Laurie H. Rubel

Revoicing in a Multilingual Classroom

The concept of revoicing has recently received a substantial amount of attention within the mathematics education community. One of the primary purposes of revoicing is to promote a deeper conceptual understanding of mathematics by positioning students in relation to one another, thereby facilitating student debate and mathematical argumentation. Our study reexamines revoicing in a multilingual high school algebra classroom; our findings challenge the assumption that revoicing is necessarily tightly connected with classroom argumentation. We demonstrate that a single discursive form, such as revoicing, can play a wide range of valuable functions within the classroom. More importantly, we investigate systematic differences in the ways that revoicing is used, by a particular teacher, across languages. Implications for policy and practice are discussed.

Teaching Mathematics for Spatial Justice: An Investigation of the Lottery

ABSTRACT 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 article 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.

Making Space for Place: Mapping Tools and Practices to Teach for Spatial Justice.

This article presents a set of spatial tools for classroom learning about spatial justice. As part of a larger team, we designed a curriculum that engaged 10 learners with 3 spatial tools: (a) an oversized floor map, (b) interactive geographic information systems (GIS) maps, and (c) participatory mapping. We analyze how these tools supported learning using notions of politicization. The floor map fed conceptual understandings of the map as a representational text and served as the terrain for an embodied activity to support proportional reasoning about inequitable distributions of resources. The data-rich GIS maps and their zoomability allowed for coordinating across multiple variables to connect patterns in inequities to other social processes. The participatory mapping enabled learners to make discoveries about, connect, and share beyond the individual classroom counterstories from people in the lived streets of their neighborhood. In aggregate, this set of spatial tools produced a complex, hybrid view of the city’s space, which contributed to learners’ political formation.

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

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.