#### Introduction

There is a clear dearth of research focused on teaching practices that increase access and equity in middle school mathematics classrooms. The magnitude of this gap and the lack of expansive research showcases the importance of understanding the most recent studies so educators can develop a sense of actions to take to foster change. In this summary, we will expand upon the importance of focusing on teaching beliefs, behaviors and practices that impact access and equity in middle level mathematics. Following, we will present recommendations based on recent research on this particular topic. It is important to note that within the articles we have selected for this summary, authors have chosen demographic terms as a personal choice and we will adopt the terms contiguous with their research to honor their choices. Therefore, you will see terms switching from Black to African American throughout our summary.

#### Overview of Research and Connection to The Successful Middle School: This We Believe

Access and equity for all in mathematics is not a new idea (Trentacosta & Kenney, 1997). When focusing on mathematics, the National Council of Teachers of Mathematics has made it clear and imperative in Principles to Actionsthat we commit to access and equity for all (National Council of Teachers of Mathematics [NCTM], 2014). Access is not simply presenting options for students but, instead, elevating expectations, supporting student learning, and providing opportunities to learn that are highly engaging. Equity requires taking a hard look at practices and policies that continue to marginalize certain student populations in order to shift environments to allow more diverse student groups to excel in mathematics. Equity occurs when we can no longer predict outcomes based on student characteristics and every student has the support they need to excel (NCTM, 2014). Student differences are strengths to be utilized in the classroom. NCTM (2014) emphasizes the need to create learning environments that honor differences by acknowledging them and being more responsive in how we teach every student group. Cai et al. (2020) called for better and more focused research on access and equity because changing results requires a significant commitment; there is no easy fix.

Just as equity and access are fundamental principles of NCTM, similar parallels exist with the Association for Middle Level Education’s position statement in The successful middle school: This we believe [TWB] (Bishop & Harrison, 2021). TWB calls for middle level education to be responsive, challenging, empowering, equitable and engaging (p.8). For mathematics classrooms, this means instructional choices include both concrete and abstract methods for each concept that will support all learners in the classroom regardless of where they might fall on the intellectual developmental spectrum (i.e. concrete to abstract thinking). It also means that students have the opportunity to engage in work with one another, consider contextual applications of mathematical principles and have opportunities to make connections between mathematics concepts and other subjects. Mathematics classrooms exhibiting all five attributes of a successful middle school also provide spaces for young adolescents to explore mathematical concepts and topics that are connected to their lives, promote agency in the classroom and allow expression of questions.

When designed to respond to the needs of young adolescents, mathematics curriculum can offer appropriately challenging learning experiences that are meaningful, relevant and rigorous. As young adolescents grow and change, they become capable of grasping more complex and abstract ideas, particularly in mathematics. Teachers can increase students’ confidence in mathematics with high expectations and build the foundation for their sense of empowerment in the classroom. Young adolescents need opportunities to question, explore, and predict as they learn mathematical concepts. Classrooms where students can have a voice and choice over curricular activities encourage students to engage in and take up responsibility for their learning. Advocating and enacting educational practices that are responsive, challenging, empowering and engaging are further strengthened by practices and structures that ensure equitable learning experiences for students.

Mathematics classrooms can be flexible as well as rigorous such that students explore concepts and show understanding in a variety of ways. Mathematics becomes more equitable when teachers allow authority to shift to students as students develop positive mathematics identities. TWB calls for “practices that respond to young adolescents’ multiple identities” (Bishop & Harrison, 2021, p.11) as they move through the phases of identity development and begin to label themselves as individuals and as learners (Erickson, 1968). Their myriad of identities grows and changes as they mature and come to better understand the world around them. Acknowledging, affirming, and encouraging the multiple identities young adolescents bring to the classroom fosters a classroom culture of exploration of self. This exploration of identities as it relates to curricular demands is appropriate and can influence a student’s perspective and perceptions of particular content areas (Bibby 2009; Darragh, 2013; Gardee, 2019). It is well-documented “that what learners learn and how they construct their identities are linked to their experiences of classroom practice” (Boaler & Greeno, 2000; Boaler & Staples, 2008; Cobb et al., 2009, as cited in Gardee, 2019, p. 236).

