Skip to main content
Log in

Enactivism and ethnomethodological conversation analysis as tools for expanding Universal Design for Learning: the case of visually impaired mathematics students

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

Abstract

Blind and visually impaired mathematics students must rely on accessible materials such as tactile diagrams to learn mathematics. However, these compensatory materials are frequently found to offer students inferior opportunities for engaging in mathematical practice and do not allow sensorily heterogenous students to collaborate. Such prevailing problems of access and interaction are central concerns of Universal Design for Learning (UDL), an engineering paradigm for inclusive participation in cultural praxis like mathematics. Rather than directly adapt existing artifacts for broader usage, UDL process begins by interrogating the praxis these artifacts serve and then radically re-imagining tools and ecologies to optimize usability for all learners. We argue for the utility of two additional frameworks to enhance UDL efforts: (a) enactivism, a cognitive-sciences view of learning, knowing, and reasoning as modal activity; and (b) ethnomethodological conversation analysis (EMCA), which investigates participants’ multimodal methods for coordinating action and meaning. Combined, these approaches help frame the design and evaluation of opportunities for heterogeneous students to learn mathematics collaboratively in inclusive classrooms by coordinating perceptuo-motor solutions to joint manipulation problems. We contextualize the thesis with a proposal for a pluralist design for proportions, in which a pair of students jointly operate an interactive technological device.

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

Similar content being viewed by others

Notes

  1. Only for purposes of text flow herein, we hence abbreviate this phrase to “blind.” This should not be taken to imply disregard to important nuances of gradients in individuals’ visual capacity.

References

  • Abrahamson, D. (2009). Embodied design: Constructing means for constructing meaning. Educational Studies in Mathematics, 70(1), 27–47.

    Google Scholar 

  • Abrahamson, D. (2012). Mathematical Imagery Trainer—Proportion (MIT-P) IPhone/iPad application (Terasoft): iTunes. Retrieved from https://itunes.apple.com/au/app/mathematical-imagery-trainer/id563185943.

  • Abrahamson, D. (2014). Building educational activities for understanding: An elaboration on the embodied-design framework and its epistemic grounds. International Journal of Child-Computer Interaction, 2(1), 1–16.

    Google Scholar 

  • Abrahamson, D., & Bakker, A. (2016). Making sense of movement in embodied design for mathematics learning. In N. Newcombe & S. Weisberg (Eds.), Embodied cognition and STEM learning [Special issue]. Cognitive Research: Principles and Implications (Vol. 1, No. (1), pp. 1–13).

  • Abrahamson, D., Gutiérrez, J. F., Charoenying, T., Negrete, A. G., & Bumbacher, E. (2012). Fostering hooks and shifts: Tutorial tactics for guided mathematical discovery. Technology, Knowledge, and Learning, 17(1–2), 61–86.

    Google Scholar 

  • Abrahamson, D., Lee, R. G., Negrete, A. G., & Gutiérrez, J. F. (2014). Coordinating visualizations of polysemous action: Values added for grounding proportion. ZDM - The International Journal on Mathematics Education, 46(1), 79–93.

    Google Scholar 

  • Abrahamson, D., & Sánchez-García, R. (2016). Learning is moving in new ways: The ecological dynamics of mathematics education. Journal of the Learning Sciences, 25(2), 203–239.

    Google Scholar 

  • Abrahamson, D., Shayan, S., Bakker, A., & Van der Schaaf, M. F. (2016). Eye-tracking Piaget: Capturing the emergence of attentional anchors in the coordination of proportional motor action. Human Development, 58(4–5), 218–244.

    Google Scholar 

  • Abrahamson, D., & Trninic, D. (2015). Bringing forth mathematical concepts: Signifying sensorimotor enactment in fields of promoted action. ZDM Mathematics Education, 47(2), 295–306.

    Google Scholar 

  • Alberto, R. (2018). Design research of pedagogical constraints on coordination dynamics: Actions, perceptions, and reasoning in learning mathematics. In D. Abrahamson (Conference chair), Coordination dynamics of mathematics education. University of California, Berkeley, October 25–26, 201.

  • Amalric, M., Denghien, I., & Dehaene, S. (2018). On the role of visual experience in mathematical development: Evidence from blind mathematicians. Developmental Cognitive Neuroscience, 30, 314–323.

