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The interconnectedness of relational and content dimensions of quality instruction: Supportive teacher–student relationships in urban elementary mathematics classrooms
... Finally, Battey et al. (2016) showed that through specific actions, teachers could dually focus on both content and relationships. They analyzed the studentteacher interactions and relationships in two classrooms that were rated as high in instructional quality and student performance. ...
... Relationships have the power to positively impact the teacher's lived experience. Successfully integrating relational and content instruction by consistently recognizing positive behavior, revoicing and highlighting student contributions, and framing students as competent, also leads to greater academic gains (Battey et al., 2016). Milatz (2015) used surveys of 83 elementary teachers to explore the impact of relationships on teacher well-being and burnout. ...
... Positive student relationships spark positive emotion in teachers (Klassen et al., 2012). A pedagogy that successfully integrates relational elements with content instruction also leads to greater student gains (Battey et al., 2016). I am particularly struck by this idea of integration because, at the time, I thought about the two as quite separate. ...
Despite research suggesting the importance of centering students and focusing on deep conceptual understandings, direct instruction and step-by-step procedures remain common in mathematics classrooms nationwide. For this self-study, I embarked on a year of striving to change how I taught. I documented that process through a reflective journal, and that journal and other artifacts together provided an intimate look into that experience and the associated challenges. I analyzed the interactions that occurred in my classroom between the teacher, the students, and the mathematics, with special attention to the teacher’s knowledge, beliefs, and emotions. My own experience was characterized by misalignment between teachers, students, and mathematics. This misalignment resulted from efforts to change and led to a lot of negative emotions. My experience was also impacted by the challenge of balancing many complementary and competing factors and practices. Despite being an intimate look at my own experience, my findings offer broader suggestions as well. Specifically, they suggest that change must be aligned and coherent throughout the entire system, that this kind of teaching must truly center students and prioritize relationships, and that the emotional side of teaching must be recognized and supported.
... Additionally, by being at school more, students receive more instructional time that positively impacts their achievement (Andersen et al., 2016). Increased instructional time means that students may not only receive more content-focused support but may also be afforded more opportunities to develop key relationships, such as with their teacher, that support their capacity for resilience (Battey et al., 2016;Bostwick et al., 2022;Granziera et al., 2022). Indeed, the joint benefits of resource support and instructional time may be key to buffering the negative effects of socio-educational adversity. ...
Academic resilience refers to academic success despite chronic socio-educational adversity. Given increases in immigration across the world in the past decade (including in Europe), there have been calls to identify factors (e.g., engagement) that can better support immigrant students’ academic resilience. With a sample of N = 17,241 immigrant students from 18 European countries, the present investigation employed multi-level probit regression to determine the extent to which cognitive, behavioral, and social-emotional engagement predict academic resilience status at both the student- and school-level. Findings revealed that cognitive engagement and behavioral engagement, at both the student- and school-level, are positively associated with academic resilience (yielding moderate and large effect sizes), while the findings regarding social-emotional engagement were more equivocal.
... The field's understanding of classroom discussions has been enriched by a large body of research, including research focused on student-teacher relationships (e.g., Battey et al., 2016), discourse (e.g., Herbel-Eisenmann & Wagner, 2010, and participation supports and structures (e.g., Cohen & Lotan, 2014;Esmonde, 2009;Featherstone et al., 2011;Foote & Lambert, 2011;Hunter & Hunter, 2018). Our work was informed by others' research but filtered through our particular goals of developing a decomposition of leading discussions useful for beginning teaching. ...
Mathematics discussions are important for helping students to develop conceptual understanding and to learn disciplinary norms and practices. In recent years, there has been increased attention to teaching prospective teachers to lead discussions with students. This paper examines the possibilities of designing a formative assessment that gathers information about prospective elementary teachers’ skills with leading problem-based mathematics discussions and makes sense of such information. A decomposition of the practice of leading discussions was developed and used to design the assessment. Nine first-year teachers who graduated from a range of different teacher education programs participated in the study. The findings reveal that our formative assessment works to gather information about teachers’ capabilities with leading discussions and that the associated tools support making sense of the information gathered. This suggests that such tools could be useful to support the formative assessment of the developing capabilities of prospective teachers.
... We first identified episodes as including an RI-any teacher-student communicative interaction that went beyond content instruction-and then coded the RI dimension (table 1). Previous qualitative work has identified five dimensions of RIs in mathematics classrooms: addressing behavior, framing mathematics ability, acknowledging student contributions, attending to culture and language, and setting the emotional tone (Battey, 2013;Battey & Neal, 2018;Battey, Neal, Leyva, & Adams-Wiggins, 2016). These dimensions, first developed using grounded theory and then validated across more classrooms and schools, are typically considered to be outside of content instruction (Battey, 2013). ...
While research has consistently shown the positive effects of having a teacher of the same race on various student outcomes, the literature has not examined how racial match affects the everyday interactions within classrooms. This research article by Dan Battey, Luis A. Leyva, Immanuel Williams, Victoria A. Belizario, Rachel Greco, and Roshni Shah addresses this underexplored area by documenting relational interactions in classrooms to find one mechanism that could be producing racialized effects on learning. Using a dataset from a study of twenty-five mathematics classrooms across predominantly white and black US middle schools, they examine the quality of relational interactions when teachers and students are racially matched and mismatched, as well as the effects on student achievement in mathematics. Their analysis shows how various dimensions of relational interactions significantly predict increases and decreases in achievement due to racial match.
