Designing Disruptions for Productive Hybridity: The Case of Walking Scale Geometry

Abstract

This article explores an alternative strategy for designing hybrid instructional environments. Rather than bridging home or community funds of knowledge with school learning, I propose designing disruptions to typical school practices to invite students to recruit out-of-school resources meaningful and sensible to them in order to grapple with school-valued concepts. I examine this design strategy first conceptually, then through a case called walking scale geometry, designed to disrupt the scale of typical classroom geometry. This major disruption has 4 interrelated consequences in that students must invent new tools and strategies for constructing geometry figures, spaces of activity and learning shift, students are positioned with new visual perspectives, and the division of labor is redistributed. I analyze how these 4 consequences played out in an episode of walking scale geometry, in relation to the deployment of student-recruited resources and conceptual agency, then comment on some implications for designing disruptions and hybrid learning settings.

Acknowledgments

Thanks to members of the Spatial Learning and Mobility Lab at Vanderbilt University for all of their incredible contributions to this work. In particular, the tireless efforts of Katie Headrick Taylor, Nathan Phillips, Jillian Oury, and Kevin Leander made the study possible. I am especially grateful to Rogers Hall for his mentorship and intellectual guidance. Thanks to Ms. O and Ms. I for allowing us into their classroom and the students at KCMS for their participation. The anonymous journal reviewers provided valuable insight and feedback on the manuscript. Additional thanks to Leona Schauble, Georgene Troseth, Noel Enyedy, members of Vanderbilt University’s and New York University’s Interaction Analysis Lab groups, Eve Manz, Molly Kelton, Chuck Munter, and Brenna Cothran.

Funding

This study was funded by grants from the National Science Foundation (DRL-0816406) and Vanderbilt University.

Notes

¹ Constructing usually refers to using only a straightedge and compass to draw geometric figures, following relations dependent on Euclid’s first three postulates. Here it means to literally build a rectangle out of the tools at hand, attending to the geometric relationships that define the figure (in this case that opposite sides are congruent and parallel).

² Names of the school, students, and teachers are pseudonyms.

³ My use of the term everyday is not meant to imply that students necessarily encountered these materials in their everyday lives. Instead it is in contrast to materials typically used in these students’ mathematics classroom, in the way Moschkovich (2002) differentiated “school” and “everyday” mathematics.

⁴ Transcripts follow a modified version of Jefferson’s transcription convention (Atkinson & Heritage, 1984). Turns at talk and new lines, determined by topic of talk or activity, are labeled with [Line#]. Nontalk activity is enclosed in ((italicized, double parentheses)). Overlapping talk across turns is signified by vertically aligned [left open brackets. Emphasis is underlined, louder utterances are CAPITALIZED, and drawn out speech is noted with co::olons. Transcriber uncertainty is indicated with (parentheses). The duration of pauses in speech is indicated in seconds by (#s). When frame-by-frame images are provided, they are labeled <Figure#>.

⁵ Readers might note that it is perfectly reasonable to use the measure of circumference in relation to spheres.

Additional information

Funding

This study was funded by grants from the National Science Foundation (DRL-0816406) and Vanderbilt University.