Abstract
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 how the 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.
Research over the last 15 years has demonstrated the positive effects of Black teachers for Black students on various student outcomes (Dee, 2004, 2005; Egalite et al., 2015; Gershenson et al., 2016, 2017; McGrady & Reynolds, 2013). This literature demonstrates how Black teachers have higher expectations of Black students, raise Black student achievement, and subsequently increase access to college. However, although these large-scale studies provide evidence that, on average, Black teachers are more effective with Black students, there are two specific limitations we aim to address in this work. First, the average effect means there are better and worse Black teachers, which can lead to general notions that all Black teachers are better for Black students. This is linked to broader narratives calling for more Black teachers, rather than a focus on which Black teachers, or which classroom practices employed by Black teachers, are actually benefiting Black students. Repeated calls to examine the effective teaching of Black teachers as a means to inform the practices of all teachers have largely gone unanswered in the literature (Acosta, 2019; Dixson & Dingus, 2008). Second, given the scale of the existing studies, none of them could examine classroom practices and learning environments to detail how the positive effects may be realized through the everyday interactions between Black teachers and their Black students.
Given that, we specifically focus on the relational interactions between successful Black teachers and their Black students. By relational interaction, we mean the communicative actions between teachers and students through verbal and nonverbal behavior, which convey meaning above and beyond instructional techniques (Battey, 2013). We focus on this construct specifically because it has been shown to be a key difference in how Black and white teachers, in the same schools, interact with their Black students (Battey et al., 2018).
Additionally, by examining the relational dimensions of Black teachers’ classrooms, we begin to trace how bell hooks’s notion of “Homeplace” may be used to conceptualize the spaces Black teachers create. hooks (2001) describes Homeplace as a site where one is humanized in resistance to broader contexts of power, as a “haven” free from negative dominant discourses. Geographer Gil Valentine (2007) elaborates on how power operates in spaces, “specific spaces (home, work, community) are produced and stabilized by the dominant groups that occupy them, such that they . . . define ways of being” (p. 18). Linking this to education, the space of mathematics classrooms, including notions of who can do mathematics and how they should do it, have predominantly been shaped by white norms (Battey & Leyva, 2016). In contrast, Black teachers who create classrooms as sites of Homeplace construct humanized spaces for their Black students to bring their fully realized ways of being inside the classroom walls. Furthermore, the concept of Homeplace provided insight into how Black teachers may encourage the success of Black students in ways that are culturally specific. By creating spaces where Black students are viewed as whole and capable—in contrast to white norms and discourses of deficit—we posit that successful Black teachers’ practices have the capacity to positively shape the space of the classroom and the bodies that interact within it.
In this paper, we posit that Homeplace is at work within these two teachers’ classrooms, where each maintains space for their students to feel that they belong and to affirm their humanity. We found that the teachers enacted this in three key ways: building collective responsibility for the mathematics, framing students as mathematically capable, and relating to students’ lives. However, as Davis, Frank, and Clark (2013) discussed previously, we caution that this does not mean that all Black teachers enact these practices nor that these are the only ways for Black teachers to be successful. This would ignore the structural challenges that Black teachers face and could falsely portray them as a monolithic group, which we discuss later in this article. Additionally, we see this focus on Homeplace as a step toward responding to Martin’s (2007) question about “Who should teach mathematics to African American children?” (p. 6). The answer to this question for us is not necessarily a simple one or one that can be teased out from large-scale studies of racial match or mismatch between teachers and students. However, that literature does raise the importance of studying the positive impact that successful Black teachers have on their Black students, specifically in mathematics. We take a stance in responding to this need by documenting the classroom practices of successful Black mathematics teachers who are affirming students’ identities through their classroom practices. The research question this study responds to is: How do successful Black mathematics teachers enact affirming mathematics classrooms with their Black students?
Homeplace
hooks (2001) centers the concept of Homeplace in the realities of Black women’s lives. In doing so, she positions Black women as the primary guides and teachers within families and communities. We caution that this concept is not meant to praise a self-sacrificing role for Black women or to position their domesticity as “natural,” a point hooks herself is careful to note (hooks, 2001). Rather, hooks explains that Black women have historically been the sole purveyors of home as a political site of resistance, detailing the ways in which Black women have created and maintained these spaces that provided shelter, comfort, care, “elevation of spirit,” and nurturance in direct contrast to the society of oppression that lives outside the home. hooks makes clear that Black women’s choices in creating and maintaining such spaces had a radical political element, regardless of explicit intent, and that the construction of a Homeplace was concerned with the eradication of racism at its core.
Throughout this research, we identified elements of comfort, care, humor, nurturance, and humanization at play in the classrooms we examined and therefore called upon hooks’s Homeplace as a means to conceptualize the ways in which Black teachers’ practices could be understood to affirm Black students and positively impact their mathematics achievement. Across hooks’s work, she repeatedly alludes to two central overarching principles in describing what constitutes a Homeplace: communicating a sense of belonging and affirming humanity in the face of a white supremacist world. Just as in the literal space of Black women’s homes that hooks writes of, where Homeplace is constructed in the classroom, it functions by way of these principles being enacted through varied means and exists as a site of resistance where Black teachers may effectively “restore . . . the dignity denied [Black students] on the outside in the public world” (hooks, 2001, p. 384).
Although we center the paper on the concept of Homeplace, we acknowledge the overlap with culturally relevant pedagogy (CRP) (Ladson-Billings, 1995). In delineating the theory, Ladson-Billings outlines three broad CRP principles: academic challenge, cultural competence, and sociopolitical consciousness. The clearest connection between Homeplace and CRP is the principle of cultural competence, which highlights teachers drawing on students’ home and language practices as assets within the classroom. In this way, cultural competence clearly aligns with the principles of communicating a sense of belonging and affirming humanity so central to Homeplace. These connections can further be seen in work documenting teacher embodiment of cultural competence as “warm demanders,” which centers the care and comfort that teachers provide as they challenge students to learn meaningful content (Ware, 2006). However, although Homeplace highlights that the choice to construct spaces of care, nurturing, and safety for Black students in a white supremacist world is in itself an arguably radically political act, the explicit sociopolitical consciousness that Ladson-Billings (1995) elaborates was not evident in the classrooms we examined. Therefore, although the classroom environments described in the findings overlap with CRP, we see the practices described in this paper more closely aligning with the notion of Homeplace.
Black Mathematics Teachers
There is a long history of scholarship on Black teachers in schools (Brown, 2009; Fairclough, 2009; Foster, 1997; Irvine, 1989; Lynn, 2006). This work has examined Black teachers during segregation, post–Brown v. Board of Education, intersectionality, and current practices and perspectives. However, only recently has research shifted to examine Black mathematics teachers to understand their perspectives and roles in classrooms (Clark et al., 2013; Frank, 2019). The majority of this work has been published in the last decade (Clark et al., 2009; Davis et al., 2013; Frank, 2019; Frank et al., 2018), put forth in dissertations (e.g., Frank, 2013; Leavitt, 2010; Peterek, 2009), or published in a single special issue of Teachers College Record (Birky et al., 2013; Chazan et al., 2013; Clark et al., 2013; Johnson et al., 2013). However, before detailing what this recent research has detailed about Black mathematics teachers, we want to clarify the perspective this paper takes on Black teachers.
First, it is critical in the documenting of their perspectives and practices that this work challenges a monolithic portrayal of Black teachers. In other words, Black teachers represent a diverse group of practitioners that cannot be essentialized. In line with Chazan and colleagues (2013), we aim to challenge deficit narratives about urban schools, which frame them as failing and defective. Instead, this research positions the practice of urban Black mathematics teachers as something to learn from and emulate. At the same time, although it is crucial to resist the tendency to essentialize Black mathematics teachers or the pedagogy they use, as many have pointed out, there are commonalities in terms of experiences and cultural practices that represent the “collective Black” (Gholson & Wilkes, 2017; Martin, 2015). Therefore, we think it critical to both disrupt portrayals of Black teachers as having one perspective and, at the same time, highlight clear cultural connections across their perspectives and practices.
Lastly, in line with Frank (2019) and Clark et al. (2013), we are not aiming to portray just any Black mathematics teachers. As noted in Clark and colleagues (2013), “We explicitly seek to avoid selecting troubled teachers or teachers sometimes described as heroic or exceptional” (p. 16). This is critical, because as Lynn (2001) argued, “Studies of Black teachers become inconsequential if [researchers] cannot provide some evidence that what these teachers do in classrooms actually makes a difference in the lives of Black students” (p. 43). We also take this lens for this paper, but we extend this work by examining successful Black mathematics teachers of Black students with a particular focus on the interactions that they have with their students. Although past work often focuses on teachers’ perspectives, that is beyond the scope of this paper, because we did not have access to interviews or data from the teachers themselves, which may have illuminated their political motivations or consciousness. Instead, we focused on specific classroom practices that teachers used to enact the concept of Homeplace for students. Therefore, by close examination of classroom interactions, we are attempting to portray the instructional practices of successful Black teachers that supported the mathematics learning of their predominantly Black students.
Homeplace in the Classroom Practices of Successful Black Mathematics Teachers
Although hooks’s concept of Homeplace has been used to describe the space of the home that Black women traditionally created and maintained, it has application to the classrooms of teachers who create a refuge and site of resistance for their Black students. The literature presents a range of practices that Black mathematics teachers employ in supporting their Black students. Here, we focus on how the practices of successful Black mathematics teachers in existing research may be understood through the lens of Homeplace; that is, where teachers have chosen to cultivate classrooms that communicate belonging and affirm the humanity of their Black students. We group the practices into three categories: designing problem contexts, using cultural forms of language and expression, and personally connecting with students. We detail each of these below, noting commonalities as well as differences.
