Positioning K-8 Classroom Teachers as Mathematics Instructional Leaders

Abstract

In this research report, we consider how to empower K-8 teachers as mathematics instructional leaders to initiate and sustain improvements within their schools, as a practical and sustainable model of enacting change in mathematics education more broadly by developing leadership from within. We share the theoretical framework and findings from a 5-year National Science Foundation project. We utilized a longitudinal mixed methods approach, collecting data on teachers’ knowledge, instructional practices, leadership practices, and self-perception of growth throughout the project, triangulated with focus group data from teachers’ school administrators and project leaders and logs of leadership activities. Findings indicate positive changes in teachers’ knowledge and practices and in their role as instructional leaders in their schools, districts, and the mathematics education community. We conclude by sharing factors that appeared to support teachers’ growth as instructional leaders and implications for practice and research.

1. Introduction

All students deserve access to effective and impactful high-quality mathematics learning experiences. However, research indicates that teaching and learning in U.S. classrooms often does not reflect the type of ambitious mathematics instruction advocated by recent policy documents (NCTM, 2014, 2020a, 2020b) and state and national standards (NGA-CSSO, 2010). We propose that a solution to promoting and sustaining instructional change is to develop the capacity of classroom teachers to act as instructional leaders who can enact and support ambitious mathematics instruction.

In this report, we share a theoretical framework and findings from Years 1–4 of a 5-year project (currently in Year 5), involving an intentional partnership between a large metropolitan research university, one of the largest school districts in the U.S., and an education-focused non-profit. We propose that advancing K-8 mathematics teachers’ mathematical and pedagogical content knowledge, ambitious instructional practices, and opportunities to serve as instructional leaders will aid in advancing their leadership capacity to initiate and support ambitious mathematics instruction, as formal or informal mathematics instructional leaders. The research questions investigated in this report include the following: (RQ1) In what ways have teachers’ mathematical knowledge for teaching and instructional practices changed throughout their participation in the project?; and (RQ2) in what ways have teachers’ roles as mathematics instructional leaders changed throughout their participation in the project? We conclude by identifying the factors (e.g., mathematical knowledge, instructional practices, school administration support) that seem to have facilitated the development of teachers as mathematics instructional leaders.

2. Theoretical Framework

The project is guided by NCTM’s Catalyzing Change framework (NCTM, 2020a, 2020b) for ambitious mathematics instruction. The framework was used to guide the focus on teachers as professionals and leaders, as well as the strong emphasis on high-quality mathematics content and pedagogy. Figure 1 represents our theory of action. The project team created and adopted a two-pronged approach to realize the key components of the theory of action. The first prong was to develop K-8 teachers’ expertise in mathematical content knowledge for teaching, encompassing mathematical and pedagogical content knowledge as defined by Hill et al. (2008), and ambitious instructional practices to equip them with the knowledge and practices to serve as mathematics instructional leaders. This was accomplished through a new K-8 Mathematics Education specialization in the Curriculum and Instruction Ed.D., a terminal professional degree program designed for educators working full-time who plan to serve as expert practitioners in their setting following degree completion. Project components intended to develop teachers’ mathematics knowledge and instructional practices included two courses on mathematical knowledge for teaching, one with a focus on elementary grades and one with a focus on middle grades. This includes a set of “Mathematics as Gateway” experiences intended to develop teachers’ own mathematical problem-solving skills, communication skills, and perseverance and strategies on how to apply these ideas in their classrooms, as well as readings and assignments throughout other courses within the Ed.D. that highlighted the value of ambitious mathematics instruction.

In general, we hypothesize that a series of sustained professional learning experiences (in this case, through coursework) that enhance K-8 teachers’ mathematical content knowledge for teaching and ambitious instructional practices will position them as experts in mathematics teaching and learning. In support of this hypothesis, we draw on research indicating that sustained professional learning experiences, connected to practice, are likely to support change in teachers’ knowledge and instructional practices (Darling-Hammond et al., 2017; Desimone, 2011). In turn, improved mathematical and pedagogical knowledge and ambitious instructional practices will support teachers’ roles as effective instructional leaders (Carver, 2012; Stein & Nelson, 2003). We draw on research indicating that enhancing school leaders’ mathematical and pedagogical content knowledge can generate shifts in the focus of classroom observations, conversations with mathematics teachers, the evaluation of curricular resources, and instructional feedback from general teacher or classroom characteristics (e.g., use of group work) to key features of ambitious instruction (e.g., connections between representations, nature of teachers’ questions, student thinking) (Boston et al., 2017; Quebec Fuentes & Jimerson, 2020; Steele et al., 2015).

