Advancing Research about Mathematics Specialists and Mathematics Teacher Leaders

KEYWORDS:

• Mathematics specialist
• mathematics teacher leader
• teacher leadership
• mathematics coaching
• professional development
• mathematics education

Introduction

The need for mathematics specialists has been well documented (e.g., Association of Mathematics Teacher Educators, 2013; Dossey, 1984; Fennell, 2006; Gojak, 2013; Lott, 2003; National Council of Teachers of Mathematics, 2000; Nickerson, 2009/2010). However, research has not yet caught up to practice and the role, responsibilities, and impact of mathematics specialists for teachers and learning are still under-investigated (Herbst et al., 2021; Hjalmarson & Baker, 2020). In recent years, there has been an increase in journal and conference submissions that focus on mathematics specialists (Baker, Saclarides, et al., 2021; Hjalmarson et al., 2020; Saclarides et al., 2020). Yet, the largest mathematics specialist submission spikes seemed to follow the implementation of key national educational events and policies (Saclarides et al., 2020). It is also important to note that although key policies and events that have advocated for mathematics specialists have spanned four decades, there are only 36 peer-reviewed research articles that address school-based mathematics specialists (Baker et al., 2021), including, at this writing, four within Investigations in Mathematics Learning (Nickerson, 2009/2010) and, more recently, Baker et al. (2022), Saclarides (2022), and Baker et al. (2022). This is of concern as state and local policies and related decisions regarding the impact, work, and responsibilities of mathematics specialists and mathematics teacher leaders are being made with little research to guide the decision-making that greatly influences the daily work, roles, and impact of the specialists on mathematics teaching and learning. Grounding practice-based decisions in research is essential as school districts’ external funding for continued support of mathematics specialists and mathematics teacher leader positions is not guaranteed.

While we recognize the importance and contributions of research related to interest in, advocacy for, and the establishment of programs for mathematics specialists, this special issue of Investigations in Mathematics Learning seeks to address and illuminate a number of the gaps in the research regarding policy, leadership, professional learning, and the impact of the mathematics specialist (Campbell et al., 2017; Fennell et al., 2013; Hjalmarson & Baker, 2020; Sun et al., 2014). As editors, we recognize the role and influence of mathematics specialists and mathematics teacher leaders at the elementary and secondary level to be a critical element of school- and district-based professional learning opportunities for teachers and ultimately students’ learning experiences. We believe the manuscripts selected for this special issue validate, challenge, and advance perspectives related to the influence and impact of mathematics specialists.

Defining and Describing Mathematics Specialists

This special issue focuses primarily on mathematics specialists’ work and development as leaders of mathematics in their schools and districts. Mathematics specialists and mathematics teacher leaders work in a variety of instructional support and leadership roles to advance the teaching and learning of mathematics (McGatha & Rigelman, 2017). However, within the mathematics specialist-focused research a challenge exists in describing this population as there is a wide variety of titles used to describe such positions (Harbour, 2015). To address this challenge and for the purpose of this special issue, we use the term “mathematics specialist” as defined by McGatha and Rigelman (2017). “A mathematics specialist is a professional with an advanced certification as a mathematics instructional leader or who works in such a leadership role” and is positioned in at least one of the following major roles: “(a) mathematics teacher, a professional who teaches mathematics to students; (b) mathematics intervention specialist, a professional who works in ‘pull out’ or ‘push in’ intervention programs; and (c) mathematics coach, a professional who works primarily with teachers” (p. xiv). We also draw on Baker and colleagues’ (2021) recent expansion of the McGatha and Rigelman framework in which they articulate additional categories of mathematics specialists captured in research, as well as “contextual descriptions and working definitions to more accurately and robustly capture the ways in which mathematics specialists are investigated and reported in research” (p. 9). The articles in the special issue may use different terms to describe the role of specialists and aspects of their work.

Mathematics specialists support the tenets of high-quality professional development by providing ongoing, focused, and interactive learning experiences for teachers (Desimone & Pak, 2017; Gibbons & Cobb, 2016). A growing body of research points to the positive impact mathematics specialists have on teachers (e.g., Gibbons et al., 2017; Polly, 2012; Saclarides & Lubienski, 2021) and students (e.g., Campbell & Malkus, 2011; Harbour et al., 2018). Additionally, mathematics specialists are positioned to make a “significant influence on curriculum, assessment and professional development decisions” (National Council of Teachers of Mathematics, 2020, p. 125) by providing on-site professional development and assistance that directly impacts K-12 mathematics teaching and learning. However, they may also play roles as resources for mathematics in the school community, broadly including parents and families (Swars Auslander et al., 2023; Association of Mathematics Teacher Educators, 2013).