... That said, there is evidence that active learning is not a silver bullet that redresses inequity, and the underlying mechanisms are not yet well understood [22]. A student-centered classroom provides more opportunities for student-student and student-instructor interactions, which has the potential to support agency in mathematics [28], but this also has the potential to trigger stereotype threat and demonstrate implicit biases [4]. This section of the paper, however, goes beyond the classroom to touch on ideas related to supporting all students, and each student, encompassing general supports in addition to those targeting students from particular backgrounds and/or demographics. ...
The Mathematical Association of America’s Precalculus to Calculus: Insights and Innovations conference brought together representatives of mathematics departments from across the country with members of two national research projects to share and discuss both research findings and on-the-ground concerns of faculty. In this article, we report on major themes that arose from the discussions at this conference, contextualized with research findings and policy recommendations. We aim to shed light on where the priorities of departments, policy, and researchers are aligned and where they are not. In doing so, we hope to support efforts to enact and sustain change in undergraduate mathematics education through connections and communication.
... These modes of creating CT opportunities were consistent with the pedagogical strategy of assigning competence, or highlighting the intellectual value of a students' contribution or thinking (Boaler 2006). Assigning competence has been shown to contribute to the development of supportive relationships between elementary teachers and students, especially for African American and Latinx students (Battey et al. 2016). Given the goal of broadening participation in computing, helping teachers learn how to recognize and highlight how students use CT practices may not only provide teachers with new contexts for assigning competence, but also allow students from traditionally marginalized groups to see that they can engage in CT ideas. ...
Incorporating computational thinking (CT) ideas into core subjects, such as mathematics and science, is one way of bringing early computer science (CS) education into elementary school. Minimal research has explored how teachers can translate their knowledge of CT into practice to create opportunities for their students to engage in CT during their math and science lessons. Such information can support the creation of quality professional development experiences for teachers. We analyzed how eight elementary teachers created opportunities for their students to engage in four CT practices (abstraction, decomposition, debugging, and patterns) during unplugged mathematics and science activities. We identified three strategies used by these teachers to create CT opportunities for their students: framing, prompting, and inviting reflection. Further, we grouped teachers into four profiles of implementation according to how they used these three strategies. We call the four profiles (1) presenting CT as general problem-solving strategies, (2) using CT to structure lessons, (3) highlighting CT through prompting, and (4) using CT to guide teacher planning. We discuss the implications of these results for professional development and student experiences.
... In addition, participants completed a focus group centered on three stimulus narratives of events from their mathematics lectures and recitation/workshop sessions. These narratives related to dynamics explored in extant literature of students taking up classroom space (Hand, 2012), stereotypes of mathematical ability (Shah, 2017), and faculty-student relationships (Battey, Neal, Leyva, & Adams-Wiggins, 2016). Participants were probed on the extent to which they observed such dynamics in mathematics classrooms and whether or not they saw themselves in similar situations. ...
While Latinxs complete undergraduate engineering degrees at lower rates than Whites and Asians, Latinx men trail behind Latinx women who recently earned over half of engineering and science degrees conferred to Latinxs. With multiple semesters of mathematics required in engineering majors, qualitative analyses of undergraduate Latinx men’s strategies of persistence and success in engineering can illuminate ways to inform more socially-affirming postsecondary educational opportunities and thus increase retention in STEM (science, technology, engineering, and mathematics). This report presents findings from a phenomenological study that characterized variation in two undergraduate Latinx men’s negotiations of their masculinities with pursuits of mathematical success as engineering majors at a large, predominantly White four-year university. Findings illuminate the Latinx men’s strategies of managing risks of mathematics classroom participation, building academically and socially supportive relationships with faculty members, and negotiating pursuits of STEM higher education with their gendered sense of commitment to family.
... An evolving theme across Lauren's and Tracey's engagements with discourses of women and Latin@s not being good at mathematics is how these gendered and racial discourses shaped the nature of instruction and teacher-student relationships in high school and college mathematics (Battey, 2013;Battey, Neal, Leyva, & Adams-Wiggins, 2016). Both Latin@ women described how their mathematics success in high school was largely attributed to establishing positive, supportive relationships with teachers who held high academic expectations of them and fellow students in alignment with notions of culturally responsive pedagogy in urban schools (Gay, 2010;. ...
In this article, the author discusses the intersectionality of mathematics experiences for two Latin@ college women pursuing mathematics-intensive STEM (science, technology, engineering, and mathematics) majors at a large, predominantly White university. The author employs intersectionality and poststructural theories to explore and make meaning of their experiences in relation to discourses of mathematics ability and pursuits of STEM higher education. A cross-case analysis of two Latin@ college women’s counter-stories details the development of success-oriented beliefs and strategies in navigating the discourses that they encountered institutionally and interpersonally in their mathematics experiences. Implications are raised for P–16 mathematics and STEM education to broaden equitable learning opportunities for Latin@ women and other marginalized groups’ construction of positive mathematics identities at intersections of gender and other social identities.
