Spatial justice by Laurie Rubel
Mathematics Thinking & Learning, 2024
Review of Skovsmose's 2023 Critical Mathematics Education
Educational Technology & Society, 2022
In this paper, we introduce Notice, Wonder, Feel, Act, and Reimagine (NWFAR) to promote social ju... more In this paper, we introduce Notice, Wonder, Feel, Act, and Reimagine (NWFAR) to promote social justice in data science (DS) education. NWFAR draws on intersectional feminist DS to scaffold critical perspectives towards systems of power and oppression and attend to students' experiences in designs for learning. NWFAR adds three practices that are typically not emphasized in learning designs for DS: feelengaging emotions and the physical body; act-challenging, inspiring, or informing others towards change; and reimagine-envisioning how data, data methods, and data technologies could pursue different problems, solutions, and perspectives. We illustrate NWFAR through two design-based research projects from prior empirical work. Through these two examples, we demonstrate what thinking with NWFAR could look like in practice and highlight future possibilities for learning. We conclude with a discussion that focuses on the reimagining dimension, in which we highlight social-justice oriented theories.
Research in Mathematics Education
Current global challenges demand changes to mathematics curricula. In this paper, we draw on inte... more Current global challenges demand changes to mathematics curricula. In this paper, we draw on intersectional feminist theories to expand current visions of mathematical literacies and real-world problem solving. This expansion is necessary as a response to current crises (e.g., the COVID-19 pandemic and climate change) and how these crises are exacerbating the precarity of girls and women. We begin with the Programme for International Student Assessment's (PISA) framework for mathematical literacy (FML), since it functions as a global guide for curriculum. We first demonstrate what we view as the inadequacy of the FML to solve current crises or to mediate the precarity of girls and women. Then we re-envision the FML by integrating concepts of critical mathematics education with intersectional feminism. We re-envision how to think about mathematical literacies, and in particular, practices of mathematical reasoning and ways of classifying real-world problem contexts. We add practices of feeling, acting, and reimagining to conventional conceptions of mathematical reasoning and explore three thematic categories for real-world problem contexts.
Educational Studies in Mathematics
Data visualizations have proliferated throughout the COVID-19 pandemic to communicate information... more Data visualizations have proliferated throughout the COVID-19 pandemic to communicate information about the crisis and influence policy development and individual decision-making. In invoking exponential growth, mathematical modelling, statistical analysis, and the like, these data visualizations invite opportunities for mathematics teaching and learning. Yet data visualizations are social texts, authored from specific points of view, that narrate particular, and often consequential, stories. Their fundamental reliance on quantification and mathematics cements their social positioning as supposedly objective, reliable, and neutral. The reading of any data visualization demands unpacking the role of mathematics, including how data and variables have been formatted and how relationships are framed to narrate stories from particular points of view. We present an approach to a critical reading of data visualizations for the context of mathematics education that draws on three interrelated concepts: mathematical formatting (what gets quantified, measured, and how), framing (how variables are related and through what kind of data visualization), and narrating (which stories the data visualization tells, its potential impacts and limits). This approach to reading data visualisations includes a process of reimagining through reformatting, reframing and renarrating. We illustrate this approach and these three concepts using data visualizations published in the New York Times in 2020 about COVID-19. We offer a set of possible questions to guide a critical reading of data visualizations, beyond this set of examples.
Journal of the Learning Sciences
This paper explores teaching mathematics for spatial justice (Soja, 2010), as an extension of tea... more This paper explores teaching mathematics for spatial justice (Soja, 2010), as an extension of teaching mathematics for social justice (Gutstein, 2006). The study is contextualized in a 10-session curricular module focused on the spatial justice of a city’s two-tiered system of personal finance institutions (mainstream vs. alternative), piloted with two 11th/12th grade mathematics classes in a high school in a low-income neighborhood. The module includes a form of participatory action research known as participatory mapping (PM), examined here as a learning activity particularly conducive to urban settings. The study investigates learning opportunities and complexities opened up by PM for students. In particular, the analysis investigates how collecting narratives through PM engaged and complicated students’ senses of place, whereby narratives that surfaced challenged the module’s narrative about predatory lending. Findings are used to generate recommendations about ways to better su...
