1. Introduction
If curriculum materials aim to guide teachers and support student learning (Remillard, 2018), it is critical to identify features of the materials that will indicate for educators and other stakeholders the quality of that guidance. This paper investigates curriculum materials through the lens of Culturally Responsive Mathematics (CRM) as a means for promoting Culturally Responsive Mathematics Teaching (CRMT), which is a multidimensional construct that encompasses “a set of specific pedagogical knowledges, dispositions, and practices that privilege mathematics, mathematical thinking, cultural and linguistic funds of knowledge, and issues of power and social justice in mathematics education” (Zavala & Aguirre, 2024, p. 6). Although this definition describes a construct that encompasses more than just teaching practices, in this paper we differentiate CRM when describing the pedagogical knowledges, dispositions, and practices from CRMT to describe specifically the teaching practices that flow from CRM. We argue that identifying the ways that written curricula adhere to the broader aims of CRM can strengthen conversations on curriculum quality and the role of curriculum in supporting CRMT and culturally responsive learning opportunities for all students.
In the United States, the push toward high-quality mathematics standards in the 1980s-1990s, along with a rise in policy and curriculum design toward alignment with such standards, shifted research from framing curriculum as a barrier to student learning to investigating ways in which such materials might support standards-based instruction and student learning (Stein et al., 2007). Such investigations showed promising results around how standards-based curricula have the potential to support student achievement (e.g., Chappell, 2003; Choppin et al., 2022; Putnam, 2003; Stein & Kaufman, 2010). However, achievement on standards-based assessments is only one, narrow representation of student learning, and an overemphasis on only standardized achievement outcomes can perpetuate dominant narratives about who can be a mathematical thinker and what mathematical activity even entails (Gutiérrez, 2012; Gutiérrez et al., 2023; Raymond, 2018). It is therefore insufficient for investigations of curricular quality to be confined to curriculum’s ability to influence standardized test scores (Buxton, 2006).
Studies have explored how conceptions of equity and cultural responsiveness are embedded within district mathematics vision-setting and reform efforts, suggesting inconsistent attention to such concepts across educational infrastructures (Comstock et al., 2024; Marshall & Khalifa, 2018). Given curriculum materials’ unique position to communicate directly to a wide range of teachers (Remillard & Kim, 2020), it is important to consider these materials’ role in supporting CRM as a critical element of educational infrastructures. In these ways, curriculum designers, school leaders, and other stakeholders could explicitly consider cultural and contextual considerations for curriculum to support the practices and dispositions embedded within CRM.
Researchers have designed tools to identify and describe the extent to which mathematics teachers’ lessons adhere to multiple dimensions of CRM (Aguirre & Zavala, 2013; Zavala & Aguirre, 2024). This study adapts these tools to the context of curriculum materials to answer the following questions.
(1). To what extent are cultural and contextual considerations included in mathematics curriculum materials?
(2). In what ways do mathematics curricula that do consider cultural and contextual considerations address such issues?
2. Literature Review
Curriculum, or the “substance or content of teaching and learning” (Stein et al., 2007, p. 321), exists in many forms throughout the education system, including national or (in the United States) state standards all the way down to the mathematical experiences of students in the classroom (Remillard & Heck, 2014). Curriculum resources play a key role in communicating to teachers specifics about how standards can be addressed (Remillard, 2018). The different manifestations of curriculum paint a picture of what teaching mathematics should look like in that school system.
In the United States, individual states or even school districts have a certain degree of autonomy in selecting curricula, often a set of materials created by a private publisher, for use in their schools. These materials (in the form of instructional resources, teachers’ guides, workbooks, etc.) can therefore serve as a tool for teachers to use and adapt as they plan their instruction (Brown, 2011). Teachers’ adaptations are necessary to turn standardized resources into learning opportunities, but the quality of instructions and guidance they receive from the mathematics curriculum is also an important factor in their teaching choices (Choppin et al., 2022; Gay, 2002; Stein & Kaufman, 2010).
As such, investigations of curriculum have recognized that there are distinctions between the intended curriculum—the instructional materials as designed—and the enacted curriculum, or how these materials are actually experienced in the classroom (Gehrke et al., 1992; Remillard, 2005). To this end, Remillard and Heck (2014) define the mathematics curriculum both “as a plan for the experiences that learners will encounter, as well as the actual experiences they do encounter, that are designed to help them reach specified mathematics objectives” (p. 707, emphasis in original). Teachers must lean on their own content and pedagogical expertise and interpret the intentions behind curriculum materials as they adapt these materials to their students’ specific needs and contexts (Ben-Peretz, 1990). It is therefore “critical that curriculum developers pay careful attention to the multiple ways that their materials communicate with the teacher” (Remillard, 2005, p. 240), as the forces that drive the design of instructional materials are not guaranteed to align with teachers’ contexts.
This participatory perspective toward curriculum, which sees educators as a “Collaborator with curriculum materials” (Remillard, 2005, p. 217), requires greater consideration of teachers’ role in enacting curriculum. Remillard (2000) describes the importance of such materials not simply speaking through teachers but speaking to them through guiding resources that recognize teachers as astute interpreters of the texts. This consideration underscores the importance of analyzing not only the supposed quality of student-facing materials, but also the included structures and resources designed to support teachers’ enactment of the materials in their own context and given their own experiences.
Although research on mathematics curricula has often focused on standards alignment and the inclusion of rigorous tasks (Stein et al., 1996, 2007), some investigations have also considered the relationship between curriculum and CRM. These studies have often emphasized this participatory perspective of curriculum (Remillard, 2005) and attributed the success of curriculum materials’ effect on culturally responsive teaching to the adaptation and practices of the teacher alongside materials themselves (Boaler, 2002; Kisker et al., 2012). Many of these studies have looked at curricula that were developed in collaboration with teachers specifically for their community of students. However, because the adoption of mass-produced curriculum materials of varying quality is prevalent across public school systems in the United States (Center for Education Market Dynamics, 2023), it is also important to consider how these types of materials may be primed for such teacher adaptation.
The very notion of “high quality” within mathematics curriculum materials also deserves critical examination. Despite aligning with notions of “high-quality instruction,” such materials often reinforce larger narratives about mathematics that play into systems of inequity already present in the school system and society (Gutiérrez, 2017b), and even reform-oriented curriculum materials require training and support to enact equitably and with fidelity (Boaler, 2002). What’s more, school district messaging in support of equitable mathematics may not be matched with district allocation of actual resources to support equitable mathematics teaching (Comstock et al., 2024). As such, it is incumbent for researchers and school leaders to strategically find opportunities to support teachers in recognizing these harmful narratives and imagining alternatives (Gutiérrez et al., 2023). Explicitly analyzing curriculum materials through the lens of CRM can therefore play an important role in developing a constellation of support for fostering CRMT in classrooms.
Fortunately, frameworks around CRM have been developed that can support such investigations. There are many aspects of culturally responsive teaching, ranging from how mathematical thinking is facilitated to how language, culture, and social justice is addressed (Aguirre & Zavala, 2013). Zavala and Aguirre (2024) have organized such knowledges, dispositions, and practices into the Culturally Responsive Mathematics Teaching Tool (CRMT2), which is in part designed to support teachers in analyzing curriculum materials to adapt for their own contexts. This tool categorizes CRMT into three conceptually related (but not wholly distinct) strands that form the basis of our present investigation: Knowledges & Identities, Rigor & Support, and Power & Participation.
Promoting access and equity in mathematics requires instruction that leverages students’ knowledges and identities (National Council of Teachers of Mathematics, 2014; Zavala & Aguirre, 2024). This can start with bringing in topics that are connected to students’ lives, but must go beyond simply adapting standard word problems. Mathematics rooted in real-life is often messier than the mathematics seen in classrooms. Simplifying contextualized math into a word problem with one process or solution can limit a student’s ability to utilize their personal funds of knowledge as they have to prioritize the sterilized classroom mathematics over contexts with which they are familiar (Boaler, 1993). This game of “make believe” deprioritizes students’ knowledges and identities by sterilizing cultural references into a neat and simplified word problem. To truly understand students’ funds of knowledge, students and their communities need to be utilized as a resource. Teachers and other actors within the education systems need to position themselves as learners, seeking out information, connections, and relationships with the adults and communities that surround students in their whole identity and experiences (González et al., 2006; Moll et al., 1992; Wachira & Mburu, 2019). Teachers and school administrators need to recognize and respect the cultures and identities of students if they want to truly capitalize on the students’ knowledge.
CRM also highlights the need for mathematical experiences that provide rigor and support for all students (Zavala & Aguirre, 2024). Open-ended tasks with many ways to solve, or with many correct answers, are often considered more mathematically rigorous in that they help to sustain high cognitive demand (Stein et al., 1996). Rigorous mathematics moves away from procedural tasks and centers the students’ thinking and knowledge. However, students who are considered behind are still often asked to perform more procedural tasks, limiting their access to rigorous, high-level mathematical thinking (Gutiérrez, 2008). Therefore, it is critical to provide all students with scaffolds that support students’ mathematical reasoning and do not inadvertently lower the rigor of the task (Boaler, 2002; Stein et al., 1996). In these ways, it is important for teachers to attend to aspects of rigor as well as support for all students to engage in such rigorous environments.