Specific to mathematics, Gardee (2019) suggests that “[personal] identity emerges from learners’ emotions, their experiences from learning mathematics, [and] their motivations…” (p. 234). Given the fact that the middle school years’ mathematics curricula are central in students’ preparation for core mathematics content such as algebra and geometry, focusing on this group of students and consciously building awareness around how to achieve equity for all students may help educators make better decisions about teaching practice and beliefs that are more effective in mitigating the unique issues facing middle level students in mathematics (Berry, 2008).

The purpose of this summary is to review the most current research examining teacher behaviors, beliefs and practices that address access and equity for all students in middle level mathematics. First, we will explore recent research focused on the importance of access to algebra in eighth grade. Second, we will discuss research that provides insights into teacher behaviors and teacher care practices that can inhibit or promote equitable student learning. Following, we will discuss research that provides effective ways to approach assignments and assessments that are more accessible and equitable for middle school students. Finally, we will highlight some of the most recent work focused on increasing success for African American students in mathematics.

#### Access to Eighth Grade Algebra

In 2013, 48% of eighth graders were taking algebra or a mathematics course higher than algebra, up from 27% in 2000 (Loveless, 2016). Though this is an impressive jump, the upward trend in enrollment does not hold true for all student demographic groups. Black and Hispanic students are less likely to enroll in or achieve in algebra in the eighth grade (McCoy, 2005; Paul, 2005) leading to disproportionate access to high level mathematics courses in high school and into college. Morton and Riegle-Crumb (2019) tackled the idea that access to algebra in the eighth grade is an integral example of the inequities in students’ opportunities to learn mathematics. These researchers sought to determine when inequities are initiated or widened in students’ course of education so educators can better disrupt the inequities with interventions. When these researchers included a prior course variable along with other prior achievement variables in their model to predict algebra enrollment, the disparities between students in different racial groups were no longer present. This result indicated that if prior placement and achievement were made equal, Black and Hispanic students were just as likely as White students to enroll in eighth grade algebra. The authors concluded that inequities in seventh grade were reproduced in eighth grade (Morton & Riegle-Crumb, 2019). Even in predominantly Hispanic schools, the disadvantages for Black students remained which highlighted the immense barriers Black students face over both White and Hispanic students.

The results from the Morton and Riegle-Crumb (2019) research indicated that in order to increase access to eighth grade algebra and consequently advanced mathematics courses, interventions must occur in early middle school or into elementary school to move toward eliminating the racialized disparities in mathematics education. The authors suggested that educators can interfere in the reproduction of inequalities if actions are taken in earlier grades. Morton and Riegle-Crumb (2019) call upon educators to analyze existing structures and practices that are constructing racial disparities and perpetuating inequities. In the following sections, we will elaborate on relevant actions and concepts from recent research that serve as potential inequity disruptors for middle school educators in support of increasing access and equity to students before those inequities are reproduced.