With respect to problem contexts, successful Black teachers have enacted a range of ways to design curriculum to connect with and support the mathematical learning of their students. In discussing Madison Morgan, a successful Black mathematics teacher, Birky, Chazan, and Morris (2013) outline how she built a coherent curriculum around supporting students’ meaning-making through the use of cultural referents or real-life contexts in mathematics lessons. Another teacher, Gloria Mirriex, drew on stories from cultural contexts such as cooking, family, and cleaning house to make mathematics more meaningful for students (Peterek, 2009). In both cases, the teachers drew on cultural practices to center problem solving in ways that affirmed students’ home practices.
Successful Black mathematics teachers often use cultural forms of language and expression in the classroom that affirm Black ways of being (Frank, 2019). A standout example of this from the literature is Floyd Lee, who used oratory similar to a sermon to communicate the purpose of learning math and succeeding educationally to students (Johnson et al., 2013). Lee used these lively speeches to challenge stereotypes and representations in the media about Black people, affirming the humanity and capability of his students. Scholar April Baker-Bell (2020) explains how Black Language, including its rhetorical styles, has been relegated to slang and questioned for its appropriateness outside of the home due to Eurocentric and racist norms. Citing Smitherman (1994), she explains how the Black church has long resisted such conformity and thus has been a “rich reservoir of terms and expressions of Black Language” (Baker-Bell, 2020, p. 69). It is no surprise, then, that Black educators constructing Homeplace as a site of refuge would communicate via these culturally specific modes of discourse. In a similar way, Peterek (2009) describes how Ms. Mirriex used Black Language rhetorical modes of call and response, chants, and rhythmic strategies with her students, again drawing on shared cultural practices from Black churches. Neal and Battey (2014) discuss Mr. Gray’s use of Black Language at times as well as cultural forms of movement, humor, personal stories to communicate the purpose of persevering with mathematics, and informal language to connect with students. Although the practices varied, these teachers employed the use of cultural forms of language and expressions, shaping a space where students could feel they belonged in the mathematics classrooms.
Lastly, successful Black teachers have been shown to connect personally with students and use their voice to advocate for them (Johnson et al., 2013; Leavitt, 2010; Neal & Battey, 2014). This is in line with creating a space that supports a sense of home. In Floyd Lee’s speeches, care is a central focus (Johnson et al., 2013). Likewise, Mr. Gray communicated care in terms of supporting students through difficulty and in communicating personal stories about his own struggles (Neal & Battey, 2014). Both teachers sometimes used Black Language in communicating with students, but we should say that the care across the two teachers looked very different. Mr. Gray had a warmer sense of care whereas Mr. Lee exhibited a more assertive care. Ms. Mirriex exhibited care through a deep commitment to her students, but also demanded much from them (Peterek, 2009). Irrespective of the way that caring comes off, all three teachers cared for students with racial awareness (Bartell, 2011), and in doing so affirmed students’ humanity.
Across the research, there is an undercurrent that the teachers all believe, expect, and support students to succeed mathematically and in school more broadly (Birky et al., 2013; Foster, 1997; Johnson et al., 2013; Lynn, 2001; Neal & Battey, 2014; Peterek, 2009). As Frank (2019) notes, “teacher expectations lay the groundwork for students’ trajectories of mathematics achievement (Clark et al., 2013; Martin, 2007)” (p. 101). Each of the practices noted here underlie a belief in students’ competence as well as it being the teacher’s job to make the curriculum engaging and comprehensible for students. However, it is important not just to have these expectations, but also to communicate them personally and through care, so they are felt by students. For us, then, conveying a belief in Black students’ mathematical competence is another connection to Homeplace because it affirms their capability to learn mathematics.
Although past work can be examined using the concept of Homeplace as background, in this study, we foreground the concept to focus on a smaller grain size of the interactional space of the classroom. In this sense, we analyzed the interactions between teachers and students to characterize the ways in which teachers created space in negotiation with their predominantly Black students. In doing this, we attempt to systematically document the kinds of practices that the teachers used to construct a space where Black students could successfully learn mathematics. However, our aim is not to boil these practices down to teacher “moves,” divorcing them from context in a way that trivializes their teaching (Dixson & Dingus, 2008). Instead, we connect the practices to patterns of interaction that constitute the construction of a Homeplace, highlighting the underlying principles of practice that enable these “moves” to carry meaning and communicate asset-based messages to students in mathematics.
Consistent with hooks’s conceptualization of Homeplace, the research aimed to learn from two Black women, aligning with Dixson and Dingus (2008), who state that “educational research should also consider how best to illuminate the pedagogy of Black women teachers in a manner that informs the practices of all teachers” (p. 831). Therefore, while drawing on the classroom practices of these Black women, we do this to inform the practices of mathematics teachers more broadly in creating affirming spaces for Black students. Finally, we focus on middle school mathematics teachers because it is a critical juncture for Black students in attaining mathematical proficiency that will give them access to higher-level mathematics, college, and participating more broadly in society (Berry, 2008; Davis et al., 2013).
Methods
This research was a secondary analysis of videos collected as part of the Gates-funded Understanding Teaching Quality (UTQ) study (http://www.utqstudy.org). The original dataset collected videos in both middle school English language arts (ELA) and mathematics classrooms during the 2009–2010 and 2010–2011 school years. All of the schools in the UTQ study were located in one metropolitan area. The dataset includes four lesson videos per teacher (two in the fall and two in the spring) as well as mathematics achievement scores prior to and during the year of data collection. There were 100 mathematics teachers in the entire dataset. A sample of 25 teachers (100 videotaped lessons) was chosen to perform additional analysis of relational interactions (RIs) between teachers and students (as previously defined). Approximately half (12) of the lessons were in predominantly white classrooms with all white teachers. The other half (13) were collected in predominantly Black classrooms with seven having Black teachers and the remaining six classrooms having white teachers. The 13 teachers in the predominantly Black classrooms were in four schools, with at least one white and Black teacher at the school.
This study used both RIs and change in achievement to select strong teachers of Black students. Using MANOVA, we selected teachers who had Black students perform at or better than other teachers across the sample. After selecting two teachers, we engaged in qualitative analysis to detail how teachers were constructing a space where their Black students were achieving mathematical success.
Participants
All 25 teachers taught in schools within the same metropolitan area in the United States. They were chosen based on having complete data in terms of lesson videos, student and teacher demographic information, and student achievement. Teachers were selected from four predominantly white and four predominantly Black schools for the purpose of a racial match analysis (see Battey et al., 2018). Of the 25 teachers included in this study, 13 taught in predominantly Black classrooms. Because this paper is focused on successful teachers of Black students, we detail those classrooms here. Demographically, the 13 predominantly Black classrooms were: 69–95% Black, 0–9% white, 4–17% Hispanic, and 0–8% Asian. Across the four schools, 86% of students qualified for free or reduced price lunch. Additionally, less than 1% of Black students were identified as gifted and 3% were identified for special education in the four schools. The 13 teachers in predominantly Black classrooms were spread across four urban schools (two to four teachers per school). The 13 teachers averaged 9 years of experience teaching mathematics.
Data Sources
Video
Four lessons were videotaped for each teacher (two in the fall, two in the spring), following the teacher for the entire lesson (40–70 minutes). Two cameras were used in each lesson, one that followed the teacher and the other that focused more broadly on students. The videos were the data source for coding RIs.
Mathematics Achievement
Achievement was measured using the state achievement test. The original dataset included scores from the year prior to data collection as well as the year data were collected for the original study. Our study used the value-added z-scores developed in the original UTQ study.
Analysis
Relational Interactions
Interactions were coded in episodes rather than turns of talk. In this choice, we used Forman and Ansell’s (2001) definition of an episode as an “entire exchange that occurred between a teacher and students” (p. 124). Although this definition focuses on exchanges around a student’s mathematical strategy, we included interactions that focused on emotion, behavior, ability, and language as well. The focus on episodes allowed us to include both teacher and student talk within the interactions.
RIs were coded in five layers. First, episodes were coded that included an RI—any teacher–student communicative interaction (not just teacher moves) that went beyond content instruction. The second layer identified the RI dimension (described in Table 1). Five dimensions of RIs have been documented in mathematics education: addressing behavior, framing mathematics ability, acknowledging student contributions, attending to culture and language, and setting the emotional tone (Battey, 2013; Battey et al., 2016, 2018). Episodes were not double-coded for dimension, and the code captured the predominant message communicated to students in the interaction.
Relational Interactions: Definitions and Examples.
Third, we coded emphases. Emphases refer to both verbal and nonverbal communication that accentuated an interaction such as stressing one’s voice or gesturing. The coded forms of emphasis included vocal stress, physical gesture, facial expression, posture, omission (explicitly ignoring a student), repeated speech, extended interaction time, and word choice. In order for an emphasis to be coded, it had to add to the intensity of the interaction. For example, a teacher may use a physical gesture that does not add emphasis to an interaction such as pointing to the board. Drawing on the emphasis, we next identified interactions as positive or negative based on the tone and type of recognition of student thinking or behavior. We also made decisions based on the student(s) with whom the teacher was interacting. Therefore, a positive interaction around behavior might be recognizing model behavior of one student when another student is misbehaving. However, focusing on the positive behavior does not send a direct message to the student misbehaving. Therefore, it is possible that indirect messages were not captured by the analysis, but it is also not clear whether students received these messages.