Power and participation are also important aspects of CRM because they require consideration of how cultural dynamics influence how students interact and are perceived (Zavala & Aguirre, 2024). These are often embodied in how schools support and respond to students’ participation, leadership, and collaboration. This is especially important in heterogeneous classrooms as peer-to-peer dynamics can reinforce inequitable participation due to the perceived status of students (Curtis et al., 2021). To develop collaboration and participation, teachers can highlight the power, intelligence, and input of students who are perceived as having lower status (Horn, 2012). This will help students in seeing themselves, and for their classmates to see them, as mathematical thinkers (Cohen & Lotan, 1995; Ladson-Billings, 1995). Acknowledging the ways that societal systems affect student experiences and participation in mathematics classrooms is critical to supporting equitable mathematics teaching.
Together, funds of knowledge, students’ whole identities, power dynamics, participation in heterogeneous classrooms, and the facilitation of rigorous mathematical experiences are all connected (Zavala & Aguirre, 2024). Teachers need to respect students’ full identities before they can be expected to push themselves academically (Ladson-Billings, 1995). Before facilitating equitable groupwork, there needs to be a move away from procedural mathematics (Cohen & Lotan, 2014). This web of ideas provides no linear path for teachers to follow to become culturally responsive in their mathematics teaching but instead informs both a professional and personal journey. Curriculum materials can provide structures, routines, and examples of what CRM could look, sound, and feel like in the classroom, inspiring and supporting teachers to try new ways to approach their teaching. We argue that bringing these ideas into all levers of teacher support, including curriculum, is key to developing a more equitable and culturally responsive education system.
Theoretical Framework
This study uses a socio-political lens when approaching mathematics education (Gutiérrez, 2013) and adapts the CRMT2 framework (Zavala & Aguirre, 2024) for the purpose of curriculum materials analysis. These two frameworks inform each other as they both consider how the positionality of education reinforces the cultural systems of power present in our society. Without acknowledging this power dynamic within mathematics education, teachers are destined to repeat it. Gutiérrez (2013) speaks more broadly, describing how students’ identities are undermined by more traditional mathematics practices, especially students of color and students with language diversity. Zavala and Aguirre (2024) propose a more specific framework intended to support teachers in “attend[ing] to teaching mathematics with strong, deep, and meaningful connections to students and their communities” (p. 18). We adapt this framework for the present study, using it as a steppingstone from CRM broadly to CRMT, and to create a similar tool as CRMT2 for mathematics curriculum resources. As such, we see this work as centered around broader knowledges, dispositions, and practices aligned with CRM, with the aim of fostering classrooms engaged in CRMT.
Though the standardized nature of curriculum may limit its ability to adapt to the cultural context of each classroom, it still holds great power as a tool that teachers use to design and adapt their instruction. This study considers the teacher-tools framework that assumes that teachers should not be expected to follow the curriculum as a script but instead use it as a tool to help make decisions (Brown, 2011). Given the need and inevitability of teacher adaptation, even reform-oriented curricula benefit from being situated within a larger system of supports for teachers to make the best use of such materials (Boaler, 2002). We therefore see this work as one means for empowering mathematics teachers to act upon their beliefs and ideals of culturally responsive teaching.
3. Materials and Methods
3.1. Context and Setting
This paper extends from the Analysis of Middle School Math Systems (AMS), a study that was conducted in partnership with four large urban school districts (serving more than 2500 schools and 1,500,000 students) during the 2021–2022 and 2022–2023 school years, involving grades six through eight (grades for students aged approximately 11–13 in the United States). While the study aimed to assess multiple facets of school systems, one primary goal was to understand how mathematics curriculum materials contributed to or hindered teachers’ enactment of culturally responsive teaching practices.
The four school districts (a local, geographic administrative unit for schools in the United States) with whom AMS partnered each brought their own policy, demographic, and instructional contexts and were in a range of stages in formulating and implementing a vision for middle school mathematics. Because the United States does not maintain a national curriculum, individual schools often partner with private companies to purchase sets of curriculum materials in line with state learning standards (Center for Education Market Dynamics, 2023). Within the districts taking part in the AMS study, there were six focal curricula of interest: Illustrative Mathematics (IM), Into Math, Eureka Math, California (CA) Math, Big Ideas, and Key Elements of Mathematics Success (KEMS). These are described in the bullets below.
IM: A grade K–8 core curriculum published by LearnZillion/Imagine Learning that is available in digital and print versions. Open-Up Resources also offers a free digital program for grade 6–8 that is authored by Illustrative Mathematics.
Into Math: A grade K–8 core curriculum published by HMH and includes print-based curriculum components as well as digital and interactive versions. Due to copyright restrictions, Into Math materials cannot be shared publicly.
Eureka Math: A grade pre-K (PK)–12 core curriculum that includes comprehensive print and digital curriculum materials and professional development. The entire PK–12 Eureka Math curriculum, along with a variety of instructional materials and support resources, can be downloaded at no charge.
CA Math: A core curriculum for grade 6–8 published by McGraw Hill Education that is based on Glencoe Math but revised to align with California’s state mathematics standards (available in digital and print). Due to copyright restrictions, CA Math materials cannot be shared publicly.
Big Ideas: A grade K–12 core curriculum published by Big Ideas Learning that includes print-based curriculum components and digital versions. Due to copyright, Big Ideas materials cannot be shared publicly.
KEMS: A grade 3–8 core curriculum developed by National Training Network, a mathematics professional development company that provides professional development and coaching services to mathematics teachers. Due to copyright, Into KEMs materials cannot be shared publicly.
3.2. Instruments
In line with the AMS study’s emphasis on supporting diverse populations of students, we sought to expand the conception of “high quality” curricula by investigating the ways in which middle school math curricula not only aligned to college- and career-readiness standards, but also provided guidance to support CRM. To understand whether and how the study curricula facilitate culturally responsive instruction and create opportunities for students to demonstrate their learning in holistic ways, we adapted the CRMT2 Lesson Analysis Tool (Zavala & Aguirre, 2024) to create an instrument that we call the CRM materials evidence tool (CRM-MET). While the CRMT2 framework was originally constructed by Zavala and Aguirre (2024) as a tool for analyzing classroom instruction, they also describe how the CRMT2 framework can be applied “to analyze or adapt existing lessons within the curriculum prior to instruction” (p. 25). In line with this use case for the CRMT2 framework, we adapted this tool as a means of quantitatively scoring the presence of guidance around CRM within curriculum materials.
To adapt this tool, the lead developer first reviewed the literature that informed Aguirre and Zavala’s (2013) CRMT lesson analysis tool and defined ways these dimensions could arise in written curricula. For example, curricula can include guidance to build on students’ cultural and community funds of knowledge (CfoK) (González et al., 2006; Moll et al., 1992) by reminding teachers to ask about and reference students’ community and home knowledge, culture, or experiences. Then the curriculum could encourage teachers to adapt problems or situations to align with their classroom. In line with Aguirre and Zavala’s (2013) original lesson analysis tool, this original draft of the CRM-MET included seven dimensions focused on mathematical thinking, language, culture, and social justice in mathematics.
The CRM-MET was then piloted on a subset of 27 lessons, which allowed coders to identify additional examples of how these dimensions were arising in the focus curricula and to resolve disagreements. For example, evidence for CFoK was revised to include more explicit guidance to coders, including the following: A potentially relatable problem context is not sufficient–to represent CFoK, there must be an indication that students are asked to think about how they themselves, or other students, could relate to the mathematized issue. Examples include the mathematics being situated in something specific in a community, and as an actual mathematical issue that would emerge from the situation. Sometimes that context is specific to the unique community represented in the school. Other times, a context might be more general or familiar to students, even though it is not unique to their specific community.
The dimension of rehumanizing mathematics (Gutiérrez, 2018) was similarly revised to include clarifications to coders about visual imagery in curriculum materials, noting that “Images on the curriculum page of non-white individuals, or use of names that are more typical of non-white cultures, does not count as evidence, unless these identities are a central aspect of the problem.” Further descriptions of the final CRM-MET dimensions and examples of evidence are described in Section 3.2.1, Section 3.2.2, Section 3.2.3, Section 3.2.4, Section 3.2.5, Section 3.2.6, Section 3.2.7, Section 3.2.8 and Section 3.2.9.
To provide further evidence of test content validity (American Educational Research Association et al., 2014), Maria Zavala, as one of the authors of the original lesson analysis tool (Aguirre & Zavala, 2013) and the (at the time unpublished) CRMT2 framework (Zavala & Aguirre, 2024), provided an expert review of the tool. Through these discussions, two additional dimensions from the CRMT2 framework—honoring student ideas and thinking and cognitive demand—were also added to the CRM-MET. These revisions allowed for greater alignment of the tool with such emerging external work involving CRM. Further psychometric analyses have not yet been conducted, but rubrics and associated training materials are available upon request.