    Google Scholar 

  • Asterhan, C. S. C., & Schwarz, B. B. (2009). The role of argumentation and explanation in conceptual change: Indications from protocol analyses of peer-to-peer dialogue. Cognitive Science, 33, 373–399.

    Google Scholar 

  • Avital, S., & Streeck, J. (2011). Terra incognita: Social interaction among blind children. In J. Streeck, C. Goodwin & C. LeBaron (Eds.), Embodied interaction: Language and body in the material world (pp. 169–181). Cambridge: Cambridge University Press.

    Google Scholar 

  • Azevedo, F. S., & Mann, M. J. (2018). Seeing in the dark: Embodied cognition in amateur astronomy practice. Journal of the Learning Sciences, 27(1), 89–136.

    Google Scholar 

  • Barnes, B., Henry, J., & Bloor, D. (1996). Scientific knowledge: A sociological analysis. Chicago: University of Chicago Press.

    Google Scholar 

  • Becvar Weddle, A., & Hollan, J. D. (2010). Professional perception and expert action: Scaffolding embodied practices in professional education. Mind, Culture, and Activity, 17(2), 119–148.

    Google Scholar 

  • Braun, S. (2008). Audiodescription research: state of the art and beyond. Translation Studies in the New Millennium, 6, 14–30.

    Google Scholar 

  • Broth, M., & Mondada, L. (2013). Walking away: The embodied achievement of activity closings in mobile interaction. Journal of Pragmatics, 47(1), 41–58.

    Google Scholar 

  • Brothers, R. J. (1973). Arithmetic computation: Achievement of visually handicapped students in public schools. Exceptional Children, 39, 575–576.

    Google Scholar 

  • Brousseau, G. (1997). Theory of didactical situations in mathematics (N. Balacheff, M. Cooper, R. Sutherland & V. Warfield, Trans.). Boston: Kluwer Academic Publishers.

    Google Scholar 

  • Burgstahler, S. (2001). Universal design of instruction. Arlington: National Science Foundation.

    Google Scholar 

  • Capiel, G. (2014). Born accessible. Journal of Electronic Publishing. https://doi.org/10.3998/3336451.0017.121

    Google Scholar 

  • Clamp, S. (1997). Mathematics. In H. Mason, S. McCall, C. Arter, M. McLinden & J. Stone (Eds.), Visual impairment: Access to education for children and young people (pp. 218–235). New York: David Fulton Publishers.

    Google Scholar 

  • Cobb, P., Yackel, E., & McClain, K. (Eds.). (2000). Symbolizing and communicating in mathematics classrooms—Perspectives on discourse, tools, and instructional design. Mahwah: Lawrence Erlbaum.

    Google Scholar 

  • de Freitas, E. (2016). Material encounters and media events: What kind of mathematics can a body do? Educational Studies in Mathematics, 91(2), 185–202.

    Google Scholar 

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

    Google Scholar 

  • Dourish, P. (2001). Where the action is: The foundations of embodied interaction. Cambridge: MIT Press.

    Google Scholar 

  • Dourish, P., & Button, G. (1998). On “technomethodology”: Foundational relationships between ethnomethodology and system design. Human-Computer Interaction, 13(4), 395–432.

    Google Scholar 

  • Due, B., & Lange, S. B. (2017). The Moses effect: The spatial hierarchy and joint accomplishment of a blind person navigating. Space and Culture, 21(2), 129–144.

    Google Scholar 

  • Duijzer, A. C. G., Shayan, S., Bakker, A., Van der Schaaf, M. F., & Abrahamson, D. (2017). Touchscreen tablets: Coordinating action and perception for mathematical cognition. Frontiers in Psychology. 8, 144.

    Google Scholar 

  • Ely, R., Emerson, R. W., Maggiore, T., Rothberg, M., Connell, O., T., & Hudson, L. (2006). Increased content knowledge of students with visual impairments as a result of extended descriptions. Journal of Special Education Technology, 21(3), 31.

    Google Scholar 

  • Encelle, B., Ollagnier-Beldame, M., Pouchot, S., & Prié, Y. (2011). Annotation-based video enrichment for blind people: A pilot study on the use of earcons and speech synthesis. In The Proceedings of the 13th International ACM SIGACCESS Conference on Computers and Accessibility (pp. 123–130). ACM.

