What is Ambitious (Mathematics) Teaching? Clarifying a Key Concept in Education Research and Practice

Abstract

Ambitious Mathematics Teaching (AMT) describes a reform-oriented vision of mathematics instruction that emphasizes conceptual rigor, student reasoning, and equitable participation. Although the term is widely used, its meaning remains variably defined. We trace the intellectual origins of AMT and synthesize three core dimensions that recur in the literature: using nonroutine, discipline-aligned tasks, eliciting and responding to student thinking, and positioning students as mathematical authorities. We also examine how equity has been conceptualized and evolved within AMT-related research. We conclude by outlining future directions, including clarifying equity frameworks and developing multilevel supports for enacting AMT in diverse school settings.

Keywords

mathematics education ambitious teaching equity literature review

Introduction

Debates over the purpose of U.S. public education have long reflected competing visions: Should schools cultivate the intellectual development and democratic participation of all students, or should they function to sort and prepare students for unequal roles in a stratified society and economy? The latter idea gave rise to the school-as-factory model and structures such as academic tracking (Oakes, 1985). Alternatively, progressive philosophers like John Dewey and educational theorists such as Jerome Bruner proposed a vision of schools as sites of intellectual adventure and student-centered inquiry, where all students engage with academic content (Cohen, 1988). Building on the lineage of progressive educational theorists, contemporary education scholars have advanced reform visions that prioritize disciplinary understanding, student agency, and conceptual rigor in classrooms. The contemporary nomenclature of ambitious teaching arose from this progressive tradition as a vision to reform teaching and learning across disciplines in K-12 schools (Kazemi et al., 2009; Lampert et al., 2011).

While ambitious teaching has been used in multiple disciplines including science (Thompson et al., 2013; Windschitl et al., 2011, 2018) and languages (Lampert et al., 2011), the phrase, along with its conceptual underpinnings, has gained substantial traction in mathematics education research and practice. This phenomenon is evidenced in the literature: over the past 10 years, multiple mathematics education researchers have used “ambitious mathematics teaching” (AMT), and “ambitious and equitable mathematics teaching” without explicitly defining the terms. For example, in a commentary that appeared in the Journal for Research in Mathematics Education, Hiebert and colleagues (2025) proposed “a new model for research on ambitious teaching.” One striking feature was Hiebert and colleagues’ inexact definition of the central focus: they implicitly defined ambitious teaching as “a kind of teaching that does more than present information to students but rather interacts with students around thinking about and doing mathematics” (p. 22). As we show in the review below, Hiebert and colleagues are not alone in using AMT with an open-ended definition. Yet, this raises a critical set of questions for those who seek to promote this form of instruction: What is AMT? What is not AMT? And, how might an agreed-upon vision of AMT be promoted in research and practice?

In this paper we used a literature review to trace the origin of AMT. We use the parenthesis in the phrase ambitious (mathematics) teaching to indicate that much of the work on AMT has roots in a broader literature on progressive education reforms, but our review focuses on this work in mathematics education. In the sections that follow, we situate the origins of AMT within the broader literature on educational reform. We then synthesize three core dimensions of AMT as described in existing research, and examine the shifting role of equity in AMT research. Then we discuss future directions—particularly the evolving relationship between AMT and equity-focused mathematics education.

Origin of Ambitious (Mathematics) Teaching

The idea of ambitious (mathematics) teaching emerged from a long tradition of efforts to reimagine school mathematics as rigorous, student-centered, and intellectually authentic. A foundational example of this shift appears in Lampert’s (1990) account of her fifth-grade mathematics classroom, where she implemented a problem-solving, discussion-based approach rooted in disciplinary practices. In introducing this approach, Lampert described the disconnect between how mathematics is typically presented in schools and how it is done in practice:

The issue of intellectual authority is central to this comparison between how mathematics is known in school and how it is known in the discipline... [in school] there is no zig-zag between conjectures and arguments for their validity, and one could hardly imagine hearing the words maybe or perhaps in a lesson (Lampert, 1990, p. 32, emphasis in original).

