Towards a Materialist Vision of ‘Learning as Making’: the Case of 3D Printing Pens in School Mathematics

Abstract

In this paper, we build on a previously developed notion of 'learning as Making' to examine mathematics thinking and learning in a highly transformative and technological Making environment: one that involves a handheld 3D printing technology which enables 3D models to be created instantly via one's moving hand. In particular, we present two examples of Maker-centred lessons for teaching and learning of primary mathematics. In these lessons, the students actively constructed artefacts with 3D Printing Pens while engaging in inquiry-based learning activities, where the target concepts were properties of prisms and cross-sections at the primary 5 (age 10-11) and primary 6 (age 11-12) levels respectively. We use diffractive analysis to capture the fine details in students' body-material interactions while engaging in the tasks with or without the 3D Printing Pens during the lessons. Through the lens of Making as a material act of creation and seeking to update Papert's constructionist view of learning, we propose to rethink Making in school mathematics according to a four-fold characterisation: Making is co-constructing meanings, Making is mathematising, Making is assembling with technology and Making is inventing. We discuss our contribution towards advancing a materialist perspective of learning mathematics and implications for a 'learning as Making' pedagogy and curriculum.

How ‘tall’ is the triangle? Constructionist learning of shape and space with 3D Pens

“…Besides the above example, I also explored other possibilities for teaching and learning mathematics as enabled by constructionist pedagogy with 3D Pens. Given that the 3D Pens allows for diagramming and manipulating with the 3D models, there are a number of mathematics topics that the 3D Pens could be complementary to teaching and learning, In the primary school level, for example, I designed lessons with classroom teachers for teaching the number of faces, edges and vertices of prisms and pyramids (Ng & Ferrara, 2020). It was found that the students' visualization of 3D solids was inextricably linked to their hand movements in Making (i.e.…”

“…In the past five years, I have been actively engaging in classroom-based interventions with primary and secondary school mathematics teachers to develop a technologyenhanced constructionist pedagogy, termed 'learning as making' (Ng & Chan, 2019;Ng & Ferrara, 2020). The notion of 'learning as making' is rooted in Seymour Papert's (1980) revolutionary theory of constructionism, which suggests that knowledge is not delivered to the learner, but is rather constructed through activities, in particular, by producing a physical and shareable product.…”

Exploring differences in primary students’ geometry learning outcomes in two technology-enhanced environments: dynamic geometry and 3D printing

“…On the other hand, the 3D Pen environment supported hands-on and flexible constructions of the 3D solids. For example, when constructing a triangular prism with 3D Pens, some students created a triangular base initially, whereas some students created one of its rectangular faces initially (Ng & Ferrara, 2019).…”

“…Specifically, 3D DGEs enable learners to construct, observe, and manipulate geometrical figures in a "3D-like space," through which their perception of spatial positions and spatial relations can be strengthened (Christou, Jones, Mousoulides, & Pittalis, 2006). On the other hand, the first author (Ng & Chan, 2019;Ng & Ferrara, 2019) has previously examined a Papert-inspired, "learning as Making" pedagogy, one that facilitates geometry learning with the hands-on construction of physical artefacts in a 3D printing environment. The author concluded that the use of 3D Printing Pens 1 provides low-floor, high-ceiling opportunities for students to utilize their hands to develop their spatial skills and enhance integrated STEM learning (Ng & Chan, 2019).…”

The Interplay Between Mathematical and Computational Thinking in Primary School Students’ Mathematical Problem-Solving Within a Programming Environment

“…By contrast, the artefact construction dimension of problem-solving contextualised with physical inputs or outputs in this study (i.e. make a device that could detect prime numbers) is very rarely presented in mathematics classrooms (Ng & Chan, 2019;Ng & Ferrara, 2020). Without explicitly stating what to do with the LED lights, the students needed to prepare the problem by setting up scenarios for how to display their results upon checking whether a number was a prime or not.…”