  • Erickson, F. (1996). Going for the zone: The social and cognitive ecology of teacher-student interaction in classroom conversations. In D. Hicks (Ed.), Discourse learning and schooling (pp. 29–62). Cambridge: Cambridge University Press.

    Google Scholar 

  • Flood, V. J. (2018). Multimodal revoicing as an interactional mechanism for connecting scientific and everyday concepts. Human Development, 6, 145–173

    Google Scholar 

  • Flood, V. J., Harrer, B. W., & Abrahamson, D. (2016). The interactional work of configuring a mathematical object in a technology-enabled embodied learning environment. In C.-K. Looi, J. Polman, U. Cress, & P. Reimann (Eds.), Proceedings of the International Conference of the Learning Sciences (ICLS) (Vol., 1, pp. 122–129). Singapore: ISLS.

    Google Scholar 

  • Fortin, M., Voss, P., Lord, C., Lassonde, M., Pruessner, J., Saint-Amour, D., Rainville, C., & Lepore, F. (2008). Wayfinding in the blind: Larger hippocampal volume and supranormal spatial navigation. Brain, 131(11), 2995–3005.

    Google Scholar 

  • Friedman, A. M. (2012). Believing not seeing: A blind phenomenology of sexed bodies. Symbolic Interaction 35(3), 284–300.

    Google Scholar 

  • Garfinkel, H. (2002). Ethnomethodology’s program: Working out Durkheim’s aphorism. New York: Rowman & Littlefield.

    Google Scholar 

  • Garfinkel, H., & Livingston, E. (2003). Phenomenal field properties of order in formatted queues and their neglected standing in the current situation of inquiry. Visual Studies, 18(1), 21–28.

    Google Scholar 

  • Garfinkel, H., & Sacks, H. (1970). On formal structures of practical actions. In J. C. McKinney & E. Tiryakian (Eds.), Theoretical sociology: Perspectives and developments (pp. 337–366). New York: Appleton-Century-Crofts.

    Google Scholar 

  • Gibson, J. J. (1977). The theory of affordances. In R. Shaw & J. Bransford (Eds.), Perceiving, acting and knowing: Toward an ecological psychology (pp. 67–82). Hillsdale: Lawrence Erlbaum Associates.

    Google Scholar 

  • Goffman, E. (1964). The neglected situation. American Anthropologist, 66(6), 133–136.

    Google Scholar 

  • Goldsmith, S. (1963). Designing for the disabled. London: RIBA Publications.

    Google Scholar 

  • Goldsmith, S. (1997). Designing for the disabled: The new paradigm. New York: Routledge.

    Google Scholar 

  • Goode, D. (1994). A world without words. Philadelphia: Temple University Press.

    Google Scholar 

  • Goodwin, C. (2000). Action and embodiment within situated human interaction. Journal of Pragmatics, 32(10), 1489–1522.

    Google Scholar 

  • Goodwin, C. (2018). Co-operative action. New York: Cambridge University Press.

    Google Scholar 

  • Goodwin, M. H. (2017). Haptic sociality. In C. Meyer, J. Streeck & J. S. Jordan (Eds.), Intercorporeality: Emerging socialities in interaction (pp. 73–102). New York: Oxford University Press.

    Google Scholar 

  • Goodwin, M. H., & Cekaite, A. (2018). Embodied family choreography: Practices of control, care, and mundane creativity. New Jersey: Routledge.

    Google Scholar 

  • Hall, R., & Nemirovsky, R. (2012). Introduction to the special issue: Modalities of body engagement in mathematical activity and learning. Journal of the Learning Sciences, 21(2), 207–215

    Google Scholar 

  • Healy, L., & Fernandes, S. H. A. A. (2011). The role of gestures in the mathematical practices of those who do not see with their eyes. Educational Studies in Mathematics, 77(2), 157–174.

    Google Scholar 

  • Healy, L., Jahn, A. P., & Frant, J. B. (2010). Digital technologies and the challenge of constructing an inclusive school mathematics. ZDM - The International Journal on Mathematics Education, 42(3–4), 393–404.

