Abstract
This paper substantiates the notion of inclusive materialism by illustrating the role of signs and micro-perception in the learning process of multiplication. Inclusive materialism, offered by de Freitas and Sinclair, considers mathematical learning a process of becoming a learning assemblage, which embodies various materials in a Deleuzian sense. Drawing on the Deleuzian notions of the sign, micro-perception, and assemblage, we analyze a classroom dynamic in which students are involved in the actualization of the concept of multiplication. The analysis shows that the scale of micro-perception modifies the material condition and leads learners to be extricated from the previous signification and previous approaches. Through gesturing and diagramming activities, the learners’ perception was structured and new habits of handling multiplicative situations were embodied. Ultimately, this paper evidences that by drawing on key ideas from Deleuze, inclusive materialism provides a new framework for theorizing the relations between materials, perception, and learning.
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Notes
In this respect, a Deleuzian perspective about learning differs from a Piagetian perspective. Piaget sees that structure is the result of organizing activity of a self-sufficient mind, and assumes a constant perception (Roth, 2011). A Deleuzian perspective explains the transformation of perception that occurs as the human body encounters with various materials, and notes the learning process by the power of materials.
References
Battista, M. T., & Clements, D. H. (1996). Students’ understanding of three-dimensional rectangular arrays of cubes. Journal for Research in Mathematics Education, 27(3), 258–292.
Battista, M. T., Clements, D. H., Arnoff, J., Battista, K., & Borrow, C. V. (1998). Students’ spatial structuring of 2D arrays of squares. Journal for Research in Mathematics Education, 29(5), 503–532.
Bennett, J. (2010). Vibrant matter: A political ecology of things. Durham, NC: Duke University Press.
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.
de Freitas, E., Ferrara, F., & Ferrari, G. (2019). The coordinated movements of collaborative mathematical tasks: The role of affect in transindividual sympathy. ZDM Mathematics Education, 51, 305–318.
de Freitas, E., & Sinclair, N. (2012). Diagram, gesture, agency: Theorizing embodiment in the mathematics classroom. Educational Studies in Mathematics, 80(1–2), 133–152.
de Freitas, E., & Sinclair, N. (2014). Mathematics and the body: Material entanglement in the classroom. Cambridge, UK: Cambridge University Press.
de Freitas, E., & Sinclair, N. (2017). Concepts as generative devices. In E. de Freitas, N. Sinclair, & A. Coles (Eds.), What is a mathematical concept? (pp. 76–89). New York, NY: Cambridge University Press.
Delanda, M. (2006). A new philosophy of society: Assemblage theory and social complexity. London & New York: Continuum.
Deleuze, G. (1993/1988). The fold: Leibniz and the baroque (T. Conley, Trans.). London, UK: The Athlone Press.
Deleuze, G. (1994/1968). Difference and repetition (P. Patton, Trans.). New York, NY: Columbia University Press.
Deleuze, G. (2000/1964). Proust and signs (R. Howard, Trans.). London, UK: Athlone Press.
Deleuze, G., & Guattari, F. (1987/1980). A thousand plateaus: Capitalism and schizophrenia (B. Massumi, Trans.). Minneapolis, MN: University of Minnesota Press.
Downton, A., & Sullivan, P. (2017). Posing complex problems requiring multiplicative thinking prompts students to use sophisticated strategies and build mathematical connections. Educational Studies in Mathematics, 95(3), 303–328.
Ferrara, F., & Ferrari, G. (2017). Agency and assemblage in pattern generalisation: A materialist approach to learning. Educational Studies in Mathematics, 94(1), 21–36.
Hoopes, J. (Ed.). (1991). Peirce on signs: Writings on semiotics by Charles Sanders Peirce. Chapel Hill, NC: The University of North Carolina Press.
Hultman, K., & Lenz-Taguchi, H. (2010). Challenging anthropocentric analysis of visual data: A relational materialist methodological approach to educational research. International Journal of Qualitative Studies in Education, 23, 525–542.
Leibniz, G. W. (1996/1765). New essays on human understanding (P. Remnant & J. Bennett, Trans.). Cambridge, UK: Cambridge University Press.
Lobato, J., Hohensee, C., & Rhodehamel, B. (2013). Students’ mathematical noticing. Journal for Research in Mathematics Education, 44(5), 809–850.
Mason, J., Stephens, M., & Watson, A. (2009). Appreciating mathematical structure for all. Mathematics Education Research Journal, 21(2), 10–32.
Mazzei, L. (2013). A voice without organs: Interviewing in posthumanist research. International Journal of Qualitative Studies in Education, 26(6), 732–740.
Mulligan, J., & Mitchelmore, M. (1997). Young children’s intuitive models of multiplication and division. Journal for Research in Mathematics Education, 28(3), 309–330.
Mulligan, J., & Watson, J. (1998). A developmental multimodal model for multiplication and division. Mathematics Education Research Journal, 10(2), 61–86.
Palatnik, A., & Abrahamson, D. (2018). Rhythmic movement as a tacit enactment goal mobilizing the emergence of mathematical structures. Educational Studies in Mathematics, 99, 293–309.
Protevi, J. (2009). Political affect: Connecting the social and the somatic. Minneapolis, MN: University of Minnesota Press.
Radford, L. (2008). Diagrammatic thinking: Notes on Peirce’s semiotics and epistemology. PNA, 3(1), 1–18.
Radford, L. (2010). The eye as a theoretician: Seeing structures in generalizing activities. For the Learning of Mathematics, 30(2), 2–7.
Radford, L., & Roth, W.-M. (2011). Intercorporeality and ethical commitment: An activity perspective on classroom interaction. Educational Studies in Mathematics, 77(2–3), 227–245.
Radford, L., Schubring, G., & Seeger, F. (2011). Signifying and meaning-making in mathematical thinking, teaching, and learning. Educational Studies in Mathematics, 77, 149–156.
Roth, W.-M. (2011). Passibility: At the limits of the constructivist metaphor. New York, NY: Springer.
Sinclair, N., & de Freitas, E. (2014). The haptic nature of gesture: Rethinking gesture with multitouch digital technologies. Gesture, 14(3), 351–374.
Singh, P. (2000). Understanding the concept of proportion and ratio constructed by two grade six students. Educational Studies in Mathematics, 14(3), 271–292.
Steffe, L. P. (1994). Children’s multiplying schemes. In G. Harel & J. Confrey (Eds.), The development of multiplicative reasoning in the learning of mathematics (pp. 3–40). Albany, NY: State University of New York Press.
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Moon, SJ., Lee, KH. Deleuzian actualizations of the multiplicative concept: a study of perceptual flow and the transformation of learning assemblages. Educ Stud Math 104, 221–237 (2020). https://doi.org/10.1007/s10649-020-09953-4
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DOI: https://doi.org/10.1007/s10649-020-09953-4