Received: 9 June 2021
|
Revised: 30 September 2021
DOI: 10.1111/ssm.12507 |
Accepted: 18 October 2021
R E S E A R C H PA P E R – ­ M AT H E M AT I C S E D U C AT I O N
Trends in mathematics specialist literature: Analyzing
research spanning four decades
Courtney K. Baker1
| Evthokia Stephanie Saclarides2 | Kristin E. Harbour3
Margret A. Hjalmarson4
| Stefanie D. Livers5 | Katherine Comey Edwards4
1
College of Education and Human
Development, Mathematics Education
Leadership, George Mason University,
Fairfax, Virginia, USA
2
College of Education, Criminal Justice
and Human Services, University of
Cincinnati, Cincinnati, Ohio, USA
3
College of Education, Department of
Instruction and Teacher Education,
University of South Carolina,
Columbia, South Carolina, USA
4
College of Education and Human
Development, Mathematics Education
Leadership, George Mason University,
Fairfax, Virginia, USA
5
College of Education, Childhood
Education & Family Studies, Missouri
State University, Springfield, Missouri,
USA
Correspondence
Courtney K. Baker, Mathematics
Education Leadership, George Mason
University, Fairfax, Virginia, USA.
Email: cbaker@gmu.edu
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1
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Abstract
For the past forty years, United States school districts have increasingly hired
mathematics specialists to support the teaching and learning of mathematics.
Despite the prevalence of this professional development structure, this is a relatively new research topic for the mathematics education field. In this paper, we
report findings from an exploration of literature between 1981 and 2018 to examine the role of mathematics specialists (MSs). In particular, we examine: (a)
MS positioning across research; (b) historical trends of school-­based MS research;
and (c) orientations of school-­based MSs within research. Using the McGatha
and Rigelman framework as an analytic lens, we found that beyond the positions
identified in their framework (coach, intervention specialist, teacher), there were
four additional MS positionings within the research (learner, other p-­12 stakeholder, university stakeholder, unknown). Ultimately, we forward an expansion
to the McGatha and Rigelman framework to include these new categories, as well
as contextual descriptions and working definitions to support future research in
more accurately and robustly capturing the ways in which MSs are investigated
and reported on in research.
KEYWORDS
math/math education, professional development < teachers and teaching, teacher education <
teachers and teaching, teachers and teaching
I N T RO DU CT ION
Mathematics education reformers have long called for
improved learning opportunities for all students across
P-­12 classrooms in the United States (U.S.). Although
instruction that promotes mathematics as sensemaking
and problem solving has been recommended (National
Council of Teachers of Mathematics [NCTM], 2000;
National Research Council [NRC], 1989), this shift
dramatically differs from the way many classroom teachers once learned and taught math (Hiebert, 1999). Thus,
local school systems are left to determine how to create
conditions that support changes in teachers’ instruction
(Hopkins et al., 2013). To address this challenge, many
schools hire mathematics specialists (MSs) as they embody key features of effective professional development
(PD; Gibbons & Cobb, 2017). Multiple models of PD (lesson study, professional learning communities [PLCs],
This is an open access article under the terms of the Creat​ive Commo​ns Attri​butio​n-­NonCo​mmerc​ial-­NoDerivs License, which permits use and distribution in any
medium, provided the original work is properly cited, the use is non-­commercial and no modifications or adaptations are made.
© 2021 The Authors. School Science and Mathematics published by Wiley Periodicals LLC on behalf of School Science and Mathematics Association
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wileyonlinelibrary.com/journal/ssm

Sch. Sci. Math. 2022;122:24–35.
math labs) often include a MS as a facilitator. For instance,
a MS might be assigned at a school to work with all first-­
grade teachers in a PLC to provide additional knowledge
and expertise in mathematics. The result of these professional learning structures is that MSs have become fixtures in U.S. schools (Fennell, 2017).
Despite the rapid spread of MS positions, research has
not caught up to practice as MSs are under-­investigated
in research (e.g., Herbst et al., 2021; Hjalmarson &
Baker, 2020). This is surprising as NCTM recommended
state certifications provide credentials for MSs in 1981
(Fennell, 2017), and there have been four decades of additional policy recommendations and initiatives since (e.g.,
Association of Mathematics Teacher Educators [AMTE],
2013b). Hence, there is an urgency for the mathematics
education field to better understand research surrounding effective MS implementation. This article aims to illuminate policy and practice surrounding MSs so that
other mathematics education researchers can build upon
and advance this work. The following research questions
guided our exploration of peer-­reviewed research articles
between 1981 and 2018: (a) How are MSs positioned?
(b) What are the historical publication trends for school-­
based MSs? and (c) What is the prevalence and emphasis
of school-­based MSs?
2
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G UI DI N G LIT E R AT U R E
Mathematics specialists work in various leadership roles
to advance the teaching and learning of mathematics
(McGatha & Rigelman, 2017), and they embody tenets
of high-­quality PD by providing teachers ongoing, focused, and interactive learning experiences (Gibbons &
Cobb, 2017). Research points to the positive influence MSs
have on teachers (Gibbons et al., 2017; Polly, 2012) and
students (Campbell & Malkus, 2011; Harbour et al., 2021).
MSs are not only positioned to “significantly influence
curriculum, assessment and PD decisions” (NCTM, 2020,
p. 125), but also to support, inform, and model a culture
of equitable mathematics so that each student can access
effective teaching practices with high-­quality curriculum
and challenging instruction (NCTM, 2014).
2.1
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Defining MSs
Using knowledge of best practice regarding PD, many U.S.
school districts have created MS positions to meet the demands of high stakes accountability and support teachers
in providing quality mathematics instruction to all students (McGatha & Rigelman, 2017). MSs lead PD within
the context of teaching and learning, rather than the
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25
traditional “sit and get” approach. The roles and responsibilities of MSs are complex and ever-­evolving. Because
the term MS has different interpretations depending on
location, mathematics specialists’ work is diverse and can
include administrative tasks, instructional tasks, PD tasks,
and data analysis.
To situate our work, we draw upon McGatha and
Rigelman’s (2017) definition of MS: “a professional with
an advanced certification as a mathematics instructional
leader or who works in such a leadership role” (p. xiv).
With MSs positioned in the broad role of instructional
leaders, McGatha and Rigelman (2017) subsequently categorized MSs into three additional positions: (a) mathematics teacher; (b) mathematics intervention specialist; and
(c) mathematics coach. Defining characteristics of these
roles broadly rely on who the instructional leader works
with for the majority of their time, with teachers and intervention specialists typically working with students and
coaches typically working with teachers. McGatha and
Rigelman (2017), along with other researchers (e.g., Chval
et al., 2010), acknowledge that while they have situated
MSs into these roles, the lines between these titles are
blurred.
Although MSs who are positioned as teachers and intervention specialists primarily work with students, these
roles have distinct characteristics. A MS as a teacher is
“a professional who teaches mathematics to students,”
whereas a MS as an intervention specialist is “a professional who works with students in a ‘pull-­out’ or ‘push
in’ intervention program” (McGatha & Rigelman, 2017,
p. xiv). On the other hand, a MS as a coach is defined
as “a professional who primarily works with teachers”
(McGatha & Rigelman, 2017, p. xiv). Depending on the
context, MSs as coaches may engage in different models
of support for teachers, including: (a) working with individuals or pairs of teachers (Barlow et al., 2014), (b) working with teacher groups (Lesseig et al., 2017), and/or (c)
working at the whole school-­level (Campbell et al., 2013;
McGatha & Rigelman, 2017). Regardless of the positioning, to provide these differing types of support, MSs need
the necessary expertise in mathematics content and pedagogy, as well as leadership skills (AMTE, 2013a; NCTM,
2012) as they work to enhance the teaching and learning
of mathematics.
2.2 | MS key historical events and calls
to action
The use of MSs to support the teaching and learning of
mathematics is not new. Drawing upon Fennell’s (2017)
work discussing MS policy recommendations from a
historical perspective, we note key events that have
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influenced the development and use of MSs across the
United States.
The 1970s saw the emergence of projects that focused on creating positions for MSs (e.g., Developing
Mathematics Enthusiasts project, Fennell, 1978). Across
these projects, school-­level MSs were identified and employed as mentors to provide content-­specific support to
other teachers and school stakeholders. In the decade
that followed, Fennell notes three key events which
underscored the importance of these newly created
positions: (a) the NCTM recommended state certification endorsement for elementary MSs, (b) John Dossey
(1984), the acting NCTM president during this time,
published a call for MSs, and (c) the NRC’s Everybody
Counts (1989) report expressed the need for elementary
MSs. The fact that these three national events occurred
within such a short time frame highlights the urgency
and significance of implementing highly competent and
prepared MSs in schools.
The 1990s were marked by a lull in policy and events
related to MSs. However, a resurgence of interest in MS
policies and events occurred in the early 2000s. Fennell
(2017) highlights nine key milestones (p. 6) during this
time, including the NCTM’s Principles and Standards
for School Mathematics (2000), the NRC’s Adding it Up
(2001), and the National Mathematics Advisory Panel
(2008) documents all making recommendations related
to MSs support the teaching and learning of mathematics. Additionally, during this time, national legislation—­
centering on No Child Left Behind (2001) and followed
by the Every Student Succeeds Act (2015) prompted the
creation of MSs to address the push for assessment and
accountability in mathematics.
In the 2010s, the call for MSs continued to advance.
The AMTE released the Standards for Elementary
Mathematics Specialists: A Reference for Teacher
Credentials and Degree Programs in 2010 (AMTE; revised in 2013). That same year, a joint position statement calling for all elementary schools to have access
to MSs was released by AMTE, the Association of State
Supervisors of Mathematics (ASSM), the National
Council of Supervisors of Mathematics (NCSM), and
NCTM. Building upon AMTE’s standards, NCTM/
CAEP released the Elementary Mathematics Specialist
Standards (NCTM, 2012), with both sets of standards
used by many preparation programs across the country. Later in the 2010s, we see MSs referenced in Linda
Gojak's NCTM president's message (2013), as well as an
AMTE research conference focused on elementary MSs
in 2015. When looked at as a whole, this timeline overview illustrates how the call for MSs has persisted for
decades and continues to be at the forefront of research,
policy, and organizational recommendations.
3
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METHOD
Below we outline the systematic procedure we used to investigate the research related to MSs across the literature
between the years 1981–­2018. Additionally, we describe
the methodological parameters of our data identification
and analysis. We note that this work is an extension of
a pilot study in which we began to explore this phenomenon in published conference proceedings (Saclarides
et al., 2020) to better understand the extent to which the
findings played out in the larger research landscape.
3.1
|
Data identification
We draw on the comprehensive sequence of steps set
forth by Cooper et al. (2019) to achieve a high-­quality literature synthesis (Sandelowski & Barroso, 2007) with the
ultimate goal of informing research and practice. MS positions have been implemented in U.S. schools for nearly
four decades, and yet this is a “relatively new research
topic for our field” (Herbst et al., 2021, p. 255). Given that
research has not caught up to practice and funding MS
positions is rather expensive (Knight, 2012), an analysis of
MS literature is warranted.