As mathematics leaders, specialists can also play an important role in mathematics education research and change initiatives. Research has pointed to the need for mathematics change initiatives to be coherent and systematic across and within levels in a school or district (e.g., Cobb & Jackson, 2015). Models for research such as design-based implementation research or research-practitioner partnerships rely on a close connection between schools, districts, and researchers. Additionally, the sustainability of a research innovation relies on school district partnerships that can create innovative learning environments grounded in practice and continue the innovation beyond the researcher team presence. Thus, school-based leaders, such as mathematics specialists, play key roles in connecting research and practice, and their influence needs to be addressed as such in both research and professional learning settings (Campbell & Malkus, 2011; Woulfin & Rigby, 2017).

However, the variety of roles and responsibilities of school-based mathematics leaders that appear in practice and in research (e.g., Swars Auslander et al., 2023; Baker et al., 2021) simultaneously present opportunity and challenge. While it can be difficult to pin down what a mathematics specialist does or should do, this variance is a distinct feature of the role that provides flexibility to respond to local needs and concerns. As mathematics education research has moved toward professional development models that are adaptive and responsive (e.g., Borko et al., 2015), implementation of any type of change in schools whether curriculum, standards, assessment, or policy must also be adaptive. Mathematics specialists are well positioned for responsiveness and adaptation if they can be seen as resources for mathematics to help guide teachers, principals, schools, and the community as change occurs. Within this special issue, Jarry-Shore et al. (2023) presents an example of how to analyze and interpret such an adaptation.

Mathematics specialist positions were initially created in response to concerns regarding the mathematics content background of elementary teachers (Fennell, 2017), who continue to be prepared as generalists, responsible for teaching all major content areas. Advocacy for mathematics specialists has come from multiple National Council of Teachers of Mathematics (NCTM) presidents (e.g., Dossey, 1984; Gojak, 2013) and numerous educational and policy-related publications (e.g., NCTM, 2000; National Research Council, 2001). Specifically, the recommendations endorse the position that all elementary schools have access to a mathematics specialist (e.g., NCTM, 2022) and encourage future “research … on the use of full-time mathematics teachers in elementary schools” (National Mathematics Advisory Panel, 2008, p. xxii). These influential recommendations have not only guided justification for state-level mathematics specialist certification but also fueled research exploring the influence of mathematics specialists on teaching and learning (Campbell & Malkus, 2011; Mills et al., 2020). Mathematics specialists are leaders. Their leadership opportunities and influence are directly related to their responsibilities and, importantly, their ability to navigate relationships with the school and school district stakeholders with whom they work (Baker et al., 2021). While the interest in and recommendations for mathematics specialists have, for the most part, been focused at the elementary school level, recent initiatives at the secondary level have involved middle school and high school mathematics specialists (e.g., Rigelman & Lewis, 2023). The purpose of this special issue is to present five articles that describe research focused on mathematics specialists in a variety of positions with a particular focus on mathematics specialist and mathematics teacher leader learning, development, leadership, support, and impact. The objective, for us, in selecting these articles was to 1) Identify articles that are suggesting new directions and innovations in research; 2) Present frameworks that might inform or shape future projects; and 3) Deepen the field’s understanding of mathematics specialists’ work and impact on mathematics teaching and learning.

Brief Synthesis of Literature

Mathematics specialists are significant partners in the teaching and learning of mathematics due to their positions as school-based or district-based leaders who support teachers. While there have been summaries and analyses of research on the topic (e.g., Baker et al., 2017; Gibbons & Cobb, 2017; Marshall & Buenrostro, 2021; McGatha, 2009; McGatha et al., 2015; Polly et al., 2013), there is a need for focused attention on not only what has been accomplished and current challenges but also future directions indicated by research. The research on mathematics specialists falls generally into two categories: first, research about specialists themselves and their responsibilities (e.g., Chval et al., 2010; Lesseig et al., 2016), and second, research about the systems in which they work and their influence on that system (e.g., schools, districts, and networks of teachers, e.g., Gibbons et al., 2017; Sun et al., 2014). These categories are symbiotic in that we must understand the responsibilities and practices related to mathematics teacher leadership and the systems where mathematics specialists are assigned to understand their influence and impact. These research categories are also evolving. As scholars in this area better understand the practices of mathematics specialists, their understanding of their influence on the systems mentioned above evolves. Furthermore, as we learn about mathematics specialists’ systems of influence, we can improve both K-12 mathematics teaching and learning and the practice of the mathematics specialist.