In contrast, in her experimental class, Lampert repositioned the teacher (herself) as a facilitator of student inquiry. Through solving open-ended, conceptually rich problems, Lampert’s students engaged in constructing and refining their own mathematical ideas. Lampert’s subsequent work examined the dilemmas that arise in the course of enacting such instruction (Lampert, 2001). In the same laboratory school where Lampert was teaching fifth grade, Ball developed a parallel approach at the early elementary level, with a similar emphasis on eliciting student reasoning and centering disciplinary understanding (Ball, 1993). Lampert and Ball also collaborated on an effort to document their teaching and to make it into an object of inquiry for others for the purpose of teacher education (Lampert & Ball, 1998). These classroom-based reforms (among others) were, and continue to be, widely influential in mathematics education research (Schoenfeld, 1992) and shaped key policy documents, including the NCTM Standards and subsequent state-level frameworks (Wilson, 2003).

Before the term “ambitious” was widely adopted to describe this vision of teaching, David Cohen (a colleague of both Lampert and Ball) described this reform vision as “adventurous” teaching—positioned explicitly against traditional models of instruction in which teachers transmit fixed knowledge and students passively receive it. In his paper Teaching Practice: Plus ça Change, Cohen (1988) linked this instructional vision to broader debates about the purposes of schooling in American society. Drawing on the tradition of progressive education from Dewey and the emerging social-psychological work from Bruner, Cohen proposed that “adventurous teaching” is an approach grounded in the belief that instruction should be intellectually challenging, attentive to students’ ways of thinking, and oriented toward exploration of disciplinary ideas (Cohen, 1988). Cohen also noted and discussed the numerous dilemmas inherent in attempting to implement adventurous teaching given the cross currents and constraints on schools and teachers in the US education system.

In sum, AMT grew from a long tradition that has been described variously as progressive education, reform teaching, or learner-centered pedagogy. Over the past 15 years, however, the term “ambitious teaching” has gained prominence—especially in mathematics and science education—as a descriptor for instructional models that prioritize conceptual understanding, student reasoning, and active participation. As mathematics education reforms advanced through the 1990s and early 2000s, the term “ambitious mathematics teaching” (AMT) was introduced to describe teaching that supports all students in learning to use academic knowledge in authentic ways. This phrase can be traced back to Lampert and colleagues who defined ambitious teaching as:

…teaching that aims to teach all kinds of students to not only know academic subjects, but also to be able to use what they know in working on authentic problems in academic domains (Lampert et al., 2011, p. 1361).

At its core, ambitious teaching seeks to close the gap between academic content as taught in school and disciplinary practices as they occur in the real world. In the sections that follow, we identify recurring features of AMT in the research literature and examine how this instructional vision has been taken up—sometimes unevenly—across educational contexts.

Review of Research on AMT

This section presents a qualitative literature synthesis of research on ambitious mathematics teaching (AMT). The review aimed to understand how AMT is defined in the literature, what supports or impedes its implementation, and what impacts are attributed to it. Our approach entailed a structured three-phase process: (1) identifying and organizing the literature, (2) summarizing and synthesizing the content of each article, and (3) analyzing recurring themes using qualitative coding. This approach balanced breadth with depth, enabling both a descriptive overview of the field and an interpretive synthesis of key conceptual patterns.

Review Methods

Phase 1: Literature Search and Selection

We began with a comprehensive search of the ERIC-ProQuest database using key terms such as “ambitious mathematics teaching,” “ambitious math,” and “ambitious teaching” restricted to the years 2000 to 2021. This initial search yielded 242 unique entries, including journal articles, dissertations, books, and public speeches. After filtering for duplicates and relevance through title and abstract review, 118 items were excluded for not focusing substantively on K–12 mathematics teaching or for referencing AMT only in passing. The remaining 124 sources were retained for full-text consideration.

