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Making Equity Considerations Explicit With Mathematics Discussion Approximations: Reflecting on Attempts and Challenges
Abstract
Supporting preservice teachers to learn to facilitate math discussions in ways that are both mathematically productive and equitable is a goal for many mathematics teacher educators (MTEs). In pursuit of this goal, MTEs may utilize approximations of practice, such as rehearsals of mathematics discussions or enactments in school settings. However, little is known about how MTEs integrate attention to equity considerations into work with such approximations. This chapter calls upon MTEs using approximations of practice to make their attention to issues of equity explicit and to engage in cycles of self-examination to hold themselves accountable for following through on commitments to equity. As an example, a self-study of one MTE's practice in an elementary mathematics methods course is shared. Findings identify challenges that the MTE encountered with maintaining an explicit equity focus with respect to mathematics discussion approximations. Implications for equity-oriented MTEs are discussed.
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Recent scholarship has explored mathematical demands faced by mathematics teacher educators and ways to support their development, but little attention has been given to the basic question of how mathematics teacher educators think about content knowledge for teaching. Knowing what they think could inform efforts to support them. Our analysis reveals that some think about mathematical knowledge for teaching as an independent, abstracted resource to be taught and learned in relative isolation from teaching, while others think about it as dynamic, situated work. We argue that this key difference matters for how they work with teachers. Further, our analysis reveals that their thinking about both teaching and justice interacts with their thinking about mathematical knowledge for teaching and that their thinking in these other two domains can be a resource for supporting their mathematical development.
Elementary mathematics teacher education often draws on research-based frameworks that center children as mathematical thinkers, grounding teaching in children’s mathematical strategies and ideas and as a means to attend to equity in mathematics teaching and learning. In this conceptual article, a group of critical mathematics teacher educators of color reflect on the boundaries of Cognitively Guided Instruction (CGI) as a research-based mathematical instructional framework advancing equity through a sociopolitical perspective of mathematics instruction connected to race, power, and identity. We specifically discuss CGI along the dominant and critical approaches to equity outlined by Gutiérrez’s (2007, 2009) framework. We present strategies used to extend our work with CGI and call for the field to continue critical conversations of examining mathematical instructional frameworks as we center equity and criticality.
Within teacher education, work on mathematics teaching often occurs separately from work on issues of race and racism. Typically, mathematics content and methods courses tackle subject matter-specific concepts and teaching practices, while the history and current dynamics of racial inequity in education, if addressed at all, tend to be the domain of social foundations or multicultural education courses (Cochran-Smith et al., 2015). Challenging this separation, this dissertation offers a vision of teaching that can serve as a guiding framework in mathematics teacher education: race cognizant math teaching, or acting on the critical race ideology of race cognizance (Frankenberg, 1993) within the teaching of mathematics. Set in a two-course elementary teacher education sequence that advances a version of race cognizant math teaching, this study explores the learning, discourse, and early practice of six white teacher candidates across those courses. Qualitative case study methods are used to pursue three research questions. First, how do focal teacher candidates take up course ideas and practices that have the potential to support race cognizant mathematics teaching, and what trajectories characterize this uptake? Second, what uptake of course ideas and practices is evident in focal teacher candidates’ early enactments of mathematics teaching? Third, how do focal teacher candidates engage with issues of race and racism in their talk and writing, and what does this reveal about their learning? Data sources consist of submitted course assignments (including video records of math teaching enactments), observation of class sessions, and four rounds of semi-structured interviews with focal participants. This study’s findings both confirm and complicate existing research on white teacher candidates’ engagement with issues of race and racism. On the one hand, focal participants exhibited anticipated patterns of race evasion. Findings include patterns of generalized and flattened uptake of race cognizant course constructs, indirect and ambiguous race talk, and alignment with aspects of color-blind ideology (Bonilla-Silva, 2018). On the other hand, however, patterns of race evasion were not uniform, nor were they mutually exclusive with evidence of race cognizant uptake and discourse. For instance, in their early math teaching enactments, several participants made deliberate efforts to act on race cognizant aims and rationales, even though they were not explicit about their attention to race until pressed. In addition, even teacher candidates who were relatively consistent in demonstrating race evasive thinking and uptake of course emphases also had moments where they indicated that they were grappling with the pervasive and persistent nature of racism and its impact on mathematics teaching and learning. An important conclusion of this study is that teacher candidates’ talk and writing about race and racism did not necessarily indicate a transparent or simple alignment with either race cognizant or race evasive ideology. Additionally, teacher candidates’ shifts towards race cognizant math teaching were not straightforward; progress was complicated by obstacles of enactment and conflicting ideas about race, racism, and mathematics teaching and learning. One implication is that teacher educators must combine consideration of teacher candidates’ language with careful attention to their practice and the ideological implications of how teacher candidates are understanding race, racism, and their roles and responsibilities as teachers. Teacher educators should also expect complexity, ambiguity, and shifts over time, rather than a binary or static division between race evasive and race cognizant learning and practice.