... Studies point to student perceptions of a 'good' mathematics teacher or lesson to involve clear, systematic and detailed explanations from the mathematics teachers (Anthony, 2013;Hill, 2017;Österling, Grundén, & Andersson, 2015;Seah & Peng, 2012). Conversely, studies find that poor mathematics teaching practices and learning outcomes are often associated with negative relationships between students and their teachers and particularly for students from minority or impoverished backgrounds (Averill, 2012;Battey, Neal, Leyva, & Adams-Wiggins, 2016;J. Hunter et al., 2016;Jerome, Hamre, & Pianta, 2009;Pianta & Stuhlman, 2004). ...
... Several recent studies emphasize the need to recognize the effects of math instruction on students' affect, identity development, and their overall relationship with mathematics (Battey, 2013(Battey, , 2016Martin, 2000;Myers et al., 2015). Yet current approaches to mathematics teacher education tend to focus on providing teachers with conceptual and practical tools for responsive instruction, with less attention to the affective aspects. ...
Extant literature suggests that pre-service teachers’ enactment of culturally responsive mathematics practices is often impacted by the duality of what is learned in preparation programs and the reality faced at school sites. For many preservice teachers, this reality typically rests within the capacities of their assigned collaborating teacher's own experiences with enacting culturally responsive practices. Through a synthesis of the reviewed literature, the author examines collaborating teachers’ experiences with enacting culturally responsive mathematics practices and argues that such experiences are both significant and central to bridging the gap between theory and practice. Afterwards, the reconceptualization of a new approach is shared.
Many scholars call for teacher educators to provide experiences that can lead prospective teachers to adopt and implement culturally responsive pedagogy in mathematics classrooms. This qualitative investigation analyzed interviews from preservice secondary mathematics teachers using Hernandez, Shroyer, and Morales framework for culturally responsive mathematics teaching. Analysis of the data demonstrates how preservice teachers grapple with enacting a culturally responsive framework at practicum sites. Findings reveal that while some participants reported comfort implementing some aspects of culturally responsive practices at placement sites, others reported apprehension. The data suggests strategies for teacher educators interested in supporting culturally responsive teacher-learners through professional modeling.
We present a finding from a literature analysis of Raza populations published in top-tiered peer reviewed mathematics education journals. We look at how narratives are perpetuated and resisted at the intersections of Raza, mathematics education, and research. The findings reveal the field of mathematics education research is perpetuating deficit narratives of Raza through 1) simplistic descriptions of Raza which perpetuate a racial hierarchy; 2) white institutional spaces group, order, and Americanize Raza populations; and 3) counter-stories of La Raza; however, we will only concentrate on the first finding for this manuscript. The examined literature continues to center Anglos' narratives and values while maintaining a social hierarchy and the assimilation and Americanization of La Raza. Finally, we provide implications for disseminating our research to go beyond simplistic demographics of social constructs.
The study presented in this article investigated the influence of lecturer biographic factors on curriculum implementation in universities in Botswana. Over the last two decades, Botswana has been transforming its education system to improve curriculum implementation in universities, particularly in terms of who should be allowed to teach and the qualification level of students they should instruct. A mixed-methods research approach that employed a structured questionnaire and semi-structured interviews was used to collect data from 306 lecturers and 25 academic middle managers (AMMs) respectively. Confirmatory factor analysis (CFA) was used to validate the questionnaire and expert opinion validated the interview guide. To analyse the resulting quantitative data, multiple regression analysis and descriptive statistics were used, while thematic analysis was employed for the qualitative data. Findings showed that lecturers’ educational level, age and teaching experience have a significant influence on effective implementation of curricula in universities, while gender has no significant influence. These results have implications for both policy and practice with regard to lecturer recruitment and curriculum implementation in universities.
This study is situated within efforts to embrace the challenge of preparing teacher candidates (TCs) for the complexities of teaching mathematics while creating shared opportunities for inquiry across teacher education programs. We developed a shared decomposition of leading mathematics discussions that could be used across our teacher education sites to provide a means to guide our work as teacher educators (TEs) and to allow us to analyze the ways that we prepare TCs to lead mathematics discussions. We address two research questions: What components of the decomposition of discussion were worked on in two different teacher education programs with particular organizational designs? What opportunities to learn about leading discussions were evident in the ways this decomposition was used? Our findings indicate that it is possible to use a common decomposition of teaching practice and engage TCs in learning the interactive work of teaching, while at the same time, adapting to meet the unique characteristics of the site context. In our study, the TEs and TCs were able to attend to all components of the decomposition and in relation to each other. The TEs used a variety of pedagogies of investigation (representations and decomposition) and enactment (including approximations) to support their work, drawing on them in ways that fit their unique organizational contexts.
Scholars continue to document that African American kindergartners bring the same competencies as their white peers (Ginsburg et al, Int J Psychol 16(1):13–34, 1981; O’Connor et al, Rev Res Educ 33(1):1–34, 2009). Research has found, however, that they experience low-quality mathematics instruction (Davis and Martin, J Urban Math Educ 1(1):10–34, 2008; Lubienski, J Negro Educ 71(4):269–287, 2002), which does not leverage the mathematical abilities of African American students. The mechanisms for how these disparities are produced are less clear (Battey, Educ Stud Math 82(1):125–144, 2013a; Lubienski, J Negro Educ 71(4):269–287, 2002). For instance, we do not understand the mechanism through which mathematics instructional quality or the cognitive demand of tasks is reduced for African American children. In this chapter, we argue that a potentially missing piece in understanding mechanisms that produce disparities in mathematics education is implicit racial attitudes. To make this theoretical case, we draw on work both inside and outside of mathematics education across four literatures: (1) the quality of mathematics instruction that African American students receive, (2) relationships developed with teachers, (3) racialized teacher perceptions of behavior and academic aptitude, and (4) racial microagressions in mathematics. The chapter ends with two examples of how implicit racial attitudes can be embedded in existing research in order to illustrate how the field could study ways to disrupt the perpetuation of deficit perspectives shaped by racial ideologies and systemic forms of oppression.