To supplement this initial search, we used a snowball sampling strategy to identify foundational and frequently cited works within the AMT literature, including texts that may not explicitly use the term “ambitious mathematics teaching” but were widely cited as conceptual anchors. We also incorporated references from key equity-oriented volumes such as Mathematics for Equity (Nasir et al., 2014). We again excluded sources that did not provide sufficient detail on the concept of focus.

Phase 2: Structured Summary and Synthesis

Each of the 88 selected sources was assigned to a member of the research team for structured summary using a shared template. The summary form included both general descriptors (e.g., citation, research questions, theoretical perspective) and project-specific questions, such as:

How is AMT defined?

What resources support AMT?

What challenges impede AMT?

What are the reported impacts of AMT on teaching and learning?

This phase also involved a secondary reduction: as individual team members read and summarized papers, additional articles were excluded for irrelevance or insufficient focus on K–12 mathematics education. In the end, 88 publications were summarized. Each structured summary was reviewed collaboratively by the team in weekly meetings. These discussions focused on clarifying core ideas, identifying emergent themes, and determining the importance of each paper. This process continued until the team reached interpretive saturation.

Phase 3: Coding and Analysis

All source materials, structured summaries, and bibliographic data were stored in Zotero and then imported into MaxQDA for coding. The qualitative coding process followed a structured approach using pre-defined descriptive codes based on our interest in understanding research that has used AMT (Saldaña, 2016). Three authors independently distilled each summary using project-specific analytic focus: (a) definitions of AMT, (b) resources that support AMT, and (c) challenges to implementing AMT. An additional team member coded contextual and descriptive characteristics of each study, including (a) Student population (e.g., primary, secondary, higher education), (b) Teacher population (e.g., pre-service, in-service, teacher leaders), (c) Instructional setting (e.g., urban, suburban, rural), and (d) Research project affiliation.

These codes allowed us to describe the distribution of AMT research across grade levels, teacher roles, and educational contexts, and to track the influence of major research programs in the field. In the final cycle of analysis, we collaboratively examined the definitions of AMT and our codes to synthesize themes across how AMT is conceptualized, practiced, and studied across mathematics education research.

In reviewing the literature that has used ambitious mathematics teaching as a framing concept, we found there is not a single, agreed-upon definition of this term. Not all references we reviewed had an explicit definition for AMT. For the 51 that did, we have collected and presented our synthesis of the definitions in the supplemental Appendix. In what follows, we present three defining features of AMT that emerged as themes in our review of the literature.

(1) using high cognitive demand, discipline-aligned tasks;

(2) eliciting and responding to student thinking; and

(3) positioning students as mathematical authorities.

We also discuss the cross-cutting theme of attending to equity, which appeared throughout the literature we reviewed.

Defining Ambitious Mathematics Teaching

First, we must note that the three themes identified above are interrelated. For example, eliciting and responding to student thinking is meaningful when students work on high cognitive demand, discipline-aligned tasks. When students solve rote exercises there is not enough grist for a meaningful discussion. In turn, reasoning about high cognitive demand, discipline-aligned tasks provides students with an opportunity to be a source of mathematical authority. In the following, we expand on each of these dimensions of AMT. While these dimensions appear frequently, we also note areas of divergence and ambiguity, which we discuss further in relation to equity-focused mathematics education.

Using Nonroutine, Discipline-aligned Tasks

Tracing AMT back to Lampert’s foundational works (Lampert, 1990, 2001), engaging students in the discipline-aligned practices of mathematical inquiry is the sine qua non of ambitious mathematics teaching. Yet, such discipline-aligned reasoning practices are unlikely to emerge when students do traditional mathematics assignments—sets of exercises focused on developing a single procedure (Schoenfeld, 1992). Rather, disciplinary reasoning emerges when teachers guide students to work on tasks that are nonroutine, focus on important mathematical concepts, and have multiple solution approaches (Boston & Candela, 2018; Jackson et al., 2017; Tekkumru-Kisa et al., 2020). Such tasks, or problems, mirror authentic problem solving in mathematics (Schoenfeld, 1992).