Background/Context
With a rationale informed by the demographic imperative, the resegregation of public schools, and our positionalities as researchers, we understand both the high stakes and the complexity of capacitating White preservice and in-service teachers capable of anti-racist praxis and race-visible teaching and learning in public school classrooms.
Purpose/Objective/Research Question/Focus of Study
Deploying the framework of colorblind racism, we systematically reviewed race-evasive White teacher identity studies and answered the question: What can we learn from 25 years of research?
Research Design
In using the method called the synoptic text, we engaged electronic databases, with special emphasis on ERIC EBSCOhost. The simple and general search term “White teachers” conducted using year-by-year parameters provided the most systematic net for capturing relevant studies. In narrowing our focus, we developed the following criteria: (a) White teachers as central topic, (b) analytical emphases on colorblind racism, (c) publication in peer-reviewed journals, (d) use of qualitative and/or narrative research methodologies, and (e) publication date between 1990 and 2015.
Data Collection and Analysis
Our general search yielded 136 (N = 136) peer-reviewed empirical qualitative and/or narrative studies between 1990 and 2015, and after narrowing our criteria, we found 47 race-evasive White teacher identity studies (n = 47, 47/136) that we reviewed here. Each study in the document universe was abstracted by authors, added to a spreadsheet, and categorized by emergent themes.
Findings/Results
The following five themes emerged and developed over the last 25 years: (a) racialized silence and invisibility (9/47), (b) resistance and active reconstruction of White privilege (12/47), (c) whiteness in institutional and social contexts (8/47), (d) fertile paradoxes in new research (9/47), and (e) reflexive whiteness pedagogies (9/47).
Conclusions/Recommendations
We believe our literature review identifies the complex contours of White preservice and in-service teachers’ silence, resistance to, engagement in, and pedagogical grappling with racism, whiteness, and White privilege. The importance of pre-service and in-service teachers being able to engage, understand, and challenge these issues becomes critically important at our crossroads in the present, especially given the recent election that bolstered open and tacit White supremacists into power. If White teachers are to engage racism, whiteness, and White privilege, they must do so with as opposed to for their students, in a Freirean sense. If teaching for social justice is important, renewed interest and investment in White teacher identity studies and related whiteness pedagogies is key for the next 25 years.
In this paper, we respond to the continued harm of deficit discourses in mathematics education, focusing on discourses that systematically devalue the knowledge and abilities of students of color in classrooms in the United States. We specifically aim to (1) develop a sociopolitical framework for conceptualizing mathematics teacher noticing and (2) conceptualize and illustrate the enactment of noticing that challenges deficit discourses about these students and their communities—anti-deficit noticing—through the lens of our framework. We address our first research aim by introducing the FAIR framework, which foregrounds the role of sociopolitical Framing as an essential component of noticing that shapes and is shaped by Attending, Interpreting, and Responding, processes that have frequently been discussed in studies of teacher noticing. We show how an analysis using FAIR can contribute to understanding deficit noticing. We then conceptualize and illustrate anti-deficit noticing using the case of Oscar, a college mathematics instructor who worked with many Black and Hispanic students and himself identified as Hispanic. We discuss the local context that supported Oscar’s anti-deficit noticing and conclude with implications for future research and practice.