International Group for the Psychology of Mathematics Education, 2016
This paper describes the role of sense of place in students’ analysis of spatial data toward unde... more This paper describes the role of sense of place in students’ analysis of spatial data toward understanding the distribution of financial services in their city. High school students participated in a 10-session module about their city’s two-tiered financial system of banks and alternative financial institutions. The paper analyzes two class sessions organized around the use of ratios, or intensive variables, to understand the distribution: an embodied distribution activity atop a large floor map and individual exploration of scalable, data-rich digital maps. Analysis investigates the role of students’ sense of place as they grappled with these ratios. Students drew on their senses of place to interpret data and generate their own sets to associate in ratios. Abstract measures and data visualizations contained in the digital maps were less accessible to students in this iteration of the module.
Mathematics Teaching in the Middle School, 2016
Take a chance on introducing the mathematics of the lottery. It will further an understanding of ... more Take a chance on introducing the mathematics of the lottery. It will further an understanding of not only probability, combinatorics, large and small numbers, and data analyses but also social justice.
Harvard Educational Review, 2016
In this reflective essay, Laurie H. Rubel, Maren Hall-Wieckert, and Vivian Y. Lim present a desig... more In this reflective essay, Laurie H. Rubel, Maren Hall-Wieckert, and Vivian Y. Lim present a design heuristic for teaching mathematics for spatial justice (TMSpJ) based on their development of two curricular modules, one about the state lottery and the other about financial services in a city. Spatial tools, including data visualizations on maps and participatory mapping, were designed for youth to 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.
Mathematical Thinking and Learning, 2020
Bu araştırmanın amacı ortaokul yedinci sınıf öğrencilerinin 'Vücudumuzdaki Sistemler' ünitesine a... more Bu araştırmanın amacı ortaokul yedinci sınıf öğrencilerinin 'Vücudumuzdaki Sistemler' ünitesine ait konuları günlük yaşamla ilişkilendirme düzeylerini tespit etmektir. Araştırmanın örneklem grubu, Kocaeli'nin Karamürsel ilçesindeki rastgele belirlenmiş dört ortaokulun 7. sınıfında öğrenim gören 195 öğrenciden (90 kız, 105 erkek) oluşmaktadır. Tarama yönteminin kullanıldığı araştırmada öğrencilere Vücudumuzdaki Sistemler Ünitesine Yönelik Günlük Yaşamla İlişkilendirme Testi (GÜYİT) uygulanmıştır. Elde edilen veriler SPSS.20 istatistik programında kullanılarak analiz edilmiştir. Analizlerde hem testin geneli hem de alt boyutları için öğrencilerin verdikleri cevaplara ait frekans ve yüzde değerleri hesaplanmıştır. Elde edilen bulgulara göre, testin genelinde öğrencilerin %75.8'i doğru cevap verirken, %9.4'ü yanlış cevap vermiştir. Bulgular her bir faktör için ayrı ayrı incelendiğinde doğru cevap verenlerin oranı 'sindirim sistemi' konusu için %84.4, 'boşaltım sistemi' konusu için %66.7, 'sinir sistemi' konusu için %84.2, 'iç salgı bezleri' konusu için %68.6, 'duyu organları' konusu için %75.1, 'vücudumuzdaki sistemlerin sağlığı' konusu için %85.9 ve 'organ bağışı' konusu için %63.3 olarak belirlenmiştir. Buna göre öğrenciler tarafından en fazla günlük yaşamla ilişkilendirilen konu 'vücudumuzdaki sistemlerin sağlığı' iken, en az ilişkilendirilen konu 'organ bağışı' olmuştur.