We used the CRM-MET to assess curricula across Zavala and Aguirre’s (2024) nine dimensions that measure the three broad strands of knowledges and identities, rigor and support, and power and participation. Each dimension was measured on a rubric that defined the type of curriculum evidence necessary, within a lesson, to meet thresholds for opportunities to enact CRMT. Table 1 describes the general rubric for these thresholds across all dimensions, while specific forms of guidance pertaining to each dimension are described below in Section 3.2.1, Section 3.2.2, Section 3.2.3, Section 3.2.4, Section 3.2.5, Section 3.2.6, Section 3.2.7, Section 3.2.8 and Section 3.2.9. Each rubric also included an overarching question that captured essential elements of the CRMT dimensions (Table 2).
In these ways, we defined evidence for how a curriculum can provide guidance, support, or opportunities for teachers to implement culturally responsive strategies and pedagogies. We recognize that such evidence does not guarantee enactment practices aligned with the CRMT2 dimensions in the classroom, and address this in our discussion. However, this tool does offer opportunities to analyze mathematics curriculum materials in a novel way, which is a contribution of this work. As such, we describe the dimensions of this instrument in detail below, include examples for how these dimensions are represented in curricula, and provide examples for ways a lesson might include explicit evidence.
3.2.1. Build on Students’ Cultural and Community Funds of Knowledge
Cultural and community funds of knowledge are the everyday knowledge and activities in students’ homes and communities that they understand and relate to (González et al., 2006; Moll et al., 1992). Culturally responsive teaching sees these as resources students bring to the classroom. Culturally responsive teachers understand that students bring ways of thinking about, reasoning with, and understanding math based on their backgrounds and the extent to which they engage in different mathematical activities (Zavala & Aguirre, 2024). For example, students may know how to calculate fares when riding the bus or have experience measuring ingredients when cooking. Math curricula can tap into students’ cultural and community funds of knowledge by encouraging teachers to practice the following: Inquire about students’ backgrounds and experiences and draw on those during math lessons. Ask students to reflect on instances where they might have seen a math concept at work in their own life and adapt it into a problem for the class. Reference students’ community and home knowledge, culture, or experiences to make math instruction more relatable and meaningful to them.
For a lesson to include explicit guidance relating to students’ cultural and community funds of knowledge, the lesson could encourage teachers to adapt one of the main math activities in the lesson to better connect with their students’ community and home knowledge or culture. If the curricula included such guidance for every activity in a lesson, then it would include strong, centered guidance on cultural and community funds of knowledge.
3.2.2. Promote Rehumanization
Rehumanizing mathematics involves broadening conceptions of what counts as mathematical knowledge (Zavala & Aguirre, 2024). Gutiérrez (2018) emphasized the verbiage of rehumanizing in recognition of the humane ways that diverse cultures have traditionally engaged with mathematics over time, stating that “we do not need to invent something new; we simply need to return to full presence that which tends to get erased through the process of schooling” (p. 3). Rehumanizing thus acknowledges that mathematics is a human activity that involves both thinking and feeling: math is not just an abstract set of rules and procedures. Rehumanizing makes clear that all students can succeed in mathematics by showing them that mathematics and strong mathematicians are found in cultures around the world (Battey & Leyva, 2016). This literature suggests that curricula can rehumanize math by prompting teachers within the curriculum materials to implement the following practices: Affirm positive math identities for all races, genders, and ethnicities by using math problems that honor students’ cultures and identity markers. Expand students’ views of mathematics by highlighting that math is more than abstract memorization. Math involves problem solving and reasoning that draw upon students’ empathy, senses, and feelings. Represent the diversity of mathematicians by introducing Black, Indigenous, Latinx, and other mathematicians to students by referencing their literature as examples in textbooks and by referencing websites such as
For a lesson to include explicit guidance relating to promoting rehumanization, the lesson could introduce how a main math activity connects to Black, Indigenous, Latinx, and other mathematicians or situate these cultures within the activity.
3.2.3. Promote and Value Diverse Student Thinking and Ideas
Research suggests that students attain deeper levels of conceptual understanding in math when they discuss their reasoning and compare different approaches to solving problems (Bennett, 2014; Curtis et al., 2021). In CRMT, attending to student thinking is even more important, given their diverse backgrounds and variety of ways they might approach problems (Zavala & Aguirre, 2024). This literature suggests that curricula can promote student thinking by directing teachers to do the following: Prompt students to share their reasoning, ask questions of one another, discuss each other’s ideas, and build shared understanding. Explicitly encourage students to use multiple forms of communication, including hand gestures, pictures or drawings, and diverse verbal responses.
For a lesson to include explicit guidance relating to student thinking and ideas, one of the main math activities would ask teachers to elicit student thinking in an effort to make student thinking public that develops shared understanding about mathematical ideas.
3.2.4. Include Math Tasks That Require High Levels of Cognitive Demand
Cognitive demand refers to the type of thinking a lesson requires of students to complete mathematical tasks (Stein et al., 1996). Engaging in challenging content is important for every student—and particularly for historically marginalized students who have not had equal access to demanding content in the past (Zavala & Aguirre, 2024). Research shows that some teachers have lower expectations for historically marginalized students and that these lower expectations may lead to worse student outcomes (Jussim & Harber, 2005). This literature suggests that curricula can support teachers to engage all students in cognitively demanding problems: Include tasks designed to allow all students to use complex, non-algorithmic thinking. Provide tips for teachers to give all students opportunities to engage in intellectually and conceptually challenging math tasks that emphasize underlying concepts, patterns, and properties.
For a lesson to include explicit guidance relating to math tasks that require high levels of cognitive demand, half of the activities within the lesson would involve complex, non-algorithmic thinking or engage students in procedures that are connected back to conceptual understanding.
3.2.5. Scaffolding Up to Maintain Rigor and High Standards for All Students
Scaffolding is a common instructional practice to support students’ access to the content when they may be struggling to understand it (Zavala & Aguirre, 2024). Although scaffolding is a valuable instructional practice, it can risk lowering the rigor of mathematical tasks for some students (Athanases & de Oliveira, 2014). This literature suggests that curricula can help all students access rigorous content through scaffolding with the following: Include a variety of scaffolding techniques designed to help students achieve success with the math tasks in each lesson that have higher levels of cognitive demand. Provide suggestions for teachers to scaffold students into formal mathematics by accessing their everyday knowledge and personal experiences. For example, children’s understanding of how to share snacks with friends can be a scaffold for solving equal sharing problems.
For a lesson to include explicit guidance relating to maintaining rigor, the lesson would include at least two pieces of guidance for how teachers could consider the diverse learning needs of their students. Should the guidance include differentiation strategies, it should reconnect students who are assigned less cognitively demanding initial content to make connections to more rigorous content.
3.2.6. Affirm Multilingualism
Classroom discourse provides students with opportunities to develop problem solving abilities and develop mathematical competence (White, 2003). Multilingual learners across the English-learning spectrum in particular need meaningful opportunities to engage in mathematical reasoning such as describing patterns, using representations, and making generalizations (Zavala & Aguirre, 2024; Moschkovich, 2013). This literature suggests that curricula can address the needs of multilingual learners by prompting teachers to do the following: Support students to develop their mathematics skills while working in their home language. Immerse multilingual children in language-rich mathematics while using strategies to develop academic language, such as reframing everyday language explanations with math terms. Encourage students to use multiple forms of communication to show their thinking, including graphic organizers, manipulatives, equations, drawings, labels, and other writing.
For a lesson to include explicit guidance relating to affirming multilingualism, the lesson would include at least two pieces of guidance for how teachers could address varying multilingual learners’ needs with at least one suggestion relying on students’ home languages.
3.2.7. Distribute Intellectual Authority
Teaching approaches that center on students pave the way for them to actively engage in meaningful mathematics conversations and deeper mathematical understanding (Michael, 2006). Students can draw on their own experiences and knowledge to make sense of and connect with the math concepts they are learning. Using student-centered approaches helps students see that teachers are not the only source of knowledge and honors the various forms of knowledge students bring to the classroom (Zavala & Aguirre, 2024; Wachira & Mburu, 2019). This literature suggests that curricula can support distributing authority in several ways, which include the following: Provide teachers with suggestions to promote students as mathematical authorities and use students’ ideas to drive mathematical conversations. For example, when students ask questions to confirm their thinking, prompt teachers to direct the question to the rest of the class to consider. Provide frequent opportunities for students to engage in group or paired activities that support them discussing and building on each other’s ideas.
For a lesson to include explicit guidance relating to distributing intellectual authority, the lesson would be designed for a teacher to facilitate the lesson, but share authority of math knowledge with students at least once.