Current research about mathematics specialists focuses primarily on the work of the mathematics specialist with and for teachers and teaching. This work occurs in several contexts: individual coaching with teachers (e.g., Gibbons & Cobb, 2016; Saclarides & Lubienski, 2021; Yopp et al., 2019), content-focused coaching (e.g., West, 2017), and ongoing work with groups of teachers such as professional learning communities (e.g., Elliott et al., 2009). Studies of a mathematics specialist’s individual coaching practice have examined how specialists develop relationships with teachers (e.g., Chval et al., 2010), the nature of the interaction (e.g., Barlow et al., 2014), tools to promote reflection of coaching practice (e.g., Baker & Knapp, 2019) and the development of coaching practice over time (Chval et al., 2010; Knapp, 2017; Saclarides, 2018). There are also multiple models of coaching that emphasize different types of knowledge and different recommendations for how the coach interacts with the teacher (Yopp et al., 2019). Important examinations of practice have come from mathematics specialists themselves in the form of self-studies or autoethnographies akin to teachers studying their own practice (e.g., Baker et al., 2022; Knapp, 2017). Another form of coaching occurs in professional learning communities (PLC), (e.g., Borko et al. (2015); Lesseig et al. (2016)) where the facilitator may be a mathematics specialist.

Related work about mathematics specialists themselves includes research that examines their own professional development needs (e.g., Baker et al., 2021), advanced programs used for mathematics specialist professional development (e.g., Campbell & Malkus, 2013; Even, 1999; Hjalmarson, 2017; Whitenack et al., 2014) and the contexts for their professional learning. Yopp et al. (2019) explored the relationships between coaching knowledge (including mathematics knowledge for teaching [MKT]), coaching practices, and influences on mathematics teaching. Many programs which prepare or support the ongoing work of the mathematics specialist focus on the mathematics content knowledge needed for coaching, but more research is needed about the formation and application of leadership knowledge and skills as they relate to supporting teacher professional learning. As a starting point, Bitto (2015) frames the requisite knowledge of the mathematics specialist by extending the MKT framework (Ball et al., 2008) to include leadership knowledge and skills as connected to a mathematics specialist’s mathematical and pedagogical knowledge.

Research including mathematics specialists also encompasses the systems in which they work and their influence on those systems. For instance, Campbell and Malkus (2011) investigated the impact of a mathematics specialist on student achievement. Sun et al. (2014) examined the influence of a coach in a school on other teachers’ mathematics knowledge for teaching. Harbour (2015) examined the impact of full-time versus part-time mathematics specialists. Such studies have the potential to help define or address policies related to mathematics specialists’ assignments and their related responsibilities in schools and districts. Thus, there is a need to do more of this type of work to advance what we know about mathematics specialists and the ways in which their positions influence school stakeholders. This research also has implications for the design of studies of the work of mathematics specialists, which could include longitudinal studies, methodological decisions, and the description of the coach’s role in an investigation/project (Hjalmarson & Baker, 2020).

Dimensions of Mathematics Specialist Research Illuminated within This Special Issue

Both the articles included within this special issue and prior research surrounding mathematics specialists can generally be positioned along three different dimensions that describe the scope of the study. The first dimension is grade level. Rigelman and Lewis’s (2023) study is an example of work that spans K-12, while Elliott and Lesseig’s (2023) work focuses on a specific grade band (6–8). The second dimension is the level of influence the study is investigating on mathematics specialists: district level (Jarry-Shore et al., 2023), school level, and classroom level (Elliott & Lesseig, 2023; Gibbons & Okun, 2023; Swars Auslander et al., 2023). The final dimension is the unit of the mathematics specialist activity in the study: cross-grade level small groups (e.g., PLCs), within-grade level, individual teachers, or the whole school community (potentially including families and caregivers). For example, Elliott and Lesseig (2023) study a community of practice model, while Gibbons and Okun (2023) explores individual coaching practices. Swars Auslander et al. (2023) includes teacher leadership that extends to the wider school community.

For the purpose of this special issue, we intentionally selected manuscripts that represented different positions on these dimensions to emphasize the wide scope and range of work that research about mathematics specialists might include. Historically, research focused on one aspect of mathematics specialist practice (e.g., working with a PLC or individual coaching), when in reality mathematics specialists have varied responsibilities across the different audiences they must attend to. Thus, we would like to emphasize that the work of the mathematics specialists represented within each of the special issue articles may not be all-encompassing. We see these practices as a set of options from which mathematics specialists may choose depending on the needs of their context while not suggesting that any one practice is more important or valuable than any other. One area where there is a need for research is in helping coaches and school leaders, and others map practices onto goals and objectives in the school context (e.g., determining instructional areas of focus for grade-level teams and developing school-level intervention programs). This flexibility is a feature and advantage of mathematics specialists’ role in schools, but it is also an ongoing complexity. Cobb and colleagues (2018) point to a need for coherence in efforts to support and improve mathematics teaching and learning. Mathematics specialists have a significant role to play in supporting that coherence.