The Mathematics Teacher, 2011
Maps at four levels of scale—global, national, regional, and local—provide a context for mathemat... more Maps at four levels of scale—global, national, regional, and local—provide a context for mathematical investigations that help teachers learn about their students.
This chapter investigates student learning in the context of a module about a city’s two-tiered f... more 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 th...
International Group for the Psychology of Mathematics Education, 2015
This paper focuses on student learning in the context of a curricular module on pawnshops piloted... more This paper focuses on student learning in the context of a curricular module on pawnshops piloted with 15 students in an urban high school. The paper describes pedagogical frameworks guiding the development of the module and summarizes key features of its curriculum. Analysis focuses on student growth with respect to mathematical understanding of percent and opinions about pawnshops. Findings include student adoption of ratio strategies indicative of conceptual understanding of percent, and development of critical opinions about pawnshops as a lending system.
Mathematical Thinking & Learning, 2020
Place-based education has traditionally had limited focus on mathematics, and critical mathematic... more Place-based education has traditionally had limited focus on mathematics, and critical mathematics education often lacks explicit attention to place and space. We explore integrating theories of place, spatial justice, and critical mathematics education. To begin, we consider various frameworks of place-including Indigenous, urban, and critical perspectives-to situate a discussion on how place acts as a shaping force on social relations like race, gender, and sexuality, and, conversely, how social relations shape place. We include mathematics as a category of social relations in that guiding framework. We next summarize and build on various notions of place and spatial justice, toward their integration with critical mathematics education. In so doing, we present teaching mathematics for spatial justice, or using mathematics 1) to identify power relations in and through place and 2) to transform the world by re-imagining and remaking place. We sidestep a false urban-rural divide and instead, illustrate the potential of teaching mathematics for spatial justice using rich examples organized around four thematic categories: geographies of opportunity, mapping, human mobility, and land relations and obligations.
2018
This paper presents a set of spatial tools for classroom learning about spatial justice. As part ... more This paper presents a set of spatial tools for classroom learning about spatial justice. As part of a larger team, we designed a curriculum that engaged learners with three spatial tools: 1) an oversized floor map, 2) interactive GIS maps, and 3) participatory mapping (PM). We anauze how these tools supported learning, using Elwood and Mitchell’s (2013) notion of political formation (similar to van Wart, Lanouette, and Parikh, 2016). Political formation includes politicization with respect to individual experiences of exclusion or unequal access, viewing inequities or injustices from collective perspectives, and creating shared, political knowledge. 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 PM 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.
Harvard Educational Review , 2016
In this reflective essay, Laurie H. Rubel, Maren Hall-Wieckert, and Vivian Y. Lim present a desi... more In this reflective essay, Laurie H. Rubel, Maren Hall-Wieckert, and Vivian Y. Lim present a design heuristic for teaching mathematics for spatial justice (TMSpJ) based on their development of two curricular modules, one about the state lottery and the other about financial services in a city. Spatial tools, including data visualizations on maps and participatory mapping, were designed for youth to 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.
This article explores integrating place-based education with critical mathematics toward
teaching... more 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.
In this reflective essay, Laurie Rubel, Maren Hall-Wieckert, and Vivian Lim present a... more 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.
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Spatial justice by Laurie Rubel
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.
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.
standards-based mathematics instruction, complex instruction, culturally relevant
pedagogy (CRP), and teaching mathematics for social justice (TMfSJ). The author
organizes these practices according to the dominant and critical axes in Gutiérrez’s
(2007a) equity framework. Among 12 teachers from 11 schools in a large urban
school district, the author presents case studies of 3 teachers who excelled with the
aforementioned dominant equity-directed practices but struggled with the critical
practices of connecting to students’ experiences called for in CRP and critical
mathematics called for in TMfSJ. The analysis explicitly explores the role of whiteness
in these struggles. The author presents implications and recommendations for
mathematics teacher education on how to better support teachers for equitable
teaching that includes these critical equity-directed practices