The fifth layer coded the intensity of the interaction as low or high. We drew on the emphasis codes to characterize the intensity. If an interaction did not contain any emphasis, it was coded low. If an interaction contained one or more emphases, we considered classification as high, depending on the extent of the emphasis. For instance, an episode with one form of emphasis in terms of vocal stress could be coded as high intensity if it was extreme (e.g., yelling). High intensity was reserved for particularly strong interactions, positive or negative.
Two previous coders trained three new coders to score the videos. Once coders achieved 85% exact agreement, they began coding the UTQ videos. Two coders were assigned per video, and pairs were randomized across lessons. Ongoing follow-up training was conducted to prevent coder drift. Intercoder agreement of 86% was achieved before reconciling codes. After finalizing codes, interrater reliability was 98%. Frequencies for each RI dimension were calculated for each teacher. We performed frequencies rather than averaging across dimensions to account for both the number and intensity of interactions for each RI dimension. Additionally, the student-level information could not be linked to who the students were in the classroom videos. Therefore, although coding relational interactions specific to individual students in the interactions would have been ideal, this was not possible in this study. Therefore, the coding of relational interactions was aggregated more as an estimate of the classroom climate.
Selection of Cases
The teachers were selected across two criteria: relational interactions and change in mathematics achievement. We used RIs because previous work has shown this is a dimension that Black teachers are more supportive of than their white counterparts when working with Black children. In addition, more positive RIs have been linked with increases in achievement for Black students (Battey & Leyva, 2015; Battey et al., 2018). To compare the classrooms based on relational interactions, we calculated average scores per lesson for each dimension. However, because attending to language and culture occurred so infrequently, we excluded it from selecting the cases. (This does not mean that these instances were excluded from analysis of the cases themselves.) To calculate the average rate of RIs by dimension, we used the number of interactions multiplied by their intensity, then summed within the dimension, and divided by the number of lessons. In other words, a high-intensity negative interaction would get one interaction multiplied by –2, whereas a low-intensity positive interaction would be multiplied by 1. The sum of those would be –1 for the lesson. This is just meant to roughly capture any particular negative or positive trends within classrooms as used in prior work (Battey et al., 2018).
We also used mathematics achievement to select classrooms where students showed the largest change in performance over the course of the year. To compare student performance, we performed an ANOVA and used Tukey’s post-hoc test as appropriate. The independent variable was teacher with the dependent variable being student performance (measured as value-added change in the standardized mathematics achievement test). After examining each of these analyses for relationships and student performance, we selected teachers that were exemplary across the two factors. We then used the qualitative analysis to characterize the relational interactions for selected cases in greater detail, presented in the results.
Relational Interactions
The classrooms differed substantially in the quality of their relational interactions (see Table 2). Not surprisingly, the teachers’ classrooms were skewed negative with respect to addressing behavior. Note, however, that the five least negative classrooms are all in suburban schools, three of which are in school 4. Teachers U2T2, U1T2, and U3T4 are the least negative teachers with respect to behavior, but this analysis would certainly exclude teachers who are hyperfocusing on misbehavior, as discussed in the literature (Gregory et al., 2010) such as U3T1, U3T2, and U4T3. There were not many interactions around framing mathematics ability, which explains the lower average scores. Particularly with Black students, we did not want to choose any teachers who could be drawing on stereotypes of students in mathematics and framing students’ abilities negatively, which excluded U1T1, U2T3, and U4T4. (U3T1 and U3T2 being excluded by the prior dimension.) U1T2 was particularly positive around student abilities among the urban classrooms. The teachers were generally more positive in acknowledging student contributions; however, this dimension would also exclude U3T1 once again. Additionally, some teachers who hadn’t been excluded yet showed particularly positive trends for this dimension, such as U1T2, U4T1, and U4T2. Lastly, setting the emotional tone generally found teachers to be positive, the exception being U3T2. From the remaining teachers, U3T4, U4T1, and U2T1, were the most positive for this dimension. Therefore, across these dimensions, we excluded six teachers: U1T1, U2T3, U3T1, U3T2, U4T3, and U4T4. Only three teachers’ interactions showed above-average positive trends in at least two of the four dimensions: U1T2, U3T4, and U4T1. Interestingly, all three of the teachers are Black. These three teachers were the only teachers included for case consideration based on supportive teacher–student relationships.
Quality of Relational Interactions by Teacher and Dimension.
Mathematics Achievement
We first report the results of the ANOVA on the measure of student mathematics performance. The ANOVA was statistically significant (F = 14.07, p < 0.001). Table 3 shows the Tukey post-hoc test to see how teachers were grouped in terms of the change in students’ mathematics achievement. In terms of teachers of Black students, two teachers show up in the highest group, U4T1 and U1T2—again, both are Black teachers. Both have similar levels of increasing student achievement by over 0.2 standard deviations more than the average teacher in the dataset. Additionally, this is not statistically different from the best teachers in the study, regardless of school type. Interestingly, the four teachers in school U4 are spread across the spectrum of change in mathematics achievement, and U3T4, who was still considered after the first criteria of selection, was around the middle. The next group of teachers of Black students have average levels of change (U3T2 and U4T3) and both teachers are white. In terms of case selection, this suggested that teachers U4T1 and U1T2 were the most successful teachers in supporting their predominantly Black students in learning mathematics.
Tukey Post-Hoc Test of Student Change (z-Score) in Mathematics Achievement by Teacher.
Case Selection Summary
In terms of relational interactions, three teachers were considered in terms of supportive relationships, U1T2, U3T4, and U4T1. Each of them was around or above average for each relational dimension. With respect to change in mathematics achievement, two teachers stood apart from the others in supporting Black students: U1T2 and U4T1. Teachers U4T1 (Ms. Townsend) and U1T2 (Ms. Carter) had students who showed a greater change in mathematics achievement compared to others. Given this analysis, we chose to examine the relational interactions within Ms. Carter and Ms. Townsend’s lessons to consider as examples of how they built successful relationships with their Black students in urban middle school mathematics classrooms.
Case Analysis
Analysis of the classroom videos started with the moments identified in the relational interaction analysis. Each member of the research team used open coding on the videos to identify additional interactions that contributed to the success of Black students (Strauss & Corbin, 1998). Once the set of interactions was identified, the team characterized patterns in the interactions separate from the RI codes. This new categorization was to identify practices specific to these classrooms rather than broad groups of categories, as with the RI coding. This categorization led to codes such as use of humor, collective responsibility, praise, expectation of understanding, and so forth. Each member of the research team built assertions from these categories about what was going on to support Black students in their mathematics participation in each classroom. Some of the categories became clear assertions such as “the teacher is building a sense of collective responsibility for students’ mathematics learning.” This was important to identify the practices as principles rather than “teacher moves” devoid of context. Other categories such as humor and praise became subtext, which were evident across the assertions. We discuss these as they arise within various examples rather than as separate themes. The assertions were then checked for confirming and disconfirming evidence across the videos, which served to adapt and nuance them (Erickson, 2012). The assertions that remained became those presented in the results.
Positionality
The first author is a Black woman and independent scholar/activist with a focus in Africana Studies and Geography, lenses that informed this research. She has taught as an adjunct in American Studies and currently consults for nonprofit organizations in the educational equity field. The second author is a white man and faculty member who researches whiteness and racism in mathematics education and thus could lend expertise with respect to the educational context but took a step back in understanding the racial dynamics. The analysis of the RI interactions and achievement was performed by a diverse team with respect to race and gender from a previous project (see Battey et al., 2018); however, the analysis for each classroom video was performed by both authors.
Findings
We identified three themes running through these classrooms that we feel constituted the construction of a Homeplace that affirmed students’ humanity and communicated to them a sense of belonging: building collective responsibility for the mathematics, framing students as mathematically capable, and relating to students’ lives (see Table 4). Although each of these themes overlaps with practices discussed in the literature, they also differ or add nuance to how these issues are currently discussed in existing work. In addition to the stated themes, undercurrents of care/nurturance, humor, praise, and the use of Black Language are clearly visible. Throughout their lessons, both teachers switched between mainstream white English and Black Language, often utilizing Black modes of expression that signaled to students that their classrooms were sites where Black ways of being were welcome. Rather than pull these undercurrents out as separate themes, we address them within each theme in an effort to interpret what these might mean for teachers and students. We present the results by theme. In some cases, one teacher was more prominent in a theme whereas in others they both exhibited behavior consistent with the theme, though manifested differently.
Analytical Themes.
Building Collective Responsibility
A practice that immediately stood out in both teachers’ classrooms was their building of collective responsibility for learning mathematics. Rather than cultivating a culture of competition or individualism, we found that both classroom spaces were maintained as sites where collectivity was not only a clearly stated expectation, but also a behavior-shaping value. Central to the principles of Homeplace, the assumptions underlying the creation of such sites is the belief that students already possess the mathematical ideas to be successful and that they belong in the mathematics classroom. The teachers used two main strategies to engender the collectivity and sense of belonging present in their classrooms. First, they built mathematical concepts with the input of multiple students. Collective contributions have long been noted as a component of African American culture that can blur the line between authority and audience while fostering a sense of community and belonging among all involved (Holloway, 2005). Both Ms. Townsend and Ms. Carter utilized collective contributions, though through different means. Ms. Townsend, for instance, regularly employed the rhetorical style of “call and response,” using culturally specific rhythmic speech patterns common in Black churches. Second, the teachers conveyed that students should look to one another for mathematics support within group and whole class settings. Both strategies encouraged students to be active rather than passive participants in acquiring and contributing to mathematical knowledge and marked the classroom space as one where collective responsibility was the norm.