To explore this phenomenon, we needed to define
the variable being studied, MSs, so that we could identify relevant and irrelevant studies (Cooper et al., 2019).
To define the conditions under which the phenomenon
we wanted to study occurs, we drew from both McGatha
and Rigelman’s (2017) framework and our diverse experiences with MSs. This lens provided us with a broader
perspective of the landscape that allowed us to capture
relevant literature. For instance, we knew many MSs are
“appointed or anointed” (Fennell, 2017, p. 9) to formal and
informal leadership positions, so describing only the experiences of MSs with advanced certification or professional
preparation excluded many specialists already engaged in
the work. We also recognized that teacher leadership and
teacher professional learning are not new phenomena. As
a result, past literature that may have captured MSs as hidden players (Hjalmarson & Baker, 2020) would be essential to examine.
In searching the literature, our goal was to conduct a
comprehensive search beyond the term “mathematics
teacher leader.” We also wanted to leave an audit trail so
that our work could be reproduced (Cooper et al., 2019).
To ensure our search maintained high recall and precision
(Sandelowski & Barroso, 2007), we compiled 11 search
terms to capture the nuanced ways MSs might be positioned in the literature (Figure 1). University librarians
provided vital assistance (Sandelowski & Barroso, 2007)
identifying these terms in each of these five bibliographic
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26
F I G U R E 1 Results of application and
inclusion criteria
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databases: (a) EBSCO Host; (b) Psych Info; (c) Education
Research Complete; (d) Science Direct; and (e) Social
Sciences Citation Index. Knowing there were multiple
variations of the word math to account for (e.g., mathematics, mathematical) and peer-­reviewed literature from
international perspectives, we applied rules of truncation and wildcard to account for spelling variations. We
limited literature publication dates to between 1981 and
2018. The lower date range was based on the call for MSs
from NCTM in 1981 (Dossey, 1984), a catalyzing event
noted by Fennell (2017), and the upper date range was
the last complete year of research available at the time.
Our initial search was targeted at maximizing the number of returned hits, which resulted in over 16,000 entries.
Many hits were not directly related to our central research
question (e.g., sports coaching, higher education) or only
mentioned mathematics achievement as a tangential outcome variable. We developed exclusion criteria to capture
a diverse body of literature while attending to the nuanced
ways MSs might appear within the literature.
We then created a shared matrix in Google Sheets with
citation information and links to each article. As we reviewed titles and abstracts, each article was assigned one
of the following preliminary codes which captured the
ways we hypothesize a MS could emerge: MS, PD, pre-­
service teacher (PST) and administrator (ADMIN). For
the purpose of this article, the analysis described includes
only the literature that was tagged with our preliminary
MS code, as these articles explicitly mentioned MSs within
the title or abstract. However, 63 of the 193 articles coded
with MS were eliminated, as upon a closer look within
the article they did not meet our criteria (see Figure 1).
Examples of excluded articles included those in which the
abstract mentioned “mathematics mentors” and the mentors were P-­12 student peer mentors or “mentoring” was
only mentioned in the implications. Ultimately, our entire
examination and application of our exclusion criteria left
us with 130 articles that we analyzed using our identified
MS positioning framework (McGatha & Rigelman, 2017).
3.2
|
Data analysis
Articles were analyzed in three distinct ways. First, we
applied the McGatha and Rigelman (2017) positioning framework (RQ1). We focused our next analyses on
school-­based MSs by determining the frequency of submissions for each year to examine historical trends (RQ2).
Finally, we examined the prevalence and emphasis of
school-­based MSs across the literature (RQ3).
3.2.1
|
MS positioning analysis
To fully attend to the nuanced and varied ways MSs are
positioned, we applied InVivo coding (Saldaña, 2021) to
capture the actual language used in the literature to describe researchers’ perceptions of the MS positioning. Our
primary code identified the population (in-­service teachers, PSTs) that the MS engaged with. A secondary code
captured the positioning of the MS (e.g., coach, mentor
teacher, classroom teacher) and a tertiary code provided
further specificity on the context (e.g., school-­based,
district-­based). This coding scheme resulted in 236 unique
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applications of codes across 130 articles, as some articles
included multiple MSs (e.g., Sun et al., 2014). However,
for the purpose of this analysis, we targeted the articles
in which MSs worked with in-­service teachers (154 instances; 16 codes). We then categorized the codes using
McGatha and Rigelman’s (2017) positions (coach, teacher
leader, interventionist). In some instances, the MS positioning was unaccounted for and new categorizations
were developed (e.g., researcher, learner). The complete
categorization of MS positioning is reported in the results
below.
T A B L E 1 Mathematics specialist positioning frequency in
research from 1981 to 2018
Categorization of MS positioning
Frequency
(%)
MS as coacha
73 (49%)
Instructional coach: District-­level
5 (3%)
Instructional coach: School-­level
9 (6%)
Mathematics coach: District-­level
8 (5%)
Mathematics coach: School-­level
36 (24%)
Organization
15 (10%)
MS as teachera
38 (25%)
Departmentalized mathematics teacher
3.2.2 | Historical trends of school-­based
MSs analysis
Teacher leader
To better understand the historical publication trends for
articles that were coded as “MS as Mathematics Coach:
School-­level”, we began by isolating the 36 unique articles that featured a school-­based mathematics coach, and
completed counts to determine the frequency of publications between our target dates of 1981–­2018. Next, we
generated a line graph to help illustrate publication trends
over time, as well as a double bar graph to explore coupling between publication trends and the implementation
of key national events (Fennell, 2017).
MS as learner
16 (11%)
MS as university stakeholder
15 (10%)
Researcher
11 (7%)
Teacher educator
4 (3%)
MS as other P-­12 stakeholder
1 (<1%)
Principal
1 (<1%)
Science coach
1 (<1%)
Technology teacher
1 (<1%)
Literacy coach
1 (<1%)
MS as unknown
2 (1%)
MS as intervention specialist
Two of the six authors labeled the 36 articles coded as “MS
as mathematics coach: School-­level” using three categories
to determine the prevalence and emphasis of MSs in the
literature: primary, secondary, and mention. “Primary”
indicated that the MS was central to the research focus
of the article. A code of “secondary” meant that a MS was
included in the peer-­reviewed article but was not the focus
of the research. The final category, “mention”, indicated
a coach or teacher leader was present within the paper;
however, beyond the noting of a MS, the data, research
questions, and/or findings did not describe/analyze their
work.
4
4.1
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R E S U LTS
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Research question 1: MS positioning
To better understand the nuanced ways MSs are positioned
in research, we examined a data corpus of 130 articles. We
found that beyond the positions identified in the McGatha
and Rigelman (2017) framework (MS as Teacher, MS as
5 (4%)
Librarian
a
3.2.3 | Prevalence and emphasis of school-­
based MSs analysis
2 (1%)
36 (24%)
0 (0%)
a
Denotes a categorization from McGatha and Rigelman (2017) framework.
Intervention Specialist, MS as Coach), there were four additional MS positionings: MS as Learner, MS as Other P-­12
Stakeholder, MS as University Stakeholder, and MS as
Unknown (see Table 1). Furthermore, we note that 74% of
the research articles were aligned with the McGatha and
Rigelman (2017) categories of MS positioning. We also
found that one specific McGatha and Rigelman (2017)
categorization (MS as Intervention Specialist) did not surface within the identified literature. In Table 1, we delineate each of the categories of MS positioning, as well as the
aligned sub codes and frequencies. Overall, MSs were most
frequently positioned as a Coach (n = 73) and Teacher
(n = 38), while the positionings of Learner (n = 16) and
University Stakeholder (n = 15) less frequently surfaced
in the data corpus. Below we describe each of the categories of MS positioning.
4.1.1
|
MS as coach
Mathematics specialists were most frequently positioned
as coaches across the data corpus (49%). Under this
broad category, we noted five different “MS as Coach”
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positionings (see Table 1 above). Using McGatha and
Rigelman’s (2017) definition as a starting point, we consider coaches to be professionals who primarily work
with teachers on issues related to instructional improvement. We also found that coaches were either instructional coaches who coached across all content areas
(e.g., Bengo, 2016), or mathematics-­focused coaches
who coached in only one content area (e.g., Campbell
& Malkus, 2011; Gibbons et al., 2017). These individuals typically had part-­ or full-­time release from teaching
responsibilities, were stationed at individual schools or
district offices, and were charged with supporting teaching and learning in one or multiple schools. Sometimes,
these coaches were part of an external organization whose
mission was to provide PD or coaching (e.g., Ancess et al.,
2007).
4.1.2
|
MS as teacher
Mathematics specialists were also frequently positioned
as teachers (25%), and more specifically, teacher leaders (24%). Individuals in this category were classroom
teachers who were tasked with providing high-­quality
professional learning opportunities to their peers while
maintaining a P-­12 classroom (e.g., Knapp, 2017). Less
frequently, these individuals were also positioned as a departmentalized mathematics teacher (1%), an elementary
classroom teacher who taught more than one section of
mathematics to students (e.g., Webel et al., 2018).
4.1.3
|
MS as learner
Some MSs were positioned as active learners across the literature (11%). Within this category, the MS was described
as actively learning within the context of the article, and
this was often part of the central research questions guiding the study. For example, the MS may have been specifically working toward a MS endorsement (e.g., Ellington
et al., 2012), or they were involved in a grant-­funded
project that afforded opportunities for coursework (e.g.,
Lesseig et al., 2017).
4.1.4
|
MS as other P-­12 stakeholder
To further speak to the nuanced ways in which MSs were
positioned in the extant research literature, we found that
MSs were also positioned as other stakeholders in P-­12 education settings (4%). In particular, these were individuals
who were stationed in P-­12 schools, and they had a vested
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29
interest in supporting teaching and learning. However,
in the context of the research article, these stakeholders
served in a coaching role supporting mathematics PD.
For example, this individual may have been a librarian
(e.g., Israel et al., 2015), literacy coach (e.g., Di Domenico
et al., 2018), principal (e.g., Garner et al., 2017), science
coach (e.g., Lotter et al., 2014), or technology teacher (e.g.,
Israel et al., 2015) who was supporting the teaching and
learning of mathematics.
4.1.5
|
MS as university stakeholder
Mathematics specialists were also positioned as university stakeholders at institutions of higher education (10%).
Within this broad category, the MS was most frequently
positioned (7%) as a university researcher or faculty member who served as a coach or mentor to in-­service teachers in school districts (e.g., Polly, 2012). Furthermore,
and within this category, the MS was also positioned as
a teacher educator or doctoral student (3%) who provided
mentoring to in-­service teachers, often in the context of
a methods or graduate-­level course, or in the field (e.g.,
Sanchez et al., 2015).
4.1.6
|
MS as unknown
Last, we noted a small subset of articles (1%) that received
the code of “MS as Unknown”. Within these articles, a MS
was present who worked with teachers and/or students on
issues related to instructional improvement (e.g., Noyes &
Sealey, 2011). However, insufficient information was provided to determine further categorization.