The lack of a specified approach for solving nonroutine tasks induces the higher cognitive processes in students (Doyle, 1988). In recent decades in mathematics education a strand of research has focused on the affordances of high cognitive demand tasks for promoting students’ learning (Boston & Smith, 2011; Stein et al., 1996, 2008). While raising the cognitive demand may seem to make mathematics less accessible, Choppin et al. (2022) note that nonroutine tasks may broaden students’ access to mathematics because such tasks allow students to use their individual and collective resources to attempt to formulate a solution. Additionally, nonroutine tasks allow students to invent strategies and approaches that emerge from their intuitive and everyday ways of thinking and acting in the world (Gravemeijer, 2004).

Eliciting and Responding to Student Thinking through Dialogic Teaching

A second recurring theme in the literature on AMT is that student thinking is a primary focus of teaching. Singer-Gabella et al. (2016) wrote, “mathematics instruction should start with and build on students’ reasoning to support students in developing increasingly sophisticated means of representing and acting on mathematical situations” (p. 412). Building on students’ thinking requires teachers to notice children’s mathematical thinking (Jacobs et al., 2010), and several studies that use noticing in the context of AMT as the guiding framework have focused on teacher education: developing teachers’ skills for and dispositions for noticing student thinking (e.g., Anthony et al., 2015; van Es et al., 2017).

What gets noticed? In the course of daily classroom interactions, one of the primary ways teachers can access student thinking is through talk—student discussions and collective participation in classroom discourse. Noting the centrality of talk, Averill et al. (2016) wrote, “orchestration of mathematical discussions that support learners to use mathematical language to express their thoughts clearly and assist with developing mathematical reasoning is central to ambitious mathematics teaching” (p. 488). This and related research emphasizes that, in the course of AMT, classroom interactions should include dialog among students and dialogue between students and teachers (Averill et al., 2016; Lampert, 1990; Stylianides & Stylianides, 2014). Creating dialogic learning environments for AMT requires “a joint production of ideas, where students offer their thoughts, attend and respond to each other’s ideas, and generate shared meaning or understanding through their joint efforts” (Staples, 2007, p. 162). The focus on classroom discourse as raw material for advancing classroom mathematical ideas leads to the next dimension of AMT in the literature, positioning students as a source of authority.

Positioning Students as a Source of Mathematical Authority

An important outcome of eliciting and responding to student thinking is the development of student agency and the positioning of students as mathematical authorities (Kinser-Traut & Turner, 2020; Lampert, 1990; Yackel & Cobb, 1996). Students exercise mathematical agency through engaging in (or even resisting) mathematical activities (Gresalfi et al., 2009). One of the initial goals of AMT reforms was to shift traditional mathematics classroom dynamics from teacher- and textbook-centered authority to more disciplinary and student-centered authority, and to promote students’ agency as doers of mathematics (Boaler, 2002; Lampert, 1990). Teachers engaging in AMT provide their students opportunities to exercise agency and share mathematical authority when they provide opportunities for students to contribute ideas, determine solution pathways, and make connections between school mathematics and out of school lives (Kinser-Traut & Turner, 2020).

An important component for the success of students exercising agency and sharing authority is accountability, that is, the norms for what are considered acceptable ways to participate and what constitutes appropriate mathematical evidence (Yackel & Cobb, 1996). Gresalfi et al. (2009) note that “accountability refers both to what students are supposed to know (be accountable for) and who students are expected to convince (be accountable to)” (p. 53). Given the focus on disciplinary practices in AMT, accountability can be understood as when students hold themselves accountable to the community and to the discipline of mathematics (Boaler, 2002). One oft-cited example of such community-based accountability is developing and adhering to established norms for what counts as mathematically valid explanations (Yackel & Cobb, 1996).