3.2.8. Disrupt Status and Power
Curricula can help overcome typical power imbalances in the classroom to ensure all students are empowered participants, regardless of their backgrounds. This is particularly important when creating opportunities for students to work together and share intellectual authority (see Horn, 2012). Popular or outgoing students may speak most often, or the top performers in class may get more attention from the teacher (Cohen & Lotan, 1995). Therefore, curricula should support teachers to intentionally attend to students’ unique mathematical, cultural, and linguistic strengths (Zavala & Aguirre, 2024). This literature suggests that curricula can ensure all students participate in meaningful ways: Include strategies teachers can use to address status imbalances, such as confronting stereotypes or using inclusive talk that builds up students and encourages multiple approaches to math. Remind teachers to build up students as mathematical authorities to each other and encourage teachers to lift up important mathematical thinking from students whose peers do not yet see them as math resources.
For a lesson to include explicit guidance relating to disrupting status and power, the lesson would include at least one strategy to minimize status differences among students.
3.2.9. Analyze and Act
Students learn mathematics in the context of meaningful problems from their lives and communities (Boaler, 1993; Zavala & Aguirre, 2024). As such, curricula can support students’ understanding by including math tasks that are related to an issue with which students will strongly connect (e.g., Gutstein, 2003, 2016). This literature suggests that curricula can provide opportunities for students to address and act on a problem: Include current or historical issues of injustice or social justice that may resonate within students’ communities. Prompt teachers to tailor problems around issues in the local community. For example, a textbook problem could ask students to discuss different ways to distribute donations among families at a local food bank.
For a lesson to include explicit guidance relating to analyzing and acting, the lesson would contain one activity that uses mathematics to analyze a socio-political context or economic, social, legal issues.
3.3. Analysis
Within each curriculum’s grade 6 teacher materials, we selected four units that covered the following topics: number sense, operations, measurement, and data displays. We chose these topics because each focus curriculum included comparable units of instruction that covered each of these topics. Within each unit, we coded nine 50-min lessons—three from the first third of each unit, three from the second third, and the last three lessons of the unit (excluding lessons that encompassed strictly review or summative assessments). The exception to this was the KEMS curriculum: because these materials were designed for 80- to 90-min lessons, we coded six lessons to code an amount of content equivalent to that of the other curricula, two from the beginning, middle, and end. This resulted in a total of 203 lessons, for which two to three coders independently reviewed the teacher’s guide and noted evidence or opportunities to enact CRM in line with the CRM-MET tool.
Prior to engaging in analysis, each coder participated in professional development focused on the theoretical background of the CRM-MET tool, in particular the CRMT2 dimensions described by Zavala and Aguirre (2024). The team then engaged in training with the CRM-MET tool itself, analyzing a set of pilot materials drawn from different units of the focus curricula and meeting to discuss and resolve differences. Every member of the coding team had experience in K-12 education (e.g., mathematics teaching experience) or education policy (e.g., experience with curriculum analysis).
Each coder would independently annotate the teacher’s guide materials for the selected lessons, taking note of the extent of evidence in line with each of the nine dimensions of CRM within the CRM-MET tool. As shown in Table 3, these annotations attended to both the extent of evidence within particular resources and instructions within the materials, as well as indications of repeated evidence of particular dimensions (e.g., multiple scaffolds provided throughout the teacher’s guide).
The pairs or triads of coders then met to discuss and resolve any disagreements and synthesized the ratings and rationale for each CRMT2 dimension, with initial ratings showing approximately 80% agreement across all rubrics and lessons. For example, in the Illustrative Mathematics (2019b) example shown in Table 3, with the full lesson coding annotations shown in the Appendix A, coders resolved the extent of evidence scores and provided rationale for each CRMT dimension as follows: For Student Ideas and Thinking, the lesson scored 5 because it included opportunities to make student thinking public and develop shared understanding throughout each part of the lesson. For Cognitive Demand, the lesson scored 5 because the entire task involved doing mathematics; that is, it required complex, non-algorithmic thinking to explore the concept of volume, fractions, and how they relate to cost. For Scaffolding Up, the lesson scored 5 because it included more than four instructions to the teacher to plan activities or supports in ways that maintain the rigor of the task for all students. For Affirming Multilingualism, the lesson scored 3 because it included at least one instruction in how to address varying multilanguage learners’ needs but did not encourage teachers to value students’ home languages. For Distributing Intellectual Authority, the lesson scored 5 because students were generating mathematical knowledge, reasoning, and solution strategies on their own while the teacher served as a facilitator for the class. For each of the remaining domains (that is, Community and Cultural Funds of Knowledge, (Re)Humanizing, Disrupting Power, and Taking Action), the tool scored 1 because the lesson included no instructions or evidence to support the domains.
After coding of the 203 selected lessons was completed, the extent of CRM evidence scores were aggregated at the unit and curriculum level to allow for descriptive analysis and reporting of the findings. This allowed for comparative analysis of each CRMT2 dimension across each of the sets of curriculum materials, as well as an overall “score” of the observed CRM evidence within each curriculum calculated by averaging across all nine dimensions. These quantitative data, along with the qualitative coding annotations and rationales, form the basis of our results.
4. Results
We designed and used the CRM-MET to understand the ways and extent to which mathematics curriculum materials provided written guidance aligned with dimensions of the CRMT2 tool (Zavala & Aguirre, 2024). We found that there were meaningful differences in how different curriculum materials provided such guidance, but overall limited evidence that such materials consistently provide support aligned with dimensions of CRMT. We did find specific dimensions of CRMT at which particular curricula included more consistent written guidance, but also some dimensions, in particular aligned with the strand of Power and Participation, with limited or no guidance within these materials. We discuss our findings in line with our two research questions below.
4.1. To What Extent Are Cultural and Contextual Considerations Included in Mathematics Curriculum?
CRM-MET ratings reflected the prevalence of guidance within the teacher-facing curriculum materials that aligned with particular dimensions of CRMT. All six curricula offered fragile or marginal explicit guidance regarding CRMT (see Figure 1). On average, the curricula provide at least one brief instruction (for example, to a subset of students or during a short task such as a warm-up) to address CRM practices in each lesson. Illustrative Mathematics (IM) held the highest average score across CRMT2 dimensions, at 2.69, suggesting that the CRM guidance in IM lessons usually included all students in the class and took place during the main activities in a lesson. IM lessons were more narrative than other curriculum materials that were more transactional, which may have provided more opportunities to include guidance that addressed the CRMT2 dimensions. No curriculum achieved an average rating of 3 or higher, meaning that the analyzed materials did not tend to provide explicit guidance that addressed CRM across their lessons.
When looking across the nine dimensions of CRMT, we found that the curricula provided more instances of explicit guidance to teachers in more traditional areas of instructional reform, such as Cognitive Demand, Student Ideas and Thinking, and Distributing Intellectual Authority (Figure 2). These CRMT dimensions emphasize student understanding of underlying concepts, patterns, and properties, communication, and ownership. In CRMT dimensions related to students’ identities, power, and participation, the curricula provided little or no guidance. For example, all six curricula scored at or near 1 (no evidence), on average, for Community and Cultural Funds of Knowledge, (Re)Humanizing, Disrupting Power, and Taking Action. This meant that the curricula typically provided no guidance for how teachers could enact or adapt the materials to recognize and affirm students’ identities, broaden students’ conceptions of themselves as doers of mathematics, or use mathematics to address community or social change.
When focusing on the three dimensions embedded within the Knowledges & Identities strand, these materials mostly attended to Honoring Student Thinking and Ideas (Figure 3). IM included the most guidance to elicit students’ ideas and thinking (an average rating of 4.25) while CA Math included the least (an average of 2.47). All curricula demonstrated only marginal evidence in connecting the mathematics concepts with student’s cultural and community funds of knowledge. None of the materials were found to help rehumanize mathematics by highlighting that mathematics is more than abstract memorization and should draw upon students’ empathy, senses, and feelings.
Within the Rigor & Support strand, on average, curricula included the most guidance to sustain a higher level of cognitive demand on the math tasks included in the curricula (Figure 4). Most curricula also included, on average, at least one instance of explicit guidance within each analyzed lesson to scaffold mathematical tasks for all students and, in particular, to affirm multilingualism. However, the analyzed materials within the KEMs curricula often did not include guidance for these two dimensions.
On average, curricula included at least one instance of explicit guidance for teachers to encourage students to take ownership over their learning by having them connect their initial thinking to mathematical concepts before teaching procedures (Figure 5). However, most curricula did not include any guidance to address status imbalances nor issues of injustice or social justice. In fact, only one curriculum (CA Math) included an instruction to address power imbalances in one of the lessons reviewed, and only one other curriculum (Into Math) included a mathematical task that addressed social justice in one of the lessons reviewed. These specific examples are described further in the results to our second research question below.
Across these results, we found that the analyzed curriculum materials were attending to dimensions of CRMT, albeit not always consistently across the analyzed materials. On average, most curricula were found to have included only fragile or marginal evidence of attention to the CRMT2 dimensions. There are also notable differences in which dimensions particular curricula addressed, and notable absences of attention to particular dimensions, namely CFoK, Taking Action, Disrupting Power, and (Re)Humanizing Mathematics.