4.2 | Research question 2: Historical
publication trends of school-­based MSs
As previously discussed, we identified 36 unique studies
that were coded as “MS as Math Coach: School-­level”. For
this sub-­set of studies, we wanted to better understand
the historical publication trends for articles featuring a
school-­based mathematics coach, and the relationship to
MS events and/or policies. Overall, there was an increasing trend in publications featuring a school-­based mathematics coach (see Figure 2). Starting with the first national
event in 1981, when NCTM suggested that states provide a
teaching credential endorsement for mathematics teacher
leaders, there were a total of zero publications featuring a
school-­based mathematics coach. In 2019, after the implementation of 22 different national events for mathematics
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FIGURE 2
Overall publication trends for “MS as school-­based mathematics coach” from 1981 to 2018
teacher leaders (Fennell, 2017), there were a total of 36
publications featuring a school-­based mathematics coach.
This suggests that the research community has an increasing interest and focus on research involving school-­based
mathematics coaches.
Furthermore, in exploring trends by decade, we observe tight coupling between the number of publications
and number of key national events identified by Fennell
(2017). That is, during the decades of 1980–­1989 and 1990–­
1999, few publications about school-­based mathematics
coaches are observed, and few key events (Fennell, 2017)
occur (see Figure 3). However, in subsequent decades, a
different trend is observed. From 2000 to 2009, there was
an increased national attention on MSs with the implementation of nine key events (Fennell, 2017), as well as
enhanced interest in MSs from the research community
as evidenced by the identification of five publications.
From 2010 to 2019, this trend continues with 10 key events
(Fennell, 2017), and 34 publications.
Overall, this analysis seems to indicate that MS policies
and events at the national level are actively shaping MS
research agendas and publication. With regards to one of
the spikes in 2017, it is important to note that eight of the
nine articles which met our criteria came from a special
issue of the Journal of Mathematical Behavior focused on
MSs.
4.3 | Research question 3:
Prevalence and emphasis of school-­
based MSs
Within the school-­based mathematics coach literature,
there were 27 instances (70%) of the categorization “primary” which indicated that the MS was central to the research focus of the article. This included articles where the
questions, data, and findings were about MSs and their work
(e.g., Chval et al., 2010). The six (15%) instances of the categorization “secondary” indicated that a MS was included
within the article, but coaching was not the focus of the research. For example, a MS might be leading professional
learning and involved in supporting teachers, but the research was not about coaching itself (e.g., Campbell, 1996)
even if the article included information about coaching.
The final category, “mention”, occurred twice (5%). These
mentions or “cameo appearances” of MSs underscore the
presence of MSs in research and professional learning projects even if the studies were not analyzing their role.
19498594, 2022, 1, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/ssm.12507 by South Korea National Provision, Wiley Online Library on [28/08/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
30
FIGURE 3
Coupling of “MS as school-­based mathematics coach” publications and national events
FIGURE 4
Mathematics specialist positions, contextual descriptors and working definitions
5 | DI S C USSION AN D
I M P L I C AT I ON S
The overarching aim of this paper was to explore
and examine the research related to MSs to discover
|
31
patterns, commonalities, and trends that will inform future research directions, such as exploring mathematics
specialists’ impact on teaching and learning, while simultaneously deepening our own understanding of how
MSs are positioned across varied contexts. Ultimately,
19498594, 2022, 1, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/ssm.12507 by South Korea National Provision, Wiley Online Library on [28/08/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
BAKER et al.
|
our search resulted in 130 unique submissions that were
analyzed for MS positioning, historical publication trends,
and prevalence and emphasis. Overall, findings indicated
there was an upward trend in MS research influenced by
national policies and events. Our exploration also added
further evidence in support of the multiple ways in which
MSs are positioned (Hjalmarson & Baker, 2020; National
Mathematics Advisory Panel [NMAP], 2008). In fact, we
identified three MS positionings that were distinct from
McGatha and Rigelman’s (2017) framework. We note that
the research presented within this paper is only a small
slice of the work our team has initiated to examine mathematics specialists’ positionality within educational research studies as a whole.
The three categories of MS positions that emerged
speak to the wide-­spread variation in ways researchers
refer to MSs, and mathematics teacher leadership more
broadly. Although prior research has already suggested
that the field lacks a common definition for MSs (e.g.,
NMAP, 2008), this study adds further evidence in support
of this trend. Hence, future research should explore the
characterization of mathematics specialists’ work and
practice in order to compare different implementation
models, better describe MS roles within schools/districts
and their work with both teachers and students, and further develop mathematics specialists’ knowledge and
skills to better support preparation programs and other
ongoing professional learning experiences.
We propose an expansion to the McGatha and Rigelman
(2017) framework (see Figure 4) to include three additional
categories (university stakeholder, other P-­12 stakeholder,
learner), possible contextual descriptions and working
definitions to more accurately and robustly capture the
ways in which MSs are investigated and reported in research. McGatha and Rigelman's (2017) framework was
intended to provide “an overview of the work” in which
MSs engage in P-­12 settings (p. xiv). However, in our examination of the research, we found not only individuals
that aligned with the McGatha and Rigelman conceptualization of MSs, but also other individuals doing the work
of MSs but positioned differently. Thus, there is a need to
capture individuals doing the work of MSs in research despite their varied positions.
Frequently, we were unable to determine contextual
features of MSs based on the little detail that was provided within the articles. For instance, only a handful of
research articles identified if the MS was employed full-­
time or part-­time or hired to work with only one or multiple schools. Not including these details in MS research
is problematic for disseminating research, as MS positions vary across contexts. More specificity is required in
how we speak about and define MSs so that the field of
mathematics education can not only come to a common
BAKER et al.
understanding, but advance both policy and practice. We
recognize that additional categorizations of MS positioning might emerge and other researchers may build upon
our proposed model.
Furthermore, within our own MS-­focused research,
we have found challenges in how we speak about these
individuals depending on the journal outlet. At times, we
have used “mathematics specialist” (e.g., Hjalmarson &
Baker, 2020), “mathematics coach and/or specialist” (e.g.,
Baker et al., 2021), “mathematics teacher leader” (e.g.,
Baker & Galanti, 2017), or “mathematics coach” (e.g.,
Saclarides & Kane, 2021; Saclarides & Munson, 2021) to
describe the same population. We are fully immersed in
MS research and have found ourselves to be unintentionally perpetuating the complexities surrounding this work.
Thus, a primary implication for future research is the use
of common definitions and descriptions that can be explicitly stated within reporting.
Currently, we do not know which MS positions have
the most potential to support teaching and learning. For
instance, zero occurrences of peer-­reviewed articles focusing on “MSs as Interventionists” emerged in our analysis.
From our work with P-­12 schools, we know that these positions exist. However, additional investigation is required
to capture this work and develop research-­informed policy and practice.
Overall, we observed an increasing trend in the number of peer-­reviewed articles published between 1981
and 2018. Furthermore, in exploring trends by decade,
we observed tight coupling between the implementation
of key national events identified by Fennell (2017) and
the number of publications. The increase in MS research
is important to note, due to the growing profession and
increasing access to MS certification programs at institutions of higher education. The hiring of MSs and surrounding policies are superseding the research. Although
a relatively new research field (Herbst et al., 2021), over
the past 40 years there have been multiple calls for MS
positions to be implemented within P-­12 education (e.g.,
Dossey, 1984; Gojak, 2013).
We are encouraged by the number of studies focused
specifically on MSs and the increasing focus on their
work, knowledge, and roles as distinct from other roles
in schools. It is not surprising that research about MSs is
likely intertwined with studies of P-­12 teachers and administrators as their work is designed to include these
groups. However, in narrowing a list of thousands of articles down, we encountered questions about what to
eliminate and what articles to keep for our review. For
instance, eliminating an article that focused on nursing,
sports management or other non-­educational fields was
a clear methodological choice. However, some of our
elimination criteria were more complicated and brought
19498594, 2022, 1, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/ssm.12507 by South Korea National Provision, Wiley Online Library on [28/08/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
32
questions to the surface that we believe are essential for
other mathematics education researchers to consider. One
question we contemplated was grounded in the following
ambiguity: What is enough mathematics for a study to
be about mathematics teaching and learning? This may
not seem like a complex question, but it is complicated
when attempting a large synthesis study. The first aspect
is when mathematics achievement is used as a student
outcome but the abstract does not include discussions
of mathematics-­focused interventions. Such studies may
provide other academic support for students, but are not
focused on mathematics specifically. A second type of
ambiguity occurred when it was not clear the PD experience within the literature was focused on teaching in a
mathematics context. We felt only having a mathematics
outcome variable was insufficient for inclusion when the
intervention was focused on other aspects of teaching and
learning.
The second question contemplated was: How similar
or different is the role of a MS in preparing in-­service
teachers from the role of a mathematics teacher educator preparing PSTs? Although not mentioned within
this analysis, a collection of studies emerged that focused on mentors of PSTs. While MSs may provide individual support to teachers in multiple positions (e.g.,
coach, teacher, university stakeholder), mentoring a PST
may have different features of professional learning that
are unique to preparation and licensure. Both MSs and
mathematics teacher educators may fall broadly under
a category of mentoring, and we propose an analysis of
mentoring PSTs needs to be conducted independently
from other types of coaching or peer mentoring that are
centered on in-­service teachers.
Regarding the third research question, we note considerations for improving the abstract of a peer-­reviewed
article. In narrowing our list of articles down to 130, we
based our decision-­making and criteria on the abstract
and title investigating some aspect of MS work. However,
there are hundreds more that do not mention that role in
the abstract. This supports our claim that MSs continue
to be “hidden players” (Hjalmarson & Baker, 2020) in the
MS research. “Hidden” in the present synthesis means
that in studies of PD, the role of the person who might be
facilitating the PD continues to be unmentioned or vague.
The second consideration involves the need for more
comprehensive, clear, or structured abstracts (Kelly &
Yin, 2007) that describe the major aspects of studies (e.g.,
questions, research design, participants). Some journals
already require such abstracts (e.g., Journal of Engineering
Education). In terms of stakeholders or participants in
teacher PD studies, abstracts within the field of mathematics education could include more about the facilitators
of such experiences.
|
33
DISCLAIMER
This material is based upon work completed while
Margret Hjalmarson was serving as Program Officer 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.
ORCID
Courtney K. Baker https://orcid.
org/0000-0002-3241-5505
Evthokia Stephanie Saclarides https://orcid.
org/0000-0002-9203-3998
Kristin E. Harbour https://orcid.
org/0000-0002-7311-3167
Margret A. Hjalmarson https://orcid.
org/0000-0001-8609-1596
Stefanie D. Livers https://orcid.
org/0000-0003-0321-1391
Katherine Comey Edwards https://orcid.
org/0000-0003-4025-1157
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BAKER et al.
Investigations in Mathematics Learning
ISSN: (Print) (Online) Journal homepage: https://www.tandfonline.com/loi/uiml20
Advancing Research about Mathematics
Specialists and Mathematics Teacher Leaders
Courtney Baker, Margret Hjalmarson & Francis Fennell
To cite this article: Courtney Baker, Margret Hjalmarson & Francis Fennell (2023) Advancing
Research about Mathematics Specialists and Mathematics Teacher Leaders, Investigations in
Mathematics Learning, 15:1, 1-10, DOI: 10.1080/19477503.2022.2154061
To link to this article: https://doi.org/10.1080/19477503.2022.2154061
Published online: 06 Apr 2023.