Teachers’ assumptions about student competence shape opportunities for students to exercise agency and have authority in the mathematics classroom. In the vision of classroom interactions typified in studies that use AMT as a framing concept, students show competence through constructing and refining mathematical arguments (Yackel & Cobb, 1996). In classrooms characterized by AMT, all students are assumed to have the ability to show competence. This is a stark contrast to “traditional” classrooms where only quick students or those with strong memorization skills are considered mathematically competent (Boaler, 2002). An implication of assuming student competence is that students’ struggles are seen as opportunities to learn rather than as deficits in students. The aspects of AMT related to positioning students as authority are closely related to the crosscutting theme in research that has used AMT as a framing concept, emphasizing multiple dimensions of equity. In the next section we discuss how equity has emerged and developed in the literature using AMT as a framing concept.

Attending to Equity

A concern for equity was woven throughout the literature we reviewed. This is evident in the earliest work that was foundational for AMT. For example, Lampert (1990) emphasized that “at every level of schooling, and for all students, reform documents recommend that mathematics students should be making conjectures, abstracting mathematical properties, explaining their reasoning, validating their assertions, and discussing and questioning their own thinking and the thinking of others” (pp. 32–33, emphasis added). In the foundational work that spawned AMT, equity was often framed as a matter of access—ensuring that all students, not just those in advanced tracks (Oakes, 1985), had opportunities to engage in lively, disciplinary reasoning.

Yet, these early studies also acknowledged the complexity of putting equity-focused ideals into practice. Lampert (1990) and Ball (1993), for instance, documented the dilemmas that arose when striving to build on students’ ideas in classroom discussions of open-ended problems. Lampert (2001) includes a detailed exegesis of a lesson vividly illustrating how she navigated competing demands during a typical lesson: advancing a mathematical discussion, attending to the diversity of students’ contributions, considering whose ideas were taken up or sidelined (and the racial, gender, and disciplinary identities of those students), finishing the day’s lesson on time, and aligning her pedagogical goals with broader commitments to disciplinary authority. These tensions foreshadow later critiques of the peripheral role of equity in the presentation of AMT. These critiques emphasize the need to foreground equity, and particularly issues of student identity, positioning, and power in equitable teaching (Rubel, 2017).

Jackson and Cobb (2010) proposed a framework to explicitly link AMT and research on equity and culturally relevant mathematics education. Their framework included:(a) unpacking the cultural suppositions in tasks and developing situation-specific images of mathematical relationships in problem contexts, (b) engaging students in multivocal discussions where authority is shared, (c) pressing students to engage in conceptual discourse and developing shared meanings for valid or acceptable mathematical explanations, and (d) explicitly negotiating the norms for participation, assigning competence, and supporting students’ engagement in the use of disciplinary language and discourse practices (Jackson & Cobb, 2010). Jackson and Cobb’s framework set the stage for subsequent studies that have merged a focus on AMT with a more explicit equity agenda (e.g., Baldinger, 2018; Crespo et al., 2021; Joseph, 2021; Kinser-Traut & Turner, 2020; Rubel, 2017; Wilson et al., 2019).

One illustration of such work is Kinser-Traut and Turner’s (2020) research that fused AMT and culturally responsive pedagogy. Since AMT rests on the assumption that students possess mathematical competencies and experiences upon which to develop key disciplinary concepts, it is an asset-based perspective on students. Yet, designing and implementing learning experiences that integrate students’ social and cultural assets with the other dimensions of AMT is non-trivial, especially for novice teachers. For example, Kinser-Traut and Turner (2020) conducted a longitudinal case study of one preservice to inservice teacher who was learning ambitious and equity-focused pedagogy. The teacher was part of a teacher preparation program that explicitly linked a focus on children’s mathematical thinking and children’s funds of knowledge. Using an analysis rooted in research on authority, they found that the teacher struggled to go beyond focusing on students’ mathematical thinking, and to connect AMT to her students’ funds of knowledge:

Sena struggled to understand connections to [children’s linguistic, cultural, and family funds of knowledge] and was inconsistent in her orientations toward families. At times Sena recognized families’ support of student learning and was open to connecting mathematics instruction to students’ experiences outside of school (recognition rules). Yet, by positioning herself as an authority on such connections, she limited her opportunities to notice or elicit ways that students and families engaged in mathematics outside of school (Kinser-Traut & Turner, 2020, p. 16-17).

The work of Kinser-Traut and Turner (2020) is a deep case study of one teacher’s uptake of ambitious practice. The struggles of this case study teacher to take up equity-based pedagogy point to one of the next directions for research on AMT. In the next section we discuss future extensions for research on AMT, and situate this mathematics-specific work in a broader disciplinary tradition.

Discussion and Next Directions

In the following sections we consider directions for future research focused on AMT. The case of AMT is a subset of the larger phenomenon of Ambitious (or “reform”) teaching writ large. In what follows, we consider three interrelated directions for future research on AMT: (1) clarifying how equity is conceptualized and operationalized in AMT literature, (2) understanding the persistent gap between the AMT vision and its limited classroom uptake, and (3) developing sustainable, multilevel frameworks to support the wider enactment of AMT in heterogeneous school settings.

Clarify Focus on Equity in Ambitious (Mathematics) Teaching Research

First, the connection between research on equity in mathematics education and research on AMT should be clarified. As noted above, AMT arose with an initial focus on equity (all students), but the realities of schools and the ways mathematics education research addresses equity have shifted since this initial effort. Scholars such as Martin (2015) have critiqued defining equity in mathematics around the goal of teaching “all students” to participate in disciplinary practices without addressing broader issues of power. Gutiérrez’s (2009) framework for equity in mathematics education is helpful for understanding this shift. The dominant axis of equity in Gutiérrez’s framework includes access and achievement while the critical axis consists of identity and power (Gutiérrez, 2009). Early research on AMT primarily focused on the dominant axis of equity—providing access to disciplinary mathematics for all students, and rethinking classroom arrangements so a wider group of students could achieve success in the discipline (Lampert, 1990, 2001). While attending to students’ identity as a mediator of learning has also been a theme throughout mathematics reform efforts (e.g., Boaler, 2002), explicitly connecting AMT and transforming relations of power in the classroom and beyond has been missing from the literature until fairly recently. Rubel (2017) and Wilson et al. (2019) are two examples of recent research that has critically examined educators’ failure to integrate conceptually focused mathematics (e.g., a part of AMT) and student identity/power. While Jackson and Cobb (Cobb et al., 2018; Jackson & Cobb, 2010), and Horn and Garner (2022) have provided the field with a vision for enacting ambitious and equitable mathematics in heterogeneous settings, more work can be done in this area.

The integration of AMT and equity can be advanced by developing frameworks for increased conceptual clarity. Crespo and colleagues (2021) wrote, “Ambitious student-centered mathematics teaching practices [are] not enough to create opportunities for historically marginalized students, including emerging multilingual students, to learn high quality mathematics and to develop a positive mathematical identity” (Crespo et al., 2021, p. 461). Other AMT-related research areas can provide a model for what advances in this area might look like. For example, researchers have provided a set of tools and frameworks for how teachers and researchers can examine mathematical tasks (Stein et al., 1996; Tekkumru-Kisa et al., 2020), facilitate discussions about students’ ideas (Stein et al., 2008), and attend to student thinking (Jacobs et al., 2010). There is an opportunity for the field to develop more widely shared frameworks for developing students’ mathematical identities and for transforming relations of power through AMT. In our search of the literature we found different possible approaches to bridging critical perspectives on equity and AMT.