This article examines the ways Hazel, a white girl entering kindergarten, became known as a child with a problem rather than a problem child in her gentrifying school. Building on a year of classroom observations and interviews with students, school staff, and parents, author Alexandra Freidus identifies the role of racialized discourses related to disposition, medicalization, family, and community in shaping Hazel’s reputation and contrasts Hazel’s reputation with that of Marquise, a Black boy in her class. Hazel’s and Marquise’s storylines teach us that to fully understand and address the differences in how Black and white children are disciplined, we need to look closely at the allowances and affordances we make for some students, as well as how we disproportionately punish others. By examining the ways educators in a gentrifying school construct white innocence and Black culpability, this study illustrates the relational nature of the “school discipline gap” and helps us understand how and why some children are disproportionately subject to surveillance and exclusion and others are not.
In this article the author shares a self-study investigation into how the quality of talk and opportunities to participate are distributed across individual students based on race and gender in her college math class. Readers will learn how to conduct a similar investigation in their classroom. A discussion of ways to use the information gathered from equitable mathematics classroom discourse investigations will follow.
Abstract
Background/Context: The Core Practice movement continues to gain momentum in teacher education research. Yet critics highlight that equitable teaching cannot be reduced to a set of “core” practices, arguing that such a reduction risks representing teaching as technical work that will be neither culturally responsive nor sustaining. Instead, they argue that, if preservice teachers are to teach equitably, they must have opportunities to develop professional reasoning that takes the specific strengths and needs of students, communities, and subject matter into account.
Purpose: This analysis takes up the question of how and whether pedagogies of investigation and enactment can support preservice teachers' development of the professional reasoning that equitable teaching requires. It conceptualizes two types of professional reasoning: interpretive, in which reasoners decide how to frame problems and make subsequent efforts to solve them, and prescriptive, in which reasoners solve a problem as given.
Research Design: This work is a qualitative, multiple case study, based on design research in which preservice teachers participated in three different cycles of investigation and enactment, which were designed around a teaching practice central to equitable teaching: making student thinking visible. Preservice teachers attended to students’ thinking in the context of the collaborative analysis of students’ writing and also through designed simulations of student-teacher writing conferences.
Findings/Results: Preservice teachers’ collaborative analysis of students’ writing supported prescriptive professional reasoning about disciplinary ideas in ELA and writing instruction (i.e., How do seventh graders use hyperbole? How is hyperbole related to the Six Traits of Writing?), while the simulation of a writing conference supported preservice teachers to reason interpretively about how to support students’ affective commitment to writing with their desire to teach academic concepts about writing.
Conclusions/Recommendations: This analysis highlights an important heuristic for the design of pedagogies in teacher education: Teacher educators need to attend to preservice teachers’ opportunities for both interpretive and prescriptive reasoning. Both are essential for teachers, but only interpretive reasoning will support teachers to teach in ways that are both intellectually rigorous and equitable. The article further describes how and why a tempting assumption—that opportunities to role play student-teacher interactions will support preservice teachers to reason interpretively, while non-interactive work will not—is incomplete and avoidable.
Despite decades of equity- and inclusion-oriented discourse and reform in mathematics education, Black learners in the U.S. continue to experience dehumanizing and violent forms of mathematics education. I suggest that equity for Black learners in mathematics education is a delusion rooted in the fictions of white imaginaries, contingent on appeasing white logics and sensitivities, and characterized at best by incremental changes that do little to threaten the maintenance of racial hierarchies inside or outside of mathematics education. Moreover, the forms of inclusion offered up in equity-oriented discourses and reforms represent contexts of containment and enclosure that keep Black people in their same relative position. Refusal is suggested as a strategy for Black learners to resist the anti-Black character of mathematics education, and as a first step in actualizing forms of mathematics education that are worthy of Black learners.