4.2. In What Ways Do Mathematics Curricula That Do Consider Cultural and Contextual Considerations Address Such Issues?
For our second research question, we examined how curriculum materials did address different dimensions of CRMT. These results consider not only the presence of guidance around the dimensions, but also the extent of evidence when guidance was observed. We describe trends in such guidance for each of the nine dimensions of CRMT and note trends in limitations of instructional guidance that may have held curricula back from attaining higher ratings for particular dimensions.
Of the 203 lessons reviewed, at most only marginal guidance to reference students’ cultural and community funds of knowledge was observed (19 lessons; nine in Into Math, three in CA Math, two in Big Ideas, one in KEMs, two in Eureka, and two in IM). For example, in the opener of a lesson from one of the target curricula, there was guidance to have student pairs discuss and share ideas of real-life situations where they may need to determine the area, allowing for students to share examples of when they had considered area in their own life. However, the remainder of the lesson drew upon traditional area examples that provided rectangles and squares and asked students to find their area without grounding these shapes in the student’s lives. To include guidance that permeates the lesson, the curricula could have, for instance, included guidance that prompted the teacher to customize the remaining math tasks in the lesson by including shapes inspired by the examples students shared for calculating area in their lives.
There were ten lessons where eliciting student ideas and thinking permeated the entire lesson (one in Big Ideas and nine in IM). These lessons encouraged students to share their reasoning, ask questions of one another, or discuss each other’s ideas during each task. For example, one lesson from IM included three explicit tasks about representing ratios with tables. During the first task, designed to represent growth in a tile pattern, the curriculum instructed the teacher to do the following: “Invite students to share their responses and reasoning. Record and display the different ways of thinking for all to see. If possible, record the relevant reasoning on or near the images themselves. After each explanation, ask the class if they agree or disagree and to explain alternative ways of thinking, referring back to what is happening in the images each time.” (Illustrative Mathematics, 2019a). The second and third task included similar instructions, emphasizing that the teacher should have students who solved the problem in specific different ways share and to have the class discuss advantages and challenges of using those methods.
There were two lessons that included tasks that predominantly involved doing mathematics, a high level of cognitive demand (Stein et al., 1996), one in CA Math and one from IM. Doing mathematics requires complex, non-algorithmic thinking, such as exploring the nature of mathematical concepts, processes, or relationships. It often requires students to access relevant knowledge and experiences and make appropriate uses of them in working through the task. For example, one curriculum encouraged students to research physical fitness by surveying students about the sports or physical activities they do in a week; researching physical activities and the calories burned per hour; creating a jogging schedule; looking up calories in fast food items; and planning for one day’s meals. Within all of these activities students would have explored means and various data displays (e.g., box plots, line graph, etc.). To share with the class, students were also then encouraged to get creative by writing an article for a food or health section of an online website or to act as a doctor and create a presentation prompting physical fitness.
There were 37 lessons that included more than three instances of explicit guidance to differentiate instruction in ways that maintain rigor for all students (eight in Into Math, two in CA Math, one in Big Ideas, one in Eureka, and 25 in IM). These instructions address supporting access to rigorous content for all students and encourage teachers to design scaffolds that do not lower the level of rigor or ensure ways to reconnect student to rigorous content. For example, one lesson began with a problem of the day and the curriculum included instructions, based on students’ responses, to jump into an interactive reteach or to complete the prerequisite skills activity. The lesson also included small-group options and math center options for students on track, almost there, and ready for more. Moreover, the lesson described a specific differentiation activity for English language learners that also could benefit all students, included various depth of knowledge questions, and brought students back together for a cumulative activity and practice problems at the conclusion of the lesson.
There was only one lesson that included explicit guidance for positioning multilingual learners as competent learners in mathematics activities. The lesson encouraged teachers to use word walls and sentence stems for vocabulary as well as modeling how to underline key words, write down equivalent words, and to draw lines between elements to make connections. The lesson encouraged teachers to have students write down equivalent words in both English and their native language to ensure connections between the two. In order to achieve a rating of strong, centered evidence for the affirming multilingualism dimension, a lesson would have had to include at least two instructions on how to attend to multilingual learners’ needs and at least two encouragements to the teacher to value multilingual learners’ home language.
There were 18 lessons where the entire lesson distributed intellectual authority between the teacher and the students (one in CA Math, one in Big Ideas, one in Eureka, and 15 in IM). In these lessons, the teacher acts as a facilitator such that the authority of math knowledge primarily resides with students. For example, one Eureka Math lesson included instructions such as, “Students should be leading the discussion in order for them to be prepared to complete the exercises”, “Students complete the volume and surface area problems in small groups”, and having students lead the closing discussion.
There was only one lesson that included marginal guidance to disrupt power and status by minimizing status differences among students. The lesson included guidance for the teacher to provide each student three counters. After each student contributed to the discussion, they would place one counter in the center of the table so that all students have an opportunity to contribute three times each.
There was only one lesson that included one activity or problem that uses mathematics to analyze a socio-political context or economic, social, legal issues that may concern students from non-dominant subgroups. This Eureka lesson had an activity to analyze data regarding the Supreme Court and its chief justices’ year appointed and length of term. The activity included an instruction to “…make connections to social studies. Ask students if they know what cases are before the current Supreme Court, whether they think any data would be involved in those cases, and whether any of the analysis techniques might involve what they have been learning about statistics.”
5. Discussion
Culturally responsive teaching necessitates being responsive to the students in the classroom. Curricula is often written with the intention that it can be used across classrooms, districts, counties, and states. This creates a tension where the materials cannot anticipate the culture or community of the classroom in which the lesson will be delivered, and where it is difficult know how the teacher will blend the instruction on the page with the culture of the students in the classroom. However, curriculum materials can provide teachers with guidance and structure to support and encourage the use of culturally responsive pedagogies in any context. The absence of explicit guidance on culturally responsive pedagogies in a textbook does not mean teachers are unable or do not layer on culturally responsive teaching; it simply means the textbook is not providing explicit guidance or support on how or when to be culturally responsive during the math lesson.
Our findings shed light on the extent to which and the ways in which middle school mathematics curriculum materials address dimensions of CRMT. These results demonstrate that standards-based mathematics curriculum materials do offer some guidance to support teacher dispositions and practices in line with certain aspects of CRMT, but that such guidance is largely sporadic and not consistent across different curricula. This suggests that curriculum materials can serve as an important part of a constellation of support for teachers but certainly not as the only means of fostering knowledges, dispositions, and practices at the heart of CRMT. Such findings have implications for educational leaders and curriculum designers in considering the affordances and limitations of curriculum materials in supporting dimensions of CRMT, but also suggest pathways for school leaders, educators, and advocates in considering which aspects of CRMT might require additional support beyond the written curriculum.
5.1. Limitations
The CRM-MET rubrics help in describing the extent to which current curriculum materials provide guidance around different dimensions of CRMT. However, there are inherently issues of power in who is represented in curriculum materials, and it is critical for students to have the opportunity “to see themselves in the curriculum or analyze the world around them” (Gutiérrez, 2012, p. 30). Therefore, this rubric alone is not intended to foster CRM in the classroom. Rather, pairing the CRM-MET with other resources such as Zavala and Aguirre’s (2024) CRMT2 rubric (from which it was adapted) can help add nuance and depth to CRM-focused work.
Additionally, our analyses solely focused on selecting lessons from select units across each curriculum’s grade 6 teacher materials. We did not review other supplementary material (such as a guide for students with disabilities or English language learners). While we assumed these trends may be similar across units and grade-levels, we did not test that hypothesis, limiting the generalizability of these findings. Future research may investigate how other grade-levels or units attend to culturally responsive math teaching.
Moreover, access to certain curriculum materials is not uniform across the nation. For example, materials developed by private developers may not be accessible to under-resourced districts. This also limits the generalizability of these findings.
5.2. Implications for Research and Practice
It is important to note that we not only included analyses that averaged guidance across dimensions, but also provided guidance on when and how these different curricula attended to each dimension of CRMT. We recognize that it is unlikely and unrealistic to expect a single lesson to score high across all dimensions. It may be more realistic to expect a range of scores across an entire unit, perhaps encouraging publishers and developers to include guidance that emphasizes different dimensions, and that ultimately attends to all CRMT dimensions across a single unit. Moreover, there isn’t going to be a single curriculum that includes strong, centered guidance across the board, at least not based on our findings. While IM included the most guidance, on average, to distribute intellectual authority, attend to multilingual learners needs, differentiate instruction, illicit students’ ideas and thinking, and included tasks that required more complex thinking, Into Math and CA Math included more guidance to attend to students’ cultural and community funds of knowledge. The implication is that no single curriculum is likely to meet all of a district’s needs, and the best curriculum for each district will be a function of district priorities.
Districts planning or considering adopting new curricula do, however, need information to understand how each set of curriculum materials aligns with district priorities. Ideally, districts would be easily able to use a single comprehensive information source to make curriculum decisions. However, there isn’t a source for this information yet, so there is no way of knowing about the quality of curricula beyond broader analyses such as EdReports. Understanding the extent to which various curricula attend to dominant and critical dimensions of CRMT could be instrumental for administrators in selecting and implementing professional learning opportunities or providing teachers with context for how they might adapt their lessons. The CRM-MET in this way can provide valuable insight to school leaders in the adoption of new curricula, or how they might best target teacher support around CRMT given the affordances and limitations of their current curriculum.