Two contrasting visions—AMT as a component of equitable pedagogy or AMT and equity as fully integrated—come from recent research. Joseph’s (2021) Black Feminist Mathematics Pedagogies (BlackFMP) is a framework for reimagining mathematics learning spaces where Black girls thrive. The four components of BlackFMP are (a) ambitious mathematics instruction, (b) critical consciousness and reclamation, (c) academic and social integration, and (d) robust mathematics identities 2.0. Joseph notes, “these dimensions are interdependent, and it is not enough to just engage in one, especially if one’s outcomes align with supporting Black girls’ limitless possibilities in mathematics” (Joseph, 2021, p. 87). Thus, Joseph positions AMT as a part of, but not the entirety of, an equitable pedagogy. Joseph’s (2021) vision is clearly grounded in the critical axis of Gutiérrez’s (2009) framework and Joseph notes the slow pace at which reform in mathematics education has progressed may be due to mathematics educators’ collective lack of focus on identity and power of both the students and the teacher in the classroom. Additionally, Joseph noted that many teachers lack the capacity to understand and productively build from students’—particularly Black girls’—identities (Joseph, 2021).

A second approach is to link the more traditional mathematically focused dimensions of AMT with more critical perspectives on equity in an integrated framework (e.g., Aguirre et al., 2013; Horn & Garner, 2022). Authors who adopt this integrated stance often write of “ambitious and equitable pedagogy” as a compound noun (Horn & Garner, 2022). One example of this integrated approach arises from the TEACHMath project, which developed resources where teachers could learn to both attend to children’s mathematical thinking and incorporate children’s funds of knowledge in instruction (Aguirre et al., 2013). As noted in the discussion above, achieving this integration is not always seamless (Kinser-Traut & Turner, 2020). Similar to TEACHMath’s framework, Baldinger (2018) developed a framework for transformative teacher learning that explicitly connects to the dimension of identity and power from Gutiérrez’s (2009) framework through highlighting teachers’ goals of “dismantling inequalities” (power) and building on all students’ “smartness” (identity) as part of AMT. In these works, ongoing and situated teacher learning is a key aspect for the success of integrating ambitious and equitable mathematics pedagogy (Horn & Garner, 2022).

One important consideration for future research that attempts to link AMT and developing a critical, equity stance in mathematics teaching is the vast difference between the social, cultural, and racial background of most teachers and students. The majority of K-12 teachers in the US are white and female, while the majority of students are not (National Center for Educational National Center for Education Statistics, 2022). Adding critical perspectives on equity to AMT would not be complete without considering the large role that race and racialization play in student experiences and education as a whole in the U.S. In a recent survey of 205 middle school mathematics teachers, Comstock et al. (2025) used Latent Profile Analysis to identify distinct groups of teachers based on the patterns of responses to items targeting three constructs: (a) culturally responsive teaching, (b) ambitious instruction, and (c) traditional instruction. Comstock et al. (2025) found that about half of the teachers emphasized classical mathematics, including more and less ambitious approaches. The vast majority of the teachers fitting this profile were white. On the other hand, about one-fourth of their sample were “multidimensional equity-focused teachers” who engaged in both classical mathematical practices and culturally relevant/responsive practices. Notably this group was overwhelmingly teachers of color (83%). This suggests that integrating ambitious and critical visions of mathematics teaching requires making a shift for most teachers, particularly white teachers, who might not agree with a critical, activist stance. We know from prior research that teachers will avoid discussing topics if those topics make them uncomfortable or they disagree with their framing (Zembylas, 2016), and in the current sociopolitical climate this phenomenon may be more salient.