As practice-based teacher education (PBTE) has become more prevalent, debates about its contribution have emerged. Critics of PBTE question whether emphasizing practice will support a technocratic approach to teacher education rather than promoting instruction that is responsive to students’ ideas. This qualitative case study was motivated by an interest in understanding whether and in what ways practice-based approaches to teacher learning can support teachers in practicing responsiveness as opposed to practicing decontextualized moves. To this end, we investigated how early-career teachers in a practice-based professional development program were supported to approximate teaching practices. We focused on the extent to which approximations of practice supported teachers to hone their skill at being responsive to students’ ideas. Findings revealed characteristics of approximations of practice that support teachers in developing their capacity to enact responsive instruction. These findings have implications for program design, teacher educator pedagogy, and future research.
In this chapter, I provide an argument for why we should stop using equity as a goal and, instead, move toward rehumanizing mathematics. I provide 8 dimensions we should consider when rehumanizing mathematics teaching and learning.
In this article, the authors provide a framework for understanding whiteness in mathematics education. While whiteness is receiving more attention in the broader education literature, only a handful of scholars address whiteness in mathematics education in any form. This lack of attention to whiteness leaves it invisible and neutral in documenting mathematics as a racialized space. Naming White institutional spaces, as well as the mechanisms that oppress students, can provide those who work in the field of mathematics education with specific ideas about combat-ting these racist structures. The framework developed and presented here illustrates three dimensions of White institutional space—institutional, labor, and identity—that are intended to support mathematics educators in two ways: (a) systematically documenting how whiteness subjugates historically marginalized students of color and their agency in resisting this oppression, and (b) making visible the ways in which whiteness impacts White students to reproduce racial privilege.
This exploratory study examined how two teachers from two New Zealand primary schools introduced and taught the same mathematics lesson to their lowest ability group of year 2 and 3 students. Emphasis was given to analysing the positioning of the teacher and students and the developing storylines and social acts from that positioning. Different positionings by teachers of themselves and their students led to inequitable opportunities for active and collaborative participation in the mathematics. The differences in pedagogy revealed through the use of positioning theory suggest that the way teachers positioned themselves and their students was more influential than the resources they were teaching with.
In this article, the author provides insight into the pedagogical processes for delegating mathematical authority to students, through the use of specific classroom structures, as a means to strive toward equity. Employing qualitative methods, the author analyzes transcripts of classroom video, along with field notes and teacher and student interviews, collected during one semester of the participating teacher's Algebra I course. The author addresses how the teacher's practice was striving toward equity through the use of classroom structures that delegated mathematical authority to students. Analyses revealed that the teacher delegated mathematical authority through the use of student presentations, Shuffle Quizzes, and Participation Quizzes. Each instance featured was chosen to highlight a different facet of the ways in which delegating authority repositioned students as competent sense-makers.
This paper examines a series of instructional activities that provide prospective elementary teachers with an opportunity to engage in one of the more difficult practices to learn within mathematics teaching—organizing a mathematical discussion. Within a mathematics methods course, representations and decomposition of practice built from the Five Practices framework (Smith and Stein in Five practices for orchestrating productive mathematics discussions. Corwin Press, Thousand Oaks, CA, 2011) were implemented and studied to examine how prospective elementary teachers set goals, selected and sequenced available student work, and planned questions within a mathematical discussion. We examined prospective elementary teachers’ strengths and weaknesses in these facets through an approximation of practice set in a lesson context familiar to the prospective elementary teachers. Our results demonstrated that although prospective elementary teachers set varying goals for a discussion, their pedagogical choices in planning their discussion tended to be consistent with the goals they have set. These results support the focused development of prospective elementary teachers’ goal setting as an implication for mathematics teacher educators.