Building Mathematical Concepts Collectively
Ms. Townsend often employed a call-and-response, “preacher” style that is a hallmark of collective contribution in African American worship and musical performance (Nelson, 1996). As detailed earlier, this mode of cultural expression has been noted in prior work with successful Black mathematics teachers, notably Floyd Lee (Johnson et al., 2013), and is considered a linguistic component of Black Language (Baker-Bell, 2020). Townsend’s method meant she would pose questions to the entire class and pause for their responses, often utilizing these responses to incrementally build mathematical concepts. Although Ms. Townsend would give praise to individuals and highlight their contributions, students were positioned as a group whose unstated goal was the pursuit of collective meaning. We see examples of this show up across her lessons when she is addressing the whole class, but here we present two extended interactions. In this lesson she is using her students’ ideas to collectively formulate a definition for a net. First, she uncharacteristically asks that students raise their hands; however, her tone is reminiscent of the opening lines of a sermon, and she also utilizes Black Language here—two key cultural forms of expression that signal to students that though the mathematics may be a challenge, the space in which they find themselves is a Homeplace.
You remember when we was working on nets? What’s a net? If you know what a net is, let me get your hand. Who wanna help me out with a net? What a net? Net. Help me, what’s a net? [points to Dante]
It’s a shape that’s laid out.
Ok, that’s good. So you said a net is a shape that’s laid out. Ok, Noah can you add to that?
A thing that you can fold into a solid figure.
Ok! So your net that’s laid out [points to Dante] that you can fold into a solid figure [turns quickly and points to Noah]. Before you can fold it into a solid figure, what do you have to do?
[Murmurings]
Ok, so let’s, let’s do it again. Dante said that a net was . . . [pauses and points to Dante] Give it to me.
A shape that’s laid out.
So a shape that’s laid out, flat, on paper. What dimension is that?
Two dimensions.
And then Noah said when you fold it together, you get what, Noah?
A solid figure.
A solid figure. Which is what dimension?
Three dimensional!
[nods her head yes] Three dimensional.
There it is, that makes sense! So a net is a drawing that is laid out . . . so that when you cut it out and fold it together, it gives you a solid figure that is three dimensional. You with me on that? So do you remember when we were talking about net of cylinders?
In this exchange we see that Ms. Townsend’s students are all expected to be active participants in doing the mathematics as she builds off students’ informal understanding to develop the concept of a net. She explicitly builds on Dante and Noah’s ideas and then connects their ideas to dimensions while using her signature “preacher style,” including tonal expressions and use of repetition. When addressing the class as a whole, Ms. Townsend is looking for all of the students’ clear, loud, quick, and uniform responses to indicate their level of comprehension. If they hesitated or diverged in opinion, she would circle back just as she did in the above transcript when they deliberated regarding the dimensions of a solid figure. Black Language also shows up frequently in her lessons; note her use of zero copula when she asked, “What a net?” This exchange ends with her connecting both surface area and nets to the composition for cylinders so that they can find the surface area of a cylinder, which is a new skill for students.
What is not apparent in written transcripts of Ms. Townsend’s interactions are the tonal and speech patterns that she used as a kind of rhythmic conductor during the whole class call and response interactions. At times her enthusiasm built to a crescendo, and the entire class would erupt in excitement with her. She would use increasing and decreasing intensity to mark meanings including as a signal to students that she was addressing the group as a whole, to stress a critical point, or to praise students for their understanding. An example of her method from the third lesson follows:
We talked a lot about surface area, who can tell us what surface area is? When people are asking you about surface area, what are they talking about?
[various answers] The inside, the outside, the faces.
[Turns towards Destiny, the student who said “the faces”] The faces—what about the faces? Destiny said the faces.
The area of the faces.
[Exclaims loudly with enthusiasm] Ok! Together y’all got it goin’ on! Destiny said they’re talking about the faces, Mya said they’re talking about the area of the faces. What do I do once I get the areas of the faces?
You multiply them?
That’s how you get the area, once I have . . .
You add ‘em.
[points to Deandrah and nods] Once I have the area of all my faces, to get the total surface area all I have to do is add it, which gives us the definition of . . . [loudly] surface area! [louder] Surface area is the sum—which means do what?
[with enthusiasm] Add!
[excitedly] Surface area is the sum of the area of all the faces! Do you think that’s gonna be the same for cylinders?
Yes!
[excitedly] Yes! Why wouldn’t it be?
In this excerpt, Ms. Townsend draws the definition of surface area from her three different students’ ideas. She pulls out the idea of faces, area, and adding the area of the faces to collectively build a definition of surface area. While doing so, the excitement in her tone increased in intensity as her students grasped the concept and she gave credit to the students either verbally, nonverbally, or both. Her voice’s rhythmic patterns, common in call and response, acted as a cue to her students. These predictable tonal expressions meant that when she posed the question, “which means do what?,” her class responded on cue by matching her level of excitement and shouted in unity, “Add!” Ms. Townsend’s use of Black Language rhetorical style coupled with utilizing students’ informal ideas to develop formal mathematical definitions not only positioned her students as a collective, but also simultaneously communicated to them that Black ways of being have a place in the mathematics classroom.
Ms. Carter had one interaction, though it was extended, that looked similar to Ms. Townsend’s style of drawing on students to collectively build mathematical definitions; however, Ms. Carter did not leverage call and response as Ms. Townsend did. In this instance, during the third lesson, she built off of students’ ideas to elicit a definition of “collinear.”
Ok, we’re going to do a little word study here and see if we can figure out what collinear means . . . Looking at this word, what is the mathematical, root word?
Linear.
Linear, very good [circles linear in collinear]. And we know when we see the word linear, what is that referring to?
An equation.
It can be a linear equation. But linear means? What’s the root word of linear?
Ear. [multiple students laughing]
[Smiling] That’s very funny.
Line.
Line [underlines line in linear]. So when we look at a linear equation, it’s the equation of a . . .
Line.
In the above excerpt, Ms. Carter drew out students’ ideas of linear and line to support them in coming up with the definition of collinear. She circled and underlined the word on the board, highlighting the ideas that came up, and focused their attention on the root words that students already knew. Note the humor shared between the students and the teacher when the student said “ear” is the root word as well. These moments of humor were common in Carter’s classroom, and it was apparent that students felt comfortable enough to joke around while doing mathematics. This interaction continued, but shifted to defining what “co” means.
Ok. So we see line. Who knows what the prefix co means? [circles co in collinear]
Like you can say co-worker, co-council, co-president, something like that. Don’t it mean like second in line?
Co-worker, co-president, they are well . . . Co-president, is one higher than the other?
No.
Co-president, what do they do with the president position?
They’re doing it together.
They’re doing it together. [brings her hands together] So co
Oh, co-operate.
Right co-operate. [points to Justin] Right, they’re doing it together. You operate together. We come together, we co-operate with each other means we’re doing it together. So as Tamira said and Justin brought out, the prefix co means together.
In this extended interaction, Ms. Carter drew on students’ ideas of co-worker, co-president, and co-operate to define “co.” She revoiced students’ contributions and gave credit to Tamira and Justin for raising that “co” means together. She then came back to the original question.
Now, look at the question. Are the points in question seven collinear? What do you think it might be asking you about the points that you used in the previous question?
Are they all on the same line?
Are they all on the same line? That is excellent.
Here, she came back to the concept of collinear, applying it to a question that they were working on and asked them to define it within that problem context. Justin applied their ideas of “co” and “line” to the problem to say they are “on the same line.” Ms. Carter finished with praise, but built on five different students’ ideas, revoicing their comments and giving students credit for their contributions. This extended interchange shows a concerted effort toward collectively defining a mathematical term in relation to students’ own knowledge, very similar to Ms. Townsend’s whole class interactions.
Students Supporting One Another
Although both teachers cultivated their classrooms as collectives, Ms. Townsend primarily enacted this via whole class instruction, building and connecting students’ ideas to the mathematics whereas Ms. Carter did this more on the individual and group level, turning students toward each other for support in learning the mathematics. In both instances, we see the nurturance and support within Homeplace is not only cultivated from teacher to student, but also encouraged between peers.
This practice was central to Ms. Carter’s classroom. In each of her four lessons, she actively monitored the expectation that students should solve problems together and discuss methods, and consistently affirmed that she believed peers had the knowledge to support each other. This value of peer support permeated her classroom such that it also visibly shaped student behavior. During the second lesson when pairs of students were collaboratively solving word problems, Ms. Carter walked from pair to pair to observe and make certain they were working collaboratively. When one student asked her a question, she responded, “Well, you and your partner are supposed to solve the problem and come up with it together.” The student acknowledged that they were aware of and fulfilled this expectation saying, “Yeah, we both did it.” After hearing their reply, Ms. Carter did not confirm the answer to the problem but instead continued to walk around the room, indicating her faith in her students’ capability. In turn, her students routinely demonstrated this capability and took responsibility for supporting one another through their words and actions, which she reinforced through her confidence in them. As an example, during group work, four students were at a table working to solve a problem when one of them stopped the teacher as she passed by. The student, Nia, voiced her difficulty with the problem. Unprompted, another student immediately turned to Nia and addressed the issue. Instead of stepping in to solve it for them, Ms. Carter affirmed the students’ handling of the difficulty by saying, “They’ve got you over there Nia,” and walked away, trusting the support that Nia’s group provided her.