#### Teacher Belief Systems, Behaviors and Practices

Educators convey their teaching and personal beliefs directly and indirectly to students, and these beliefs, along with the way in which teachers show care for their students, affects how they learn (Yurekli et al., 2020; Maloney & Matthews, 2020). Because of this, teachers for young adolescents need to be specifically prepared for the unique needs of the age group, have a deep understanding in their content area and “respect and value” the students with whom they will work. (Bishop & Harrison, 2019, p. 11). Yurekli et al. (2020) focused on middle level teacher beliefs related to students’ conceptual understanding of mathematics through making connections to determine if teacher beliefs aligned with their practices. Making these connections is recommended by NCTM as it helps ensure success for all students (NCTM, 2014). Enacting these recommended teaching practices is at the core of moving toward greater access and equity in mathematics. However, Yurekli, et. al (2020) found that teacher beliefs about making connections were higher than their actual enactment of those beliefs in their classrooms. Even though teachers believe in the importance of these practices to facilitate learning, they do not report using them very often (Yurekli, et. al, 2020, p. 241). When the researchers looked further, they found that teachers strongly believed students should deepen understanding past making connections to making generalizations but, like the initial result, the teachers reported this practice was difficult to enact. Additionally, the researchers found that students’ backgrounds impacted teachers’ enactment of the practice: the more a teacher perceived students’ backgrounds to affect how they can make connections, the less they enacted the practices. The authors concluded that if teachers believe some students cannot make mathematics connections, professional development may be the course of action to correct these beliefs about students’ abilities and eliminate constraints on enacting recommended teaching practices to ensure all students have access to quality mathematics instruction.

Maloney and Matthews (2020) argued that when Black and Latinx students in particular feel more connected to their mathematics classrooms, they are more resilient in mathematics and find more value in the subject. In their study, they investigated the relationship between characteristics and types of teacher care (the way a teacher relates to their students as an obligation to the students’ welfare [Noddings, 1984]) and students’ perceived value and relevance of mathematics mediated by how connected students felt to their mathematics classrooms. A major theme from their research is the idea of developing trust with Black and Latinx students in mathematics classrooms. Teachers who show empathetic care have a relationship with students through an “authentic expression of identifying with the challenges of their students and prioritizing students’ well-being above their own” (Maloney & Matthews, 2020, p. 408). Teachers with transactional care characteristics were those who focused mostly on learning and less on their students’ experiences outside of the classroom. These teachers still very much want their students to be successful but their focus is more conditional, less active, and more superficial. In their study, these researchers found that the students who were most connected to their mathematics classrooms were those who had empathetic caring teachers. There are several characteristics to highlight from Maloney and Matthews (2020) for teachers seeking to employ pedagogies of empathetic care and increase Black and Latinx students’ connectedness to mathematics and, therefore, sense of relevance and empowerment. Empathetic care teachers actively manage students’ frustrations and form partnerships with students to overcome struggles. These teachers handle emotions and students’ mathematics identities before the content as a means to promote productive learning behaviors. Empathetic teachers correct students but protect their students’ mathematics identities at the same time and avoid taking deficit views on student performance. Promoting connectedness to mathematics for those students who have felt like outsiders is multifaceted but Maloney and Matthews (2020) encouraged teachers to start with making genuine connections with students and their families, truly understand students’ situations inside and outside of school, and become partners to share their burdens while forging through challenges. Position mathematics as a tool of personal growth; a way to empower Black and Lantinx students to resist inequities (Maloney & Matthews, 2020).

#### Creating Effective Assignments

When assignments and assessments are answer-focused, such pedagogies prohibit students from being creative in exploring how they do mathematics. In middle level classrooms, the educator’s role is to foster creativity and discovery as well as provide opportunities for divergent thinking through open-ended questions while encouraging the use of different language, flexibility in how students respond, and valuing originality (Luria et al., 2017). Open-ended problems give students options in which they can draw from their life experiences, their cultural differences, and be clever in creating mathematics ideas. A study by Equity Trust (Dysarz, 2018) which collected and scored over 1,800 assignments based on various criteria showed that although most assignments in middle level mathematics were aligned to standards, they were very low-level based on cognitive demand. Dysarz’s (2018) results showed that in high poverty schools, only 6% of assignments required strategic thinking, and none of the assignments analyzed required the highest level on the Depth of Knowledge scale (p. 10). Also, very few assignments showed opportunities for students to discuss and the assignements lacked choice in content or process. Even fewer assignments connected the mathematics content to relevant student experiences. Dysarz (2018) also found that assignments were mostly answer-focused and, even when more rigorous problems appeared, those problems were isolated and not integrated with the rest of the assignment. This collection of results is alarming. There are ways to create better situations for students to complete academic work and reveal their mathematics thinking. Taking up the characteristics of TWB (Bishop & Harrison, 2021) helps educators develop “[c]urriculum is challenging, exploratory, integrative and diverse (p.27).

