The Power of Place: Spatializing Critical Mathematics Education

Proceedings of the Eleventh International Mathematics Education and Society Conference, 2021

Contemporary discourse about the 'opening'/'closing' of schools and what is 'inside'/'outside' the curriculum potentially exacerbates existing inequities in mathematics education. This paper explores how different spatial imaginaries might advance or hinder efforts to deeply and systematically pursue equity. We use critical postcolonial thought for our (re)imaginings in the South African context. We argue that viewing the school, the mathematics curriculum, and language as nouned, bounded, spatial objects highlights what needs attention and for whom, but also points to the indelible, structural nature of exclusion. We propose a notion of spatiality as experienced encountering. This recognises all people and their practices as strategic agents, and emphasises relations between people, but also between the mind, body and Earth.

In this reflective essay, Laurie Rubel, Maren Hall-Wieckert, and Vivian Lim present a design heuristic for teaching mathematics for spatial justice (TMSpJ), based on the development of two curricular modules, one about the lottery and the other about financial services in a city. Spatial tools, including data visualizations on maps and participatory mapping, were designed for youthto examine spatial injustices in these systems. The authors’ findings report reflections about supporting students to “read and write the world with mathematics” (Freire & Macedo, 1987; Gutstein, 2003). These reflections inform an expanded design heuristic for TMSpJ.

2015

Although equity-oriented discourse is working to move the mathematics education community from achievement-gap rhetoric toward a focus on opportunity gaps, it does not currently recognize the role of space and the politics of space in creating and maintaining opportunity gaps as it relates to mathematics education in urban settings. The purpose of this paper is to engage the task of re- conceptualizing urban mathematics education by proposing a framework for scholarship, policy, and practice. The authors engage scholarship in mathematics education, urban education, critical geography, and urban sociology to substantiate a socio-spatial framework for urban mathematics education, which features a visual schematic that locates mathematics teaching and learning—vis-à- vis a mathematics-instructional triad—within a system of socio-spatial considerations relevant to U.S. urban contexts.

2016

This article explores integrating place-based education with critical mathematics toward teaching mathematics for spatial justice. Local Lotto, a curricular module with associated digital tools, was designed to investigate the lottery as a critical spatial phenomenon and piloted in urban high schools. This paper describes findings from the second iteration in a remedial class in a low-income neighborhood. The research questions consider how the spatial focus supported the learning of mathematics and provided opportunities for students to think critically about the lottery using that mathematics. Findings include student interest in and engagement with the theme of the lottery familiar from outside of school with associated social justice implications. Students used mathematics and spatial evidence, at various levels of spatial scale, to support arguments about the lottery with greater success at narrower levels of scale. Suggestions about further innovations to scaffold place in a “critical pedagogy of place” in mathematics are provided.

Data literacy—the ability to work with, analyze, and make arguments with data—is essential in a data-driven society and can be instrumental toward engaging powerfully with civic issues.1 This paper illustrates how City Digits: Local Lotto, a high school curriculum and supporting web application, supported students in building data literacy. Local Lotto included opportunities for qualitative data collection and quantitative analysis, enabling youth to develop data-informed arguments about the lottery’s impact on local communities.

The purpose of this paper is to re-engage the task of conceptualizing urban mathematics education by proposing a theoretical framework for schol- arship, policy, and practice in urban mathematics education. The authors engage scholarship in mathematics education, urban education, critical geography, and urban sociology to consider a socio-spatial framework for urban mathematics education, which includes a visual schematic that locates mathematics teaching and learning—vis-à-vis a now-classic math-instructional triad—within a system of socio-spatial considerations relevant to urban contexts in the United States. The authors also consider the potential for such a framework for considering a more global perspective of urban within mathematics education scholarship.

n Mathematics and the Body: Material Entanglements in the Classroom by Elizabeth de Freitas and Nathalie Sinclair (2014), the authors call for a "radical reconfiguring" (p. 225) of mathematics education. Similarly, argues that "theories are living and breathing reconfigurings of the world" (p. 207) and that putting new materialist and posthumanist theories to work in mathematics education could open up a space for this radical reconfiguring. This book review is based on our developing thinking about the use of theory and its possibilities within urban mathematics education. We situate ourselves in what de Freitas and Sinclair call a "stretchy space of continuous transformation" (pp. 90-91)-continuing to think and re-think issues like equity with this text, letting the words wash over us , opening up and questioning urban mathematics education research. As two White women mathematics educators and emerging scholars in the field, we do not assert that theory alone or theory removed from practice can address the complex, prevalent, and long-lasting inequities present in mathematics education; however, we view theory in concert with practice as having potential to advance the field. de Freitas and Sinclair's theories, which they use to question school mathematics in general, could be built upon and deployed to expose the problematic presence of White rationality in urban classrooms. We encourage the reader to

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.

n Mathematics and the Body: Material Entanglements in the Classroom by Elizabeth de Freitas and Nathalie Sinclair (2014), the authors call for a "radical reconfiguring" (p. 225) of mathematics education. Similarly, argues that "theories are living and breathing reconfigurings of the world" (p. 207) and that putting new materialist and posthumanist theories to work in mathematics education could open up a space for this radical reconfiguring. This book review is based on our developing thinking about the use of theory and its possibilities within urban mathematics education. We situate ourselves in what de Freitas and Sinclair call a "stretchy space of continuous transformation" (pp. 90-91)-continuing to think and re-think issues like equity with this text, letting the words wash over us , opening up and questioning urban mathematics education research. As two White women mathematics educators and emerging scholars in the field, we do not assert that theory alone or theory removed from practice can address the complex, prevalent, and long-lasting inequities present in mathematics education; however, we view theory in concert with practice as having potential to advance the field. de Freitas and Sinclair's theories, which they use to question school mathematics in general, could be built upon and deployed to expose the problematic presence of White rationality in urban classrooms. We encourage the reader to

Journal of Urban Mathematics Education, 2018

It has been almost 25 years since Tate’s (1994) “state of the union address” on mathematics education for Black students invoked Woodson’s (1933/1990) passage as a clarion call to reject the foreign “pedagogy” of mathematics for Black students: And even in the certitude of science or mathematics it has been unfortunate that the approach to the Negro has been borrowed from a “foreign” method. (p. 4) Having read Tate’s article soon after beginning my PhD studies (circa 2000), it was one of my earliest awakenings in the field. It had crystalized a prior visit to a Wisconsin classroom on culturally relevant pedagogy taught by Professor Gloria Ladson-Billings and the admonition she spoke to me after class: “Lou, we don’t need another study on functions” (referencing the cognitively guided instruction dominant mathematics culture at my university). I understood this we. Our people. My people. It was the felt presence of my community and communities of the African and Caribbean diaspora upon whose hopes and dreams this work is pursued. Yet, Tate’s call was the harbinger of a more intrusive element in the mathematics of our people—the mathematics education reform enterprise itself.