Understand the Lack of Uptake of Ambitious (Mathematics) Teaching

There is a significant disconnect between vision of mathematics classrooms found in the literature on AMT and mathematics teaching experienced by most students. This disconnect is especially pronounced in schools serving low-income and minoritized student populations. While mathematics education literature includes multiple case studies of teachers enacting AMT (Boaler & Staples, 2008; Nasir et al., 2014), such teaching appears to be rare in practice. Many of the studies we reviewed reported on challenges with implementation (e.g., Kinser-Traut & Turner, 2020). We know AMT is rare from our first-hand experiences as researchers and teacher educators, and from anecdotes we hear from colleagues. Comstock et al. (2025) also noted this trend appears in nationally representative studies of teaching practices:

Scholarship examining mathematics teaching in large samples in urban U.S. districts suggests that mathematical instruction tends to emphasize routine mathematical procedures and explicit instruction, which we refer to as traditional instruction, and devote much less time to conceptually-focused tasks and ambitious practices such as discourse-rich and student-driven activities (p. 4).

If the vision of AMT is to become a reality, then researchers and teacher educators need to understand why this vision is removed from most students’ experiences. One overarching explanation can be found in Cohen’s (1988) essay on the challenges of transforming teaching practice in U.S. schools. Among the challenges that Cohen described are (a) deep-rooted beliefs about academic knowledge as a set of facts, and corresponding instructional traditions such as “teaching as telling”, (b) the vision of reform coming from “elite” institutions, which clashes with a decentralized and generally “anti-elite” system, and (c) the inherent challenges of making changes when teachers depend on their students’ cooperation for the success of implementing reform. While Cohen described these challenges nearly 40 years ago, it is striking how relevant they are in the current social, political, and academic climate. In addition to the enduring issues named by Cohen, more recent work on understanding the implementation of reform (and challenges thereof) has examined social networks and sources of advice for teachers (Coburn et al., 2012), and the capacity of those charged with implementing ambitious reforms (Spillane et al., 2018).

Turning more specifically to the research on AMT, one of the issues that may be limiting uptake of the research is the use of a limited number of cases, both as sites for research as well as for motivating research. Lampert and Ball worked in the same laboratory school in Michigan, where much of this work started. In the window from 2000–2015, multiple studies that are highly cited in the AMT literature were conducted at one high school. In the past 10 years, a large body of work has come from one large study spanning four urban school districts. While all of these contributions are valuable, the field of mathematics education will benefit from a broader research base.

Consolidate Frameworks for Wider Uptake of AMT

A key next step for the field is to consolidate how ambitious mathematics teaching (AMT) is defined and used across research and professional development. Although the term ambitious mathematics teaching is widely invoked, the defining features of AMT are rarely made explicit. This lack of clarity poses challenges for researchers who seek to study AMT and for teacher educators and practitioners who aim to implement this vision. With greater conceptual clarity, researchers can better articulate the instructional and systemic demands of AMT and examine how these demands align with—or come into tension with—those created by other policies and initiatives (Choppin et al., 2024). Achieving such alignment has important implications for developing both teacher and organizational capacity to enact and sustain AMT.

Conclusion

Ambitious (Mathematics) Teaching remains a central, yet variably defined concept in mathematics education research and practice. In this review, we traced the origins of ambitious teaching in progressive education reforms, synthesized common features of AMT from across the literature, and examined how AMT is entangled with evolving understandings of equity in the field. We identified three interrelated dimensions in the definitions of AMT—engaging students in high cognitive demand tasks, eliciting and responding to student thinking, and positioning students as mathematical authorities—and highlighted the growing imperative to attend to equity, including identity, power, and systemic inequity within these practices. We note that the trends we observed for AMT have parallels in the broader effort to reform teaching and learning. As the framing of AMT continues to shape research, teacher education, and instructional reform, we call for deeper integration of critical equity frameworks and the development of sustainable, multilevel support systems to bolster and sustain implementations of AMT. Such work is essential to make ambitious and equitable mathematics teaching a reality in schools serving diverse learners.

Footnotes

William Zahner

Kristin Tenney

Jeffrey Choppin

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This material is based upon work supported by the National Science Foundation under Grant No. 2010111. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

Declaration of Conflicting Interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Appendix

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