The Geometry of Movement: Encounters with Spatial Inscriptions for Making and Exploring Mathematical Figures
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The Geometry of Movement: Encounters with Spatial Inscriptions for Making and Exploring Mathematical Figures Justin Dimmel 1,2
& Eric
Pandiscio 1 & Camden Bock 1
# Springer Nature Switzerland AG 2020
Abstract In this article, we examine spatial inscriptions marked in real or rendered spaces, rather than on two-dimensional surfaces, conceptualize spatial inscriptions from an inclusive materialist perspective and consider realizations of spatial inscriptions that are possible with emerging technologies (e.g. 3D pens, immersive virtual reality). We then describe two cases of immersive environments that allowed learners to make and interact with spatial inscriptions. Next, we analyze how movements of participant–environment– inscription assemblages realized diagrams. Our analysis highlights how varying scale and changing perspective can become resources for doing mathematical work with spatial inscriptions. Keywords Immersive environments . Virtual reality . Dynamic geometry
Mathematical work can be categorized by the quality, volume and materiality of the inscriptions with which communities of mathematicians generate and disseminate mathematical knowledge (Artemeva and Fox 2011; de Freitas 2016; Greiffenhagen 2014). We take inscription as an undefined term (Panciera 2012). Among others in mathematics, inscriptions include writing, symbols, pictures, graphs or diagrams (Roth, 2005). From Archimedes sketching in sand to children touching screens (Ng and Sinclair 2015), acts of inscribing have called to mind inscribable surfaces (de Freitas 2016; Dimmel and Bock 2019; Ng et al. 2018). But emergent technologies (e.g. 3D pens; virtual or augmented reality) are disrupting this status quo by transforming space into a canvas for making inscriptions (Dimmel and Bock 2019; Ng and Sinclair 2018). * Justin Dimmel [email protected]
1
School of Learning and Teaching and the Research in STEM Education (RiSE) Center, University of Maine, Orono, ME, USA
2
College of Education and Human Development, University of Maine, 330 Shibles Hall, Orono, ME 04469, USA
Digital Experiences in Mathematics Education
In the study detailed in this article, we explored two questions that concern spatial inscriptions – namely those marked in real or rendered spaces, rather than on twodimensional surfaces (Dimmel and Bock 2019). How might spatially inscribed realizations of mathematical figures be encountered by learners? How might such encounters affect the learning and teaching of mathematics? These broad questions reflect the emergent nature of our subject of inquiry. We aim to describe encounters with spatial inscriptions to the goal of generating hypotheses about how they partake in mathematical activity. We focus on (im)material spatial inscriptions that are rendered in immersive environments. Examples of such environments have been fixtures in research settings for decades (Lai et al. 2016; Kaufmann et al. 2000; Robinett and Rolland 1992; Steinicke and Hinrichs 2006; Sutherland 1968), but the advent of affordable, reliable equipm
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