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INVESTIGATIONS IN MATHEMATICS LEARNING
2023, VOL. 15, NO. 1, 1–10
https://doi.org/10.1080/19477503.2022.2154061
EDITORIAL PERSPECTIVE
Advancing Research about Mathematics Specialists and
Mathematics Teacher Leaders
Courtney Baker
a
, Margret Hjalmarson
b
, and Francis Fennell
c
a
College of Education and Human Development, George Mason University, Fairfax, VA USA; bNational Science
Foundation, Alexandria, VA USA; cEducation Department, McDaniel College, Westminster, MD USA
KEYWORDS Mathematics specialist; mathematics teacher leader; teacher leadership; mathematics coaching; professional develop­
ment; 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 underinvestigated (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 mathe­
matics 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
CONTACT Courtney Baker
cbaker@gmu.edu
© 2023 Research Council on Mathematics Learning
George Mason University, 4400 University Drive MS IE8 Fairfax, VA USA
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C. BAKER ET AL.
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 partner­
ships rely on a close connection between schools, districts, and researchers. Additionally, the sustain­
ability 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 connect­
ing 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,
INVESTIGATIONS IN MATHEMATICS LEARNING
3
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 under­
stand 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), contentfocused 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
4
C. BAKER ET AL.
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 responsi­
bilities 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 care­
givers). 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 mathe­
matics specialist practice (e.g., working with a PLC or individual coaching), when in reality mathe­
matics 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
INVESTIGATIONS IN MATHEMATICS LEARNING
5
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 descrip­
tion 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 districtlevel 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
6
C. BAKER ET AL.
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 mathe­
matics 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 mathe­
matics 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 knowl­
edge 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
INVESTIGATIONS IN MATHEMATICS LEARNING
7
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 mathe­
matics 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 leader­
ship. 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.
ORCID
Courtney Baker
http://orcid.org/0000-0002-3241-5505
Margret Hjalmarson
http://orcid.org/0000-0001-8609-1596
Francis Fennell
http://orcid.org/0000-0002-7944-4581
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Investigations in Mathematics Learning
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Leveraging Mathematics Teacher Leaders in
Support of Student and Teacher Learning
Nicole Rigelman & Chandra Lewis
To cite this article: Nicole Rigelman & Chandra Lewis (2023) Leveraging Mathematics Teacher
Leaders in Support of Student and Teacher Learning, Investigations in Mathematics Learning,
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INVESTIGATIONS IN MATHEMATICS LEARNING
2023, VOL. 15, NO. 1, 85–102
https://doi.org/10.1080/19477503.2022.2140989
Leveraging Mathematics Teacher Leaders in Support of Student
and Teacher Learning
Nicole Rigelman
a
and Chandra Lewisb
a
Department of Curriculum and Instruction, Portland State University, Portland, Oregon, USA; bRMC Research
Corporation, Portland, Oregon, USA
ABSTRACT
KEYWORDS
Transforming mathematics learning and teaching toward more equitable
and effective approaches is critical to student mathematics learning and
identity development. This task at-scale in a district takes time, commitment,
and mathematics expertise that may not be widespread in the absence of
focused professional development. District and regional mathematics lea­
ders with university mathematics and mathematics education faculty part­
nered to address this challenge by designing a professional development
program that prepared K-12 teachers of mathematics as leaders at the class­
room, school, and district level. Described are specific aspects of
a professional learning model focused on developing mathematics content,
pedagogical, and leadership knowledge and skills. Also provided are findings
related to the impact of the project’s professional development on shifts in
instructional practice and student achievement.
Mathematics specialists;
teacher leaders; coaches;
professional development;
teacher learning; student
learning
Introduction
As schools and districts aspire to transform the teaching of mathematics to be problem-based and
discourse-rich, many turn to using mathematics specialists to support instructional shifts (National
Council of Teachers of Mathematics, 2014). Because having a mathematics specialist who serves as
a coach, working with adults, is an added expense for schools and often removes highly skilled teachers
from their work with students, examining the influence and impact of both mathematics coaches and
classroom-based teacher leaders is critical. An NCTM research brief detailed 24 research studies of
mathematics coaches (McGatha et al., 2015). Across the studies, researchers saw improvements in teaching
practices connected to the focus of the professional learning (e.g., questioning, mathematical discourse,
student engagement, conceptual understanding, formative assessment); however, there were only six
studies that examined student achievement. At present, there is minimal research on how mathematics
specialists that remain at least partially in the classroom can support improved teaching practice across
a school and on how both types of specialists can positively influence student achievement.
An examination of the student achievement literature pertaining to mathematics specialists (MSs)
revealed that almost all the studies examined student achievement at either the elementary or middle
grades, and most of the research focuses on the impact of mathematics specialists in a coaching role
(Balfanz et al., 2006; Brosnan & Erchick, 2010; Campbell et al., 2017; Campbell & Malkus, 2013; Coniam,
2010) rather than as classroom teachers (Meyers & Harris, 2008; Nickerson, 2010; Zollinger et al., 2010).
When studying the impact of mathematics specialists on student achievement, the research designs
typically included either school level (Brosnan & Erchick, 2010; Nickerson, 2010; Zollinger et al., 2010) or
student level data on state administered assessments (Balfanz et al., 2006; Campbell et al., 2017; Coniam,
2010; Meyers & Harris, 2008). Of the six studies that included student level data, one was limited by
CONTACT Nicole Rigelman
rigelman@pdx.edu
© 2022 Research Council on Mathematics Learning
PO Box 751 Portland Oregon, Portland, Oregon 97207-0751
86
N. RIGELMAN AND C. LEWIS
a small student sample size (Coniam, 2010), another was unable to obtain true baseline data (Campbell
et al., 2017), and only one reported specifically on closing the achievement gap among subgroups
(Balfanz, MacIver, & Byrnes, 2006). One study (Meyers & Harris, 2008) revealed that students who
were in schools with more than one mathematics specialist experienced significantly greater gains than
students in schools with only one mathematics specialist. Studies by Campbell and Malkus (2013) &
(2017)) indicated that increases in student achievement were often not seen within a year of treatment
but that several years were needed to see a significant impact on student achievement.
The present study focuses on the preparation, influence, and impact of well-prepared mathematics
teacher leaders (MTLs) by providing evidence of their content and pedagogical knowledge growth,
their use of research-proven teaching practices in their classrooms, and the achievement of their
students. The 3-year East Metro Mathematics Leadership (EaMML) Math-Science Partnership project
was a collaboration among David Douglas School District (District 1), Centennial School District
(District 2), the Multnomah Education Service District, Portland State University, and RMC Research.
The EaMML districts sought to develop district-wide mathematics leadership teams (MLTeams)
representing every school in the districts, and including individuals serving a variety of roles: teachers,
elementary instructional coaches, principals, and district mathematics leaders. These teams would
engage in deepening their mathematics content, pedagogical, and leadership knowledge and skills to
better serve students in their schools. A subset of the MLTeam members were also mathematics
leadership cadre (MLC) members who, in addition to leading through their roles as teachers, coaches,
or administrators, were charged with disseminating their learning by providing professional learning
for non-EaMML teachers at the grade, course, school, or district level.
There are several unique features of the EaMML project that add to the research base. One unique
feature of the EaMML project is the K-12 representation of math specialists engaging in both acrossthe-grades and within-grade-band professional learning. The math specialists included both formal
(i.e., coaches) and informal leaders (i.e., elementary teachers teaching all subjects as well as middleand high-school mathematics teachers). A second unique feature is studying the preparation and
positioning of classroom teachers as mathematics leaders, as most of the research focuses on mathe­
matics specialists as coaches. Few studies examine the impact of classroom-based mathematics
specialists on student achievement. Not only did the EaMML project utilize student-level state
assessment data in a rigorous quasi-experimental design, but the project also examined data across
elementary and middle school (grades 3–7) and from an equity perspective, investigating if student
achievement gains were experienced consistently across gender, race, ethnicity, and socio-economic
status. Finally, to provide more information about translation of teacher learning to instructional
practice, the EaMML project collected pre-post, K-12 teacher-level artifact and observation data.
While several studies include observation data, there were no studies that also included artifacts.
Research Questions
EaMML’s research questions focus on the project’s impact on both the MTLs and their students.
RQ1: What was the influence of EaMML professional development on MTL mathematical content
knowledge, pedagogical knowledge, and leadership knowledge and skills?
RQ2: To what extent has the EaMML project increased the school and district capacity to provide
mathematics professional development?
RQ3: To what extent did EaMML MTLs use research-proven instructional practices that develop
deeper student understanding of mathematics in their classrooms?
RQ4: Did students who had an EaMML MTL demonstrate higher achievement on state assessments
than students who did not have an EaMML MTL?
INVESTIGATIONS IN MATHEMATICS LEARNING
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Table 1. EaMML leadership types.
Leadership Type
Project Leadership
(n = 8)
Mathematics Leadership
Team (MLT)
(n = 94)
Mathematics Leadership
Cadre (MLC)
(n = 29)
Description
Individuals from each partner who guided project development and supported implementation
through their facilitation of various professional learning components.
Individuals from every school in the districts were identified to serve as the MLT and engaged in
ongoing learning through project professional development (described in upcoming section).
This group included teachers, elementary instructional coaches, principals, and district
mathematics leaders. They led by supporting effective and equitable mathematics teaching
through their role (i.e., modeling effective and equitable practices, actively engaging in
mathematics professional learning communities serving as a “more knowledgeable other”).
Beginning in year 2, 29 of the 94 MLT members volunteered to serve as part of the MLC. This
included teachers, elementary instructional coaches, and district mathematics leaders. As
informal or formal leaders, MLC members led by designing and facilitating professional learning
for their grade-level or course team, school, and district colleagues.
Note: The n’s reflect the total number of recruited participants.
Definition of Mathematics Teacher Leaders for the EaMML Project
Table 1 provides a description of the three leadership participant types for the EaMML project.
EaMML focused on two types of leaders–those who participated through the MLTeam and those
who also served through the MLC. While the project focused on these two types of leaders holding
varied roles (i.e., teachers, instructional coaches, administrators), this manuscript focuses on the
teaching and learning outcomes for the EaMML MTLs; specifically, these are the MLTeam’s class­
room-based teachers who completed the 3-year project (i.e., 51 of the 67 teachers), of which 19 were
also part of the MLC.
A potentially surprising characteristic of the MLC was that formal leadership roles did not
guarantee engagement with providing school- and district-level mathematics professional develop­
ment for the EaMML project. For example, of the 14 elementary instructional coaches in the project,
only three chose to participate in the cadre. The vast majority (i.e., 76%) of the MLC members were
classroom teachers, this in contrast with having the majority in formal leadership roles (i.e., schoollevel coach, district-level specialist, or administrator). This is similar to the overall relationship
between informal and formal leaders among the MLTeam members, suggesting that EaMML mathe­
matics teacher leader participants were not only leading from within their classroom but also outside
their classrooms through their role on the MLC.
