Search

Background: The field of mathematics education has made progress toward generating a set of instructional practices that could support improvements in the learning opportunities made available to groups of students who historically have been underserved and marginalized. Studies that contribute to this growing body of work are often conducted in learning environments that are framed as “successful.” As a researcher who is concerned with issues of equity and who acknowledges the importance of closely attending to the quality of the mathematical activity in which students are being asked to engage, my stance on “successful learning environments” pulls from both Gutiérrez’s descriptions of what characterizes classrooms as aiming for equity and the emphasis on the importance of conceptually oriented goals for student learning that is outlined in documents like the Standards. Though as a field we are growing in our knowledge of practices that support these successful learning environments, this knowledge has not yet been reflected in many of the observational tools, rubrics, and protocols used to study these environments. In addition, there is a growing need to develop empirically grounded ways of attending to the extent to which the practices that are being outlined in research literature actually contribute to the “success” of these learning environments.Purpose: The purpose of this article is to explore one way of meeting this growing need by describing the complex work of developing a set of classroom observation rubrics (the Equity and Access Rubrics for Mathematics Instruction, EAR-MI) designed to support efforts in identifying and observing critical features of classrooms characterized as having potentialfor “success.” In developing the rubrics, I took as my starting place findings from an analysis that compared a set of classrooms that were characterized as demonstrating aspects of successful learning environments and a set of classrooms that were not characterized as successful. This paper not only describes the process of developing the rubrics, but also outlines some of the qualitative differences that distinguished more and less effective examples of the practices the rubrics are designed to capture.Research Design: In designing the rubrics, I engaged in multiple cycles of qualitative analyses of video data collected from a large-scale study. Specifically, I iteratively designed, tested, and revised the developing rubrics while consistently collaborating with, consulting with, and receiving feedback from different experts in the field of education.Conclusions: Although I fully acknowledge and recognize that there are several tensions and limitations of this work, I argue that developing rubrics like the EAR-MI is still worthwhile. One reason that I give for continuing these types of efforts is that it contributes to the work of breaking down forms of practice into components and identifying key aspects of specific practices that are critical for supporting student learning in ways that make potentially productive routines of action visible to and learnable by others, which may ultimately contribute to the development of more successful learning environments. I also argue that rubrics like the EAR-MI have the potential to support researchers in developing stronger evidence of the effectiveness of practices that prior research has identified as critical for marginalized students and in more accurately and concretely identifying and describing learning environments as having potential for “success.”

Background/Context: Instructional policy aims to shift the nature of teaching and learning. Decades of policy studies have highlighted the challenges inherent in these aims and the conditions necessary to support such change, including a robust infrastructure to support teacher learning. Further, teachers themselves must perceive and experience their policy environment to be supportive of calls to shift instruction.Purpose/Objective/Research Question/Focus of Study: In this study, we examine the connection between teachers’ perceptions of their policy environments and their instructional practices over time, in the context of college-and-career-readiness (CCR) standards implementation. While conducted in the context of standards implementation, our findings apply to supporting instructional change through policy more broadly.Setting: We examine implementation of CCR standards in two unique state contexts: Texas and Ohio. These states represent important differences in demographics and in their approaches to CCR standards implementation over time.Research Design: We use a convergent mixed-methods design that draws on state-representative teacher survey data at two points in time (allowing for a trend analysis to understand how teachers’ perceptions and experiences evolve), longitudinal interview data with state education leaders, and interview data with educators in one case study district in each state.Data Collection and Analysis: Surveys measured teachers’ perceptions of their policy environments, as well as their self-reported instructional practices. Interviews focused on understanding state- and district-level policies, guidance, and resources, and educators’ enactment of standards. Survey analysis included descriptive analysis of patterns over time and hierarchical linear modeling. To unpack broad-based survey patterns, we coded qualitative data and developed assertions based on emergent patterns.Findings/Results: We found that Texas teachers agreed more strongly than Ohio teachers that their policy environment had aligned, specific, and stable resources, as well as accountability mechanisms in place. Specificity of guidance and resources for standards implementation predicted teachers’ use of standards-emphasized instruction in 2019. These patterns reflected each state’s approach to policy implementation: a robust state-level infrastructure for guidance and support in Texas, compared with fewer state-developed resources in Ohio in favor of local control. Still, aspects of teachers’ local context—in particular, lack of infrastructure for ongoing, embedded professional learning—limited teachers’ ability to engage in state-developed guidance.Conclusions/Recommendations: Our study offers enduring lessons about how to establish the policy conditions necessary to support teachers to change instruction. Findings suggest a need for states to develop resources that clarify instructional shifts for teachers, and districts must balance these top-down resources with ongoing opportunities for educators to adapt resources to suit their students’ needs.