Assignments need to change to require students to justify or argue about their responses in order to value how students communicate their mathematics thinking, regardless of their answers. Any form of justification leads to reflection and better discourse. Discourse provides more students access to content when the assignments foster safe interactions rather than indirectly creating fear when the focus is only on one correct answer. It is the teacher’s role to encourage and value students’ varying ideas thus showing students that they are being mathematically productive, regardless of their accuracy. According to Bieda and Staples (2020), justification takes place when students not only make claims about their work, but they support those claims with reasoning. In classrooms that focus on justification, instead of simply focusing on correct answers, students may take more risks in their mathematics choices because their classroom values not only different mathematics ideas but also the ideas of the students engaged in learning. This type of instruction empowers students through engagement and allows students to develop positive mathematical identities. Additionally, when justification becomes a recurring component of lessons, rigor will increase leading to better mathematics understanding. Students will more likely gain agency (sense that they can do and create mathematics) when they are asked to justify their mathematical decisions (Bieda & Staples, 2020). It is important for teachers to make mathematics assignments into tools for students, not barriers. Particularly for students who have been historically underserved in mathematics, more engaging, open content in assignments that connects to students’ backgrounds and provides choice helps students see themselves within mathematics. Subsequently, students become motivated to do mathematics rather than positioning themselves as just another member of a class (Dysarz, 2018, p. 16). When teachers redirect assignments toward justification, discourse, creative thinking, and relevance, traditional answer-focused assessments will not be an appropriate pedagogical match whereas formative assessment may provide more flexibility in evaluating and eliciting student learning in real-time (Dukor et al., 2017).

#### Using Formative Assessment

Just as assignments need to shift away from answer-focused structures, the same can be said about assessments. TWB (Bishop & Harrison, 2021) advocates varied and ongoing assessments [that] advance learning as well as measure it” (p. 40). The effective use of formative assessment allows a bridge between assignments that cultivate students’ mathematics thinking and how teachers gauge the depth of students’ learning. Dukor, et al. (2017) presented their framework to conceptualize formative assessments based on empirical research. These authors discussed ways to formatively assess students to create more dynamic environments in middle level mathematics classrooms that promote equity. If teachers shift the way they create assignments, there must be a matching shift in how they assess students. Dukor, et al. (2017) referred to seven teacher moves as priming, posing, pausing, probing, bouncing, tagging, and binning. These authors discussed how a teacher’s role is to create opportunities for students to interact, and using the teacher moves just mentioned, demand higher-level thinking. The teacher moves are akin to an acting lesson using improvisation; teachers need to be ready to change things as needed to engage students. For example, teachers conduct class, and if they take one student’s question, they can prime the class to get them ready to discuss, bounce the question to other students who can share a variety of ideas, pose another question to the class and then probe the class for responses. Throughout the lesson, teachers can pause to allow students time to reflect or tag groups of ideas from students that need further development. Using a variety of teacher moves like these normalizes student thinking, creates a safe exploratory learning environment, gives value to novel ideas and empowers students within the classroom. Safe environments allow middle school students to take academic risks that will benefit their learning. The goal of formative assessment is not just checking for understanding but developing teacher moves that will involve all students and elicit student thinking so teachers can facilitate learning transparently (Dukor et al., 2017). This is the type of instruction and assessment that “fosters learning that is active, purposeful, and democratic” (Bishop & Harrison, 2021, p.35)

Teachers can conceptualize formative assessments as a way to allow middle school students to think creatively around mathematics and feel safe doing so. Creativity in classrooms can occur when lessons involve exploration and less direct instruction which allow for teachers to formatively assess throughout a lesson. Open-ended instruction interwoven with formative assessment gives students options in which they can draw from their life experiences, their cultural differences, and be clever in creating mathematical ideas (Luria et al., 2017). To use formative assessment strategies like teacher moves that involve priming, pausing, tagging among the others mentioned, student-centered, open instruction and assignments pair well to allow for conversations and active problem-solving which leads to deeper understanding for all students.