In this article, we theorize the relation between race and schooling and consider the implications for learning. While the body of research on culture and learning has come to define learning as an inherently cultural and social process, scholars have few theoretical tools to help us think about the role of race and racism in relation to students' access to identities as learners and to learning. We draw on both theoretical and empirical literature to make three core arguments: (a) racial 'storylines' or narratives are prevalent in our society and have powerful implications for learners, particularly for youth from marginalized communities; (b) these racial storylines are a critical aspect of life in schools, which serve the purpose of racially and academically socializing students; and (c) as these storylines are invoked in school settings, certain identities are made available, imposed, or closed down. Such identities have important implications for students' opportunities to learn and their engagement in learning settings. As we conclude, we consider the potential of alternative spaces, which can serve to counter dominant narratives about who is capable of learning and how learning takes place, and open new spaces for identity and learning. Copyright (C) 2013 S. Karger AG, Basel
We develop theory within the field of mathematics education based on analysis of an imported theory—positioning theory—and the way it is used in the field. After summarizing positioning theory, we identify some conceptual fuzziness, particularly in core terms “positioning” and “storyline.” We offer Lemke’s idea of timescales as a way to refine the theory. We then use the refined theory to analyze strong examples from mathematics education literature as a source of insight into how this theory is being and could be used in the field. We identify the need to be clear about scale in describing positioning and storyline, to recognize that multiple storylines and positionings are at play in any interaction, to be specific about the role of communication acts in development of positioning and storyline, and to differentiate among different kinds of positioning. We claim that attention to these issues will help researchers recognize narratives and relationships at play that may be outside their expectation and also underpin stronger warranted claims.
This article focuses on using simulations of practice in teacher education. We studied preservice teachers’ engagement with a popular simulations platform, which creates mixed-reality simulations of five digital avatars controlled by a single live interactor. Because simulations are only an approximation of real practice, our overarching goal was to understand how mathematical stereotypes might arise in simulated spaces. We used Discourse analysis to classify the stereotypes present and the EQUIP observation tool to understand how PTs made participation opportunities available. We found that the simulations might have perpetuated overtly racist and sexist stereotypes and that negatively stereotyped students were afforded lower-quality opportunities to participate. We discuss how to mitigate potential harm caused and offer guidance for redesigning more equitable and antiracist simulations. Our goal is to raise critical questions for our field around the use of simulations of practice.
We introduce a teacher learning practice called EQUIP-ing , which aims to foster sociopolitical noticing by leveraging EQUIP, an equity-oriented classroom observation tool. We detail our iterations of EQUIP-ing to a field-based Number Talk experience in a secondary mathematics methods course with 25 White prospective teachers (PTs). We offer empirical accounts of how EQUIP-ing empowered PTs to connect their teaching practices with racialized and gendered patterns of student participation; as a result, PTs began to reconsider taken-for-granted practices. However, we also found that PTs demonstrated potentially detrimental ways of attributing marginalizing patterns to minoritized students without actionable plans to redress the inequity. We conclude by inviting mathematics teacher educators to apply EQUIP-ing while emphasizing purposeful support for asset-based noticing.
Approximations of practice are opportunities for preservice teachers (PSTs) to engage in components of teaching. However, how the varying levels of complexity or authenticity of teaching create different learning opportunities for PSTs is underexplored. Forty-one studies related to approximations of mathematics teaching were reviewed to explore how approximations are embedded in PST education, how authenticity represents itself in approximations, and how mathematics teacher educators report approximations facilitating PSTs’ learning. The review identified eight types of approximations used, indicating that PSTs developed aspects of specific practices such as professional noticing, conducting a meaningful mathematics discussion, as well as generic lesson planning and implementation. We propose teacher education programs consider a continuum of authenticity to capture the complexity of approximations of practice as well as the recomposition of decomposed practices. We discuss how varying levels of authenticity in approximations of practice creates different opportunities for PSTs.
Couched within a larger critique of assessment practices and how they are used to stigmatize African American children, the authors examine teachers’ instructional practices in response to demands of increasing test scores. Many mathematics teachers might be unaware of how these test-driven instructional practices can simultaneously reflect well-intentioned motivations and contribute to the oppression of their African American students. The authors further argue that the focus of assessing African American children via comparison to white children reveals underlying institutionally-based racist assumptions about the competencies of African American students. Strategies are suggested for helping teachers resist test-driven instructional practices while promoting excellence and empowerment for African American students in mathematics.
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.