    Google Scholar 

  • Healy, L., Ramos, E. B., Fernandes, S. H. A. A., & Peixoto, J. L. B. (2016). Mathematics in the hands of deaf learners and blind learners: Visual–gestural–somatic means of doing and expressing mathematics. In R. Barwell, P. Clarkson, A. Halai, M. Kazima, J. Moschkovich, N. Planas, M. Setati-Phakeng, P. Valero, M. Villavicencio & Ubillús (Eds.), Mathematics education and language diversity: The 21st ICMI Study (pp. 141–162). Cham: Springer.

    Google Scholar 

  • Heath, C. (1986). Body movement and speech in medical interaction. Cambridge: Cambridge University Press.

    Google Scholar 

  • Heath, C. (1989). Pain talk: The expression of suffering in the medical consultation. Social Psychology Quarterly, 52(2), 113–125.

    Google Scholar 

  • Heath, C., & Luff, P. (2000). Technology and social action. In Technology in action (pp. 1–30). Cambridge: CUP.

    Google Scholar 

  • Heft, H. (1989). Affordances and the body: An intentional analysis of Gibson’s ecological approach to visual perception. Journal for the Theory of Social Behaviour, 19(1), 1–30.

    Google Scholar 

  • Heritage, J. (1984). Garfinkel and ethnomethodology. New York: Polity Press.

    Google Scholar 

  • Herzberg, T. S., & Rosenblum, L. P. (2014). Print to braille: Preparation and accuracy of K-12 mathematics materials. Journal of Visual Impairment & Blindness, 108(5), 355–367.

    Google Scholar 

  • Horvath, J., & Cameron, R. (2017). 3D printed science projects (Vol. 2): Physics, math, engineering and geology models. Berkeley: Apress.

    Google Scholar 

  • Hutto, D. D., Kirchhoff, M. D., & Abrahamson, D. (2015). The enactive roots of STEM: Rethinking educational design in mathematics. In P. Chandler & A. Tricot (Eds.), Human movement, physical and mental health, and learning [Special issue]. Educational Psychology Review, (Vol. 27, No. 3, pp. 371–389).

  • Ingram, J., Pitt, A., & Baldry, F. (2015). Handling errors as they arise in whole-class interactions. Research in Mathematics Education, 17(3), 183–197.

    Google Scholar 

  • Ishigaki, T., Imai, R., & Morioka, S. (2017). Association between unintentional interpersonal postural coordination produced by interpersonal light touch and the intensity of social relationship. Frontiers in Psychology. 8, 1993.

    Google Scholar 

  • Iwarsson, S., & Stahl, A. (2003). Accessibility, usability and universal design—positioning and definition of concepts describing person–environment relationships. Disability & Rehabilitation, 25(2), 57–66.

    Google Scholar 

  • Iwasaki, S., Bartlett, M., Manns, H., & Willoughby, L. (2018). The challenges of multimodality and multi-sensoriality: Methodological issues in analyzing tactile signed interaction. Journal of Pragmatics. https://doi.org/10.1016/j.pragma.2018.05.003

    Google Scholar 

  • Jackiw, N., & Sinclair, N. (2009). Sounds and pictures: Dynamism and dualism in dynamic geometry. ZDM Mathematics Education, 41, 413–426.

    Google Scholar 

  • Jay, M. (1993). Downcast eyes: The denigration of vision in twentieth-century French thought. Berkeley: University of California Press.

    Google Scholar 

  • Kelso, J. A. S. (1984). Phase transitions and critical behavior in human bimanual coordination. American Journal of Physiology: Regulatory, Integrative and Comparative, 246(6), R1000–R1004.

    Google Scholar 

  • Kelso, J. A. S. (1995). Dynamic patterns: The self-organization of brain and behavior. Cambridge: MIT Press.

    Google Scholar 

  • Koschmann, T., & Mori, J. (2016). “Its understandable enough, right?” The natural accountability of a mathematics lesson. Mind, Culture, and Activity, 23(1), 65–91.

    Google Scholar 

  • Koschmann, T., Stahl, G., & Zemel, A. (2007). The video analyst’s manifesto (or the implication of Garfinkel’s policies for studying instructional practice in design-based research). In R. Goldman, R. Pea, B. J. Barron & S. Derry (Eds.), Video research in the learning sciences (pp. 133–144). Mahwah: Lawrence Erlbaum.