Encouraging Directions Within & Beyond This Special Issue

In selecting articles for this special issue, we aimed to prioritize research that was innovative and would advance the field by providing new directions for mathematics specialist research. The initial description of the issue sought articles that addressed a variety of questions, issues, and topics related to mathematics specialists and mathematics teacher leaders including: 1) the selection and preparation of mathematics specialists; 2) supporting and sustaining the role of the mathematics specialist; 3) the influence and impact of mathematics specialists; and 4) mathematics specialists’ professional learning. With nearly 40 proposals initially submitted for consideration and 24 manuscripts received, we were encouraged by the large response to the call for this special issue. The response provides a signal that the field of mathematics education is taking the work of mathematics specialists seriously, as an important and valued component of ongoing teacher professional learning, school change, and the continuing need for attention to equity and culturally relevant teaching and learning environments. Ultimately, five manuscripts were accepted after peer and editorial review, which resulted in an acceptance rate of 21% for the special issue.

Each of the five articles for this special issue on mathematics specialists and mathematics teacher leaders represents an underexplored concept or new direction for future mathematics specialist research and practice. Whether a new framework (Elliott & Lesseig, 2023), preparation model (Swars Auslander et al., 2023), or coaching tool (Gibbons & Okun, 2023) or an initial foray into exploring mathematics specialist work across the K-12 continuum Jarry-Shore et al., 2023, these five articles extend what is known and offer insight into future opportunities for research and practice. For example, Rigelman and Lewis’s (2023) longitudinal study offers a unique model for researching mathematics specialists (i.e., mathematics coaches and classroom-based teacher leaders) that draws on both observational data from practice in addition to student achievement scores. This not only extends the limited research connecting leadership actions to student learning but also speaks to the influence and impact of K-12 mathematics specialists.

Swars Auslander and colleagues (2023) also speaks to multiple positions of mathematics specialists (i.e., mathematics coach and teacher leader) as they investigate the preparation and professional learning of mathematics specialists during the first year of a formal, university-based mathematics specialist program. Through a mixed methods approach, Swars Auslander and colleagues illuminate the influence of mathematics specialists’ leadership activities and explore the constraints and the agency fostered within the program. Importantly, this research intentionally supports a diverse group of elementary mathematics specialists who work in schools that serve students who have been historically marginalized and underserved in mathematics education.

Jarry-Shore et al.’s (2023) article speaks to the role of a variety of district-level mathematics specialist positions (e.g., coach and content specialist) in sustaining and adapting teacher leadership professional learning. Specifically, they investigate how district-level mathematics specialists build on researcher models of system-wide professional learning to integrate district initiatives, experiences, and specialized knowledge. They provide an authentic and honest analysis of what happens to a professional learning model once it is implemented and after the researchers are gone and address considerations and decisions that are made at the district level to ensure coherence with other district initiatives while simultaneously building capacity in others. This perspective adds to the limited literature on district-level mathematics specialists and launches a conversation on the role of district-level mathematics specialists in research–practice partnerships.

Elliott and Lesseig (2023) use the classroom design and analytic framework of Productive Disciplinary Engagement (PDE) to examine the work of 73 mathematics specialists (i.e., school or district mathematics teacher leaders) in professional learning. The authors’ use of the PDE framework reveals facilitator practices that support and hinder Productive Disciplinary Engagement. Like the authors, we feel strongly that adapting frameworks such as PDE can provide valuable insight for both future mathematics specialist research and practice, as well as teacher professional learning, more broadly.

Extending the research on individual coach–teacher interactions via coaching cycles, Gibbons and Okun’s (2023) research examines a mathematics specialist (i.e., coach) and classroom teachers’ interactions with students. Specifically, the teacher and coach duo use Teacher Time Outs (TTO) within a Math Lab to create opportunities for professional learning interactions that deepen mathematics content and pedagogical knowledge. In this manner, Gibbons and Okun illuminates that professional learning should be situated in contexts where teachers can engage in in-the-moment implementations and adaptations of their practice to promote and advocate for ambitious and equitable teaching.