This paper uses quantitative analytics to study talk-based participation in 100 mathematics classrooms across one racially diverse urban school district in the USA. Using the EQUIP observation tool and hierarchical linear modeling, we characterize the quantity and quality of participation for students across 3025 coded turns, by race and gender. We found that in general, boys participated significantly more than girls. We also found that Latinx and Asian/Pacific Islander students had significantly fewer turns than Black and White students. To interpret these findings in context, we analyzed interviews from 29 district leaders using a poststructural framework organized around D/discourse.
In this conceptual article, Niral Shah critically analyzes how the narrative that “Asians are good at math” positions Asian people as racial subjects. Despite being false, the “Asians are good at math” narrative is prominent in STEM education and is also familiar to the general public. To analyze the narrative's discursive impact on Asian personhood, Shah uses poststructural race theory and Mills's notion of the racial contract, focusing on the interaction between discourses of STEM and discourses of race. Rather than a harmless compliment, Shah argues that the type of mathematical success implied in the narrative dehumanizes Asian people and perpetuates White supremacy, and calls for racial equity and justice work in STEM education to account for ontological questions of personhood alongside traditional concerns about academic content learning and economic access to STEM careers.
Research on collaborative learning has focused on its potential to foster successful problem solving. Less attention, though, has been given to issues of equity. In this article, we investigate how inequity can become amplified and attenuated within collaborative learning through small interactional moves that accumulate to produce broader patterns of equity or inequity. Our theoretical perspective utilizes Boaler’s notion of relational equity and introduces what we term participatory equity. Research was conducted in a computer science course co-taught by the authors and taken by upper-elementary students. Data sources include audio recordings of students’ collaborative interactions, ethnographic field notes, student work, and student surveys. This article focuses on a single student, Jason, and his dyadic interactions, and builds upon our previous analyses of his interactions with four higher-performing partners. Findings reveal how the interplay between classroom structures and student enactments shaped two types of inequity during collaborative learning. We conclude by discussing implications for theorizing and analyzing equity and inequity, as well as pedagogical considerations for structuring collaborative learning to attenuate inequity.
This study is situated within efforts to embrace the challenge of preparing teacher candidates (TCs) for the complexities of teaching mathematics while creating shared opportunities for inquiry across teacher education programs. We developed a shared decomposition of leading mathematics discussions that could be used across our teacher education sites to provide a means to guide our work as teacher educators (TEs) and to allow us to analyze the ways that we prepare TCs to lead mathematics discussions. We address two research questions: What components of the decomposition of discussion were worked on in two different teacher education programs with particular organizational designs? What opportunities to learn about leading discussions were evident in the ways this decomposition was used? Our findings indicate that it is possible to use a common decomposition of teaching practice and engage TCs in learning the interactive work of teaching, while at the same time, adapting to meet the unique characteristics of the site context. In our study, the TEs and TCs were able to attend to all components of the decomposition and in relation to each other. The TEs used a variety of pedagogies of investigation (representations and decomposition) and enactment (including approximations) to support their work, drawing on them in ways that fit their unique organizational contexts.
This article explores teaching practices described in NCTM’s Principles to Actions: Ensuring Mathematical Success for All. Investigating and mitigating implicit bias in questions are discussed in this article, which is another installment in the series.
Equity in mathematics classroom discourse is a pressing concern, but analyzing issues of equity using observational tools remains a challenge. In this article, the authors propose equity analytics as a quantitative approach to analyzing aspects of equity and inequity in classrooms. They introduce a classroom observation tool that focuses on relatively low-inference dimensions of classroom discourse, which are cross-tabulated with demographic markers (e.g., gender, race) to identify patterns of more and less equitable participation within and across lessons.
Frankenberg explores the unique intersection of race and sex as she examines the way that white women relate to racism. She writes from the assumption that whiteness is socially constructed rather than naturally pre-existing. She theorizes "from experience" to offer a unique perspective that retains the strength of a theoretical foundation as well as the relatability of personal narratives. She interviews thirty white women to get their perspectives on various racial topics and gain a critical standpoint for thinking about individual and social forces that construct and maintain whiteness in contemporary society. She begins with the question, "What is white women's relationship to racism?" The women discuss various aspects of interracial courtship, the role of power in acknowledging racial differences, and the function of language in facing and overcoming the negative effects of this difference.