    Google Scholar 

  • Krause, C. M. (2015). The mathematics in our hands: How gestures contribute to constructing mathematical knowledge. Wiesbaden: Springer Spektrum.

    Google Scholar 

  • Krejtz, I., Szarkowska, A., Krejtz, K., Walczak, A., & Duchowski, A. (2012). Audio description as an aural guide of children’s visual attention: evidence from an eye-tracking study. In Proceedings of the Symposium on Eye Tracking Research and Applications (pp. 99–106). ACM.

  • Lemke, J. L. (1998). Multiplying meaning: Visual and verbal semiotics in scientific text. In J. R. Martin & R. Veel (Eds.), Reading science: Critical and functional perspectives on discourses of science (pp. 87–113). London: Routledge.

    Google Scholar 

  • Lerman, S. (2000). The social turn in mathematics education research. In J. Boaler (Ed.), Multiple perspectives on mathematics teaching and learning (pp. 19–44). Westport: Ablex.

    Google Scholar 

  • López, A. P. (2010). The benefits of audio description for blind children. Approaches to Translation Studies, 33, 213–225.

    Google Scholar 

  • Mace, R. L., Hardie, G. J., & Place, J. P. (1991). Accessible environments: Toward universal design. In W. E. Preiser, J. C. Vischer & E. T. White (Eds.), Design intervention: Toward a more humane architecture (pp. 155–175). New York: Van Nostrand Reinhold.

    Google Scholar 

  • Merleau-Ponty, M. (2005). Phenomenology of perception (C. Smith, Trans.). New York: Routledge. (Original work published 1945).

    Google Scholar 

  • Mondada, L. (2011). Understanding as an embodied, situated and sequential achievement in interaction. Journal of Pragmatics, 43(2), 542–552.

    Google Scholar 

  • Mondada, L. (2012). The conversation analytic approach to data collection. In J. Sidnell & T. Stivers (Eds.), The handbook of conversation analysis (pp. 32–56). Boston: Blackwell Publishing Ltd.

    Google Scholar 

  • Mondada, L. (2016). Challenges of multimodality: Language and the body in social interaction. Journal of Sociolinguistics, 20(3), 336–366.

    Google Scholar 

  • Morash, V., & McKerracher, A. (2014). The relationship between tactile graphics and mathematics for students with visual impairments. Terra Haptica, 4, 13–22.

    Google Scholar 

  • Nishizaka, A. (2007). Hand touching hand: Referential practice at a Japanese midwife house. Human Studies, 30(3), 199–217.

    Google Scholar 

  • Núñez, R. E., Edwards, L. D., & Matos, J. F. (1999). Embodied cognition as grounding for situatedness and context in mathematics education. Educational Studies in Mathematics, 39(1), 45–65.

    Google Scholar 

  • O’Loughlin, M. (2006). Embodiment and education: Exploring creatural existence. Dordrecht: Springer.

    Google Scholar 

  • Packer, J., Vizenor, K., & Miele, J. A. (2015). An Overview of Video Description: History, Benefits, and Guidelines. Journal of Visual Impairment & Blindness, 109(2), 83–93.

    Google Scholar 

  • Quek, F., & Oliveira, F. (2013). Enabling the blind to see gestures. In P. Marshall, A. N. Antle, E. v.d. Hoven, & Y. Rogers (Eds.), The theory and practice of embodied interaction in HCI and interaction design [Special issue]. ACM Transactions on Human–Computer Interaction (Vol. 20, no. (1), pp. 1–32).

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

    Google Scholar 

  • Rapp, D. W., & Rapp, A. J. (1992). A survey of the current status of visually impaired students in secondary mathematics. Journal of Visual Impairment & Blindness, 86, 115–117.

    Google Scholar 

  • Reed, E. S., & Bril, B. (1996). The primacy of action in development. In M. L. Latash & M. T. Turvey (Eds.), Dexterity and its development (pp. 431–451). Mahwah: LEA.

    Google Scholar 

  • Reid, D., Brown, L., Coles, A., & Lozano, M.-D. (Eds.). (2015). Enactivist methodology in mathematics education research [Special issue]. ZDM Mathematics Education, 47(2).