Background and Context: Racialized disparities in curricular tracking have long been ascribed to narrow tests that create a hierarchy of perceived ability. Consequently, teachers are urged to reject deficit views of ability and embrace more expansive techniques to reveal and respond to the real-life needs of students, especially those from minoritized groups. Paradoxically, these tools, upheld as equity strategies today, had prior careers racializing populations along a hierarchy of perceived needs. That hierarchy, which gave a humanitarian basis for curricular tracking, continues to produce racializing effects today.Purpose: This article rethinks how teachers are taught to distinguish the real-life needs of students from marginalized communities. As a history of the present, it examines how demographic distinctions in health-related needs emerged historically and became tied to lower track science and mathematics instruction. We ask: To what extent do current strategies persist in dividing populations and prescribing distinct pedagogies? Have the normalizing impulses of past tools been removed or rearticulated in recent reforms that promote educational and health equity?Research Design: We first analyzed articles reviewed as exemplary of culturally responsive science and mathematics education to identify techniques recommended to uncover students’ real-life needs. Next, we compared these techniques with similar tools promoted in early 20th-century U.S. science and mathematics education journals, when these fields began distinguishing types of students and matching them with distinct tiers of instruction.Conclusions: Despite key shifts over the century (e.g., from treating inherent pathologies to redressing inequities), similar tools operate as humanitarian techniques today. That is, they classify populations as having “immediate needs” for intervention in daily life that preempt “future needs” for academic preparation. The resulting hierarchy of perceived needs orders students and subject matter from applied relevance to abstract rigor. This yields four dangers: (1) positing target students and families as not-yet-capable of self-direction, (2) prioritizing for target groups an applied and often lower prestige curriculum with consequences for their academic trajectories, (3) depoliticizing systemic inequities as problems of attitude adjustment, and (4) depoliticizing mainstream science and mathematics education by isolating sociopolitical concerns as compensatory interventions. We argue that school science and mathematics are not unique in these respects but epitomize risks present whenever social scientific tools offer an ostensibly neutral basis for seeing and sorting difference.

Background/Context: In New Orleans, Louisiana, in the years following Hurricane Katrina, predominantly white education reformers have used entrepreneurial support to dismantle the predominantly Black city’s public education system. Using racial domination without community approval, these education reformers have educationally disenfranchised the Black community by implementing No Excuses (NE) Charter School Management Organizations (CMO). The rise in these organizations has also led to the mass firing of the city’s majority Black educator base and the hiring of majority white educators. Scholarship on NE CMOs notes their use of dehumanizing behavioral practices meant to control their student populations. Accounts, however, are limited from those who have witnessed, experienced, or resisted these dehumanizing behavioral practices.Purpose/Objective/Focus of Study: Through the critical race theory (CRT) lens of racial realism, this paper provides a critical race personal counternarrative (CRPCN) that characterizes the racist and racialized disciplinary and surveillance practices used to control Black students’ bodies. It examines my experiences as a teacher within an NE CMO, the Knowledge Is Power Program (KIPP) school in New Orleans. Furthermore, this paper underscores my own Black fugitive pedagogic acts alongside my Black students, acts that allowed us to create fleeting moments of freedom inside and outside our classroom.Research Design: I relied on critical race methodology to construct a CRPCN against KIPP, which prides itself on positive behavior practices and social justice. The evidence I drew on included free-written notes, conversations with former students and teachers, media (e.g., photos and videos), and scholarly literature. To analyze data, I drew on CRT concepts of racial realism and the permanence of racism in U.S. society to underscore Black fugitivity, anti-Black surveillance, and discipline.Conclusion/Recommendations: Racial realism provides a lens for identifying the evolution of racialized surveillance technologies on Black bodies within the United States. Although critics characterize racial realism as overly pessimistic, this paper notes one way that scholars, educators, students, and parents can draw on this tool of racial resistance to accept the current racial reality, uncover racially oppressive schooling practices, and highlight strategies of survival through fugitive acts.

There is a significant body of research in mathematics education suggesting that historically excluded learners (Black, Latinx, Indigenous, and poor) experience devaluation, inequities, exclusion, and violence (Berry, 2008; Gutiérrez, 2002; Gutstein, 2003; Martin, 2015; McGee & Martin, 2011). Research, policies, and reforms in education “[have] been violent to marginalized peoples who are represented by perspectives that are neither kind to their cultural worldview nor accurate regarding their priorities” (Leonardo, 2013, p. 603). This commentary unpacks how the four articles in this special issue prioritize historically excluded learners’ cultural worldviews. Specifically, this commentary focuses on practices across the four articles that respond to historically excluded learners’ mathematical, social, and cultural needs.