5.3. Future Directions for Curriculum Design and Adaptation
It is important to consider culturally responsive pedagogies because the content covered and pedagogical approach that mathematics teachers use is heavily influenced by the curriculum (Stein et al., 2007). Curriculum developers ultimately hold great power in guiding the narratives about what does and does not count as mathematics in our educational systems (Gutiérrez et al., 2023). As such, the decisions that curriculum developers make regarding the inclusion or avoidance of guidance aligned with CRM can have a meaningful impact on the constellation of support that teachers have in fostering and sustaining CRMT. In our review, it is clear that while curricula often do provide guidance on more traditionally dominant aspects of instruction (e.g., maintaining rigor, scaffolding up), guidance on the critical elements is limited.
In first addressing more dominant aspects of instruction, several considerations do still stand out regarding curriculum design. First, almost twenty percent of all analyzed lessons in our focus curricula included more than three instructions for differentiation. While this dimension had the most lessons that scored the highest category on the rubric, it is important to note that even more lessons could have scored higher in this category. Many such lessons did not also include guidance on how to help students reconnect with rigorous content, a requirement for higher ratings of evidence for this dimension. By adjusting the content of a lesson to support students below grade-level, teachers may meet students where they are at, but without reconnecting students with the rigorous content a teacher is essentially creating a microcosm of a tracked environment.
Second, 96 lessons (out of 203) did include at least two instructions to attend to multilingual learners’ needs (a rating of three—explicit evidence—on our rubric). However, none of these lessons encouraged the use of students’ native language, a prerequisite for attaining a sustained (4) or strong (5) rating. Other than using vocabulary in English and students’ native language to make connections, curricula could provide additional suggestions or could use digital technologies that connect mathematical concepts in students’ native language. In the meantime, teachers could consider instructional resources and strategies (e.g., Chval et al., 2021) that not only describe how to adapt materials to engage multilingual learners through reading, writing, discourse, and gesture, but also on how to position multilingual learners as capable mathematical thinkers and doers in the classroom. As noted by Zavala and Aguirre (2024), supporting multilingual learners ultimately “is about using all the resources, even if you as a teacher don’t have every resource, to reach out to families and communities” (p. 85). This dimension is rooted in asset-orientation and relationship-building, and thus beginning from a place of affirmation–regardless of support built into curriculum materials–is essential.
Curricula also only provided brief instructions to attend to students’ cultural and community funds of knowledge, most likely because the students in classrooms across a range of geographical, cultural, and political settings vary. The curricula appeared to usually attend to these funds of knowledge in introductory questions framing a process in the real-world, such as asking students to consider how the topic at hand has related to their own personal experiences. However, curricula could do more by including guidance for how teachers can adapt problems, based on their students’ interests and aspirations, and perhaps share examples of such adaptations. This would frame the curriculum as more pliable, underscoring the importance of critical examination and responsiveness necessary for teachers to more equitably use such standardized materials (e.g., Gutiérrez, 2012). Regardless of curriculum guidance, teachers should also be critical observers, considering how they might adapt task contexts to their particular students. Neihaus et al. (2023), for example, describe a cycle through which teachers can identify and revise “problematic faves,” or tasks that have valuable mathematical ideas but for which the contexts–sans revision–might be inauthentic or damaging to students’ identities and experiences. Consistently building in such critical review practices could help teachers address these observed limitations in curriculum materials.
Considering more critical elements of CRM, there were no observed lessons that included any guidance for rehumanizing mathematics. Given the relatively stronger findings concerning the strand of Rigor & Support, lessons that attended to this strand—such as by providing higher cognitive demand tasks or scaffolds for students—could serve as an entryway toward seeing such rigorous mathematics in new, broader, and more diverse terms (i.e., rehumanizing). Gutiérrez (2018) describes eight specific concepts that can contribute to rehumanizing mathematics: “(1) participation/positioning, (2) cultures/histories, (3) windows/mirrors, (4) living practice, (5) creation, (6) broadening mathematics, (7) body/emotions, and (8) ownership” (p. 4). Curriculum designers and teachers alike could consider how such concepts could strengthen the emphasis on more academically rigorous mathematics by providing students with opportunities to see their full selves as capable mathematical thinkers within the context of such content.
Curriculum materials offering windows and mirrors (Style, 1996) through which students can broaden their conception of what mathematics is and who can be a mathematician is especially a means by which developers and teachers alike could support rehumanizing mathematics. Numerous resources exist that demonstrate that mathematical contributions are confined to no particular culture, race, or gender [e.g.,
Such approaches could also serve to disrupt issues of status and power, another dimension of CRMT that was only observed as brief guidance in one lesson from the focus curricula. Because status ultimately reflects students’ perception of their own academic capability and social desirability (Horn, 2012), teachers could address this dimension by considering how students collaborate and demonstrate their understanding around the lessons that compose these curriculum materials. For instance, Zavala and Aguirre (2024) describe three strategies—humanizing assessment (focusing on asset or strength based formative assessments), assigning competence (publicly stating students’ mathematical contributions), and co-constructing group norms (establishing a groupwork focus on collaboration and respect)—that can support this dimension. In short, the absence of guidance within curriculum materials need not preclude teachers from taking charge in disrupting status and power in their classrooms by supplementing their instruction with such strategies.
There was also only one lesson that included a brief, optional instruction to explore a socio-political context, the supreme court. While there may not always be an opportunity in a lesson to analyze socio-political contexts or economic, social, legal issues that may concern students from non-dominant subgroups, when there is, these activities may permeate an entire lesson. Curricula could build on existing resources that address how to explore, understand, and respond to issues of social injustice with mathematics (e.g., Berry et al., 2020) to better attend to issues of power relevant to students. For example, students in Michigan–or in other locales impacted by failing public water systems–could engage with the context of the Flint water crisis as an avenue for understanding the role of mathematics in issues of justice (e.g., modeling the water needs of citizens during such crises). Indeed, encouraging teachers to first engage in the exploration of such topics could help in fostering educators committed to mathematics for social justice (Aguirre et al., 2019). Another example would be to explore functions in tables and arrays using electoral votes and popular votes to understand if one is a function of the other (see
5.4. Navigating Culturally Responsive Mathematics Teaching in the Present Climate
It is ultimately impossible to consider issues of CRM and curriculum without considering the broader policy and political climate around education, particularly in the context of the United States where many of these curricula have been adopted (Center for Education Market Dynamics, 2023). Curriculum developers hold significant power in shaping dominant narratives about what counts as mathematics (Gutiérrez et al., 2023), and visions of mathematics instruction heralded by district leaders often emphasize dominant aspects of equitable mathematics while downplaying critical dimensions of equity (Comstock et al., 2024). Additionally, the design of a standards-based curriculum could never alone foster the individualized knowledges, dispositions, and practices necessary for CRMT (Zavala & Aguirre, 2024). As we have laid out in this investigation, curriculum can offer opportunities and guidance around CRM, but we recognize that it is ultimately through the alignment of curriculum with other educational resources, along with teacher and school leader desire and ability to foster culturally responsive practices, that CRMT can be achieved. For such reasons, it is necessary to contextualize the role of curriculum materials in light of the broader climate of educational policy.
Of particular concern are recent legislative threats and federal executive orders that seek to dismantle diversity, equity, and inclusion policies and programs (see Ostrager et al., 2025). Given CRM’s emphasis on valuing (1) a diversity of student backgrounds and mathematical perspectives, (2) equitable practices that promote success for traditionally marginalized student populations, and (3) an inclusive classroom environment for all learners, it must be assumed that efforts to promote CRM will be impacted by such actions. Indeed, this political environment is understood as not only shuttering public policies and programs that might support diversity, equity, and inclusion, but also creating a chilling effect on the private sector as well (Ng et al., 2025). We therefore recognize that the challenges in calling for greater inclusion of guidance aligned with CRM from private curriculum developers will be further exacerbated in the present climate.
As such, we see investigations such as this, which take a critical look at curriculum design, as necessary in illuminating the affordances and limitations of standards-based curriculum materials. To engage in critical conversations that both foster greater attention toward CRMT in classrooms and counter potential rollbacks of the limited progress made within the domain of curriculum design, it is vital for education stakeholders and advocates to have tangible tools to address such issues. In this way, tools like the CRM-MET, in coordination with other analytical tools and frameworks, can help provide measurement and language to advocate for policies and programs that support CRMT, and hold to account actors who might attempt to counter such progress.