  • Rose, D. H., & Meyer, A. (2002). Teaching every student in the digital age: Universal design for learning. Alexandria: Association for Supervision and Curriculum Development.

    Google Scholar 

  • Saerberg, S. (2010). Just go straight ahead. The Senses and Society, 5(3), 364–381.

    Google Scholar 

  • Saxe, G. B. (2012). Cultural development of mathematical ideas: Papua New Guinea studies. Cambridge: Cambridge University Press.

    Google Scholar 

  • Schegloff, E. A., & Sacks, H. (1973). Opening up closings. Semiotica, 8, 289–327.

    Google Scholar 

  • Scherer, P., Beswick, K., DeBlois, L., Healy, L., & Opitz, E. M. J. Z. (2016). Assistance of students with mathematical learning difficulties: How can research support practice? ZDM Mathematics Education, 48(5), 633–649.

    Google Scholar 

  • Sebanz, N., & Knoblich, G. (2009). Prediction in joint action: What, when, and where. Topics in Cognitive Science, 1(2), 353–367.

    Google Scholar 

  • Sedaghatjou, M. (2018). Advanced mathematics communication beyond modality of sight. International Journal of Mathematical Education in Science and Technology, 49(1), 46–65.

    Google Scholar 

  • Shvarts, A. (2017). Eye movements in emerging conceptual understanding of rectangle area. In B. Kaur, W. K. Ho, T. L. Toh, & B. H. Choy (Eds.), Proceedings of the 41st Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 268). Singapore: PME.

    Google Scholar 

  • Shvarts, A., & Abrahamson, D. (2018). Towards a complex systems model of enculturation: A dual eye-tracking study. Paper presented at the annual conference of the American Educational Research Association, New York.

  • Sinclair, N., & de Freitas, E. (2014). Rethinking gesture with new multitouch digital technology. Gesture, 14(3), 351–374.

    Google Scholar 

  • Siu, Y. (2016). Designing for all learners with technology. Educational Designer, 3(9). Retrieved December 17, 2017 from http://www.educationaldesigner.org/ed/volume3/issue9/article34/index.htm.

  • Solfo, A., & van Leeuwen, C. (2018). From adult finger tapping to fetal heart beating: Retracing the role of coordination in constituting agency. Topics in Cognitive Science, 10(1), 18–35.

    Google Scholar 

  • Streeck, J. (2013). Interaction and the living body. Journal of Pragmatics, 46(1), 69–90.

    Google Scholar 

  • Suchman, L. A. (1987). Plans and situated actions. New York: Cambridge University Press.

    Google Scholar 

  • Summers, E., Langston, J., Allison, R., & Cowley, J. (2012). Using SAS/GRAPH to create visualizations that also support tactile and auditory interaction. In SAS Global Forum.

  • Urton, G. (1997). The social life of numbers: A Quechua ontology of numbers and philosophy of arithmetic. Austin: University of Texas Press.

    Google Scholar 

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

    Google Scholar 

  • Vérillon, P., & Rabardel, P. (1995). Cognition and artifacts: A contribution to the study of thought in relation to instrumented activity. European Journal of Psychology of Education, 10(1), 77–101.

    Google Scholar 

  • vom Lehn, D. (2010). Discovering “experience-ables”: Socially including visually impaired people in art museums. Journal of Marketing Management, 26(7), 749–769.

    Google Scholar 

  • Wittgenstein, L. (1953). Philosophical investigations (G. E. M. Anscombe, Trans.). Upper Saddle River: Prentice Hall.

    Google Scholar 

  • Wittmann, M., Flood, V., & Black, K. (2013). Algebraic manipulation as motion within a landscape. Educational Studies in Mathematics, 82(2), 169–181.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Contributions

Contributions on ethnomethodological conversation analysis were written by VJF.

Corresponding author

Correspondence to Dor Abrahamson.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Abrahamson, D., Flood, V.J., Miele, J.A. et al. Enactivism and ethnomethodological conversation analysis as tools for expanding Universal Design for Learning: the case of visually impaired mathematics students. ZDM Mathematics Education 51, 291–303 (2019). https://doi.org/10.1007/s11858-018-0998-1

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11858-018-0998-1

Keywords

Navigation