Cultural myths about mathematics as a set of known facts pose unique obstacles for inquiry instruction. What is there to discover if everything is already known? At the same time, decades of mathematics education research shows the potential for inquiry instruction to broaden participation in the discipline. Taking a classroom ecology perspective, this chapter uncovers common obstacles to inquiry in school mathematics and identifies three leverage points for redesigning instruction toward this goal. These include: teachers’ knowledge for inquiry mathematics, curricular connections to other contexts, and classroom norms and practices. The chapter proposes that design thinking around these leverage points holds promise for wider-spread implementation of inquiry instruction in mathematics classrooms.
Background
Within mathematics education research, policy, and practice, race remains undertheorized in relation to mathematics learning and participation. Although race is characterized in the sociological and critical theory literatures as socially and politically constructed with structural expressions, most studies of differential outcomes in mathematics education begin and end their analyses of race with static racial categories and group labels used for the sole purpose of disaggregating data. This inadequate framing is, itself, reflective of a racialization process that continues to legitimize the social devaluing and stigmatization of many students of color. I draw from my own research with African American adults and adolescents, as well as recent research on the mathematical experiences of African American students conducted by other scholars. I also draw from the sociological and critical theory literatures to examine the ways that race and racism are conceptualized in the larger social context and in ways that are informative for mathematics education researchers, policy makers, and practitioners.
Purpose
To review and critically analyze how the construct of race has been conceptualized in mathematics education research, policy, and practice.
Research Design
Narrative synthesis.
Conclusion
Future research and policy efforts in mathematics education should examine racialized inequalities by considering the socially constructed nature of race.
To succeed, groups need skills to jointly regulate their shared task work. The current study examines variation in other-regulation, or efforts by one student to regulate their group's work. We consider the relationship of directive and facilitative forms of other-regulation with efforts to negotiate competence, given that directive other-regulators may raise doubts about relative ability. Three groups of four 7th grade students were observed while working on two collaborative activities during an inquiry-based science unit. Results suggest the nature and quality of facilitative and directive other-regulation varies, with directive regulators focused on controlling the task product in ways that excluded others' attempts to contribute. In response, teammates worked to renegotiate their positions of competence within the group to ensure their ideas were considered for integration. The focus on relative competence promoted by directive other-regulation may diminish a focus on group learning, given the social nature of joint activity.
Complex Instruction (CI) is a response to the paradox that group work offers much potential but often creates circumstances where few students seem to learn. CI is a set of ideas and strategies that address the problems that confound group work, but that create powerful learning for children. This book offers guidance to readers on how to use these strategies and ideas. The authors describe the lessons they learned using group work, explain how complex instruction helps unsuccessful students, and analyze how to design assignments that support group learning—using group-worthy tasks—giving readers examples of good tasks and help in adapting math problems from their own curricula.
My aim in this article is to explore 3 perspectives on bilingual mathematics learners and to consider how a situated and sociocultural perspective can inform work in this area. The 1st perspective focuses on acquisition of vocabulary, the 2nd focuses on the construction of multiple meanings across registers, and the 3rd focuses on participation in mathematical practices. The 3rd perspective is based on sociocultural and situated views of both language and mathematics learning. In 2 mathematical discussions, I illustrate how a situated and sociocultural perspective can complicate our understanding of bilingual mathematics learners and expand our view of what counts as competence in mathematical communication.
The gap in achievement across racial and ethnic groups has been a focus of education research for decades, but the disproportionate suspension and expulsion of Black, Latino, and American Indian students has received less attention. This article synthesizes research on racial and ethnic patterns in school sanctions and considers how disproportionate discipline might contribute to lagging achievement among students of color. It further examines the evidence for student, school, and community contributors to the racial and ethnic patterns in school sanctions, and it offers promising directions for gap-reducing discipline policies and practices.
This article explores how schools reproduce race, class, and gender inequality through the regulation of students' bodies. Using ethnographic data from an urban school, I examine how assumptions guiding bodily discipline differed for different groups of students. First, adults at the school tended to view the behaviors of African American girls as not "lady-like" and attempted to discipline them into dress and manners considered more gender appropriate. Second, school officials tended to view the behaviors of Latino boys as especially threatening, and members of this group often received strict, punitive discipline. Third, school officials tended to view the behaviors of white and Asian American students as nonthreatening and gender appropriate and disciplined these students less strictly. To conclude, I discuss the importance of viewing race, class, and gender in schools simultaneously and the problems associated with disciplinary reform in education. © 2005 by Pacific Sociological Association. All rights reserved.
This analysis joins together two lines of work: research on students' mathematical identities and on curricular organization that supports equitable academic outcomes. This article conceptualizes students' sense of mathematical competence as emerging through the interaction between their extant identities and the mathematical worlds they encounter in the school. Using data from a five-year mixed-methods longitudinal study comparing students' mathematical experiences in two high schools (Boaler, 20063.
