Participatory Mapping Tools for Teaching Mathematics for Spatial Justice

• In Event: Reinscribing the City in Design Studies of Critical STEAM Conceptual Practice

Abstract

Introduction. How can youth claim their “right to the city” (Lefebvre, 1968)? Critical, spatial perspectives are crucial, because “everything that is social is simultaneously and inherently spatial” (Soja, 2010, p. 24). This paper describes a participatory mapping (PM) tool piloted in high schools in low-income, urban neighborhoods as part of mathematics investigations about the lottery and about financial institutions. Alternative financial institutions (AFI’s), like pawnshops or check-cashers, are predatory because they charge higher rates than banks and proliferate in low-income areas. With poor rates of return, lotteries are similarly predatory because advertisements and ticket-locations target low-income people. Mathematics is fundamental to understand the basis of both systems and to how they shape and are shaped by socio-spatial inequalities. PM in this project utilized geolocative mobile devices to capture media and ground-truth locations.

Frameworks. Maps invite questions about who has participated in whose mapping, what information has been overlooked, and who is empowered/disempowered (Chambers, 2006). PM positions students as agentive actors, turning map into text that “works for them” (Wood, 2010). PM encourages students to engage in “decolonization” and “reinhabitation” (Gruenewald, 2003). “Decolonization” recognizes critical factors impacting place and occurs through analyses of inequalities. “Reinhabitation” occurs through exploration of the local neighborhood. “Reinhabitation” and “decolonization” co-constitute the development of a mathematically-informed, critical perspective on place.

PM in education literature is transdisciplinary, cross-cutting literacy and social studies (e.g., So, Seow, & Looi, 2009) to quantitative reasoning around data and geometry (e.g., Taylor & Hall, 2013). The literature includes using mobile technologies for out-of-school mapping (e.g., So, Seow, & Looi, 2009; Burke, Greene, & McKenna, 2014; Santo, Ferguson, & Trippel, 2010), with others limited to mapping in school (e.g., Literat, 2013; Mukhophadyay & Enyedy, 2007). Storytelling in PM through photography (e.g., Santo et al., 2010) or interviews (e.g., Mitchell & Elwood, 2012) is emphasized. This paper studies how youth engage with PM tools in the context of mathematics for spatial justice investigations.

Results. Students enthusiastically used the PM tool across five iterations to produce stories (Figure 1) and to investigate and document place with mathematics (Figure 2), culminating in a multi-layered and multi-indexed map (Figure 3). Patterns of student participation were disrupted as Spanish-speaking, ELL students became leaders in the field. PM revealed unexpected stories, such as a person who buys lottery tickets in wealthy neighborhoods, or finding local AFI’s welcoming in contrast with banks. Unexpected stories that arose through PM were unaddressed by the pre-designed digital maps and present challenges to coordinating PM with data-analysis mapping tools.

Significance. Mobile technologies open up PM opportunities for mathematics education. This project demonstrates potential for and student interest in engaging in PM to inform spatial analyses. PM mediates between students’ local knowledge and institutionalized knowledge about their neighborhoods (Lefebvre, 1991), and across levels of scale. In future iterations, our goals are to extend the field research experience, to foreground stories/counterstories more explicitly with students, and to find ways to better draw out the mathematics in those stories.

Authors

• Laurie Rubel, Brooklyn College - CUNY

• Maren Hall-Wieckert, The City University of New York

• Vivian Y. Lim, University of Pennsylvania

• Mary Candace Raygoza, University of California - Los Angeles

• Lauren Shookhoff, New York City Department of Education