Agency and assemblage in pattern generalisation: a materialist approach to learning

Abstract

In this paper, we draw on the contemporary perspective of inclusive materialism offered by de Freitas and Sinclair to contribute to current discussions on the role of the body in the learning of mathematics. Using the notions of distributed agency and assemblage, we illustrate the way in which three students engage with a patterning task. We discuss this as an example to show how the mathematics activity involves, besides the students' bodies, other materialities that populate the classroom, and how all the human and non-human bodies form a moving assemblage that constantly reconfigures and reorients learning. The inclusive materialism helps us talk about learning as a dynamic assemblage rather than in terms of individual achievements and directs attention to the material learning environment.Taking the new materialist perspective proposed by de Freitas and Sinclair (2014), this article contributes to current discussions on the role of the body in learning mathematics. The inclusive materialism of de Freitas and Sinclair offers a new way of theorising the nature of embodiment and embodied mathematics, moving away from essentialised views of the body Band towards a more temporal and contingent sense of becoming^(p. 47). It suggests that we must Btalk about the 'perceptuo-motor possibilities' of the body while also addressing the social entanglement of bodies^, as well as address Bthe way meaning and matter are entangled^(p. 22). De Freitas and Sinclair propose to focus less on human will and intention and more on distributed agency, so that the human body is not conceived as the principal administrator of its own participation or the only centre of activity. Decentralising agency allows us to shift attention to how the material conditions of the classroom partake in mathematical thinking and learning. This approach questions the acquisitionist view that learning occurs through mental schemas or mechanisms that students are expected to acquire, Educ Stud Math (2017) 94:21-36

Teaching Novice Teachers to Enhance Learning in the Hybrid University

“…However, they showed special interest in ‘knowing-in-practice’ (Orlikowski 2002 ) rather than in knowledge as a given object. This finding is also particularly important in order to avoid representational perceptions of knowledge and to reintegrate the body and the environment into the learning processes (Ferrara and Ferrari 2017 ).…”

“…In sociomaterial terms, a learning space is made by material, digital and social relations that shape the formats (Lamb and Ross 2021 ) and boundaries (van de Oudeweetering and Decuypere 2019 ) of the learning experience. Thus, learning is configured as ‘situated and embodied’ (Networked Learning Editorial Collective (NLEC) et al 2021 ), while at the same time being ‘distributed’ (Ferrara and Ferrari 2017 ) and ‘emergent’ (Biesta 2010 ). New configurations of learning spaces mean new actors involved and new possibilities for the learner.…”

Proses Generalisasi Pola Bilangan Siswa SMP dalam Memecahkan Masalah Matematika Berdasarkan Gaya Belajar

“…Hal ini menyebabkan generalisasi pola terkadang tidak lagi berfokus terhadap permasalahan yang diberikan namun lebih berfokus kepada prosedur dan hubungan-hubungan yang terdapat dalam permasalahan tersebut. Generalisasi pola bertujuan untuk membedakan keteraturan, kesetaraan dan fungsi (Björklund & Pramling, 2014;Ferrara & Ferrari, 2017) serta suatu objek yang menghubungkan antara variabel dengan rumus (Ferrara & Sinclair, 2016).…”

The Mutual Involvement of Gesture and Diagramming in the Process of Mathematical Meaning-Making: Case of Statistical Thinking through Diagrammatic Reasoning

“…Figure 1에 나타난 상호 수반적인 제스처-다이어그래밍은 교환법칙이 성립하는 기존 곱셈 개념에 대한 의미체계 에서 벗어나, 방향이라는 정보가 포함되어 있으며 교환법칙이 성립하지 않는 새로운 곱셈 개념으로 나아가게 되는 계 기로 작용했다 (Châtelet, 2000;de Freitas & Sinclair, 2014). 결국, 제스처-다이어그래밍은 새로운 수학적 개념이 나 의미를 발견하는 사건에 깊이 연루된 움직임일 수 있으며, 더 나아가 수학 교수 학습이 이루어지는 맥락에서도 학 생이 새로운 개념 및 절차를 익히는 과정에서 매우 중요한 역할을 수행하는 것으로 알려져 있다 (Ferrara & Ferrari, 2017;. The slice gesture that embodies the abstract concept of fractions (Edwards, 2009, p. 132) Figure 3 The slight movement of the body that tilts the diagram (Noh et al, 2021, p. 143) 430 https://doi.org/10.29275/jerm.…”