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Growing-making mathematics: a dynamic perspective on people, materials, and movement in classrooms

Abstract

Recent theoretical advances on learning (mathematics) emphasize the fact that what results from engagement with curriculum materials is not entirely in the control of the students in the way classical theories of knowing and learning suggest. These new theories distinguish themselves by either invoking distributed agency, some of which is attributed to non-human aspects of the environment, or by emphasizing the essential (radical) passivity that characterizes coming to know. In this study, an alternative is offered: making as a modality of growing. This move allows us to capture theoretically that both growers-makers and their materials grow (old) together. The proposed approach troubles existing ones because it shifts our perspective from a transitive relation between students and the curricular objects to an intransitive one, where the becoming of each is described in terms of Deleuzian lines of flight. A case study involving two girls and tangram pieces is described in terms of growing together and becoming-hexagon. Implications are discussed for how researchers can capture the non-agential, non-causal dimensions of coming to know.

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Notes

  1. Grammatically, a transitive verb expresses an action that passes from the subject S to the object O (e.g., “The student constructs a hexagon”); an intransitive verb expresses an action does not have a direct object (e.g., “the tree grows).

  2. In classical, Newtonian mechanics, the movement of an object is described by the equation F = m · a, that is, a force that causes acceleration in the direction of the force. In Lagrangian mechanics, the forces F i are orthogonal to the displacement of the object δ r i. A description of the motion can be derived based on the fact that the inner product F i · δ r i = 0.

  3. An alternative to Fig. 1e models classroom interactions by means of knot diagrams (de Freitas, 2012). Future work has to determine whether these “knot works” are similar to those that Ingold (2015) offers despite their differences with respect to the notion of “assemblage.”

  4. Perpendicularity (orthogonality) is used in the sense of vector algebra, where there is no overlap when two vectors include a 90° angle, that is, when the inner (dot) product equals 0.

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Acknowledgments

Data collection for this study was supported by a research grant from the Social Sciences and Humanities Research Council of Canada. I thank Alfredo Bautista, Maria Inês Mafra Goulart, Jean-François Maheux, and Jennifer Thom for their contributions to the implementation of the curriculum and the data collection.

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Correspondence to Wolff-Michael Roth.

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Roth, WM. Growing-making mathematics: a dynamic perspective on people, materials, and movement in classrooms. Educ Stud Math 93, 87–103 (2016). https://doi.org/10.1007/s10649-016-9695-6

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  • DOI: https://doi.org/10.1007/s10649-016-9695-6

Keywords

  • Transitivity
  • Intransitivity
  • Materialism
  • Flow
  • Deleuze