Conceptual Framework for the Preparation of EaMML Mathematics Teacher Leaders
NCTM’s Principles to Actions (NCTM, 2014) was used to develop a shared vision for effective and
equitable mathematics teaching among project leaders and participants while providing a foundation
for the various professional development (PD) components. Central to all the PD components was the
emphasis on implementation of high cognitive demand tasks, connected representations (i.e., physical,
visual, verbal, symbolic, and contextual), and meaningful student mathematical discourse in support
of deep mathematics learning, which provided coherence across the PD components.
EaMML’s desired outcomes included both deepening teachers’ professional knowledge and skills as
well as increasing the district and school capacity for providing effective mathematics learning
experiences for teachers and students. Because of this, EaMML’s PD model included a combination
of job-embedded professional development approaches for all EaMML participants (i.e., book studies,
lesson studies, curriculum mapping, assessment development) and the option to participate in
standards-aligned graduate-level mathematics specialist (MS) coursework (Association of
Mathematics Teacher Educators, 2013; NCTM, 2014; Sutton et al., 2011). Summarized in Table 2
are the various components of the EaMML Professional Development program, the total number of
hours, the facilitators, and the participating groups (i.e., MLTeam, MLC, other teachers).
88
N. RIGELMAN AND C. LEWIS
Table 2. EaMML professional development activities.
Facilitators*
Activity Description
Kick Off Events. Beginning in Spring 2014 and again in Fall 2015 and 2016,
teacher, coach, and administrator participants in each district engaged in
daylong events focused on connecting EaMML professional learning with
research-proven instructional and leadership practices. In Fall 2017, there was
a project wide celebration that included a presentation and celebration of the
research results (i.e., EaMML effect on teacher and student learning) as well as
planning for continued work following the project.
Book Studies. Book studies, offered 3 times in Spring 2014 and 4 times in each
subsequent year for 2 hours, supported development of teacher and coach
knowledge about pedagogy and leadership; the first read, Principles to Actions
(NCTM, 2014), supported development of a shared vision for effective and
equitable mathematics teaching and learning. Additional books were selected
to help teachers and coaches develop the skills (a) eliciting and using student
mathematical thinking to inform instruction, (b) designing/adapting tasks to be
responsive to and relevant for students, and (c) honing leadership skills.
Lesson Studies. Lesson studies, offered Spring 2014 and 3 times in two
subsequent years to grade band teams, supported development of specialized
mathematical content and pedagogical knowledge. The groups convened in
a lead team member’s classroom for a 1-day modified lesson study (Hurd &
Lewis, 2011; Watanabe, 2002). Instead of tuning a lesson, this work focused on
tuning practice through collaboratively “doing the math,” planning for student
engagement in high-level thinking and discourse, observing for student
mathematical discourse, debriefing, and planning next steps–all keeping
effective and equitable teaching practices at the fore.
District-Based Curriculum Work. Each summer, district mathematics specialists
convened teachers and coaches to work on a combination of activities that
included: establishing a mathematics vision, engaging in curriculum review,
developing curriculum and assessment maps and associated resources.
Common features across the collaborative work were examination of standards
and progressions, analysis of tasks and curriculum materials including
assessments to identify and address potential gaps.
Optional:** Mathematics Specialist Coursework. EaMML teachers and coaches
were invited to participate in graduate-level courses aligned with AMTE’s EMS
Standards (AMTE, 2013). These courses were clustered into content-focused
pedagogy and leadership courses–seven 30-hour courses in all. Focal content
for the included Base Ten Numeration and Operations; Whole Number and
Fraction Operations; Generalizations about Operations; Patterns and Functions;
Measurement; Data Analysis where DMI materials served as the foundation.
Participants completed 5 of the 6. The leadership course and practicum focused
on leading both within and outside the classroom.
Building- and District-Based Professional Learning. Beginning in Fall 2016,
Mathematics Leadership Cadre Members began supporting project-sponsored
professional learning such as the book studies and lesson studies. They also
offered professional learning through coaching and mentoring colleagues
individually or through their grade-level or course teams as well as leading
colleagues in book studies or lesson studies.
Participants
Total
Hours
28
Project
Leaders
l
14
l
s
•
•
49
l
s
•
•
28
l
•
•
210
l, s, +
•
•
169
s
MLC MLT MLC Others
•
•
l
•
•
*l = led, s = supported, + = included other PSU facultyHT
**Mathematics Specialist Courses were completed by a subset of MLT and MLC members. The courses were also open to district
colleagues.
The purpose of selecting job-embedded PD approaches not only supported careful study and
transformation of day-to-day instructional practice (Ball & Cohen, 1999; Smith, 2001; Sztajn et al.,
2017), but it also allowed MLC members to replicate these structures and content as they shared
learning with their colleagues. Similarly, the MS coursework centered on learning from practice with
expectations to implement course-based learning when working with their students and colleagues.
The intended by-product of the project was to cultivate leaders who would help sustain ongoing
mathematics PD for all district teachers.
INVESTIGATIONS IN MATHEMATICS LEARNING
89
Garet et al. (2001) identified three structural features of effective professional development as (1)
the form of the activity, (2) the duration of the activity, and (3) the degree to which the activity
promotes collective participation. These structural features along with the unique core features defined
by Desimone (2009)–content focus, active learning, coherence – were considered in the EaMML PD
design. The PD model included six components described in Table 2. All the PD components reflect
reform-type PD. On the surface, the MS Coursework might be considered traditional PD but the casebased curriculum design (i.e., written and video cases, cases of one’s own students) supports teacher
leaders with developing deepened mathematical understanding simultaneous to developing pedago­
gies responsive to their students’ thinking. Four of the six activities included all participants (i.e.,
kickoff events, book studies, lesson studies, and district-based curriculum work) with a subset of
participants–specifically 20–completing four or more courses in the mathematics specialist program
and 29 engaged as MLC members, leading professional learning within their team, school, or district.
Taken together, all EaMML participants engaged in sustained professional learning logging more than
50 hours during each of the full two years. The 20 participants engaged in coursework had an
additional 90 contact hours per year. MLC members–not including district leaders–led an additional
169 hours of professional learning in the second full year. Across the professional learning compo­
nents teachers engaged in purposeful collaboration both within-grade or across-the-grades focused
squarely on transforming students’ opportunities to learn.
The desired pedagogical outcomes from the EaMML professional learning were to enhance
participants’ professional knowledge and skills so they could make shifts in instructional practice
that would positively impact students’ mathematics learning. Each component of the EaMML PD
supported participants with deepening their understanding of the content they taught and the ways
students learn that content. Through participation in the lesson studies, teachers and coaches put their
learning from the book studies and the courses into action while they also developed skills with
noticing, analyzing, and responding to students’ thinking. As described in Doerr et al. (2010) a focus
on student thinking and classroom practice can lead to developing productive habits of mind focused
on continuously learning from teaching.
The desired leadership outcomes from the EaMML professional learning were to prepare partici­
pants for their leadership role by broadening their perspectives about leadership and equipping them
to support collaborative professional learning. Instead of viewing leadership as an individual, EaMML
project leaders wanted participants to view leadership as a shared practice (Harris, 2003; Muijs &
Harris, 2003). This view of shared or distributed leadership positioned teacher leaders to lead formally
and informally, sharing their expertise both within and beyond their classrooms (c.f. Wasley, 1991).
EaMML participants had the opportunity to deepen their understanding of how adults learn and
models for supporting that learning while simultaneously developing their identity as a teacher and
leader of mathematics. Through participation in the book studies and lesson studies, teachers and
coaches experienced learning in the ways project leaders hypothesized could be used to support
continued learning at the grade, course, school, and district levels. Teachers and coaches participating
in the MS coursework also completed field-based projects where they engaged in a coaching cycle
supporting a new or experienced teacher and facilitated professional learning at their grade or school
level. In the last year of the grant, MLC members not only supported facilitation of grant sponsored
events but also led learning for their team, school, district, and beyond.
Methods
Participants
The project was a 3-year collaboration from 2014 to 2017 among one large city school district (14
schools, approximately 9,800 students, 75% free and reduced lunch (FRL), and 55% Black and
Indigenous People of Color (BIPOC)), a large suburban district (9 schools, approximately 6,000
students, 77% FRL, and 60% BIPOC), an education service district, a university, and a research
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N. RIGELMAN AND C. LEWIS
firm. In the 2016–2017 school year, approximately 75% of the students in both districts had access to
free and reduced lunch, and 55% of the students were BIPOC in District 1 and 60% in District 2. Of the
94 recruited EaMML MLTeam members, 67 were classroom teachers, and 51 completed the 3-year
project and provided both pre and post data, hereafter referred to as EaMML teachers. Of the 51
EaMML teachers, four taught Grade K, four taught Grade 1, three taught Grade 2, six taught Grade 3,
four taught Grade 4, one taught Grades 4 and 5, five taught Grade 5, six taught Grade 6, one taught
Grade 7, two taught Grade 8, four taught Grades 6–8, and eleven taught a range of mathematics
courses in Grades 9–12.
Research Question 1: Mathematics Teacher Leader Learning
Design
Research Question 1 is addressed using two pretest-posttest designs. EaMML teachers completed
a survey at the onset of the project (pretest) and at the conclusion of the project (posttest). The
matched pre-post completion rate was 76% (51 of 67). The research team developed the survey to
measure changes in teachers’ pedagogical and leadership knowledge and skills. The research team
reviewed a 121-item teacher survey developed by the Arizona Mathematics Partnership (AMP),
a 5-year Mathematics and Science Partnership project funded by the National Science Foundation
(Weaver et al., 2018). The research team selected items from the AMP survey, modified some wording
of the items, and developed items that aligned with the instruments for the other designs. The survey
includes one scale measuring leadership with three items that directly aligned with the definition of
leadership for this project. These focus on teacher collaboration, sharing instructional materials, and
leading professional learning. There were six scales measuring different types of pedagogical knowl­
edge: (1) addressing Common Core State Standards in Mathematics, (2) developing mathematical
tasks, (3) addressing students’ learning needs, (4) assisting students in sense making, (5) encouraging
student discourse, and (6) developing students’ mathematical reasoning. The research team calculated
the Cronbach’s alpha score for each scale to determine the reliability and internal consistency of each
scale. The Cronbach’s alpha scores for all scales exceeded 0.67.
For the second pre-post design, EaMML teachers completed one of the Mathematical Knowledge
for Teaching (MKT) assessments (Hill et al., 2004) at the beginning of the project (pretest) and at the
end of the project (posttest). The matched pre-post completion rate was 76% (51 of 67). The MKT
measures changes in participants’ specialized knowledge for teaching mathematics. This project used
the Number Concepts and Operations (elementary school and middle school versions with elementary
and middle school participants respectively) and the Patterns, Functions, and Algebra (with highschool participants) assessments, because these assess topics addressed in the EaMML professional
development. Utilizing Item Response Theory, the MKT assessment scales have reliabilities between
0.75 and 0.85.
Analysis
Paired t-tests were used to assess differences between pre and post. Differences were deemed
statistically significant if p < .05. Significance tests were only conducted at the aggregate level; however,
the data were broken out by key subgroups to determine descriptive differences between MLC and
MLTeam participants, those teaching Grade K–5 and Grades 6–12, and those who completed the MS
coursework through the practicum (i.e., 24 quarter credits of graduate-level coursework) and those
who had not. Significance tests were not conducted for each subgroup due to limited sample sizes and
to reduce the probability of a false-positive finding.