Background/Context
There is evidence that race affects students’ learning experiences in mathematics, a subject typically thought of as “race-neutral” and “culture-free.” Research in psychology and sociology has shown that racial narratives (e.g., “Asians are good at math”) are pervasive in U.S. culture and play a critical role in shaping people's lived experiences. However, racial narratives have received little explicit attention in the mathematics education literature.
Purpose
The purpose of this study was to examine the racial ideological context of mathematics education, specifically in terms of how students made sense of racial narratives about academic ability.
Participants
Thirty-five students identifying as Asian, Black or African American, Latinx, Polynesian, White, and mixed race were interviewed. These students were recruited from four mathematics classrooms observed by the author at a racially diverse high school in Northern California.
Research Design
This qualitative study employed an ethnographic research design to gather data on the meanings students constructed around issues of race in the context of mathematics.
Data Collection and Analysis
A semistructured interview protocol was used to conduct individual interviews with each student participant. Field notes were taken during 130 hours of participant observation over the course of a school year. Interview transcripts and field notes were analyzed for instances in which participants invoked racial narratives. Each of these narratives was first coded by topic and by the racial group to which the narrative referred. Narrative clusters were then identified and analyzed in order to understand how the narratives were related to each other.
Findings
Students invoked a variety of racial narratives about both mathematical and nonmathematical topics (e.g., athletic ability, general intelligence, parenting practices). Importantly, students did not invoke these narratives in isolation. Instead, nearly all of these narratives were invoked in conjunction with at least one other narrative. This relationality among racial narratives shows how the academic abilities of learners from diverse racial backgrounds are constructed in relation to each other, often in ways that position non-Asian students of color as inferior in mathematics.
Conclusions/Recommendations
This article suggests the need for study designs and analytical approaches that theorize race as a relational construct that transcends the Black-White paradigm. Further, this article challenges researchers and practitioners to reconsider boundaries between what is deemed “mathematical” and “nonmathematical” in classroom discourse, specifically with respect to sociopolitical phenomena like race. Two African American boys, Will and Derrick, wait patiently as their math teacher circulates the room. She is passing back the results of the latest math test. Will receives his grade: He earned an ‘A.’ Derrick sees Will's grade and exclaims: “Oh you're hecka smart in math! You must have some Asian in you!”
This article takes a critical approach to unsettling the apathy around Black girls’ and women’s mathematics achievement and participation. I discuss how prevailing narratives about White girls and women, as well as Black boys and men, make the existence of coherent narratives of Black girls and women in mathematics essentially impossible. I argue that Black girls and women serve as a referent group providing a quiet, invisible, and menial labor of sanitizing theoretical and empirical spaces for other demographic groups. Using an example, I describe the process through which Black girls and women are rendered invisible in mathematics. To conclude, I call for the creation, occupation, and sharing of positive, socio-epistemic spaces that allow for the visibility of Black girls and women in mathematics.
Students do not all benefit equally from participation in collaborative discussions. Issues of equity can be seen in mathematical group work in a variety of ways if equity is defined as a fair distribution of opportunities to learn (Esmonde, 2009). Studies investigating how equity issues arise have typically focused on whether students have access to correct mathematical explanations.
Managing mathematical discussion is known to be challenging for novice teachers. Coaching within student teacher rehearsals of teaching has been shown to develop mathematics teaching practice, but can be time consuming. To examine how coaching using questions could assist novice teachers to promote mathematical thinking and discussions within time-constrained programmes, videos of rehearsals, reflective debriefs, and student teacher surveys were collected across a range of courses over 4 years. Findings included that student teacher roles in rehearsals were enhanced through coaching with questions and co-construction was enabled. Coaching questions exposed effective practice, particularly in relation to orchestrating mathematical discussion, enabling student teachers to reflect, discuss, make decisions, and immediately trial teaching strategies. Questions appeared to lengthen rehearsals but improved their effectiveness through enhancing participation and enabling co-construction of meaning. Findings indicate that questions used in coaching of rehearsals inform and empower novice teachers, essential factors within initial teacher education for equitable and ambitious mathematics teaching.