Background: Traditional mathematics logics lead to inequities that reproduce narratives such as the myths of racialized and gendered hierarchies of mathematical ability (Hottinger, 2016; Martin, 2009). Black girls sit at the bottom of both racialized and gendered hierarchies; however, research over the past decade has provided evidence that Black teachers challenge these hierarchies for their Black students. Therefore, we show how two teachers work against these logics to create space for their Black girl students to flourish as learners and producers of mathematics.Focus of Study: This research documents the logics that lead to supportive spaces for Black girls in two Black mathematics teachers’ classrooms: What are the supportive logics of successful mathematics teachers who support Black girls’ achievement in middle school classrooms?Setting: This research was a secondary analysis of videos collected as part of the Gates-funded Understanding Teaching Quality (UTQ) project.Case Study Selection: The study used MANOVA to quantitatively select teachers based on change in mathematics achievement. Two teachers were selected based on number and percentage of Black girls in the top 5% of change in achievement across the dataset. Although not part of the selection criteria, both mathematics teachers identified as Black.Research Design: The study used a case study design to describe the mathematics practices and the logics that they supported for the two successful Black mathematics teachers.Data Collection and Analysis: The dataset included four lessons per teacher with two cameras for each lesson. Open coding was used to identify the practices used by teachers drawing on logics as an orienting concept.Findings: Interestingly, both classrooms were fairly procedural in their mathematics focus; however, the classrooms challenged logics of individualism, racialized and gendered hierarchies of mathematics ability, and carceral pedagogy. Teachers supported Black student autonomy in terms of both behavior and intellectual contribution, and specifically positioned Black girls as experts and highlighted collective responsibility for peers’ mathematics learning.Conclusions: Although the classrooms did not display the cultural competence or sociopolitical consciousness foundational to culturally relevant pedagogy, the Black teachers did challenge traditional logics found in mathematics classrooms. Through a focus on collectivity, autonomy, and competence, the relational ways in which teachers positioned Black girls ran counter to logics that too often frame them as incapable mathematically.

Background/Context: Unconscious racial bias (URB) can be a pernicious form of racism. In light of increased awareness of and research on the subject, URB work has become a key focus of equity work in health care, education, and corporate contexts as part of broader calls for racial justice. In Canada, targeting URB in education has become a policy priority at the national, provincial, and school board levels. The role of individual and organizational URB is now widely recognized in policy as central to equitable outcomes in schooling; however, research is limited on how to engage these forms of racism in educational contexts. Prevailing approaches to URB work in schools often include truncated one-off workshops, which leave unaddressed the connections between the individual racial biases, and the operations of white supremacy and racism at the institutional, systemic, and structural levels.Purpose/Objective/Research Question/Focus of Study: While URB is increasingly well-understood by social psychologists, there has been limited engagement from critical scholars working in areas such as critical race theory (CRT), anti-colonialism, and critical whiteness studies—despite the popularity of interrogating URB as an anti-racism strategy in education. CRT in education has laid bare and problematized the central function of schooling in the safeguarding and management of white supremacy. This project emerged from a dual recognition of URB as a productive entry point for racial awareness and anti-racism work, alongside a significant concern about the failure of mainstream URB discourse to address structural racism and white supremacy—masking at times the deeper ways that Euro-colonial racism underpins social relations in contemporary U.S., Canadian, European, and other contexts. This work seeks to address these limitations in the design of the study through deep work with participants. Specifically, the study sought to understand better the impacts of reading critical texts focusing on systemic, structural, and institutional racism on teachers’ understandings of their own racial biases, as well as teachers’ perspectives on the impacts of reading critical texts in terms of their professional practices.Research Design: This article reports on the findings of a 10-month study with secondary teachers in Toronto, Canada, focusing on critical approaches to racial bias mitigation in education. In addition to asking participants to enact a series of URB mitigation strategies developed in the field of social psychology, this study also required participants to read and reflect on one of the following critical anti-racism nonfiction texts: White Fragility: Why It’s So Hard for White People to Talk About Racismby Robin DiAngelo (2018); Policing Black Lives: State Violence in Canada From Slavery to the Presentby Robyn Maynard (2017); Everyday Antiracism: Getting Real About Race in School, edited by Mica Pollock (2008); Unsettling the Settler Within: Indian Residential Schools, Truth Telling, and Reconciliation in Canadaby Paulette Regan (2014); and Monstrous Intimacies: Making Post-Slavery Subjectsby Christina Sharpe (2010). The project was designed using multiple data sources from participants, including electronic survey responses, ongoing journaling/reflection, a midpoint check-in questionnaire, and a final interview. These multiple entry points, as well as the duration of the project, aimed to go beyond the taken-for-granted and toward deeper understanding over time.Conclusions/Recommendations: Findings suggest that reading these works impacted teachers’ understandings of race and racism in terms of their teaching, as well as in terms of their personal relationships to race and racism, increasing their inclination and ability to address race and anti-racism. This work allowed for critical reflection to seep into the most intimate and invisible moments of operationalized whiteness in the professional and personal spheres of participants. This suggests an important complementarity between teacher intervention practices emerging from social psychology, and the introduction and engagement of critical anti-racist and anti-colonial texts in terms of teachers’ work for racial justice.