INVESTIGATIONS IN MATHEMATICS LEARNING
91
Table 3. EaMML survey pre and post data (Means) by subgroup.
Instructional
Leadership*
Overall
Grade K-5
Grade 6–12
Practicum
MLT
MLC
n
51
27
24
10
32
19
Pre
3.29
3.17
3.43
3.50
3.20
3.46
Post
3.52
3.53
3.50
3.83
3.47
3.60
Common Core
State Standards*
Pre
3.22
3.07
3.38
3.25
3.17
3.29
Post
3.67
3.69
3.65
3.90
3.64
3.71
Mathematical
Tasks*
Pre
2.91
2.74
3.10
2.97
2.86
2.98
Post
3.53*
3.47
3.60
3.67
3.56
3.47
Learning
Needs*
Pre
3.31
3.12
3.51
3.00
3.28
3.35
Sense
Making*
Post Pre Post
3.55 3.15 3.55
3.44 2.96 3.56
3.67 3.37 3.53
3.50 3.08 3.78
3.49 3.08 3.49
3.65 3.27 3.65
Discourse* Reasoning*
Pre
2.97
2.82
3.14
2.95
2.90
3.09
Post
3.45
3.47
3.42
3.80
3.42
3.49
Pre
2.74
2.54
2.96
2.70
2.72
2.77
Post
3.34
3.27
3.42
3.50
3.32
3.37
Survey Response Options: 1 = Not at all, 2 = A little, 3 = Somewhat, 4 = Very. Only matched pre and post data are included. Paired
t-tests used to assess differences between pre and post at the aggregate level. *Differences deemed significant if p < 0.05
Results
The results indicate that EaMML teachers (n = 51) increased their leadership knowledge and
pedagogical knowledge after completing the EaMML professional development program. EaMML
teachers’ scores on all seven four-point scales increased significantly over time (see Table 3). The
average post scores were all high (i.e., three or higher). An examination of subgroup differences
revealed that those who completed the practicum had the highest post scores (M = 3.83) along with
MLC members (M = 3.60) for leadership knowledge. For the pedagogical knowledge scales, those who
completed the MS coursework through the practicum had the highest post score for five of the six
scales and MLC members’ post scores were higher than the MLTeam members’ post scores for five of
the six scales.
Closer examination of the items that comprise the leadership scale indicated which aspects of
leadership were strongest for MTLs. Two of the survey items increased significantly from pre to post:
“talk about math teaching and learning with colleagues” (Pre, M = 3.55; Post, M = 3.73) and “design
and lead professional learning sessions for peers” (Pre, M = 2.69; Post M = 3.06). The item “share
instructional materials with colleagues” did not increase significantly from pre to post (Pre, M = 3.65;
Post, M = 3.75); however, teachers already felt confident in this area at the time of the Pre. Although
MTLs significantly increased in terms of designing and leading professional learning for their peers,
this was the area in which they rated themselves the lowest.
The MKT results indicate that EaMML teachers increased their mathematical and pedagogical
knowledge; scores improved on all assessments and elementary and high-school participants’ scores
increased significantly (see Table 4). An examination of subgroup differences reveals that the MLC
members’ post scores were higher than the MLTeam members’ post scores on all assessments. The
results for the mathematics leadership practicum subgroup were mixed: those completing the ele­
mentary version of the assessment obtained the highest post score; however, those completing the
middle school version had the lowest post score.
Research Question 2: Increased Capacity
Design
Research Question 2 is addressed by collecting data on the mathematics leadership support MLC
members provided to their colleagues. In the 2016–2017 school year, the research team documented
the number of professional development events, the number of hours, and the specific audience for
each event (i.e., grade level or course team, school-based, district-based, and outside the district)
provided by the MLC teacher leaders. Because expectations for leading professional learning for
colleagues were late in the EaMML project, the research team collected data a year and a half after
the conclusion for the grant by surveying MLC members (18 of the 19 were still at the district) and
interviewing the remaining district mathematics specialist to determine which, if any, activities
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N. RIGELMAN AND C. LEWIS
Table 4. Mathematical knowledge for teaching pre and post results by subgroup.
Number Concepts and Operations (ES)*
Practicum*
MLC
MLT
Number Concepts and Operations (MS)
Practicum
MLC
MLT
Patterns, Functions, and Algebra (HS)*
MLC
MLT
n
30
8
11
19
12
2
6
6
9
2
7
Pre
0.3793
0.8196
0.6251
0.2370
0.5604
0.5907
1.1922
−0.0715
0.9249
0.7178
0.9841
Post
0.9315
1.7798
1.1064
0.8303
0.9646
0.0892
1.3630
0.5662
1.5614
1.9500
1.4503
Only matched pre and post data are included. n = 30 for NCOP (ES). n = 12 for NCOP (MS). n = 9
for Patterns, Functions, and Algebra (HS). Scale: NCOP ES ranges from −2.75 to 3.02; NCOP MS
ranges from −2.80 to 2.53; Patterns, Functions, and Algebra ranges from −3.35 to 2.19. Paired
t tests were used to determine whether aggregate gains were significant. *Differences were
deemed significant if p < 0.05.
continued, how often, and the supports and hindrances faced as they continued the mathematicsfocused work.
Analysis
The research team used the project records to report on the frequency and duration of professional
learning events. The follow-up survey data were summarized using descriptive statistics and openended items were analyzed for themes. The follow-up interview was analyzed to identify themes and
used to better understand the contexts influencing the follow-up survey results.
Results
Across the two districts, there were 98 events led by MLC teacher leaders in the 2016–2017 school year,
60 in District 1 and 38 in District 2, for a total of 169 hours, 116 hours in District 1 and 53 hours in
District 2. Figure 1 shows the range of professional learning activities including by grade level, school
based, district based, and outside of the district.
The follow-up survey results revealed the positive impact of the project-purchased lending
libraries for book studies and protocols for analyzing student work or students at work such as
in lesson study. These resources supported MLC members to lead book studies (41%), lesson
studies (59%), or aspects of lesson study (59%) and were the most common ways the MLC teacher
leaders continued to lead once the project ended. These MTLs, with the support of their grantinspired school-based mathematics leadership teams and MTL roles (i.e., mathematics resource
teachers in District 1, and mathematics residents in District 2), regularly facilitated or co-facilitated
learning for their teams, schools, and districts (41%). Fifty-nine percent reported leading profes­
sional learning on a weekly/bi-weekly basis, 35% on a monthly/quarterly basis, and 6% reported
only annual opportunities to lead professional learning. In the interview, the district mathematics
specialist reflected “we are seeing teachers opt in to more professional learning and begin to assist
with the planning and facilitation of district professional learning. Those who were part of EaMML
are often quicker to step into the lead facilitator role than those who have not had as much
training.”
MLC teacher leaders also revealed supports and hindrances to improving mathematics teaching
and learning. Following EaMML, each district created MTL roles. Most saw these leadership oppor­
tunities as a lasting success of EaMML, with 76% of the MLC members serving in these roles. Others
reflected positively on opportunities to influence their colleagues’ instructional practices through
opening their classrooms for colleagues to visit and collaborating within their teams. The most
INVESTIGATIONS IN MATHEMATICS LEARNING
93
Figure 1. Percent of professional development activities by audience.
common challenges identified were skepticism or resistance from colleagues (~24%) and lack of time
to collaborate (19%). Finally, a hindrance for some was also the way MTLs are positioned as voluntary
or supplemental rather than central supports to leading change (i.e., math focused coaches, compen­
sated roles).
Research Question 3: Mathematics Teacher Leader Instructional Practices
Design
Research Question 3 was addressed using a mixed-method approach utilizing both artifacts and
observations. Both were scored using the Instructional Quality Assessment (IQA; M. Boston &
Wolf, 2004) which focused on Academic Rigor in both tools, and added Accountable Talk, and
Accountability to Knowledge and Rigorous Thinking for the observations. These domains are aligned
with focus areas in the EaMML professional development. Artifacts were scored using the three
academic rigor rubrics: Potential of the Task, Implementation of the Task, and Teacher
Expectations. Each domain on the artifact rubric could receive a slightly different score range;
Potential of the Task had a range of 0 to 4, Implementation of the task 1 to 4, and Teacher
Expectations, 1 to 4 and not applicable. For the observation rubrics the following domains could
receive a score of 0 to 4: Potential of the Task, Implementation of the Task, Student Discussion
Following the Task, and Mathematical Residue. The Questioning, Participation, Teacher Linking,
Student Linking, Asking, and Providing domains could receive a score of 0 to 4 or not applicable.
EaMML project leadership deemed scores of 3 and 4 as reflective of optimal teaching practices. Scores
3 and 4 focused on, for example, high cognitive demand tasks and conceptual understanding rather
than a focus on procedural skill; 3 s and 4 s focused on questions pressing for justification of why
versus telling how; and 3 s and 4 s focused on sharing and comparing multiple strategies rather
privileging a single solution path.
EaMML teachers submitted classroom artifacts at the onset of the project (pre) and at the
conclusion of the project (post). The matched pre-post completion rate was 75% (50 of 67 teachers
submitted artifacts at the onset and completion of the project). The classroom artifacts included (a)
a cover sheet for the teacher to record general information, (b) a mathematics task that either the
teacher developed or borrowed from a curriculum resource, (c) the rubric the teacher used to score the
student work, and (d) four examples of student work (i.e., work receiving a low score, middle score,
and high score, as well as an example the teacher found interesting).
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N. RIGELMAN AND C. LEWIS
The research team designed an objective and rigorous artifact scoring training. The artifact scoring
process involved each member of EaMML project leadership team (a) reviewing the artifact and cover
sheet, the student task, the rubric the teacher used to score the student task, and examples of student
work; (b) scoring the artifact independently using IQA Rubrics, (c) discussing the individual IQA
scores and discrepant scores, and (d) determining and recording a final consensus score for data
analysis. The research team calculated pre and post interrater reliability. Reliability was at least 0.67
before coders conferred.
For the observations, a random stratified sample of 31 EaMML teachers were selected for pre and
post observation. Of the 31 teachers, 26 were observed in Year 1 (pre) and Year 3 (post) for a pretestposttest design. As with the artifacts, the research team used the IQA Classroom Observation Rubrics
due to their alignment to the project’s professional learning goals and artifact rubrics.
The observation training and scoring processes were similar to those used for the artifacts. The ten
coders met multiple times in Fall 2015 to view classroom videos and code videos in an effort to
increase reliability between coders prior to conducting the baseline observations. During the training,
and through the duration of the project, the research team conducted analyses to assess interrater
reliability among observers. Overall, the reliability of the observers’ independent scores was high (i.e.,
at least 0.73); however, there were some domains with lower reliability. Therefore, there were always
two observers at each observation, each observer independently recorded scores, and then discussed
and arrived at consensus scores for each domain.
Analysis
Independent t-tests and Mann–Whitney U-tests were used for between-group comparisons, paired
t-tests, and Wilcoxon tests were used for within group comparisons. For all tests, differences were
deemed statistically significant if p < .05. As with the prior research question, significance tests were
only conducted at the aggregate level and key subgroup differences are provided descriptively.