Ms. Carter regularly reminded students to look to one another for support and to be proactive in providing that support. At the whole class level, during the fourth lesson, groups of students shared their strategies for solving a complex word problem at the board. Ms. Carter repeated that groups were responsible for each other, stating, “If the person at the board is having a problem, the people in the group can help . . . so we can understand what’s going on. Ok?” She stated this twice during the student sharing to encourage group members to support their representative at the board in explaining their thinking. She would also take the opportunity to praise her students’ capability by affirming that their mathematical competence was a resource for others. When one student in a pair explained his solution to a difficult problem, she responded first with praise, saying, “Very, very good Maurice. Excellent, excellent, excellent. Now so, you [Maurice] might want to give him [the partner] a hint for that next one that he’s working on. Very good.” At the end of the interaction, she directed Maurice to support his partner on the next problem that extended the concept he had clearly stated. In each lesson, Ms. Carter made a practice of conveying that students were responsible to support each other, that they needed to substantively interact when solving problems, and that they were capable of supporting each other.
Ms. Townsend also conveyed her belief that students should act as a support to one another. In the two lessons with in-class assignments, Ms. Townsend walked around the room and checked that students who worked quickly through problems were offering their peers assistance. Similar to Ms. Carter, we see her directing students toward one another as resources rather than stepping in to provide support or an answer. She also verbally stressed that the responsibility to provide support should inform students’ behavior. For example, on one occasion she noticed that a struggling student was not offered help by her classmate so she questioned the student, saying, “Deandrah, did you offer your assistance? [Deandrah shakes head no] That’s what you shoulda did. Next time.” On another occasion she again voiced the importance of taking responsibility for others in the collective by asking a student, “Asha, can you help explain it to Naima for me?” Although Asha nodded her head in the affirmative, Ms. Townsend continued to prod her in a calm, serious tone, “She’s gonna need an explanation of how to convert decimals to fractions. Can you handle that? Are you sure? That’s a huge responsibility.” Ms. Townsend reinforced the idea that students should support one another, communicating that her classroom was one where responsibility for others in the collective was not only possible because of their capability, but also an expected behavioral norm.
The collectivity across both classrooms set students up to support each other, but also to take ownership for the mathematics rather than relying solely on their teacher for answers. Both teachers exhibited their belief that students had informal ideas to develop the formal mathematics, could successfully do the mathematics, and could support each other in their learning. As sites of Homeplace, a common thread of affirming students’ humanity and competence runs within each episode, as well as a sense of belonging where Black ways of being could show up through nurturance, praise, and cultural modes of expression.
Framing Students as Mathematically Capable
Given societal messages conveying a myth of a racial hierarchy of mathematics ability (Martin, 2009), classroom contexts that challenge racial stereotypes in mathematics, both explicitly and implicitly, can be pivotal for Black students. The construction of a classroom that is a Homeplace specifically calls for this challenge to be enacted, because it is a space of respite from racist discourses. We found that the teachers sent messages of students’ competence in three ways. First, both Ms. Carter and Ms. Townsend conveyed an expectation that students would understand the material, encouraging them with praise as they progressed. Second, both teachers also empathized with mathematical difficulties, normalizing these for students as part of the learning process. Finally, Ms. Carter in particular owned up to her mistakes, at times joking about them rather than ignoring or denying their occurrence. Across these three practices, students were positioned as capable to learn mathematics.
Expectation of Understanding
Both teachers displayed unwavering expectations of competence throughout all four lessons, and though the feel of each classroom differed, praise was central in both teachers’ support of their students’ mathematical progress. Ms. Carter encouraged students and created space for their responses, displaying a quiet confidence in the fact that her students would be successful and praising them generously when they were. In contrast, Ms. Townsend’s enthusiasm and energy were often high and her infectious excitement and effusive praise established a classroom environment where her students’ mathematical knowledge was openly celebrated. Despite that praise is often critiqued in the literature (see, for example, Dweck, 1999), the praise shown by these teachers was often for hard work or detailed descriptions of students’ thinking. Each of these forms of praise challenges a discourse of mathematical ability being innate as well as stereotypes regarding whether Black youth can learn difficult mathematics. Therefore, just as with hooks’s description of Homeplace, we believe that classroom spaces shaped by a purposeful “elevation of spirit” do radical work where Black students are concerned.
Ms. Carter approached students as if they could always understand mathematics. It might take hard work, but she expressed confidence that they could do it, often drawing on her knowledge of students’ past ability as evidence. During the fourth lesson, students solved a problem in groups to subsequently share their solution with the whole class. Ms. Carter watched a group as they solved for L in the equation P = 2(L + 1½W). Ishmael helped another student, Javon, distribute the 2 to make it P = 2L + 3W. Javon was struggling with how to both distribute and isolate the L. Ishmael responded, “Man, you don’t remember the distributive property? Let me get my notes out.” Javon responded, “Man shut up! You don’t know how to do it!” Ms. Carter walked up and said, “He might! He knew how to use the distributive property. Oh, look at him, going to his handy-dandy notebook.” She patted him on the shoulder, “School ‘em. . .. Right, you were exactly right, that’s the distributive property.” In this instance, Ms. Carter asserted Ishmael’s competence as well as praising his notes. There is a sense of humor in the moment with her reference to his “handy-dandy notebook,” and she utilized Black Language to give reassurance when she says with endearment, “School ‘em,” lightening any frustration. Afterward, Ishmael leaned over to Javon, sharing his notes, and explained how to distribute the two across the parentheses, and Javon realized he could divide both sides by two to get L alone. As he did this, Ms. Carter began walking away, but twirled her hands in a flourish, adding “Tada! You can do it.” Javon smiled and mimicked the gesture to the group. Both Javon and Ishmael left this interaction as competent, even when one started in frustration. This type of positive, steady confidence in her students was typical of Ms. Carter’s classroom. She acknowledged hard work and believed that understanding was attainable for her students.
In another episode, Daron was at the board showing students how to solve 2X + 3Y = 12 for Y. He started by subtracting 2X from both sides and then divided by 3. As he did this, a student interrupted before he could write the subtraction sign in front of –2X/3. At this point he had 3Y/3 = 12/3 – 2X/3. Ms. Carter created space for him saying, “Wait, let him finish.” A moment later, he started moving the term with X to the left, but still on the right side of the equation, to get Y = –⅔ X (before he could write the +4) and another student interrupted. Ms. Carter again created space, “Daron, keep going darling.” In this instance, she provided space for him to complete his thinking in addition to the “darling” that again made the interaction endearing. Daron finished by writing the equation Y = –⅔X + 4. “Daron, that was really an excellent . . . you did an excellent job. Very good, very good, very good. Y’all’s group did very good. Very well done, very well done Daron” [students clap]. Again, we see her effusive praise throughout this interaction and the classroom also takes it as a cue to clap. In each of these moments, it was not clear what Daron would do, but Ms. Carter consistently expected he could do it and created space for him to complete his work.
Praise was central to Ms. Carter’s belief in students’ capabilities and she regularly praised them with the words “very good.” Often it was in a calm, reassuring tone, but infrequently she also expressed excitement. As an example, one student, Sharice, shared a concise but complete explanation to a problem, with all of the correct units, something that Ms. Carter had stressed. Ms. Carter responded with, “Mmm! Now that is some good algebra there! Alright, very well described, very good.” Though it was not her usual practice, Ms. Carter did express excitement within her praise of students’ understanding.
Ms. Townsend, however, regularly expressed excitement for students’ hard work with loud, joyful praise. In the first lesson, students converted mixed fractions to decimals and vice versa, but had been struggling with reading decimals, especially if the tenths place had a zero in it. This threw them off in converting to fractions. Ms. Townsend identified this and had a student who was typically soft-spoken, Byron, read the decimal 10.02 before converting it. When he read the number successfully, she practically yelled she was so excited: Byron, you get it, boy! Let’s give you a ticket. You already know Byron gets a ticket. Any time Byron has something to say he’s gonna get a ticket. You go ‘head [hands him a ticket]. He said that there was ten . . . he said it so perfectly! I’m so proud of him! . . . He said ten and two hundredths.
Her pride in his accomplishment was for both his confidence and his mathematical ability, and she celebrates him with a ticket she would hand out as part of a reward system as well as unrestrained, boisterous praise. In the same lesson, when another student named Jasmine read 2,321.1 accurately, Ms. Townsend likewise responded by shouting excitedly, “Go ahead, Jasmine! You got it! You feelin’ me on that?” Here, she encouraged Jasmine before asking the rest of the class if they were “feelin’ her” on that. This elated recognition of students’ contributions and highlighting their capability with enthusiastic praise continued throughout all four lessons, and often her celebrations were infectious to the point that other students would join in. During another episode in lesson three, she praised a student for his mathematical reasoning, saying, “You get it, Vaughn. Hot dog, Vaughn! Hot dog!” Immediately following this, Vaughn’s classmate, James, exclaimed, “Hot diggity dog, Vaughn!” Though this interaction could be read as sarcastic, James appeared genuinely excited for his classmate, and Vaughn’s smile beamed. Another time, she responded to James while the class was working in small groups, “That is looking good! Doggone it James, you rock!” Other members of the group then responded to James, “You rock!” and gave him high fives. The collective celebration of students’ accomplishments was palpable in the classroom. Not only was Ms. Townsend excited by her students’ success with the mathematics, but students were excited for one another’s success as well.