Background: Current efforts to promote reasoning, problem solving, and discussion are often framed as advancing equity, but scholarship suggests individual students’ opportunities to learn can vary considerably in classrooms that attempt to take up these approaches to teaching mathematics. Noticing students’ mathematical strengths and positioning their contributions as competent is among aspects of instruction associated with more equitable learning outcomes for students from marginalized groups, but research has yet to comprehensively examine the range and nuance of this aspect of teachers’ practice in classrooms that feature broad distributions of participation.Purpose: The purpose of this study was to examine teachers’ instructional practice with respect to assigning competence in two mathematics classrooms that demonstrated high levels of student participation. We investigated the kinds of situations in which teachers positioned students as competent, and the ways assigning competence opened opportunities to participate.Setting: Data were collected at a public elementary school in a culturally, linguistically, and economically diverse neighborhood in southern California.Participants: Participants included two teachers and 45 students from two third-grade classrooms. Teachers had participated in ongoing professional development focused on leveraging children’s mathematical thinking in instruction.Research Design: We drew from qualitative methods for analyzing video to investigate classroom interactions from 12 mathematics lessons. Data sources included video recordings, transcripts, and student work. We used Studiocode software to parse each lesson into phases and episodes. Drawing from previous studies, we identified a subset of episodes in which teachers explicitly positioned a student’s contribution as competent. An iterative process of coding and discussion was used to analyze patterns with respect to student participation, teacher support, and the unfolding of rights and obligations related to participating in mathematical activity.Findings: Analyses revealed different kinds of situations in which students participated in mathematically substantive ways (in terms of providing detailed explanations of their ideas or engaging with the details of a peer’s idea) and teachers positioned their contributions as competent. These situations included highlighting, clarifying, and amplifying contributions; supporting the specificity of student contributions; recognizing emergent ideas; and validating unprompted attention to mathematical details. Assignments of competence emerged in ways that were integrated into teachers’ ongoing efforts to surface and make explicit the details of their mathematical ideas, while also broadening the kinds of contributions students could make to joint mathematical work.Conclusions: Helping students to know what it could look and sound like to participate in the moment while recognizing a wide range of contributions as competent created openings for students who in many classrooms might be excluded or relegated to the periphery of conversations. Making competence explicit was a contingent, relational practice that required teachers to find specific ways of leveraging student strengths to support their participation. Recommendations for advancing mathematics teaching must attend to the nuances with which particular practices unfold to open or constrain individual students’ opportunities to learn.

Background: Although large-scale research over the last 15 years demonstrates the positive effects of Black teachers for Black students on various student outcomes, these studies focus on average effects. This leaves space to examine classroom practices to detail howthe positive effects may be realized through the everyday interactions between Black teachers and their Black students, specifically in mathematics. To conceptualize the mathematics classroom we draw on hooks’s (2001) concept of “Homeplace” as a site where one is humanized in resistance to broader contexts of power, as a “haven” free from negative dominant discourses.Focus of Study: This research documents the classroom practices of successful Black mathematics teachers who are affirming students’ identities through their classroom practices: How do successful Black mathematics teachers enact affirming mathematics classrooms with their Black students?Setting: This research was a secondary analysis of videos collected as part of the Gates-funded Understanding Teaching Quality (UTQ) project. All of the schools in the UTQ study were located in one metropolitan area.Case Study Selection: The study used MANOVA to quantitatively select teachers based on mathematics achievement and quality of relational interactions. Two teachers were selected and, although not part of the selection criteria, both mathematics teachers identified as Black.Research Design: The study used a case study design to describe the mathematics practices of two Black teachers.Data Collection and Analysis: The dataset included four lessons per teacher with two cameras for each lesson. Open coding was used to identify the practices used by teachers drawing on Homeplace as an orienting concept.Findings: The classrooms enacted Homeplace through affirming students’ humanity and communicating a sense of belonging in three ways: building collective responsibility for the mathematics, framing students as mathematically capable, and relating to students’ lives. In addition to the themes, undercurrents of care, humor, praise, and the use of Black Language were clearly visible.Conclusions: Although the classrooms did not display the sociopolitical consciousness foundational to culturally relevant pedagogy, the Black teachers did create an environment consistent with Homeplace. Through cultivating a classroom that affirmed Black students’ humanity and dignity and communicated to them a sense of belonging, they resisted negative racialized narratives and increased students’ mathematics achievement.