Results
The results indicate that EaMML teachers increased their use of research-proven instructional
practices after completing the EaMML professional development program. Artifact data (n = 50)
indicate that teachers increased their use of research-proven instructional practices that develop
deeper student mathematics understanding: scores increased over time in all areas and significantly
for two of the three areas as shown in Table 5. EaMML teachers’ post scores were highest for Potential
of the Task. None of the average post scores were within the range of strong mathematical practices
(i.e., a score of 3 or higher).
The research team examined key subgroups to determine if there were differences. An examination
of subgroup differences reveals that the MLC members’ post scores were higher than the MLTeam
members’ post scores for all three components, those teaching Grade K–5 demonstrated higher post
Table 5. Pre and post artifact data (Means) by subgroup.
Potential of Task
Overall
Grade K-5
Grade 6–12
Practicum
MLC
MLT
n
50
30
20
10
19
31
Pre
2.60
2.63
2.55
2.70
2.42
2.71
Post
2.86
2.80
2.95
3.20
2.95
2.81
Implementation of Task*
Pre
2.20
2.23
2.15
2.10
2.05
2.29
Post
2.58
2.60
2.55
2.80
2.63
2.55
Teacher Expectations*
Pre
2.26
2.36
2.11
2.30
2.22
2.29
Post
2.65
2.71
2.56
2.80
2.72
2.61
Only matched pre and post data are included. n = 45–50 for all indicators. Possible Ratings: Potential of the Task
0–4, Implementation of the Task 1–4, and Teacher Expectations 0–4 or not applicable. Wilcoxon tests were
used to compare pre to post for overall scales only, not subgroups. *Differences were deemed statistically
significant if p <0.05.
INVESTIGATIONS IN MATHEMATICS LEARNING
95
scores for two of the three components compared to those teaching in Grades 6–12, and for all three
components the mathematics leadership practicum subgroup had the highest post score.
By the end of the project, observation data indicated EaMML teachers were using more researchproven practices in their classroom than they were at the onset of the project. Teachers (n = 26) were
observed at the beginning and end of the project and were rated in ten areas: observation scores
increased over time in all ten areas and significantly in three areas: Questioning, Student Linking, and
Providing (Students’ Responses). Teachers’ scores were highest for Participation and Potential of the
Task with mean post scores of 3 or higher as shown in Table 6. Teachers’ scores were lowest for
Student Linking: the mean was 1.77 at post.
The research team examined key subgroups to determine if there were differences. An examination
of subgroup difference reveals that the MLC post scores were higher than the MLTeam post scores for
six of the ten components, those teaching Grades K–5 had higher post scores for eight of the ten
components compared to those teaching Grades 6–12, and those who completed the mathematics
leadership practicum did not have higher scores than other groups for any components.
Research Question 4: Student Learning
Design
Research Question 4 was addressed using a quasi-experimental study. The initial sample was com­
posed of 47,672 records representing 21,496 students in Grades K through 11, in two participating
school districts. A total of 692 duplicate records were removed from the sample.1 Student membership
in the treatment or comparison group was determined based on receiving instruction from an EaMML
teacher. In the participating districts, a total of 56 teachers served as EaMML teachers (nDistrict 1 = 20,
nDistrict 2 = 36) and 328 (nDistrict 1 = 148, nDistrict 2 = 180) served as comparison teachers. EaMML
teachers engaged in project professional development during the final four months of the baseline year
(2014–2015). As such, students taught by an EaMML teacher during this time period (n = 3,579) were
removed from the analytic sample to ensure that students included in the treatment group were
exposed to at least one full year of instruction from an EaMML teacher. Students were included in the
treatment group if they were taught by an EaMML teacher in at least one of the treatment years (2015–
2016 or 2016–2017) and students were included in the comparison group if they did not receive any
instruction from an EaMML teacher during this time. The final analytic sample included data from the
students of 287 teachers, 36 EaMML teachers (nDistrict 1 = 14, nDistrict 2 = 22), and 251 comparison
teachers (nDistrict 1 = 94, nDistrict 2 = 157).
Analysis
Two HLM Models were used to assess the impact of EaMML on student achievement as measured by
the Smarter Balanced Assessment of Mathematics. HLM Model 1 was a two-level longitudinal model
(i.e., growth model with scores nested within students) that tested whether student achievement scores
increased at a greater rate if taught by an EaMML teacher versus a comparison teacher and included
a time by treatment interaction term. HLM Model 2 included 3-way interaction to test whether the
EaMML effect was moderated by student subgroups. All models included grade level of the student in
2015, district, and controlled for baseline achievement.
1
All duplicate records included identical Smarter Balanced Assessment scores. In 356 of these records a student was linked to
multiple teacher types. In these cases, if a student was assigned to an EaMML teacher the record for the EaMML teacher was
maintained in the sample. For those with both dropped teachers and non-EaMML teachers the record for the dropped teacher was
maintained.
n
26
8
12
5
10
15
Pre
2.81
2.75
2.85
3.00
2.90
2.75
Post
3.08
3.13
3.00
3.00
3.30
2.94
Pre
2.46
2.38
2.62
2.60
2.50
2.44
Post
2.65
2.75
2.69
2.60
3.00
2.44
Implementa- tion
of Task
Pre
1.96
2.25
1.77
2.60
2.10
1.88
Post
2.23
2.63
1.85
2.60
2.10
2.31
Student Discussion
Following Task
Pre
2.27
2.50
2.15
3.20
2.40
2.19
Post
2.88
3.00
2.77
3.00
2.90
2.88
Questioning*
Pre
1.85
2.13
1.69
2.40
2.30
1.56
Post
2.15
2.50
1.92
2.40
2.10
2.19
Mathematical
Residue
Pre
2.92
2.75
2.75
2.60
2.70
3.70
Post
3.16
3.25
3.08
3.20
3.00
3.27
Participation
Pre
2.12
2.13
2.00
2.20
2.40
1.94
Post
2.23
2.38
2.15
2.40
2.40
2.13
Teachers
Linking
Pre
1.38
1.50
1.38
1.80
1.60
1.25
Post
1.77
1.75
1.85
1.80
1.80
1.75
Students
Linking*
Pre
2.35
2.75
2.15
3.40
2.50
2.25
Post
2.62
2.75
2.62
2.60
2.70
2.56
Pre
2.08
2.13
2.00
2.60
2.10
2.06
Post
2.54
2.38
2.62
2.40
2.60
2.50
Asking
Providing Students
Teachers Press
Responses*
Only matched pre and post data are included. Possible Ratings 0–4: Potential of the Task, Implementation of the Task, Student Discussion Following the Task, and Mathematical Residue. Possible
Ratings 0–4 or not applicable: Questioning, Participation, Teacher Linking, Asking, and Providing. Wilcoxon tests were used to compare pre to post at the aggregate level. The participation n is 25
rather than 26 due to a score of not applicable on the pre. *Differences were deemed statistically significant if p <0.05.
Overall
Grade K-5
Grade 6–12
Practicum
MLC
MLT
Potential of
Task
Table 6. Pre and post observation data (Means) by subgroup.
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N. RIGELMAN AND C. LEWIS
INVESTIGATIONS IN MATHEMATICS LEARNING
97
Results
The results of the first HLM model are presented in Table 7. Smarter Balanced Assessment scores for
all students increased significantly over time with, on average, scores increasing 31.4 points at each
subsequent administration. In addition, students who had an EaMML teacher at any point during the
study, scored significantly higher than those of comparison teachers with EaMML students scoring, on
average, 23.6 points higher at each administration (Hedges g = .02). A significant time by EaMML
interaction was also observed with scores increasing, on average, 7.72 points more per administration
for EaMML students than for comparison students. The covariate for district was also significant with
students in District 1 scoring, on average, 11.24 points higher than students in District 2. The grade
level in 2015 indicators were also significant predictors in the model. This is to be expected as scores on
the Smarter Balanced Assessment are scaled to increase with each grade level. The predicted scores at
baseline, first, and second follow-up for EaMML and non-EaMML students by grade level and district
are presented in Table 7 for students in Grade 3, Grade 4, Grade 5, and Grade 6 at baseline.
The second HLM model tested whether the EaMML effect differed by student subgroup, results for
this model are presented in Appendix A. The EaMML effect was consistent across students by gender,
race (Underrepresented vs. White, Asian, Pacific Islander), ethnicity (Hispanic vs. Non-Hispanic), and
SES (Free-and-Reduced Lunch vs. Non). After controlling for demographic variables a significant
effect of having been instructed by an EaMML teacher was observed with EaMML students scoring, on
average, 22.91 points higher than non-EaMML students. The time by EaMML interaction was also still
significant with scores increasing, on average, 6.13 points more per administration for EaMML
students than for comparison students. District and the grade level indicators were also still significant
in this model.
Among the 2,515 students who did not pass their baseline Smarter Balanced Assessment, students
taught by an EaMML teacher (n = 832) had greater odds (0.44) of passing a follow up Smarter
Balanced Assessment than comparison students (n = 1,683; 0.27). The odds ratio (2.20) indicates that
students not passing their baseline Smarter Balanced Assessment and were taught by EaMML teachers
in subsequent years were over 2 times more likely to pass a future Smarter Balanced Assessment than
their peers who were not taught by EaMML teachers in subsequent years.
Study Limitations
There are limitations in this study that could be addressed by future research. Limitations of the
teacher-level data include: the teachers were volunteers, there is not a comparison group for teacherlevel data, the overall sample size is small, and data were collected pre/post rather than continuously
over the course of the project. The survey was self-report data and participants may have reported
socially desirable answers. In terms of assessing student achievement, the study was limited to the
Table 7. EaMML effect model.
Estimate
Standard Error
Fixed Effects
Intercept
EaMML
District
Grade 3
Grade 4
Grade 5
Grade 6
Grade 7
Time
Time * EaMML
***p < .001.
2341.64
23.60
11.24
55.40
85.79
123.17
146.38
203.44
31.41
7.73
8.28
3.15
2.95
8.46
8.55
8.68
8.87
9.19
0.67
1.05
t
df
p
282.69
7.49
3.81
6.55
10.04
14.16
16.49
22.14
47.02
7.34
4120.70
3848.80
3708.86
4024.10
4019.69
4011.93
3999.72
4006.77
3768.80
3551.22
***
***
***
***
***
***
***
***
***
***
98
N. RIGELMAN AND C. LEWIS
grades in which statewide assessments were administered so the student achievement data was not
representative of all the teachers in the project.
