# “So We Only Have One We Share with More, and Then They Have Way More and They Share with Less”: Mathematics and Spatial Justice

## Abstract

This chapter investigates student learning in the context of a module about a city’s two-tiered financial system of banks and alternative financial institutions (i.e., pawnshops), held in ten sessions in a high school advisory class led by a mathematics teacher. The module exemplifies teaching mathematics for spatial justice, by extending teaching mathematics for social justice (Gutstein, 2006) with the idea that place matters (Gruenewald, 2003) and that justice has a geography (Soja, 2010). In this module, students use the concepts of percent to mathematize the costs of loans, and they analyze intensive variables to investigate spatial data about the density of these categories of institutions across their city. Spatial data is presented with GIS maps, layerable with demographic data and locations of financial institutions. The spatial distribution of the financial institutions reflects the inequalities of the spatial patterns in the city’s social demographics. Contextualized in the disparity of interest rates across these financial institutions, the spatial pattern not only reflects but reinforces those social inequalities. This chapter presents findings from one round of piloting and pursues the question: How did the module’s spatial justice orientation support the development of conceptual understanding of percent and ratio? Analysis focuses on growth with respect to mathematical understanding of percent and learning in class sessions organized around the use of ratios to understand the distribution. Findings include student adoption of strategies indicative of conceptual understandings of percent and development of critical opinions about their city’s two-tiered personal lending system.

## Keywords

Mathematics education Critical mathematics Critical geography Youth geography Spatial justice High school education Cartography Mapping Participatory mapping## Notes

### Acknowledgments

This material is based upon work supported by the National Science Foundation [NSF] under Grant No. DRL-1222430. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the NSF. We acknowledge the significant contributions of MIT’s Civic Data Design Lab in the design of the digital maps and mapping tools described in this manuscript. This research would not have been possible without the generosity of time and spirit of teachers and students from the New York City Department of Education. This material extends findings presented in conference papers presented at Psychology of Mathematics Education North America in 2015 and 2016.

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