In both classrooms, students’ mathematical thinking was lifted up and given due recognition by their teachers, reinforcing the idea that they could do difficult mathematics and that they belonged in the mathematics classroom.
Empathizing with Difficulties
Another practice common to both teachers is that they positioned difficulties as a normal part of learning mathematics. What often happens in classrooms is that when a difficulty arises, it is individualized or the student is made to feel that a mistake implicates their intelligence (Battey & Stark, 2009). Instead, Ms. Townsend and Ms. Carter created an environment where mistakes were anticipated, acceptable, necessary, and nonthreatening. Although this positioning is important for any classroom, it is particularly important when addressing a difficulty with mathematics that could align with racialized discourses. Given this, we see the designing of these spaces of empathy as congruent with the concept of a Homeplace.
Ms. Carter was constantly attentive to any confusion that might be present in her classroom and made it her aim to reassure students. In the first lesson, one student, Natasha, shared her solution for the problem X/2 – 4 = –5 from her seat while Ms. Carter recorded it on the overhead. Ms. Carter noticed that students were struggling and addressed the confusion: “Very good, I see some perplexed looks so let me just. . . . You’re absolutely correct, Natasha. You all understood that we need to add 4 to both sides, but how do we get X alone?” She noted that Natasha was correct and gave verbal recognition that the class understood the first part of the problem in adding 4 to both sides. She then asked them if it was ½, how would they make it one? A number of students responded with, “multiply by two.” Ms. Carter related this to X/2 to connect what they knew about fractions back to the variables, saying to think about it as “What do I need to do to make it one?” As shown in this interaction, Ms. Carter’s custom was to first note students’ competence and then relate any difficulty that emerged back to skills her students already possessed.
She also verbally empathized with difficulties and normalized that learning mathematics can be challenging at times. As an example, as the class reviewed how to solve X/3 + 4 = –3, she said, “Now, let me remind you students. Just let me remind you. I know why this throws you off. I understand why.” She continued by relating it to a problem they had already solved where they had Y/8 = and were asked to evaluate the expression if Y = 32. Students had known the answer was 4, but were confused about where to record the answer, in addition to thinking Y had to be less than one due to the fraction notation. She then related this back to the current problem and how they could figure out that X must be less than –3 (X/3 = –7). This showed students a way to reason around equations they were struggling with. After this interaction, she checked in with students, saying, “How are we with those two-step equations? Are we feeling a little bit more confident?” Here, she opened up emotional space to share how they felt about the mathematics and any challenges they might be facing. This sent a message that the mathematics was something collective to struggle through, and that any difficulties were expected, important, and could be overcome.
Ms. Townsend likewise anticipated potential student difficulties across all lessons, but she made it clear that if there were difficulties, it was her responsibility to provide clarity and explanation. One example of anticipating such difficulties arose around a video that Ms. Townsend showed about making pizza boxes. The context was a relevant one to the content students were working on—nets and surface area. They had calculated surface area for rectangular objects prior to this, so the video was a way to access prior knowledge. Ms. Townsend used the video to remind them what a net was in order to extend the understanding to the net and surface area of a cylinder. The video showed flattened pizza boxes being manufactured and then folded to make a box. However, the formula for surface area of the box in the video looked different from the formula they had been using. She anticipated there might be confusion and preemptively stated, “Don’t get overwhelmed with their formula. It’s just a little different from ours, but truly it’s the exact same formula. You will continue to use the formula that we’ve derived to find the surface area. . .. It’s just another way.”
Her practice of addressing potential confusion before it could even be voiced by students occurred again during lesson four when showing students a video about expected outcomes related to probability. The language in the video was different from what they’d been using in the classroom, so Ms. Townsend introduced it by saying: She said “chosen outcomes,” we say “favorable.” They both mean “What we want.” If I want a one, this is how many ways I can get a one.. . . If I want the color blue, how many ways can I get it. Ok?
In this instance, she not only anticipated the difference in language, but also stated the relationship between terms in addition to giving an informal way to understand “favorable outcomes” as “what we want.” The underlying message in her classroom was that if students had difficulties, it was because she had not made the explanation clear enough or had not done enough to illustrate the mathematical reasoning. During the same lesson about probability, Ms. Townsend again anticipated student difficulties and took the responsibility upon herself to make the concepts clear. This time she did it using coin flips to show that the more times you flip, the closer and closer it will get to 50%. Note her comments: I’m trying to prove to you because . . . I want you to believe me. So I want to prove to you that yes, indeed, the more times you do the experiment, the closer and closer you’re gonna get to theoretical probability.
The class ran through multiple coin flips, calculating the results of the experiments and comparing them to the theoretical probability. During this proving, she continuously checked in with her students to validate their understanding.
Check-ins were a typical way for Ms. Townsend to gauge comprehension and, like Ms. Carter, these actions sent a message that difficulties were expected and could be overcome. She regularly checked in with her students with comments like “Are you following me?,” “Anybody have a question?,” “You feelin’ me?,” “You understand what I’m sayin?,” and “We good?” These frequent check-ins for clarity put the onus for explanation and understanding on her as the teacher, and her use of Black Language lent a warm, reassuring tone to the space. This was evidenced by the fact that students were willing to say they didn’t understand, either with verbal collective “Nos,” breaking the rhythm of call and response with prolonged pauses, or by shaking their heads, to which Ms. Townsend responded with phrases like, “Did you understand that? No? So let’s try it again,” “That’s a good question,” and her ubiquitous, “OK. Let’s just do one more, I want to make sure you got it.”
Both teachers anticipated student difficulties, though in somewhat different ways. Ms. Carter normalized difficulties in her classroom and noted when certain mistakes were actually important learning moments. Ms. Townsend took responsibility for moments when students may not understand and provided multiple check-ins during each lesson to make sure students were following her. Both strategies served to diffuse rather than reinforce or confirm racialized mathematical stereotypes, and the message across both classrooms was that mistakes or misunderstandings did not signify a lack of ability to succeed mathematically.
Admitting Instructor Mistakes
This subtheme was only found within Ms. Carter’s interactions, but it registers as significant in that mistakes were framed as a normal part of life in the mathematics classroom. Ms. Carter made a mistake in each of the four lessons and in every instance she took responsibility for them and either apologized or joked about them, frequently resulting in playful exchanges. In one such instance, Ms. Carter wrote “mart” instead of “mark” on the board and when the students pointed it out she replied, “Now y’all are always catching me when I goof. Yes. [pauses and adds slyly, smiling] Although, you don’t have many opportunities.” Students responded with “Oooh” and then laughter erupted in pockets throughout the classroom before they moved on. In these interactions, their level of comfort was clearly evident, illustrating how Homeplace is one where students can be their whole selves in the classroom. In another lesson, Ms. Carter was confused about why the mathematics problem necessitated multiplying by 11 months since there are 12 in a year.
You said you multiplied 35 times. . .
11.
There 11 months in the year?
The first month is already done for you.
Ms. Carter: Ohhh! Because it’s an additional month, ok. So it’s only for 11 [drops head and starts laughing]. Alright [students laughing].
You trippin’.
No you trippin’ [smiling]. Alright, and that’s very key, that’s a very key part of this information that if we’re doing this in our head, we’re only going to multiply 35 by 11. . . . Now see, why you all snickerin’? [smiling broadly as class continues to laugh]
In this interaction, her student notably felt comfortable enough to tell her in Black Language that she’s “trippin” and she responded in turn by joining in the banter and laughing at herself with the class. In another instance where she misheard a student and missed that the number given to her was negative, she apologized by saying, “Oh, did you say that? I’m sorry. I didn’t hear the negative part. I’m sorry, my bad. Thank you.” In some classrooms, teachers can be concerned with always being right, but that was not the case here. Across all episodes, Ms. Carter was responsible for her mistakes and was able to laugh at herself and move beyond them, framing mistakes as a typical, nonthreatening part of life in the classroom.
Relating to Student Lives
Although both teachers found ways to relate to students, in some ways, neither classroom was consistent with CRP, as noted at the outset. Examples of cultural competence were rare, and we did not see instances where sociopolitical consciousness was made evident. However, the teachers did use Black Language in conversing with their students. They also used two practices in order to relate to their students. First, both teachers led with care, meaning that they first approached students as humans with complex lives. Additionally, they used concepts and activities to relate to students’ everyday experiences. Although neither practice was fully aligned with CRP, we argue that the care, language, and everydayness of the classrooms did reflect hooks’s notion of Homeplace.
Leading with Care
A key aspect of Homeplace is that it operates as a site of nurturance, comfort, and care, where dignity that may have been denied in the outside world can be restored to individuals. Though some of the interactions may appear small or insignificant, as a whole, they reflect impactful practices for Black students that challenge systemic injustices around school discipline for behavior (Gregory et al., 2010). When teachers see a student who is not doing what they want, their assumptions and response can speak volumes regarding how they think about students. A student with their head down could be a sign of laziness, disinterest, or resistance, or it could signal that a student is in need of something, such as sleep or food. Both teachers checked in with students with concern, giving them the benefit of the doubt and affirming their dignity, instead of seeing themselves as disciplinarians first. This made both classroom environments more humanizing.