#### Teacher Actions for African American Student Success

As highlighted early, the Morton and Riegle-Crumb (2019) study showed that Black students are the most marginalized group of students in mathematics. Black students continue to be placed in lower mathematics courses and receive less demanding instruction (Anderson & Tate, 2008; Lubienski, 2002). To help identify practices that work to increase African American student success in mathematics rather than perpetually impede these students, Wilson et al. (2019) focused specifically on African American students and middle level classrooms. These researchers looked at classes in which African American students were successful on state assessments in order to determine the characteristics of teaching practices that led to such success. The researchers identified six effective teacher actions for improving mathematics achievement for middle level, African American students: making expectations explicit (participation and mathematics work), coaching students (teacher intervention), attending to students’ local context (connection to cultural or social context of student), attending to language (revoicing to appreciate student contributions), attributing mathematics authority to students (time for student reflection, discussion), and attending to classroom community(explicit action taken to build a productive environment). These teaching practices support classrooms which provide high cognitive demand lessons, whole-class discussion and value a variety of student thought. For African American students, these six teaching practices may be the catalyst to higher achievement when used in conjunction with other engaging teaching practices without decreasing rigor (Wilson et al., 2019).

#### Normalizing Black Girls in Mathematics

Joseph et al. (2019) powerfully argued for particular attention to be given to Black girls and their success in mathematics due to a lack of research focused specifically on this student population. These authors detailed the immense hurdles that Black girls in particular must overcome to be successful academically as they have been devalued, dehumanized, and excluded from opportunities and achievement in mathematics. In their recent study on normalizing Black girls’ humanity in mathematics classrooms, Joseph, et al. (2019) looked at Black girls’ experiences in middle level mathematics to make clear what Black girls need and want from those experiences. In an effort to change the systemic exclusion of Black girls from mathematics, these authors provided pedagogical recommendations to increase Black girls’ access to mathematics. There are two main tenets from their study: social interaction and sharing power. The authors found that Black girls thrive in mathematics classrooms that value different perspectives and in which the teacher shows empathy. Instead of a punitive environment, the classroom that increases access to mathematics for Black girls will be characterized by patience, approachability, and safety. The authors stated that a “key theme was the inextricable links between Black girls’ performance and participation in mathematics and the patience and approachability of their mathematics teachers” (Joseph et al., 2019, p. 143). When asked what makes a teacher a good teacher, one student said, “he doesn’t yell at you for the wrong answer” (Joseph et al., 2019, p. 144). Classrooms in which Black girls feel safe help them trust their teachers which leads to higher levels of comfort and engagement. Teachers must share power with students in knowledge creation to give access to these students. The authors suggest teachers move away from focusing on answers and move toward building knowledge together, relinquishing power in service of students (Joseph et al., 2019, p. 138), and capitalizing on Black girls’ tendency toward being collective learners by allowing them to productively struggle in groups and interact. “When mathematics teachers give…[Black girls] dedicated time to explain mathematics ideas, teachers are also acknowledging the girls’ vulnerability as children and adolescents” (Joseph et al., 2019, p. 144). Teachers can empower Black girls to believe in their mathematics abilities when they commit to teaching in ways that utilize their strengths. If teachers acknowledge the realities of Black girls’ marginalization by changing the way they teach to be more inclusive, teachers can normalize Black girls’ involvement and success in mathematics.

