Students Operating as Points on a Walking Scale Number Line

• In Event: Movement, Environment, and Meaning in Learning

Abstract

“Walking Scale Number Lines” (WSNL; 4) was situated in this symposium’s two dimensions of investigation in the following ways. The technical augmentation of embodiment restructured a familiar place (school gym) to resemble a familiar representational form (number line), scaled up to disrupt the representational infrastructure of school number line mathematics. Students’ views were shifted to being inside and a part of the representations (their bodies were points on the line). Their movements made “drawing” ephemeral rather than lasting (students’ movements left no trace of their paths). Finally, students simultaneously represented points along the line, providing newly salient meanings (“Kian is Morgan’s opposite”).

The WSNL setting’s correspondence to the learning content was disruptive rather than augmentative. The design explored mathematical concepts (addition, multiplication, equivalence) using a typical school mathematical representation. WSNL was not meant to immerse students more authentically in the phenomena. Instead, the environment-plus-body complex transformed “number line” and “operations” on it on one hand, and the gym and students’ typical embodied gym activity on the other, into a hybrid blend where bodies and embodied activity became representations of quantities and operations.

Our purpose is to understand the features of WSNL and students’ engagement, given these two dimensions, to support future designs for learning.

The framing relies on the two dimensions of the symposium. Additionally, we take a situative (Lave & Wenger, 1991) and distributed (Hutchins, 1995) view of cognition and learning. Further, we treat the body’s activity as integral to doing and learning mathematics (Stevens, 2012), not as merely a reflection of or instrument for mental activity. In other words, we view cognition as, in part, constituted by the body’s engagement with its material setting.

Data included recordings of five iterations of a WSNL workshop (~45 minutes each), designed and conducted by mathematics educators. These records were made with seven total stationary and wearable video cameras and four audio recorders. Methods included multimodal interaction analysis (Jordan & Henderson, 1995; Goodwin, 2010) to track and construct concepts (Charmaz, 2006) around students’ engagements in WSNL.

WSNL tasks focused on “operations,” movements along the line with distance and direction specified (Table 1 for more detail). Conclusions explore how this new experience of the number line produced surprising (for students, designers, and researchers) confusions and insights. Representational disruptions of the technical augmentation troubled students’ taken-as-stable understandings of quantity. For example, the experience of “doubling” for a student whose spot was eleven away from the origin was so surprising (“I’m confused…I was like way over there…everyone else is closer together”) that she questioned her own counting. The setting’s hybrid relation to the learning content and place supported playful embodied imaginariness that blended rhythmic and performative embodiments of operation with important quantitative relations and transformations.

The paper’s significance lies in contributions to conceptual development of how a multi-party whole-bodied mathematics can support learners’ engagement in important mathematical concepts as well as the development of positive dispositions for learning mathematics.

Author

• Jasmine Y. Ma, New York University