As an example, Ms. Townsend walked by Nathan, a student who had his head down on his outstretched arm on his desk during lesson two. Instead of chastising him for a lack of attention, she asked, “You alright, Nathan?” He responded, “Yeah, I’m just hungry.” Ms. Townsend assured him, “Ok, we’ll be eating soon.” When Townsend saw students not doing what she wanted them to do, she did not assume it was because they were lazy, intentionally unengaged, incapable, or challenging her authority. Instead, Ms. Townsend always checked to see if the student was alright and had their needs met, approaching them with concern rather than with the goal of bringing a student in line. Even during a lesson when a student appeared genuinely distracted by something at his desk while they watched a video, Townsend gave the student the benefit of the doubt. When he responded with, “I don’t understand,” she gently whispered, “But you weren’t watching. I’m going to help you, but you need to watch the video.” After the video ended, she came to this student first and said, “What can I do to help?” As was her practice with addressing difficulties, Ms. Townsend followed through on supporting students and never put the blame for not understanding on the student. In another instance, she saw a student talking excitedly when she was supposed to be working and asked her, “You straight? There’s a lot going on today. You gettin’ your hair done? Let’s focus on this for now and we will talk about that part later.” The student was excited about her hair, and Ms. Townsend acknowledged this (in Black Language), provided space for it, but also communicated that she wanted her to focus on the task at hand. Throughout these moments, students were treated with dignity, as human beings who have interests and needs outside mathematics. Note, though, that in spite of this, Ms. Townsend was still firm in wanting her students to attend to instruction.
Similarly, Ms. Carter always approached students with concern, whether it be for their physical well-being or for their ability to succeed mathematically. During the first lesson, as students worked on a problem to begin their day, Ms. Carter walked around passing back graded papers. One student, Lonnie, had her head in her hands and as Ms. Carter passed by, she stated, “I’m sorry you don’t feel good, but you’ll be alright.” She put her hand on Lonnie’s shoulder before continuing to walk around the room. About 10 minutes later, she came back to Lonnie, who now had her head to the side, resting on one arm. She asked her, “Do you want to go see the nurse? [student shakes her head no] Ok, well, do what you can then.” Ms. Carter expressed concern and sympathy for Lonnie without viewing her as resistant to doing her work, and took the time to check back in. A similar occurrence happened during the third lesson with another student. Instead of chastising students for not doing work, being lazy, or considering their behavior as a problem, Ms. Carter allowed space for students to not feel well.
In addition to leading with care when students were not feeling well, Ms. Carter looked out for students who had missed class to make sure they kept up with the material. During the third lesson, Ms. Carter spoke with two students who missed the prior day and would not understand what the class was reviewing. Ms. Carter stated, “Freddy and Sierra, just follow along with us because we’re going to review what we need to do.” She then gave the two students different practice problems to make the mathematics more accessible given what they had missed. Here, Ms. Carter adjusted her instruction to students’ needs and had specific supports to catch them up with the material. Later in the same lesson, as students solved problems individually, one student who had been absent had his head down on his textbook with his eyes closed. Ms. Carter approached him, “You got to wake up, baby. You haven’t been here. You can’t, you know you can’t afford to be asleep.” The student picked his head up and began working again. Where some teachers might chastise a student, Ms. Carter used a term of endearment, but was still firm in asking the student to get back on track.
Notably, there were no examples in either class where teachers framed students as behavioral problems, as not caring about their work, or as being mathematically incapable. Instead, the first response from these two teachers was to check in to see if their students needed to go to the nurse, were hungry, or were tired. Both teachers still wanted students to attend to instruction, but they also realized they were human beings that sometimes didn’t feel their best or could lose focus. None of the moments escalated into disciplinary issues, none of them led to the teacher raising her voice, and none of the interactions was made public. Each interaction was kept private and caring, and the teachers avoided calling out or embarrassing students in front of their peers. This practice of leading with care is critical in classrooms with Black students, who often endure treatment informed by racialized preconceptions.
Using Concepts and Activities to Relate to Students’ Interests
Both teachers related mathematics to students’ lives. Ms. Carter designed activities and utilized games and humor as modes of connection, but more commonly for both teachers, finding ways to relate to their students was done in the moment. They utilized the everydayness of mathematics to communicate its usefulness to students in the real world, building connections to outside interests where they saw an opportunity.
Ms. Carter primarily related to students through humor, games, and connecting to their interests. In the first lesson, students had been working, mostly individually, to solve equations with one variable when Ms. Carter decided to have the class play a game in order to introduce two-step equations. She explained that because she knew many students liked to play cards, she wanted to make two-step equations interesting through a card game. She explained the rules of the game, called, “I Declare 2-Step!” and students were excited and began chatting. They used cards to represent coefficients (e.g., 8, 2, and 5), and then had to solve the problem to see who had a greater value for x (e.g., 8x + 2 = 5). Ms. Carter asked for a volunteer to model the game for the class and asked, “What do you say when you win?” The student modeling it with her said, “Bingo!” Ms. Carter smirked, then demonstratively laid her arms out in front of her and said “2-Step! Alright! No, we’re not playing Bingo [smiling].” Students began playing the game in pairs as Ms. Carter monitored. She approached one pair and asked, “And who won?” When students told her the answer, Ms. Carter feigned annoyance with her hand on her hip and said, “Well, did she say ‘2-Step’?” The student responded, “I’m gonna say it now.” Ms Carter replied to her partner, “She didn’t say it though, did she? Did she say it? [showing excitement] Oooh, we might have to play games more often!” Another time Ms. Carter listened to two students, then moved back dramatically when one yelled “2-Step” like she was blown away, then smiled, said good job, and patted the student on the shoulder. Carter intentionally set out to connect mathematics to students’ interests through the development of a card game and often related to them through humor and by exhibiting playfulness.
As another example of her playful exchanges with students, in the second lesson, Ms. Carter asked how many remembered to bring in their textbooks that day. She said, “I appreciate it” and reached for a book that a student offered her, but the student held on, smiling mischievously. She smiled and made a sound as she pulled it “uh, uh, uh, uhhh” and the student laughed and let go. Later in the same lesson, students had a choice between three situations to translate into a system of equations. Ms. Carter stressed that this is not just abstract math and strove to relate it, with humor, to real life. She said: Now remember, we’re not trying to just solve for x and y. We have a real life situation here. So if it’s, how much chips and soda did Ms. Carter buy? Well you need to tell me Ms. Carter can buy 12 drinks and five. . . What was the other thing I said?”
One student responded with “soda” and she replied no, and then another responded “chips.” She turned to the one who said soda, because she had remembered that one already and said, “Chips baby, chips [smiling]. Ok, alright. So you need to state the solution in the context of the problem. Is everybody straight with what we’re doing?” Students began solving problems in pairs about credit card charges when going to the store, which Ms. Carter designed to model real-life situations. In three of the four lessons, Ms. Carter made connections to student interests, always with humor and playfulness.
Ms. Townsend also found ways to relate mathematics to students’ everyday lives. In the lesson where she showed her students a video on pizza boxes, she initiated a discussion about what was mathematical about pizza boxes before connecting this to the mathematical terms of nets and surface area. Another example occurred when she compared the idea of circumference to the freeway that encircled their metropolitan area. She related it to perimeter for rectangles, but explained that circumference is for finding the distance around a circle, saying “If we wanted to find the circumference of [city name], we would just go around [freeway number], cuz it goes around [city name] in a circle.” Here, she used a reference to the major highway to show how mathematics related to students’ geographic location. Typically, these moments were more in the moment for Ms. Townsend rather than a prepared activity.
In another instance, within the lesson about converting decimals and mixed fractions, she related where students could see them in their lives: When you go to the grocery store you’re gonna see decimals. When you go to the meat counter, you might ask for ¼ pound of meat. But when they weigh it on the scale, they’re gonna give it to you in decimals and I want you to be able to tell the difference.
In each lesson, Ms. Townsend communicated a way that students would see the mathematics in their everyday lives. Even in communicating the meaning of inverse she gave them an everyday example of, “When I get out of bed, the inverse is if I would get back in.” Again, Ms. Townsend’s interactions were not necessarily worked into the design of the lesson, but she regularly communicated how the mathematics could be seen in students’ experiences.
The practice of relating mathematics to students’ lives served to illustrate for them the real-world application of mathematical concepts. It also functioned as a way for the teachers to build connections with their students while acknowledging that they all have lives and experiences beyond the classroom.
Discussion
Looking across the two teachers’ classrooms, we see themes of collectivity, affirming Black students’ competence, and finding ways to relate to students. These practices are consistent with prior findings noted in the literature review, but in taking an interactional lens, Ms. Townsend and Ms. Carter’s practices are displayed in a more concrete way than much of that work, which centers on teacher interviews and teachers’ intentions. However, we caution against any interpretation of the interactions as teacher moves—practices that can be divorced from the context in which they occur. Instead, we frame the practices within the concept of Homeplace to make clear how these teachers build a space of belonging and affirmation for students because the classroom is crafted into a safe haven from the stereotypes and racist structures common in mathematics. In the following, we discuss three ways in which the findings add to existing literature and point to directions for future work: the contribution of Homeplace, critical care and praise, and Black Language.