#### Taking Action Now

There are distinct themes that run through the findings of the aforementioned authors and each connects to the Association for Middle Level Education’s essential attributes and characteristics of a successful middle school (Bishop & Harrison, 2021). What can you do now to take action to increase access and equity in your middle level mathematics classrooms? First, make a commitment. There is overwhelming consensus that this topic matters and the goal is to create a culture of access and equity, not just incremental changes (Bieda & Staples, 2020). As an educator you can step back, acknowledge historical and current inequities for Black and Latinx students and commit to make more equitable pedagogical changes a priority. Next, maintain rigor and offer high-quality, high-cognitive demand content in your lessons. TWB (Bishop & Harrison, 2021) calls for “curriculum [that] is challenging, exploratory, integrative and diverse” (pg.27). Release some authority in your classrooms to give authority to students to think creatively and have choice in their mathematical approaches. Such an approach will empower your Black students in their mathematical work, especially girls. Responsive middle school mathematics curriculum is not only appealing to young adolescents, but offers “them opportunities to pose and answer questions that are important to them” (Bishop & Harrison, 2021, p. 27). Through lessons, give students a voice and value different ideas; overtly display openness to students’ mathematical ideas whether they are correct or not to create a safe space where all students can explore mathematics and take risks in their learning. Equity through empathy can be an important component of creating better experiences for students, particularly Black students. Also, connect student mathematics tasks to authentic experiences and place activities within contexts to which students can connect. Learning opportunities for all depends upon evaluating classroom-level choices and activating the approaches to learning that will engage every student and deconstruct barriers. These opportunities also create a classroom community that “is welcoming, inclusive, and affirming for all” (Bishop & Harrison, 2021, p. 12).

#### References

Anderson, C. R., & Tate, W. F. (2008). Still separate, still unequal: Democratic access to mathematics in U.S. schools. In L. D. English, M. B. Bussi, G. A. Jones, R. A. Lesh, B. Sriraman, & D. Tirosh (Eds.), Handbook of international research in mathematics education (2nd ed., pp. 299–318). Routledge.

Berry, R. Q. (2008). Access to upper-level mathematics: The stories of successful African American middle school boys. Journal for Research in Mathematics Education, 39(5), 464-488.

Bibby, T. (2009). How do pedagogic practices impact on learner identities in mathematics?

A psychoanalytically framed response. In L. Black, H. Mendick, & Y. Soloman

(Eds.), Mathematical relationships in education: Identities and participation (pp.

123-136). Routledge.

Bieda, K. N., & Staples, M. (2020). Justification as an equity practice. Mathematics Teacher, 113(2), 102-109.

Bishop, P., & Harrison, L. (2021). The successful middle school: This we believe. Association for Middle Level Education.

Boaler, J., & Greeno, J. G. (2000). Identity, agency, and knowing in mathematics worlds. In J. Boaler (Ed.), Multiple perspectives on mathematics teaching and learning (pp. 171–200). Ablex Publishing.

Boaler, J., & Staples, M. (2008). Creating mathematical futures through an equitable teaching approach: The case of Railside school. Teachers’ College Record, 110(3), 608–645.

Cai, J., Morris, A., Hohensee, C., Hwang, S., Robison, V., Cirillo, M., Bakker, A., Kramer, S., & Hiebert, J. (2020). Maximizing the quality of learning opportunities for every student. Journal for Research in Mathematics Education, 51(1), 12-25. https://doi.org/10.5951/jresemathematicseduc.2019.0005

Cobb, P., Gresalfi, M., & Hodge, L. L. (2009). An interpretive scheme for analyzing the identities that students develop in mathematics classrooms. Journal for Research in Mathematics Education, 1, 40–68.

Darragh, L. (2013). Constructing confidence and identities of belonging in mathematics at the transition to secondary school. Research in Mathematics Education, 15(3), 215–229.

Duckor, B., Holmberg, C., & Becker, J. R. (2017). Making moves: Formative assessment in mathematics. Mathematics Teaching in the Middle School, 22(6), 334-342. https://doi.org/10.5951/mathematicsteacmiddscho.22.6.0334

Dysarz, K. (2018). Checking in: Are mathematics assignments measuring up? Equity in Motion. https://edtrust.org/resource/checking-in-are-mathematics-assignments-measuring-up/

Erikson, E. H. (1968) Identity: Youth and crisis. Norton.