Boaler , J. 2006. Promoting relational equity through complex instruction and mathematical reasoning. Theory into Practice, 45 Winter: 40–46. [Taylor & Francis Online], [Web of Science ®]View all references), I focus on seven students who showed initial and unexpected success in mathematics. One department provided more resources for students to develop identities of mathematical competence, while the second department naturalized differential outcomes for students. An examination of two student trajectories, one from each school, illustrates how mathematical identities were constructed across, as well as within, classrooms. I argue that students' mathematical identities emerge beyond a single classroom, and to achieve equitable outcomes, we must look not only at the work of individual teachers but also at teacher collectives who support mathematical achievement.
This article presents an analysis of two low-performing students' experiences in a first- grade classroom oriented toward teaching mathematics for understanding. Combining constructs from interactional sociolinguistics and developmental task analysis, I investigate the nature of these students' participation in classroom discourse about fractions. Pre- and post-instruction interviews documenting learning and analysis of classroom interactions suggest mechanisms of that learning. I propose that three main factors account for these two students' success: use of tasks that elicited the students' prior understanding, creation of a variety of participant frameworks (Goffman, 1981) in which the students were treated as mathematically competent, and frequency of opportunities for identity-enhancing interactions.
Scholars have documented that Black students enter kindergarten with weaker reading skills than their White counterparts and that this disparity sometimes persists through secondary school. This Black-White performance gap is even more evident when comparing students whose parents have equal years of schooling. This article evaluates how schools can positively affect this disparity by examining two potential sources for this difference: teachers and students. It provides evidence for the proposition that teachers' perceptions, expectations, and behaviors interact with students' beliefs, behaviors, and work habits in ways that help to perpetuate the Black-White test score gap.
In this paper we describe and discuss the language practices of mathematics, science and English language teachers and learners in a sample of urban and rural, primary and secondary schools in South Africa. We focus particularly on the reception and production of language through code-switching, exploratory talk and discourse-specific talk. We situate the article in the policy and practice environment of post-apartheid South African education in which additive bi/multilingualism is officially advocated. We use the metaphor of a journey to describe how teachers and learners move from informal, exploratory talk in learners’ main languages to discourse-specific talk and writing in English. A key finding from our study is that few teachers and learners completed this complex journey and that the constraints differed across classroom context, level and subject being taught.
Past studies have noted that black students' classroom behavior is rated more favorably by black teachers than by white teachers. This pattern could be a function of white teachers' bias--rating black students more harshly than they deserve--or black students' misbehavior--acting out more when placed with white teachers versus black teachers. If explanations emphasizing black students' misbehavior (oppositional culture) are accurate, matching effects should be more substantial among adolescents than among young children. To assess this possibility, the authors estimated matching effects among kindergartners in the Early Childhood Longitudinal Study--Kindergarten Class of 1998-99 and eighth graders from the National Education Longitudinal Study of 1988. They found that the effects of matching are comparable across both kindergartners and adolescents, a pattern that is more readily understood from the position of white teachers' bias than from that of oppositional culture.
Abandoning conventional assumptions about skills hierarchies leads to a new set of curricular principles focusing on complex, meaningful problems, embedding basic skills instruction within more global tasks, and connecting instruction to students' experience and culture. Teachers can then model powerful thinking strategies, encourage multiple problem-solving approaches, and stress dialogue in teaching and learning. (25 references) (MLH)
Classroom discussion practices that can lead to reasoned participation by all students are presented and described by the
authors. Their research emphasizes the careful orchestration of talk and tasks in academic learning. Parallels are drawn to
the philosophical work on deliberative discourse and the fundamental goal of equipping all students to participate in academically
productive talk. These practices, termed Accountable TalkSM, emphasize the forms and norms of discourse that support and promote equity and access to rigorous academic learning. They
have been shown to result in academic achievement for diverse populations of students. The authors outline Accountable Talk
as encompassing three broad dimensions: one, accountability to the learning community, in which participants listen to and
build their contributions in response to those of others; two, accountability to accepted standards of reasoning, talk that
emphasizes logical connections and the drawing of reasonable conclusions; and, three, accountability to knowledge, talk that
is based explicitly on facts, written texts, or other public information. With more than fifteen years research into Accountable
Talk applications across a wide range of classrooms and grade levels, the authors detail the challenges and limitations of
contexts in which discourse norms are not shared by all members of the classroom community.
In this paper we draw on two research projects in South Africa to describe and discuss the language practices of teachers
in primary multilingual mathematics classrooms. We focus particularly on code-switching – moving across languages and discourses.
We situate the paper in the policy and practice environment of post-apartheid South African education in which code-switching
is encouraged. Through our descriptions and discussion, we argue that while at a general political and pedagogical level it
makes sense for teachers to encourage and use code-switching as a learning and teaching resource, this is not a straight forward
matter. We argue that different English language infrastructures present primary mathematics teachers with different challenges
for communicating mathematics. Furthermore, we show how the movement across mathematical discourses relates to movement between
languages in classroom communication.