6. Conclusions
The CRM-MET provides not only guidance to teachers and school leaders regarding curricular decisions, but also is a charge to curriculum developers to consider ways in which their products might foster (or hinder) culturally responsive instruction. This extends considerations of curricular quality beyond a focus on alignment to standards to also address the ways in which these materials might better encourage opportunities for CRM. Including support structures aligned with different dimensions of culturally responsive teaching does not guarantee enactment of such structures in the classroom but may, over time, afford teachers opportunities to focus and strengthen their own culturally responsive practices, in line with CRM instructional tools (e.g., Zavala & Aguirre, 2024).
Conceptualization, R.S., E.P.S. and R.J.E.; methodology, R.S.; validation, R.S.; formal analysis, R.S.; investigation, R.S.; resources, R.S.; data curation, R.S.; writing—original draft preparation, R.S., E.P.S. and R.J.E.; writing—review and editing, E.P.S. and R.J.E.; visualization, R.S. and E.P.S.; supervision, E.P.S.; project administration, E.P.S.; funding acquisition, R.S. and E.P.S. All authors have read and agreed to the published version of the manuscript.
The study was conducted in accordance with the Declaration of Helsinki, and approved by the Institutional Review Board of HML IRB (protocol code 939MATH21 and 19 July 2021).
Informed consent was obtained from all subjects involved in the study.
Data can be made available upon request.
The authors declare no conflicts of interest.
The following abbreviations are used in this manuscript:
| CRM | Culturally Responsive Mathematics |
| CRMT | Culturally Responsive Mathematics Instruction |
| IM | Illustrative Mathematics |
| KEMS | Key Elements of Mathematics Success |
| CFoK | Community and Cultural Funds of Knowledge |
Footnotes
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.
Figure 1 Prevalence of CRMT guidance in curricula.
Figure 2 Average prevalence of CRM guidance in curricula by dimension.
Figure 3 Knowledges & Identities strand ratings, by curriculum.
Figure 4 Rigor & Support strand ratings, by curriculum.
Figure 5 Power & Participation strand ratings, by curriculum.
Coding Rubric for CRMT Evidence Across Dimensions.
| Rubric Score | Extent of Evidence |
|---|---|
| 1. No evidence | No guidance across lessons within a dimension. |
| 2. Fragile/Marginal evidence | Brief instance of guidance (e.g., during the warm-up or closing) that may not include all students. |
| 3. Explicit evidence | One instance of explicit guidance (e.g., during one of the lesson’s main math tasks) for all students. |
| 4. Sustained, explicit evidence | At least two instances of explicit guidance, with at least one including all students. |
| 5. Strong, centered evidence | The entire lesson includes guidance pertaining to the relevant dimension. |
Culturally Responsive Measurement Strands, Dimensions, and Essential Curricular Questions.
| Strands | Dimensions | Essential Question |
|---|---|---|
| Knowledges and Identities | Community and Cultural Funds of Knowledge (CFoK) | How does the lesson as written help students connect mathematics with meaningful issues or situations in their lives? |
| (Re) Humanizing | How does the lesson as written support creativity, broaden what counts as mathematical knowledge, and affirm positive mathematics identities for all students? | |
| Student Ideas and Thinking | How does the lesson as written create opportunities to elicit, express, and build on student mathematical thinking in a variety of ways? | |
| Rigor and Support | Cognitive Demand | How does the lesson as written enable all students to closely explore and analyze mathematics concept(s), procedure(s), and problem-solving or reasoning strategies? |
| Scaffolding Up | How does the lesson as written maintain high rigor with strong support for all students? | |
| Affirming Multilingualism | How does the lesson as written position multilingual learners as competent learners in mathematics activities? | |
| Power and Participation | Distributing Intellectual Authority | How does the lesson as written distribute mathematics authority and make space for a variety of forms of knowledge and communication? |
| Disrupting Power | How does the lesson as written disrupt status differences, entrenched stereotypes, and inequitable power relationships present in all mathematics classrooms? | |
| Taking Action | How does the lesson as written support students’ use of mathematics to analyze, critique, and address power relationships and injustice in their lives (economic, social, environmental, legal, political, patriarchal)? |
Note. The strands and dimensions for this framework are adopted from
Excerpt of Coding Annotations for
| Lesson (Teacher’s Guide) | Coding Annotations |
|---|---|
| … | |
| |
Note. See
Appendix A
The following coding annotations are drawn from IM Grade 6, Unit 4, Lesson 17. The latest version of this lesson (updated after the time of coding) can be found on the IM website (
| Lesson (Teacher’s Guide) | Coding Annotations |
| This lesson is broken up into three main parts. The objective of the lesson is for students to use volume and fractions to calculate shipping costs for a variety of boxes to determine which is the most economical option for delivering 270 jewelry boxes. | |
| In the first part of the lesson, students should make sense of the task and determine what they need to know and do to find the most economical shipping box combination. Encourage students to work together to systematically minimize omissions and errors and to create drawings or models. Reflective questions you can ask students include, “Which orientations are possible? How much empty space would result?” | |
| Give students 1–2 min to read the task individually and ask any clarifying questions. Model the task by putting a small box inside a larger box in different orientations. After individual review, place students in groups of 4 and give them 5 min to individually brainstorm what information is needed to solve the task. Then, give another 5 min to plan in groups, followed by time to measure boxes or research box options and dimensions for themselves. | |
| | |
| | |
| In part 2, students will now calculate the cost of shipping the boxes in each of the larger USPS boxes. Notice groups using different strategies for division with fractions, asking students to think about the different ways they have used fractions in calculations. If students are stuck, remind them that drawing the boxes or modeling them out of paper might help to visualize how to calculate a solution. | |
| Students will stay in their groups of four, selecting one of each of the different sized shipping boxes. Give students quiet time to work through a few box orientations and calculations. Two additional scaffolds ( | |
| | |
| In the last phase of the lesson, students will present, reflect on, and revise their work within their small group. They will discuss their decisions, accuracy, and revise any steps taken, if needed. The goal will be for the group to decide on the shipping box size or combination of sizes that will be most economical for shipping 270 boxes. | |
| Still working in the same group of 4, give students 10–12 min to discuss each group member’s work and make revisions as needed. Display the following questions and ask students to use them to guide their discussion: | |
| Once each group member has shared, give students 4–5 min to decide on the least expensive option to ship 270 boxes and to write down ideas explaining why they selected that option. | |
| | |
| | |
| Consider the following questions as | |
| | |
| | |
| Note. The quoted teacher’s guide materials are drawn from | |
Aguirre, J. M.; Anhalt, C. O.; Cortez, R.; Turner, E. E.; Simic-Muller, K. Engaging teachers in the powerful combination of mathematical modeling and social justice: The Flint water task. Mathematics Teacher Educator; 2019; 7,
Aguirre, J. M.; Zavala, M. D. R. Making culturally responsive mathematics teaching explicit: A lesson analysis tool. Pedagogies: An International Journal; 2013; 8,
American Educational Research AssociationAmerican Psychological AssociationNational Council on Measurement in Education. Standards for educational and psychological testing; American Educational Research Association: 2014.
Athanases, S. Z.; de Oliveira, L. C. Scaffolding versus routine support for Latina/o youth in an urban school: Tensions in building toward disciplinary literacy. Journal of Literacy Research; 2014; 46,
Battey, D.; Leyva, L. A. A framework for understanding whiteness in mathematics education. Journal of Urban Mathematics Education; 2016; 9,
Bennett, C. A. Creating cultures of participation to promote mathematical discourse. Middle School Journal; 2014; 46,
Ben-Peretz, M. The teacher-curriculum encounter: Freeing teachers from the tyranny of texts; SUNY Press: 1990.
Berry, R. Q., III; Conway, B. M., IV; Lawler, B. R.; Staley, J. W. High school mathematics lessons to explore, understand, and respond to social injustice; Corwin Press: 2020.
Boaler, J. The role of contexts in the mathematics classroom: Do they make mathematics more “real”?. For the Learning of Mathematics; 1993; 13,
Boaler, J. Learning from teaching: Exploring the relationship between reform curriculum and equity. Journal for Research in Mathematics Education; 2002; 33,
Brown, M. W. The teacher–tool relationship: Theorizing the design and use of curriculum materials. Mathematics Teachers at work; Routledge: 2011; pp. 37-56.
Buxton, C. A. Creating contextually authentic science in a “low-performing” urban elementary school. Journal of Research in Science Teaching; 2006; 43,
Center for Education Market Dynamics. K-8 math curriculum products and publishers: The state of district-led selection; 14 September 2023; Available online: https://www.cemd.org/k-8-math-curriculum-products-and-publishers-the-state-of-district-led-selection/ (accessed on 30 May 2025).
Chappell, M. Senk, S. L.; Thompson, D. R. Keeping mathematics front and center: Reaction to middle-grades curriculum projects research. Standards-based school mathematics curricula: What are they? What do students learn?; Lawrence Erlbaum Associates: 2003; pp. 285-296.
Choppin, J.; Roth McDuffie, A.; Drake, C.; Davis, J. The role of instructional materials in the relationship between the official curriculum and the enacted curriculum. Mathematical Thinking and Learning; 2022; 24,
Chval, K. B.; Smith, E.; Trigos-Carrillo, L.; Pinnow, R. J. Teaching math to multilingual students, grades K-8: Positioning English learners for success; Corwin: 2021.