Gardee, A. (2019). Social relationships between teachers and learners, learners’

mathematical identities and equity. African Journal of Research in Mathematics, Science, and Technology Education, 23(2), 233-243.

Joseph, N. M., Hailu, M. F., & Matthews, J. S. (2019). Normalizing black girls’ humanity in mathematics classrooms. Harvard Educational Review, 89(1), 132-155. https://doi.org/10.17763/1943-5045-89.1.132

Loveless, T. (2016). The 2016 Brown Center report on American education: How well are American students learning? Washington, DC: Brown Center on Education Policy, Brookings Institution.

Lubienski, S. T. (2002). A closer look at Black-White mathematics gaps: Intersections of race and SES in NAEP achievement and instructional practices data. Journal of Negro Education, 71(4), 269–287. https://doi.org/10.2307/3211180

Luria, S. R., Sriraman, B., & Kaufman, J. C. (2017). Enhancing equity in the classroom by teaching for mathematics creativity. ZDM: Mathematics Education, 49(7), 1033-1039. https://doi.org/10.1007/s11858-017-0892-2

Maloney, T., Matthews, S.M. (2020). Teacher care and students’ sense of connectedness in urban mathematics classrooms. Journal for Research in Mathematics Education, 51(4), 399-432.

McCoy, L. P. (2005). Effect of demographic and personal variables on achievement in eighth-grade algebra. The Journal of Educational Research, 98(3), 131–135. https://doi.org/10.3200/JOER.98.3.131-135

Morton, K. & Riegle-Crumb, C. (2019). Who gets in? Examining inequality in eighth-grade algebra. Journal for Research in Mathematics Education, 50(5): 529-554.

National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematics success for all. NCTM.

National Middle School Association. (2010). This we believe: Keys to educating young adolescents. Author.

Noddings, N. (1984). Caring: A feminine approach to ethics and moral education. University of California Press.

Paul, F. G. (2005). Grouping within Algebra I: A structural sieve with powerful effects for low-income, minority, and immigrant students. Educational Policy, 19(2), 262–282. https://doi.org/10.1177/0895904804274056

Trentacosta, J., & Kenney, M. J. (1997). Multicultural and gender equity in the mathematics classroom: The gift of diversity. Reston, VA: NCTM.

Wilson, J., Nazemi, M., Jackson, K., Wilhelm, A.G.. (2019). Investigating teaching in conceptually oriented mathematics classrooms characterized by African American student success. Journal for Research in Mathematics Education, 50(4): 362-400.

Yurekli, B., Stein, M.K., Correnti, R., Kisa, Z. (2020). Teaching mathematics for conceptual understanding: Teachers’ beliefs and practices and the role of constraints. Journal for Research in Mathematics Education, 51(2): 234-247.

#### Selected Annotated Resources

Duckor, B., Holmberg, C., & Becker, J. R. (2017). Making moves: Formative assessment in mathematics. Mathematics Teaching in the Middle School, 22(6), 334-342. https://doi.org/10.5951/mathematicsteacmiddscho.22.6.0334

Duckor, Holmberg, and Becker presented a framework to better define what formative assessment looks like in middle level mathematics classrooms. They included seven teacher moves as part of their framework: priming, posing, pausing, probing, bouncing, tagging, and binning. These teacher moves can be used in a feedback loop system to engage students in deeper mathematics thinking and guide mathematics inquiry. Duckor, Holmberg, and Becker used a video-based lesson study conducted by a middle school teacher to present their formative assessment framework. The authors highlighted examples of each of the teacher moves and the reflections made by the participating teacher. The goal of this article was to showcase the formative assessment moves as a means for teachers to better elicit student thinking and amplify all student voices in middle school mathematics classrooms.