This article reviews two sets of research studies from outside of mathematics education to consider how they may be relevant
to the study of bilingual mathematics learners using two languages. The first set of studies is psycholinguistics experiments
comparing monolinguals and bilinguals using two languages during arithmetic computation (language switching). The second set
of studies is sociolinguistic research on young bilinguals using two languages during conversations (code switching). I use
an example of a mathematical discussion between bilingual students to illustrate how sociolinguistics can inform analyses
of bilingual mathematical conversations.
Drawing on socio-cultural theory, we understand the norms regulating the practices within the mathematics classroom as resulting from the social representations of the socially dominant groups and of the school culture related to what constitutes learning mathematics. Immigrant students, having their own personal histories as members of particular social groups, and having been in school traditions other than the one predominant in the host society, have their own images of what mathematics in school is about. Individuals interacting in the classroom are all re-interpreting the different episodes from the perspective of the social representations of the larger groups with which they identify themselves. In multiethnic classrooms different re-interpretations of the same norms clash. The lack of negotiation gives rise to obstacles to immigrant students' participation in the mathematical conversations and, therefore, interferes with the students' learning process.
In a small-scale, 8-month teaching experiment, the author aimed to establish and maintain mathematical caring relations (MCRs) (Hackenberg, 2005c) with 4 6th-grade students. From a teacher's perspective, establishing MCRs involves holding the work of orchestrating mathematical learning for students together with an orientation to monitor and respond to energetic fluctuations that may accompany student–teacher interactions. From a student's perspective, participating in an MCR involves some openness to the teacher's interventions in the student's mathematical activity and some willingness to pursue questions of interest. In this article, the author elucidates the nature of establishing MCRs with 2 of the 4 students in the study and examines what is mathematical about these caring relations. Analysis revealed that student–teacher interaction can be viewed as a linked chain of perturbations; in student–teacher interaction aimed toward the establishment of MCRs, the linked chain tends toward perturbations that are bearable (Tzur, 1995) for both students and teachers.
All students have beliefs about what to do in school in order to learn. These beliefs-their "folk learning theories"-are an expression of what our culture believes about school knowledge and how it is acquired.
Could your kids be learning a fourth R at school: reading, writing, 'rithmatic, and race? Race in the Schoolyard takes us to a place most of us seldom get to see in action-our children's classrooms-and reveals the lessons about race that are communicated there. Amanda E. Lewis spent a year observing classes at three elementary schools, two multiracial urban and one white suburban. While race of course is not officially taught like multiplication and punctuation, she finds that it nonetheless insinuates itself into everyday life in schools. Lewis explains how the curriculum, both expressed and hidden, conveys many racial lessons. While teachers and other school community members verbally deny the salience of race, she illustrates how it does influence the way they understand the world, interact with each other, and teach children. This eye-opening text is important reading for educators, parents, and scholars alike.
Direct assessments of instructional practice (e.g., classroom observations) are necessary to identify and eliminate opportunity gaps in students’ learning of mathematics. This study examined 114 middle school mathematics classrooms in four instructionally focused urban districts. Results from the Instructional Quality Assessment identified high percentages of lessons featuring cognitively challenging tasks, but declines in cognitive challenge during implementation and discussions. Overall instructional quality exceeded results from studies with nationally representative samples and paralleled results of studies of instructionally focused urban middle schools. Significant differences existed between districts, favoring the district with veteran teachers, long-term use of Standards-based curricula, and professional development initiatives.
Drawing from the 1990, 1996, and 2000 National Assessment of Educational Progress, this study examines Black-White disparities in 4th-, 8th-, and 12th-grade mathematics achievement and instruction. Substantial Black-White achievement gaps were identified, such as 12th-grade Black students scoring below 8th-grade White students. Furthermore, an analysis of race and SES together in the 1996 data revealed that student SES failed to account for much of the Black-White achievement gaps. Several instruction-related factors were also found to differ by race even after controlling for students' SES. This study provides evidence that, despite current reforms promoting high-quality mathematics education for all, Black students of both low and high SES are being left behind.
In a small-scale, 8-month teaching experiment, the author aimed to establish and maintain mathematical caring relations (MCRs) (Hackenberg, 2005c) with 4 6th-grade students. From a teacher's perspective, establishing MCRs involves holding the work of orchestrating mathematical learning for students together with an orientation to monitor and respond to energetic fluctuations that may accompany student—teacher interactions. From a student's perspective, participating in an MCR involves some openness to the teacher's interventions in the student's mathematical activity and some willingness to pursue questions of interest. In this article, the author elucidates the nature of establishing MCRs with 2 of the 4 students in the study and examines what is mathematical about these caring relations. Analysis revealed that student—teacher interaction can be viewed as a linked chain of perturbations; in student—teacher interaction aimed toward the establishment of MCRs, the linked chain tends toward perturbations that are bearable (Tzur, 1995) for both students and teachers.
Assessments of instructional quality based on classroom observations and artifacts have the potential to measure and improve mathematics instruction and learning. This article describes the Instructional Quality Assessment (IQA) Mathematics Toolkit and examines its ability to identify the nature and quality of classroom instruction. The IQA assesses elements of ambitious instruction in mathematics; specifically, the level of instructional tasks and task implementation, opportunities for mathematical discourse, and teachers' expectations. Results are reported from a study of 13 middle school teachers in a mid-sized urban district, following a professional development initiative and the adoption of standards-based mathematics curricula. The IQA identified high-quality assignments and student work, and that teachers who utilized cognitively challenging tasks could maintain the cognitive demands in lesson observations. The IQA also identified that observed instruction lacked high-quality whole-group discussions. The article closes by discussing how IQA can provide feedback for instructional improvement at the district level.