However, before discussing the results in relation to existing literature, we do want to note three main limitations of the study. First, we were not able to use community nominations to select successful mathematics teachers of Black students as was done in Clark, Chazan, and colleagues’ work (Birky et al., 2013; Chazan et al., 2013; Clark et al., 2013; Johnson et al., 2013). This was due to the project focusing on secondary analysis of classroom videos. We do think selecting teachers for strong relational interactions and producing significant student mathematics learning was a strong alternative. This study was limited by analyzing only two teachers, which does not represent Black mathematics teachers broadly and shouldn’t lead to any generalizations of practice. What we do hope is that drawing on the notion of Homeplace may allow for a conceptualization of successful Black mathematics teachers’ practice. Finally, and most significantly, this study would have been improved by having teachers and students discuss their interactions to understand how intentional teachers were being and to flesh out how students interpreted these moments. We think future work could add these features to provide insight between an interactional approach and teachers’ and students’ perspectives on their relationships.
Homeplace
Despite these limitations, we see a number of ways in which these findings build on existing literature. The concept of Homeplace certainly overlaps with CRP, as discussed at the outset of the paper. CRP centers three principles: academic success, cultural competence, and sociopolitical consciousness (Ladson-Billings, 1995). The teachers enacted views that students could fundamentally succeed mathematically, which is consistent with all of the literature documenting successful Black mathematics teachers reviewed previously (see Frank, 2019). This view of Black students succeeding also connects to work on CRP highlighting a focus on academic challenge and success for students. Both Ms. Townsend and Ms. Carter built this collectively in their classrooms, explicitly drawing on students’ ideas and having them rely on each other for support.
Related to the second CRP principle of cultural competence, both teachers found ways to relate the mathematics to students’ lives, even if these were brief at times. Although aligned with prior literature, some of that work has more elaborated contexts than the ones described in these classrooms (Birky et al., 2013; Foster, 1997; Peterek, 2009). Ms. Townsend and Ms. Carter were clearly connecting with students, getting to know them, sharing about their likes and dislikes, and other everyday experiences. More importantly, the teachers did not approach students as needing to comply with their demands. Instead, they approached students with concern, humor, and understanding (Clark et al., 2013; Johnson et al., 2013; Neal & Battey, 2014). This way of approaching students allowed them to be more fully human than just completing tasks that teachers demanded them to do.
The last principle of CRP, sociopolitical consciousness, was not evident in these teachers’ interactions. It is possible that the teachers brought this understanding to their teaching because their interactions resisted stereotypes about Black students’ ability in mathematics. However, activities that use mathematics to critique the social world were not evident across the eight lessons analyzed here. This finding has been less consistent in the prior literature. Although some teachers have used social justice as a context in which to apply the mathematics (Lynn, 2001), other teachers have tried to establish meaningfulness within the mathematics (Birky et al., 2013). It is possible that viewing more lessons could reveal interactions related to this principle, but no evidence was captured within this dataset. As such, we see Homeplace as a concept that better fits the classroom environments designed by the teachers.
Homeplace, which previously hasn’t been applied to mathematics classrooms, supported our understanding of communicating a sense of belonging and affirming students’ humanity in the face of racism. Across the central themes of building collectivity, framing students as mathematically competent, and relating to students’ lives, the teachers created a safe haven in the midst of systemic inequities in mathematics. For example, collectivism runs in direct contrast to the competition and individualism that are embedded in so many math classrooms. Instead, these classrooms created space for students to be recognized for their contributions, for multiple students to have their contributions recognized, and for the responsibility for learning to be shared across the teacher and students. Although not explicitly sociopolitical, these are direct contradictions to the way that mathematics is often taught to students. Likewise, the affirming of Black student competence counters the myth of a racial hierarchy of ability in mathematics (Martin, 2009). In these ways, the classrooms provide a refuge for students from racist stereotypes and ideologies that position Black students as incapable (Leyva, 2021).
Critical Care and Praise
Leading with care is a way to create belonging in mathematics classrooms, consistent with hooks’s concept within the home. This notion of approaching students with care represents a shift discussed in much of the discipline literature around Black students, in which they are framed as discipline problems in need of control (Gregory et al., 2010). In fact, the interactions in these classrooms seem to frame behavior as the last concern of the teachers. They were first concerned with students’ health and well-being, and then with learning the mathematics; only after that, if students were not engaged or behaving in a way that may be limiting their learning, did they address behavior. Teachers handled any issues privately, quietly, and without escalating the behaviors in a way that would harm their relationship with students (Weinstein et al., 2004). These practices align with literature on culturally responsive classroom management that challenges the production of discipline gaps. However, the teachers also acted as warm demanders (Ware, 2006), focusing students, reengaging them in instruction, and not letting them drift from learning mathematics. Therefore, in leading with care, the teachers disrupted common patterns for Black students that suggest discipline and disparagement as more common responses to their behavior.
As Ms. Townsend and Ms. Carter disrupted these patterns, both humor and praise were central. This, despite research on the dangers of praise in classrooms because it can demotivate students or teach them that ability is innate (Dweck, 1999). Although this study did not examine the impact of praise on students’ motivation, students certainly learned relative to other classrooms considered for case selection and seemed motivated in both the fall and spring videos. Both teachers regularly used praise, for specific and general purposes, which makes us wonder about how praise functions with respect to race, something that has not been examined in much depth in the literature. Possibly, Black students interpret praise differently, because it can challenge negative stereotypes about mathematics ability that are passed on in schools and society more broadly. Additionally, it is not clear to us that Black students hearing praise from Black teachers would necessarily read it in the same ways compared to when their teachers are white. Praise has been central in much of the prior work on relational interactions documenting successful mathematics teachers of both Black and Latinx students (Battey et al., 2016; Neal & Battey, 2016), which raises the issue of whether a more detailed understanding of how praise functions within and across race is needed. But more generally, it may be dangerous to position praise outside the broader ways in which teachers care for and nurture their Black students. And the centering of caring with awareness (Bartell, 2011) may disrupt narrow interpretations of praise divorced from racial contexts.
Additionally, the teachers disrupt many of the ways in which students are racially marginalized in mathematics classrooms. These practices around mistakes, difficulty, and the expectation of understanding protect students, and specifically Black students, from having incorrect answers and struggles turn into incompetence. The classroom practices enacted here served to affirm students’ capability to learn and succeed mathematically. This is consistent with the literature cited previously about the expectation for understanding (e.g., Frank, 2019), but shows in what specific ways these teachers are creating mathematics classrooms as refuges from mathematical logics where mistakes mean incompetence and struggles connote a lack of motivation. Therefore, we see the critical care in these classrooms as disrupting traditional math logics and stereotypes about what it means to do mathematics for Black students, creating a safe haven where they can have their humanity affirmed.
Black Language
The use of Black Language is another affirming practice that showed up in both classrooms. In the literature review we noted how Floyd Lee and Gloria Mirriex are examples of successful Black mathematics teachers who communicated with their students via Black Language. Ms. Townsend drew on the rhetorical style of call and response, using expressions and rhythmic speech patterns borrowed from Black churches, similar to Mr. Lee. Both Carter and Townsend spoke Black Language with their students across lessons, and regarded students who used it as expressing competence and valid mathematical thinking.
Interestingly, we also noted that both teachers appeared to converse in Black Language during specific moments in order to convey warmth or comfort—moments of personal connection, humor, or praise, or when students encountered new or difficult material. The overlap with hooks’s description of Homeplace as a space that provided shelter, comfort, care, elevation of spirit, and nurturance speaks to the utility of its application in conceptualizing the relational interactions in these classrooms. Although it was beyond the scope of our research to concentrate on exactly how and why Black Language was used, or if it was purposeful or subconscious, the creation and maintenance of these spaces as Homeplace were undoubtedly shaped by ways of being, including practice plus language.
Though Black Language is yet another way that Black students can be framed as “incompetent,” “uneducated,” and “improper,” Baker-Bell (2020) critiques these racialized assumptions, noting that Black Language is often “viewed from a deficit perspective with the goal to eradicate it” (p. 72). She details how it has persisted in Black communities for generations as a “counter language” and has functioned as a “tool to resist, rebel, and reclaim power in the context of domination” (p. 71). We think there is much more to explore with respect to Baker-Bell’s (2020) conceptualization of Black Language within math classrooms that affirm Black students’ identity and create space for them. Meanwhile, we underscore the fact that Black educators constructing Homeplace as a site of refuge communicate via these culturally specific modes of discourse as a signal that their Black students belong in the mathematics classroom.
Conclusion
In documenting the practices of successful Black mathematics teachers, we think it important to note that focusing on an interactional level allows for a detailed examination, as well as looking at the consistency of practices, that can make such practices more interpretable for teachers and teacher educators. We think a future goal should be to capture both the perspectives and the interactions of teachers, noting consistencies and inconsistencies between the two, an undertaking that was beyond the scope of this research. But we want to end with caution by saying again that divorcing these practices from the people and their perspectives is not possible. The classrooms looked and felt quite different. A teacher trying to normalize problem difficulty without also authentically noting students’ competence runs counter to what these teachers were trying to do. Although the paper necessarily separated practices into themes, we argue that it is the convergence of these practices and prevailing ways of being that shaped the classroom into a Homeplace, a haven free from negative discourses, where Black students could show up and learn substantive mathematics as they built strong relationships with their teachers and peers.
Footnotes
Declaration of Conflicting Interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Funding
The author(s) received no financial support for the research, authorship, and/or publication of this article.