Discussion
There are several unique features of the EaMML project that add to the research base. One unique
feature of the EaMML project is the K-12 representation of math specialists engaging in both acrossthe-grades and within-grade-band professional learning. The EaMML project advances the field by
providing an example of a professional development design that strengthens MTL content knowledge,
pedagogical knowledge, and leadership knowledge and skills while engaging leaders throughout an
entire district and across all grade levels. Yet questions remain about effectiveness of the model at scale
that is, in varied contexts, with different facilitators (Borko, 2004; Marrongelle et al., 2013), and with
earlier expectations for teacher leadership (c.f. Implementing the Problem-Solving Cycle (iPSC),
Koellner & Jacobs, 2015). It would be worthwhile to examine components of the EaMML professional
development model through the lens of the professional development continuum described by
Koellner and Jacobs (2015). When considering this continuum from “highly specified” to “highly
adaptive,” the overall model might fall somewhere in the middle because there is a mix across the PD
components in terms of level of specification. As an example, the MS courses are more highly specified
than the lesson studies which may have common broad professional learning goals but varied greatly
by grade band, task selected, classroom learning environment, and student discourse levels. An aspect
of the mix of professional learning experiences may contribute to EaMML’s success. Future research
could study various professional development models to determine if this model, or others, are more
effective in terms of developing and sustaining leadership structures over time.
The second unique feature of this project is studying the preparation and positioning of classroom
teachers as mathematics leaders, as most of the research focuses on mathematics specialists as coaches.
In this study, classroom teachers engaged in informal (i.e., sharing resources with colleagues) and
formal (i.e., leading professional development sessions) leadership efforts within their school, district,
and outside of their district. As noted earlier, coaches are an added expense for schools and often
remove the highly skilled teachers from their work with students, so the findings from this research are
critical to show that these leadership roles can be effectively filled by classroom teachers and under
what conditions. The responses from MLC MLTs two years after completion of the project offer
preliminary evidence for how schools or districts might successfully support and sustain such
engagement. Future research could study classroom teachers as leaders and address some of the
limitations of this study by including a comparison group for teacher-level data, collecting data more
frequently than pre and post, and collecting instructional practice data from teacher leaders’
colleagues.
Few studies examine the impacts of math teacher leaders on student achievement. Prior research
typically focused on school level data or included student level data with several limitations and
primarily examined the role of leaders in a coaching role, not as a classroom teacher. This research
examined classroom teachers as leaders, utilized student-level state assessment data in a rigorous
quasi-experimental design, included data across elementary and middle school (grades 3–7), and
incorporated an equity perspective in the analysis. Additionally, as called for by Sloane and Wilkins
(2017), this research employed a quantitative methodology and hierarchical linear modeling
(HLM) to assess student achievement gains over time. Students with an EaMML teacher scored
significantly higher on the state assessments than students of comparison teachers and the EaMML
effect was consistent across students grouped by gender, race, ethnicity, and SES. By using HLM,
this research was able to make a unique contribution to the field by connecting leadership to
student achievement. Future research should utilize these types of rigorous methods to analyze
impacts on student achievement and should ensure models are included that address potential
differences in achievement among subgroups (e.g., gender, race, ethnicity, and SES). Use of these
models are necessary to determine if an intervention was able to minimize or close achievement
INVESTIGATIONS IN MATHEMATICS LEARNING
99
gaps. Due to the limitations of state-standardized assessments, future research could use common
school or district assessments that may be more closely aligned with the project’s student learning
goals.
What is less clear is the relationship between student achievement and research-proven practices.
Project leaders defined strong mathematical practices as scores of 3 and 4 on the IQA as descriptions at
these levels are consistent with the research-proven effective mathematics teaching practices (NCTM, 2014)
and equity-based practices (Aguirre et al., 2013) as they go deep with mathematics (Academic Rigor
rubrics), assigning competence as well as affirming and positioning students as doers, knowers, and sense
makers (Accountable Talk rubrics). The artifact and observation data reveal that even though average
scores were not well within the range of strong mathematical practices at the time of the post assessment,
there was a significant positive impact on student achievement. This finding raises questions regarding the
level, frequency, and duration of strong mathematical practice needed to impact students’ opportunities to
learn. It also raises questions about the content, structure, frequency, and duration of the professional
learning that would be needed for more post scores to be in the strong mathematical practices range.
Furthermore, might this be related to a disconnect between expectations of students on the Smarter
Balanced Assessment and strong mathematical practices with the latter pressing further with regard to
rigor?
Finally, this research was unique because it collected artifact and observation data while most of the
previous research has focused on observations. Consistent with many studies of classroom practice, the
data reveal stronger instructional practice with task potential than with task implementation
(M. D. Boston & Smith, 2009; Henningsen & Stein, 1997; Stein & Lane, 1996) for both measures,
however stronger performance was evident in the observation. This difference observed between the
artifact and observation was not expected, in that observations represented one point in time of a lesson,
artifacts could be collected from many lessons potentially leading to stronger performance because the
teacher had more control over what they submitted. Project leaders speculated the weaker performance
on the post artifact, when compared to the observation, could be related to some participants not taking
the final data point as seriously as the other data points. The difference could also be attributed to the
fact that the observations were from only a subset of teachers, so even though the observations were of
randomly selected teachers, this group may not have been representative of the whole. This raises
a question about the extent to which the artifact scores can be a predictor of the observation scores for
the Potential of the Task and the Implementation of the Task. Project leaders also wondered if there are
additional areas explicitly connected to the Accountability to Knowledge and Rigorous Thinking
Rubrics (i.e., Asking (Teacher’s Press), Providing (Students’ Responses)) that could be scored for
artifacts (e.g., if student samples included teacher feedback and students’ responses), or if the observa­
tions are simply a more complete picture of teachers’ classroom practice. Conducting observations and
engaging in consensus conversations after scoring was more time-consuming for researchers than
engaging in similar conversations about classroom artifacts, yet in a large project with fewer resources,
collecting more robust classroom artifacts may be a good option.
Conclusion
The EaMML project, in an effort to build district-wide mathematics leadership, engaged both formal
(i.e., coaches and administrators) and informal leaders (i.e., elementary teachers teaching all subjects
as well as middle- and high-school mathematics teachers) in common professional learning. The
EaMML professional learning increased MTLs’ mathematical content knowledge, pedagogical knowl­
edge, leadership knowledge, and use of research-based practices. This research showed that students
with an EaMML teacher scored significantly higher on the state assessments than students of
comparison teachers and the EaMML effect was consistent across students by gender, race, ethnicity,
and SES.
100
N. RIGELMAN AND C. LEWIS
Acknowledgments
The authors would also like to thank Jennifer Weston-Sementelli for conducting a thorough statistical review and
Caroline Qureshi for her instrumental contributions both during the study and for this manuscript.
Disclosure Statement
No potential conflict of interest was reported by the author(s).
Funding
This work was supported by the Mathematics and Science Partnerships grant program, a competitive grant through the
Oregon Department of Education [Office of Elementary and Secondary Education, Title IIB].
ORCID
Nicole Rigelman
http://orcid.org/0000-0003-1868-3076
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Appendix A. EaMML Effect Equity Model
Estimate
Standard Error
Fixed Effects
Intercept
EaMML
District
Grade 3
Grade 4
Grade 5
Grade 6
Grade 7
Female
Underrepresented
Hispanic
FRL Eligible
Time
Time * Female
Time * Underrepresented
Time * Hispanic
Time * FRL
Time * EaMML
EaMML * Female
EaMML * Underrepresented
EaMML * Hispanic
EaMML * FRL
Time * EaMML * Female
Time * EaMML * Underrepresented
Time * EaMML * Hispanic
Time * EaMML * FRL
2360.24
22.91
13.54
52.17
83.12
120.30
142.40
199.17
0.35
−28.13
−3.03
−5.39
37.71
1.39
−5.46
2.34
−6.75
6.13
2.32
7.40
−14.66
−2.99
1.71
3.61
−5.62
0.11
n.s. non-significant, * p < .05, ** p < .01, ***p < .001.
8.51
5.39
2.87
8.19
8.28
8.40
8.60
8.90
3.59
5.00
5.59
2.32
1.53
1.33
1.93
2.13
1.63
2.32
5.86
8.46
9.61
3.89
2.11
3.17
3.54
2.50
t
df
p
277.22
4.25
4.72
6.37
10.04
14.32
16.56
22.38
0.10
−5.63
−0.54
−2.32
24.69
1.04
−2.83
1.10
−4.14
2.64
0.40
0.87
−1.52
−0.77
0.81
1.14
−1.59
0.04
4292.46
4687.05
3742.02
3989.76
3986.01
3978.38
3968.37
3979.33
3990.91
4300.72
4200.38
4823.60
4068.52
3735.42
3911.30
3891.16
4429.83
3843.62
3893.24
4147.54
4028.38
4942.26
3539.30
3701.32
3654.89
4149.50
***
***
*
***
***
***
***
***
n.s.
***
n.s.
**
***
n.s.
***
n.s.
***
***
n.s.
n.s.
n.s.
n.s.
n.s.
n.s.
n.s.
n.s.
Investigations in Mathematics Learning
ISSN: (Print) (Online) Journal homepage: https://www.tandfonline.com/loi/uiml20
Advancing Research about Mathematics
Specialists and Mathematics Teacher Leaders
Courtney Baker, Margret Hjalmarson & Francis Fennell
To cite this article: Courtney Baker, Margret Hjalmarson & Francis Fennell (2023) Advancing
Research about Mathematics Specialists and Mathematics Teacher Leaders, Investigations in
Mathematics Learning, 15:1, 1-10, DOI: 10.1080/19477503.2022.2154061
To link to this article: https://doi.org/10.1080/19477503.2022.2154061
Published online: 06 Apr 2023.
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INVESTIGATIONS IN MATHEMATICS LEARNING
2023, VOL. 15, NO. 1, 1–10
https://doi.org/10.1080/19477503.2022.2154061
EDITORIAL PERSPECTIVE
Advancing Research about Mathematics Specialists and
Mathematics Teacher Leaders
Courtney Baker
a
, Margret Hjalmarson
b
, and Francis Fennell
c
a
College of Education and Human Development, George Mason University, Fairfax, VA USA; bNational Science
Foundation, Alexandria, VA USA; cEducation Department, McDaniel College, Westminster, MD USA
KEYWORDS Mathematics specialist; mathematics teacher leader; teacher leadership; mathematics coaching; professional develop­
ment; 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 underinvestigated (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 mathe­
matics 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
CONTACT Courtney Baker
cbaker@gmu.edu
© 2023 Research Council on Mathematics Learning
George Mason University, 4400 University Drive MS IE8 Fairfax, VA USA
2
C. BAKER ET AL.
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 partner­
ships rely on a close connection between schools, districts, and researchers. Additionally, the sustain­
ability 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 connect­
ing 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,
INVESTIGATIONS IN MATHEMATICS LEARNING
3
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 under­
stand 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), contentfocused 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
4
C. BAKER ET AL.
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 responsi­
bilities 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 care­
givers). 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 mathe­
matics specialist practice (e.g., working with a PLC or individual coaching), when in reality mathe­
matics 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
INVESTIGATIONS IN MATHEMATICS LEARNING
5
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 descrip­
tion 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 districtlevel 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
6
C. BAKER ET AL.
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 mathe­
matics 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 mathe­
matics 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 knowl­
edge 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
INVESTIGATIONS IN MATHEMATICS LEARNING
7
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 mathe­
matics 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 leader­
ship. 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.
ORCID
Courtney Baker
http://orcid.org/0000-0002-3241-5505
Margret Hjalmarson
http://orcid.org/0000-0001-8609-1596
Francis Fennell
http://orcid.org/0000-0002-7944-4581
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