In considering “good teaching” in mathematics, scholars usually refer to teacher knowledge and instructional practices that promote understanding. However, researchers have found that these two elements of instruction are often not as prevalent in urban contexts, a space where high percentages of students of color and the poor are educated. Additionally, recent work calls for understanding other classroom mechanisms that impact the mathematics learning of students of color. Using video, field notes, and an interview, this research examines a case study of one urban classroom of Latino and African American students. Their teacher engages them in substantive mathematics and reform-minded pedagogical strategies, but a number of relational interactions raise issues of how these micro-interactions can mediate access to mathematics. The study found four dimensions in which relational interactions mediated access to mathematics: addressing behavior, framing mathematics ability, acknowledging student contributions, and attending to culture and language. The paper ends with raising questions for future research and calling for a broader framing of instruction that incorporates relational dimensions of the classroom.
Value-added models have become popular in research and pay-for-performance plans. While scholars have focused attention on some aspects of their validity (e.g., scoring procedures), others have received less scrutiny. This article focuses on the extent to which value-added scores correspond to other indicators of teacher and teaching quality. The authors compared 24 middle school mathematics teachers’ value-added scores, derived from a large (N = 222) district data set, to survey- and observation-based indicators of teacher quality, instruction, and student characteristics. This analysis found teachers’ value-added scores correlated not only with their mathematical knowledge and quality of instruction but also with the population of students they teach. Case studies illustrate problems that might arise in using value-added scores in pay-for-performance plans.
This study examined teachers' perceptions of African American males' aggression and achievement and the need for special education services based on African American students' cultural movement styles (i.e., walking). The participants, 136 middle school teachers, viewed a videotape and completed a questionnaire. To study interaction effects between student ethnicity and student movement and teachers' ratings of student achievement, aggression, and need for special education, a completely randomized factorial analysis of variance was employed. The results indicated that the teachers perceived students with African American culture - related movement styles as lower in achievement, higher in aggression, and more likely to need special education services than students with standard movement styles. Implications for research are discussed.
We observed 223 largely suburban or rural public school kindergarten classrooms in 3 states to describe classroom activities and child-teacher interactions involving I child per classroom. We also observed global classroom quality and assessed its relation to teacher, school, classroom, and family characteristics and target child outcomes. Classrooms were observed once for 3 hours starting at the beginning of the school day. Time samplings of activities, teacher behaviors, and child behaviors as well as global ratings of teacher-target child interactions and the classroom environment were obtained. The most frequently observed forms of activity were structured teacher-directed activity and whole-group instruction. There was tremendous variation in the occurrence of these activities across classrooms, ranging from 0% to 100% of the observation period. Global ratings of teachers' positive interactions with the target child, classroom instructional climate, and classroom child-centered climate were lower when the concentration of poverty in the school was high, when the target child's family income was low, and when the number of staff available to work with children in that classroom was low. Target students' observed social and on-task behavior and teachers' reports of social and academic competence for target children were higher when these global ratings indicated higher quality, even controlling for family background factors. These data may have implications for educational policies on class size and composition, and issues of equity in early school experiences.
This study documents how teachers who participated in a professional development program on understanding the development of students’ mathematical thinking continued to implement the principles of the program 4 years after it ended. Twenty-two teachers participated in follow-up interviews and classroom observations. All 22 teachers maintained some use of children’s thinking and 10 teachers continued learning in noticeable ways. The 10 teachers engaged in generative growth (a) viewed children’s thinking as central, (b)possessed detailed knowledge about children’s thinking, (c) discussed frameworks for characterizing the development of children’s mathematical thinking, (d) perceived themselves as creating and elaborating their own knowledge about children’s thinking, and (e) sought colleagues who also possessed knowledge about children’s thinking for support. The follow-up revealed insights about generative growth, sustainability of changed practice and professional development.
uriosity about the crowd forming on the next block attracted me to the scene in time to witness Kevin's1 arrest. I watched him struggle futilely against the police officer's determined hold of his upper body. Kevin's winced expression was briefly visible as the handcuffs were placed around his restrained wrists. His body seemed limp and defeated as he was moved from the grassy plot into the back of the police car, sobbing. As the climax of the arrest slowly subsided, clipped thoughts and questions flooded my mind. Kevin was an eighth grade kid from my school. I had never seen a 13-year-old in the back of a police car; definitely never anyone that young in police custody. Why? What happened? What now? Unfortunately, I had arrived too late to know how the arrest had been set in motion. Some of the other onlookers said that Kevin had tried to rob someone; others commented that the incident was drug related. As strands of truth and speculation shaped Kevin's story, I turned and walked back to the school campus. He was in my sec- ond period class. I knew that I would learn the details of the story at work. The form of notification soon arrived from the district office. Beside Kevin's name were the expected words. Sta- tus: Suspended. Location: Juvenile detention. The document provided a crisp and matter-of-fact conclusion to the story. Yet, my own experiences with Kevin, coupled with observations by students and colleagues, raised compli- cated questions about the situation. Already struggling academically, what effect would Kevin's incarceration have on his intellectual development? How would he readjust to mainstream society and school following his release? What life implications did juvenile detainment hold for a young adolescent, particularly a black male? Unfortunately, such questions surround the lives of many African American youths as crime continues to be a familiar component of the nation's urban landscape.
