pp. 251–270). Cham: Springer.

    Google Scholar 

  • Wager, A. A. (2014). Noticing children’s participation: Insights into teacher positionality toward equitable mathematics pedagogy. Journal for Research in Mathematics Education, 45(3), 312–350.

    Article  Google Scholar 

  • Walkoe, J. (2015). Exploring teacher noticing of student algebraic thinking in a video club. Journal of Mathematics Teacher Education, 18, 523–550.

    Article  Google Scholar 

  • Whitehead, A. N. (1959). The aims of education. Daedalus, 88(1), 192–205.

    Google Scholar 

  • Whitehead, A. N. (1978). Process and reality. New York: The Free Press.

    Google Scholar 

Download references

Acknowledgements

This article is based on research supported by the National Science Foundation (NSF) under Grant no. 1253822. Any findings, claims, or recommendations included in this article are those of the author and do not necessarily reflect the views of NSF.

Author information

Authors and Affiliations

  1. College of Education, Michigan State University, 620 Farm Lane, 116K Erickson Hall, East Lansing, MI, 48824-1034, USA

    Higinio Dominguez

Authors
  1. Higinio Dominguez
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Higinio Dominguez.

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

Dominguez, H. Students and teachers mobilizing mathematical concepts through reciprocal noticing. ZDM Mathematics Education 53, 43–55 (2021). https://doi.org/10.1007/s11858-020-01209-y

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11858-020-01209-y

Search

Navigation