The totality of these five articles not only validates the importance of mathematics specialists but extends the current literature by providing possibilities of future research. The issues surrounding mathematics specialists and mathematics teacher leaders are complex and hard to examine due to the varied position titles, responsibilities, and support provided. It is essential for us as researchers to account for and describe these different skill sets, responsibilities, and contexts so that we as a field can begin to understand the nuances of not only these individuals and their professional learning needs but also the impact and influence they have on others within K-12 settings. It is for those reasons that it is important for research to illuminate both productive and unproductive practices so that the field as a whole can improve.

Beyond this special issue, there are also tremendous implications for the field based on the lack of proposals received in certain areas. For instance, we did not receive many proposals about equity, which is surprising as it is essential to know how leadership efforts in mathematics education can support equity work (Marshall & Buenrostro, 2021). What is the professional learning required to advance ambitious and equitable instruction? We were also surprised by the lack of proposals on policy considerations and decision-making. How does a state, a school system, or a school decide that there is a need for mathematics specialists and how best to structure their positions? What influences such decision-making? How are mathematics specialist programs developed, monitored, and assessed? While Rigelman and Lewis’s (2023) research highlights the evidence of change one might look for, as a field we need to know the impact of these specialists that allows one to continue to fund and support mathematics specialist positions. If we are unable to define a mathematics specialist’s impact, how can the field move forward?

Furthermore, there is still a limited understanding and discussion around leadership and mathematics specialists. The field of mathematics education should be asking questions about a mathematics specialist’s enactment of leadership. What do we mean by leadership knowledge and skills? How do we know this is happening? How can we support the development and acquisition of leadership knowledge that will advance efforts for ambitious and equitable teaching? Too often the field emphasizes mathematics content knowledge over leadership knowledge. However, we are at a point where we recognize that more is needed for mathematics specialists than additional content courses, and it is not enough to be “appointed or anointed” to a mathematics specialist position at any level simply because one is “good at math” (Fennell, 2017, p. 9). However, what does this enactment of leadership look like across the span of a mathematics specialist’s career? What are the elements of leadership that make them successful in different school and district contexts?

There is also a need to move the field away from coaching cycles as the sole model of mathematics specialist work as this model is costly (Knight, 2012). This is not to say that coaching cycles do not have value or place in educational reform. This work is important and should be one of the many models available when bringing instructional change to scale. However, as a field, we must consider both the fiscal and contextual reality of K-12 settings in addition to the opportunities that are provided (or limited) by this model of professional learning. For example, who determines who the mathematics specialist collaborates with (e.g., mathematics specialist, principal, and district-leader)? What are the criteria for gaining access to a mathematics specialist (e.g., exemplar teacher, willingness of teacher, and teacher on probation)? Does the specialist have time to meet with teachers in this way? Each of these decisions is critical in nature in that they are providing opportunity for some but not all educators within a school to access professional learning.

We are encouraged that researchers are asking deeper questions about the work of mathematics teacher leadership. While work around the roles and responsibilities of mathematics specialists is important, there are significant questions the field of mathematics education must ask about mathematics specialists to not only better support teacher professional learning but also bring initiatives around ambitious and equitable teaching to scale. If we are to truly transform mathematics education as we strive toward ambitious and equitable teaching, we need to consider ways to engage entire school communities with professional learning and create a “toolbox” of strategies for mathematics specialists to draw upon depending on their context and audience needs. If part of a cohesive and coherent program for the professional learning of mathematics specialists, then each of these tools can be utilized in conjunction with one another to address the challenge of building capacity across school contexts.

We also see potential for mathematics education research to engage with school and district partners in deeper, more meaningful ways if mathematics specialists are involved in the work of research. There have been long-standing needs to develop and sustain partnerships that both help mathematics education researchers learn about what is happening in schools and that help schools learn about mathematics education research. We see a potential way forward for mathematics specialists and teacher leaders to help bridge this gap between research and practice.

Acknowledgments

We wish to thank the following 14 individuals that served as external peer reviewers for this special issue: Robert Berry, Laura Bitto, Johnna Bolyard, Cynthia Callard, Jeffrey Choppin, Ryan Gillespie, Kristin Harbour, Melinda Knapp, Beth Kobett, Paula Jakopovic, Erin Lehmann, Denise Spangler, John Staley, and Corey Webel. Each reviewer was intentionally selected for the specialized knowledge they possess regarding mathematics specialists and mathematics teacher leadership. Without their time and expertise, this special issue would not have been possible. We also thank the editors of IML, especially Jonathan Bostic, for their support and encouragement.

Disclosure Statement

This material is based upon work completed by Margret Hjalmarson while serving at the National Science Foundation. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.