The work in this article has a basis in a long-term research paradigm investigating the "funds of knowledge" of diverse populations. This conceptualization adopts an anthropological perspective for viewing the households of low-income and minority students as repositories of diverse knowledge bases. In the BRIDGE project, the focus has been on understanding the mathematical potential of households, as well as "mathematizing" household practices. The transformation of mathematical knowledge, however, has been somewhat problematic. Our experience until now indicates that, whereas other classroom knowledge domains (language arts, social studies, etc.) may draw in a rather straightforward fashion from households, mathematical knowledge may not be so easily incorporated. This article describes a theoretical refinement of the concept of funds of knowledge, and will endeavor to conceptualize the distributed nature of mathematical community capital.
This article describes the ways in which the mathematics department of an urban, ethnically diverse school, brought about high and equitable mathematics achievement. The teachers employed heterogeneous grouping and complex instruction, an approach designed to counter status differences in classrooms. As part of this approach teachers encouraged multi-dimensional classrooms, valued the perspectives of different students, and encouraged students to be responsible for each another. The work of students and teachers at Railside was equitable partly because students achieved more equitable outcomes on tests, but also because students learned to act in more equitable ways in their classrooms. Students learned to appreciate the contributions of students from different cultural groups, genders and attainment levels, a behavior that I have termed relational equity. This article describes the teaching practices that enabled the department to bring about such important achievements.
In this article, the author first sets forth theoretical reasons for African American males' location in national disciplinary trends. Special emphasis is placed on the role of culture as a key factor in why Black boys lead the most measures of behavioral sanctions. Next, she analyzes how research findings centered on African American and boys' cultural orientations may shape classroom life to promote positive results. She sketches and discusses pedagogical strategies and teaching resources for K-12 educators. Finally, she concludes with a brief discussion of how future scholars may extend the ideas raised to remedy the discipline gap and further assist the academic pursuits of Black youth.
Investigated changes over four years for three elementary teachers participating in Cognitively Guided Instruction (CGI), which emphasized students' mathematical thinking and supported teachers through workshops, mentoring, and collaboration. Interviews and observations indicated that CGI allowed teachers to engage in ongoing practical inquiry directed at understanding their students' thinking, thus helping them to engage in self-sustaining, generative growth. (SM)
This article addresses equity in mathematics classrooms through a focus on students’ co-constructed trajectories of identity and engagement in cooperative learning groups. I examine how two students who served as group leaders in a projects-based algebra classroom constructed markedly different trajectories of identity and engagement across the academic year. Results showed that group members differentially interpreted their respective project-related directives in gendered ways such that the female group leaders’ displays of authority were positioned as inappropriate, while the male group leaders’ displays were positioned as desirable.
The central concern of the philosophy of mathematics is to give an account of the nature of mathematics. Views of the nature of mathematics are particularly important in the teaching of mathematics, where they can strongly influence the mathematics curriculum as taught to pupils. However, the distinction must be drawn between stated beliefs as to the nature of mathematics and views as inferred from actual classroom practice. In mathematics education there is increasing emphasis on the process (as opposed to the product) view of mathematics. This orientation is snared by a new wave in the philosophy of mathematics, represented in the works of Imre Lakatos, which rejects the traditional product orientation of the philosophy of mathematics for deep philosophical reasons. Thus there is a growing school of thought in the philosophy of mathematics which is able to account for the nature of mathematics in a way which is fruitful for the philosophers, educationists, teachers and students of mathematics alike.
This article examined general trends in teacher-reported conflict and closeness among 878 children from kindergarten through sixth grade, and examined early childhood characteristics that predict differences in initial levels and growth of conflict and closeness over time. Results indicated modest stability of teacher-perceived conflict and closeness through sixth grade, with relatively greater stability in perceptions of conflict. Levels of conflict at kindergarten were higher for children who were male, Black, had greater mean hours of childcare, had lower academic achievement scores, and had greater externalizing behavior. Children identified as Black and those with less sensitive mothers were at greater risk for increased conflict with teachers over time. Levels of teacher-reported closeness were lower when children were male, had lower quality home environments, and had lower academic achievement scores. The gap in closeness ratings between males and females increased in the middle elementary school years. Additional analyses were conduced to explore differences in teacher ratings of conflict between Black and White students.
This study examined the relationship between fall teacher expectations and year-end achievement among 561 children in 1st, 3rd, and 5th grades. Specifically, we hypothesized that children from academically stigmatized groups (African Americans generally and girls in mathematics) are more likely to be responsive to negative teacher expectancies than are children from nonstigmatized groups. Controlling for prior achievement and class membership, moderator effects were tested with hierarchical linear models in the whole sample and with loglinear models in a subsample of children who were targets of extreme teacher over- and underestimates of ability. Among targets of extreme teacher over- and underestimates, in 3rd and 5th grade, ethnicity moderated expectancy effects in reading; and in 5th grade, gender moderated expectancy effects in math but not reading. Members of stigmatized groups were more susceptible to teacher underestimates of ability. Implications are discussed in terms of differential response to teacher expectations and in terms of how susceptibility to teacher expectations is conceptualized and inferred.