Dysarz, K. (2018). Checking in: Are mathematics assignments measuring up? Equity in Motion. https://edtrust.org/resource/checking-in-are-mathematics-assignments-measuring-up/

Dysarz conducted an analysis of over 1,800 assignments from 12 schools to determine their level of alignment to standards, cognitive challenge, rigor, promotion of communication of mathematics understanding, and engagement. The author presents examples to showcase typical assignments versus those that reach higher levels on the measured scales. Those most of the assignments analyzed aligned to standards, they were not cognitively demanding nor did they provide opportunities for students to express their mathematics understanding. Most assignments had a procedural focus and did not provide opportunities for choice. Dysarz provides suggestions for educators to deepen understanding through assignments and provide a better balance of assignments for their students in order to increase engagement, reasoning, and problem solving for all students.

Joseph, N. M., Hailu, M. F., & Matthews, J. S. (2019). Normalizing black girls’ humanity in mathematics classrooms. Harvard Educational Review, 89(1), 132-155. https://doi.org/10.17763/1943-5045-89.1.132

Joseph, Hailu, and Matthews used longitudinal mixed-methods data with a focus on the interviews of 10 black girls in grades 6-9 and their experiences in mathematics. The researchers analyzed what made for good experiences in mathematics for these girls and how educators can adjust their teaching to humanize Black girls in mathematics. Looking at themes from the interviews and these girls’ experiences, the researchers found that, in mathematics, Black girls seek opportunities to work together in more relaxed environments where their personalities are welcomed, are more engaged when their teachers are approachable, inclusive, and patient, and want classrooms that are centered around respect.

Maloney, T., Matthews, S.M. (2020). Teacher care and students’ sense of connectedness in urban mathematics classrooms. Journal for Research in Mathematics Education, 51(4), 399-432.

Maloney and Matthews explored types of teacher care (empathetic, transactional, blended) in order to determine if Black and Latinx students valued mathematics more and felt it was more relevant with teachers who demonstrated a specific type of teacher care. They used a mixed-methods approach combining interviews with qualitative analysis from coding to investigate impacts of students’ teacher care type and connectedness to their mathematics classrooms. Maloney and Matthews defined each of the types of teacher care types and provided examples to demonstrate the differences in care types. They found that students with empathetic care teachers felt more connected to their mathematics classrooms and that students’ connectedness to mathematics mediated the relationship between teacher care type and perceived value and relevance of mathematics.

Wilson, J., Nazemi, M., Jackson, K., Wilhelm, A.G.. (2019). Investigating teaching in conceptually oriented mathematics classrooms characterized by African American student success. Journal for Research in Mathematics Education, 50(4): 362-400.

Using comparative analysis or teaching practices, Wilson, Nazemi, Jackson, and Wilhelm worked to identify what works for African American students in middle school mathematics classrooms. They looked at classrooms in which African American students were more successful on state assessments and those in which students were not as successful. Their analysis revealed themes concurrent with the successful classrooms such as attending to context and language, attributing authority to the students, and special attention paid to the classroom as a community of learners.

Yurekli, B., et al. (2020). Teaching mathematics for conceptual understanding: Teachers’ beliefs and practices and the role of constraints. Journal for Research in Mathematics Education, 51(2): 234-247.

Yurekli, B., Stein, M.K., Correnti, R., Kisa, Z. sought to better define teacher beliefs and how teachers enact the Common Core State Standards for Mathematics teaching standards in order to determine the mismatches between teacher beliefs and self-reported teaching practices. Using survey data from 248 teachers in two-level measurement models with a focus on teaching practices related to making mathematics connections, these researchers found that even when a teacher found a standards item important, they reported implementing recommended strategies with less frequency. And, they found that if teachers thought multiple solutions strategies were too difficult for students, they tended to not implement recommended teaching strategies. These researchers identified two constraints that impacted teachers’ decisions to implement strategies: standardized tests and students’ backgrounds.