Cohen, E. G.; Lotan, R. A. Producing equal-status interaction in the heterogeneous classroom. American Educational Research Journal; 1995; 32,
Cohen, E. G.; Lotan, R. A. Designing Groupwork: Strategies for the heterogeneous classroom third edition; Teachers College Press: 2014.
Comstock, M.; Backup, D.; Johnson, A.; Smith, E. P.; Desimone, L. M. Promise and pitfalls of crafting coherence around a district-wide vision for equity-centered mathematics instruction. National Council of Teacher of Mathematics Research Conference; Chicago, IL, USA, September 25–28; 2024.
Curtis, K.; Lindo, K.; Jansen, A. Discourse can create a learning culture. Mathematics teacher: Learning and teaching PK–12; 2021; 114,
Gay, G. Preparing for culturally responsive teaching. Journal of Teacher Education; 2002; 53,
Gehrke, N. J.; Knapp, M. S.; Sirotnik, K. A. In search of the school curriculum. Review of Research in Education; 1992; 18, pp. 51-110. [DOI: https://dx.doi.org/10.2307/1167297]
González, N.; Moll, L. C.; Amanti, C. Funds of knowledge: Theorizing practices in households, communities, and classrooms; Routledge: 2006.
Gutiérrez, R. Research commentary: A gap-gazing fetish in mathematics education? Problematizing research on the achievement gap. Journal for Research in Mathematics Education; 2008; 39,
Gutiérrez, R. Herbel-Eisenmann, B.; Choppin, J.; Wagner, D.; Pimm, D. Context matters: How should we conceptualize equity in mathematics education?. Equity in discourse for mathematics education: Theories, practices and policies; Springer: 2012; pp. 17-33. [DOI: https://dx.doi.org/10.1007/978-94-007-2813-4]
Gutiérrez, R. The sociopolitical turn in mathematics education. Journal for Research in Mathematics Education; 2013; 44,
Gutiérrez, R. Living Mathematx: Towards a Vision for the Future. Philosophy of Mathematics Education Journal; 2017a; 32,
Gutiérrez, R. Kastberg, S. E.; Tyminski, A. M.; Lischka, A. E.; Sánchez, W. B. Political conocimiento for teaching mathematics. Building support for scholarly practices in mathematics methods; Information Age Publishing: 2017b; pp. 11-37.
Gutiérrez, R. Goffney, I.; Gutiérrez, R.; Boston, M. Introduction: The need to rehumanize mathematics. Annual perspectives in mathematics education 2018: Rehumanizing mathematics for black, indigenous and latinx students; National Council of Teachers of Mathematics: 2018; pp. 1-12.
Gutiérrez, R.; Myers, M.; Kokka, K. The stories we tell: Why unpacking narratives of mathematics is important for teacher conocimiento. The Journal of Mathematical Behavior; 2023; 70, 101025. [DOI: https://dx.doi.org/10.1016/j.jmathb.2022.101025]
Gutstein, E. R. Teaching and learning mathematics for social justice in an urban, Latino school. Journal for Research in Mathematics Education; 2003; 34,
Gutstein, E. R. “Our issues, our people—Math as our weapon”: Critical mathematics in a Chicago neighborhood high school. Journal for Research in Mathematics Education; 2016; 47,
Horn, I. S. Strength in numbers: Collaborative learning in secondary mathematics; National Council of Teachers of Mathematics: 2012.
Illustrative Mathematics. Grade 6, unit 2.11: Representing ratios with tables; 2019a; Available online: https://curriculum.illustrativemathematics.org/MS/teachers/1/2/11/index.html (accessed on 30 May 2025).
Illustrative Mathematics. Grade 6, unit 4.17: Fitting boxes into boxes; 2019b; Available online: https://curriculum.illustrativemathematics.org/MS/teachers/1/4/17/index.html (accessed on 30 May 2025).
Jussim, L.; Harber, K. D. Teacher expectations and self-fulfilling prophecies: Knowns and unknowns, resolved and unresolved controversies. Personality and Social Psychology Review; 2005; 9,
Kisker, E. E.; Lipka, J.; Adams, B. L.; Rickard, A.; Andrew-Ihrke, D.; Yanez, E. E.; Millard, A. The potential of a culturally based supplemental mathematics curriculum to improve the mathematics performance of Alaska Native and other students. Journal for Research in Mathematics Education; 2012; 43,
Ladson-Billings, G. Toward a theory of culturally relevant pedagogy. American Educational Research Journal; 1995; 32,
Lumpkin, B.; Strong, D. Multicultural science and math connections: Middle school projects and activities; Walch Publishing: 1995.
Marshall, S. L.; Khalifa, M. A. Humanizing school communities: Culturally responsive leadership in the shaping of curriculum and instruction. Journal of Educational Administration; 2018; 56,
Michael, J. Where’s the evidence that active learning works?. Advances in Physiology Education; 2006; 30,
Moll, L. C.; Amanti, C.; Neff, D.; González, N. Funds of knowledge for teaching: Using a qualitative approach to connect homes and classrooms. Theory Into Practice; 1992; 31,
Moschkovich, J. Principles and guidelines for equitable mathematics teaching practices and materials for English language learners. Journal of Urban Mathematics Education; 2013; 6,
National Council of Teachers of Mathematics. Principles to action: Ensuring mathematical success for all; NCTM: 2014.
Neihaus, A.; Kalinec-Craig, C.; Prasad, P. V.; Wood, M. B. My problematic fave. Mathematics Teacher: Learning and Teaching PK-12; 2023; 116,
Ng, E.; Fitzsimmons, T.; Kulkarni, M.; Ozturk, M. B.; April, K.; Banerjee, R.; Muhr, S. L. The anti-DEI agenda: Navigating the impact of Trump’s second term on diversity, equity and inclusion. Equality, Diversity and Inclusion: An International Journal; 2025; 44,
Ostrager, A.-E.; Jordan, J.; High, T. R. President Trump acts to roll back DEI initiatives; The Harvard Law School Forum on Corporate Governance: 10 February 2025; Available online: https://corpgov.law.harvard.edu/2025/02/10/president-trump-acts-to-roll-back-dei-initiatives/ (accessed on 10 September 2025).
Putnam, R. T. Senk, S. L.; Thompson, D. R. Commentary on four elementary mathematics curricula. Standards-based school mathematics curricula: What are they? What do students learn?; Lawrence Erlbaum Associates: 2003; pp. 161-178.
Raymond, K. M is not just for STEM: How myths about the purposes of mathematics education have narrowed mathematics curricula in the United States. Education Sciences; 2018; 8,
Remillard, J. T. Can curriculum materials support teachers’ learning?. Elementary School Journal; 2000; 100,
Remillard, J. T. Examining key concepts in research on teachers’ use of mathematics curricula. Review of Educational Research; 2005; 75,
Remillard, J. T. Examining teachers’ interactions with curriculum resource to uncover pedagogical design capacity. Research on mathematics textbooks and teachers’ resources: Advances and issues; Springer: 2018; pp. 69-88.
Remillard, J. T.; Heck, D. J. Conceptualizing the curriculum enactment process in mathematics education. ZDM—Mathematics Education; 2014; 46, pp. 705-718. [DOI: https://dx.doi.org/10.1007/s11858-014-0600-4]
Remillard, J. T.; Kim, O. K. Beyond the script: How curriculum authors communicate with teachers as curriculum enactors. Elementary mathematics curriculum materials: Designs for student learning and teacher enactment; Springer: 2020; pp. 141-160.
Stein, M. K.; Grover, B. W.; Henningsen, M. Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms. American Educational Research Journal; 1996; 33,
Stein, M. K.; Kaufman, J. H. Selecting and supporting the use of mathematics curricula at scale. American Educational Research Journal; 2010; 47,
Stein, M. K.; Remillard, J.; Smith, M. S. Lester, F. K., Jr. How curriculum influences student learning. Second handbook of research on mathematics teaching and learning; Information Age Publishing: 2007; Vol. 1, pp. 319-369.
Style, E. Curriculum as window and mirror. Social Science Record; 1996; 33,
Wachira, P.; Mburu, J. Culturally responsive mathematics teaching and constructivism: Preparing teachers for diverse classrooms. Multicultural Learning and Teaching; 2019; 14,
White, D. Y. Promoting productive mathematical classroom discourse with diverse students. The Journal of Mathematical Behavior; 2003; 22,
Zavala, M. D. R.; Aguirre, J. M. Cultivating mathematical hearts: Culturally responsive mathematics teaching in elementary classrooms; Corwin Press: 2024.
© 2025 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
Details
; Smith, Ethan P 2
; Ebner, Raisa J 2 1 Mathematica, 600 Alexander Park Dr., Princeton, NJ 08540, USA
2 College of Education, Sport, and Human Sciences, Washington State University Tri-Cities, 2710 Crimson Way, Richland, WA 99354, USA; [email protected] (E.P.S.); [email protected] (R.J.E.)