Video cases and video clubs have become popular tools for supporting teacher learning. One concern is that many of the video projects discussed in the research literature may unintentionally continue to perpetuate deficit perspectives about students by focusing more on their gaps in understanding than on the strengths they bring to their learning. This article describes a video club that is part of a multidimensional professional development network that aims to re-culture mathematics classrooms so that all students have challenging and empowering learning experiences. I discuss shifts in teachers' ways of seeing and talking about students' mathematical activity that the video club has made possible, as well as features of the video club that have supported these shifts.
Central to ambitious teaching is a constellation of practices we have come to call “leveraging student thinking.” In leveraging, teachers position students’ understanding and reasoning as a central means to drive learning forward. While leveraging typically is described as a feature of mature practice, in this article we examine approximations of leveraging as enacted by elementary teachers who are just beginning their careers. In addition to providing an existence proof that novices can leverage when teaching elementary mathematics, the analysis surfaces and illustrates four pressure points—epistemic, academic, developmental, and managerial—that can short-circuit the development of novices’ efforts. Our framing of these pressure points both spotlights the complex dynamics at play, and establishes an agenda for supporting the development of this practice: learning to leverage student thinking is a challenging and long-term endeavor, rather than a routine easily acquired.
This book considers in unprecedented detail one of the most confounding questions in American racial practice: when to speak about people in racial terms. Viewing "race talk" through the lens of a California high school and district, Colormute draws on three years of ethnographic research on everyday race labeling in education. Based on the author's experiences as a teacher as well as an anthropologist, it discusses the role race plays in everyday and policy talk about such familiar topics as discipline, achievement, curriculum reform, and educational inequality. Pollock illustrates the wide variations in the way speakers use race labels. Sometimes people use them without thinking twice; at other moments they avoid them at all costs or use them only in the description of particular situations. While a major concern of everyday race talk in schools is that racial descriptions will be inaccurate or inappropriate, Pollock demonstrates that anxiously suppressing race words (being what she terms "colormute") can also cause educators to reproduce the very racial inequities they abhor. The book assists readers in cultivating a greater understanding of the pitfalls and possibilities of everyday race talk and clarifies previously murky discussions of "colorblindness." By bridging the gap between theory and practice, Colormute will be enormously helpful in fostering ongoing conversations about dismantling racial inequality in America.
In recent years, work in practice-based teacher education has focused on identifying and elaborating how teacher educators (TEs) use pedagogies of enactment to learn in and from practice. However, research on these pedagogies is still in its early development. Building on prior analyses, this article elaborates a particular pedagogy of enactment, rehearsal, developed through a collaboration of elementary mathematics TEs across three institutions. Rehearsals are embedded within learning cycles that provide repeated opportunities for novice teachers (NTs) to investigate, reflect on, and enact teaching through coached feedback. This article shares a set of insights gained from 5 years of developing, studying, and learning how to support NTs’ enactment in rehearsal. The insights we share in this article contribute to building a knowledge base for pedagogies of teacher education.
Engaging students as active participants in mathematics classroom discussions has great potential to promote student learning. Less well understood is how teachers can promote beneficial student participation, and how teacher-student interaction relates to student achievement. This study examined how the kinds of teacher practices that may encourage beneficial student participation relate to student achievement in elementary school mathematics classrooms. Using videotaped recordings, we examined the extent to which students explained their own ideas and engaged with others’ ideas and how teachers supported these kinds of student participation. Linking teacher practices, student participation, and achievement all at the individual student level, we found that student achievement was best predicted by the combination of teacher practices and student participation. The results show that taking into account student participation is necessary for understanding how teaching practices relate to student mathematics learning. © 2015, Springer Science+Business Media Dordrecht (outside the USA).