The second prong is to develop K-8 teachers’ leadership capacity, to establish them as mathematics instructional leaders within their schools and school districts. In this project, this is accomplished through a set of components designed to engage K-8 teachers as mathematics teacher leaders through the use of a cognitive apprenticeship system of modeling, coaching, and fading (Collins et al., 1987) and job-embedded support and mentoring (Cobb & Jackson, 2011). These components include a Teacher Leader Academy (TLA) throughout the project; a course on school structures and change; a course on instructional coaching; “Milestone” practice-based research projects at key points in the program; a “research in practice” dissertation in Year 3 required to have direct applicability in and impact on mathematics teaching and learning in teachers’ schools; and other specific assignments and readings throughout the program. In general, we hypothesize that engaging K-8 teachers in intentional, developmentally sequenced leadership activities will create space for them to develop into (informal or formal) mathematics instructional leaders. We envision the embedded leadership experiences for beginning teacher leaders as serving as “rehearsals” and “approximations of practice,” analogous to Grossman’s (Grossman, 2021; Grossman et al., 2009) description of rehearsals and approximations of practice for beginning teachers. Both prongs—the expertise and the space to exercise this expertise- are necessary for K-8 classroom teachers to develop into mathematics instructional leaders.

Note that the grant supporting this project requires teachers to remain in the classroom throughout the five years of the project. Hence, we conceptualize a “teacher leader” as a “teacher who leads.” This framing is consistent with Warren and definition, as “teachers who maintain K-12 classroom-based teaching responsibilities, while also taking on leadership responsibilities outside of the classroom” (p. 5), and also with definitions of hybrid or semiformal teacher leaders offered by Margolis (2020, 2016). Recent work by Pynes et al. (2024) also identifies the important role of teacher leaders who actively work beyond the scope of their own classrooms to motivate others (e.g., colleagues, early career and/or preservice teachers, school administrators, and other stakeholders) to enhance teaching and learning.

3. Methods

A longitudinal mixed methods approach was selected to study the outcomes from this project, which drew on the strengths and minimized the weaknesses of both quantitative and qualitative approaches (Creswell & Plano Clark, 2007; Creswell, 2003).

3.1. Participants

The participants in this study comprise all 14 “Fellows” selected to participate in a project at a large University in the southeastern U.S.. Recruitment for the project drew heavily from an existing relationship and close collaboration between a large urban school district and the University’s K-8 Mathematics and Science Education Master’s program, a program centered on improving the quality of mathematics and science teaching and developing teacher leaders. Recruitment criteria for the project included teaching K-8 mathematics within the school district, a master’s degree in education, and other project-specific criteria based on individual interviews with applicants. The group of 14 Fellows was selected from a set of over 30 applicants. Throughout the project, all 14 Fellows taught K-8 mathematics (4 elementary generalist teachers, 6 elementary mathematics teachers, and 4 middle-level mathematics teachers) in the same school district, which is one of the largest school districts in the U.S. The district has over 200,000 students, and at the beginning of this project (fall 2021), the district’s student population was 25% White, 24% Black, 43% Hispanic, 5% Asian, and 2% multi-cultural (as identified by the district). The district has a high population of students on free or reduced-priced meals.

The majority of Fellows are (1) graduates of the K-8 Mathematics and Science Master’s program at the University (11 of 14 Fellows; 78.6%), and (2) teachers working in Title 1 schools (11 of 14 Fellows; 78.6%). At the beginning of the project, Fellows had an average of 12 years of teaching, with 7 Fellows with 5–10 years of teaching, and 7 Fellows with more than 10 years of teaching.

3.2. Data Sources

Data collection aligns with the two prongs, and hence with RQ1 and RQ2. Data related to the first prong (RQ1; teachers’ mathematical content knowledge for teaching and ambitious instructional practices) consists of the following:

• selected modules in elementary and middle-level mathematics from the Learning Mathematics for Teaching (LMT) assessments (Hill et al., 2008) administered at three timepoints. The elementary was completed with the application process, prior to project activities (pre; April 2021), following one semester of content-focused coursework (post; December 2021), and at the conclusion of the Fellows’ coursework (post-post/maintenance; June 2024). The middle-level modules were completed prior to project activities (pre; August 2021), following the second semester of content-focused coursework (post; December 2022), and at the conclusion of the Fellows’ coursework (post-post-maintenance; June 2024).
• videos of Fellows teaching mathematics lessons in their own classrooms, analyzed with the Instructional Quality Assessment (IQA) Toolkit in Mathematics (Boston, 2012). Fellows self-record a lesson of their choosing using a video-tracking platform (e.g., SWIVL). Videos were collected during Fellows’ Year 1 (pre; Fall 2021), Year 3 (mid; January 2023), and Year 4 (post; January 2024). The IQA is a set of classroom observation rubrics that specifically target ambitious mathematics teaching practices. The rubrics assess the rigor of the following components of ambitious mathematics instruction (rubric titles in parentheses): instructional tasks (Task), task implementation (Implementation), students’ mathematical contributions to the discussion (Discussion), teacher’s questioning (Questioning), teacher’s discourse actions (Teacher Linking and Teacher Press), and students’ responses (Student Linking and Student Providing) during mathematical discussions. In the IQA coding scheme, a score of 0 indicates the construct was absent, scores of 1–2 indicate low cognitive demand or low rigor in a construct, and scores of 3–4 indicate high cognitive demand or high rigor in a construct. In each data collection, a subset of 10 of 14 (71%) randomly selected lessons were rated by discussion and consensus between the external evaluator and a trained rater; the other 4 lessons were rated by the external evaluator.

Data related to the second prong (RQ2) consist of project artifacts (course-based assignments related to leadership and a self-reported log of Fellows’ leadership activities) and focus group interviews with Fellows, project leaders, and school administrators. Focus groups occurred toward the end of each project year and were held using Zoom.

• Focus groups for Fellows were held in groups of 4–5 Fellows for approximately one hour, in each year of the project. Prompts for the Fellows’ focus groups are provided in Appendix A, with prompts that align with the main goals of the project (mathematics, teaching mathematics, and leadership) in bold font. Qualitative data from focus groups and project artifacts were used to assess Fellows’ roles as instructional leaders in their schools and how those roles changed over time. Focus group responses were also used to assess Fellows’ self-perception of (and confidence in) their roles as instructional leaders over time, as another indication of their development as instructional leaders. For the Discussion, we examine data from RQ1 and RQ2 to identify factors that seem to support Fellows’ engagement as mathematics instructional leaders.
• A focus group was conducted for the four project leaders, for approximately an hour in each year of the project. Each project leader was invited to share events and insights from their specific role on the project and to reflect on Fellows’ overall growth and change over that year. In this report, data from project leaders’ focus groups are used to support and triangulate other data sources.
• Focus groups for school administrators were conducted each year of the project. School administrators (e.g., principals, assistant principals, and/or instructional coaches) signed up for 1-hour time slots, with focus groups consisting of 4–6 participants. In this report, data from project leaders’ focus groups are used to support and triangulate other data sources.

3.3. Data Analysis

The LMT and IQA were analyzed quantitatively by the project’s external evaluator, using descriptive statistics and statistical tests such as the Wilcoxon Signed Rank tests (non-parametric t-tests for repeated measures and paired data) to examine Fellows’ growth across pre-, post-, and post-post administrations. The LMT is a national standardized assessment. Fellows completed a pre-, post-, and post-post assessment for a set of three elementary LMT tests and a set of four middle-grade LMT tests. After Fellows complete the online modules, the LMT system generates results including a number-of-items-correct score, an item response theory (IRT) score, and an analysis of change over time in IRT scores. In this report, we share the change in IRT scores over time for the group of Fellows.

Observation data were analyzed using descriptive statistics and statistical tests. Changes over time in overall lesson scores were analyzed with t-tests for paired data. For individual rubrics, Wilcoxon Signed Rank tests for ordinal (non-parametric) paired data were used to identify changes in classroom practice over time. For samples with sufficient changes in data, the Wilcoxon test yields p-values and a z-score. For samples with an insufficient number of changes in data (e.g., in our study, 8 or fewer changes in paired data from pre to post), the Wilcoxon test provides p-values only for critical values of statistical significance of W(ns/r), where ns/r is the number of data points exhibiting change, and does not provide z-scores. Note that for ordinal data, descriptive statistics should include medians rather than means. However, we also chose to share means in our tables because they are provided with the Wilcoxon test for ease of interpretation and comparison by the reader.

Focus group interviews were analyzed systematically through data reduction and connection (Dey & Astin, 1993; LeCompte et al., 1993). The external evaluator conducted the focus groups and utilized Zoom to create audio-recordings and transcripts. For the Fellows’ focus groups, the external evaluator and a graduate research assistant (GRA) on the project (doctoral student; not a project Fellow) coded the transcripts line-by-line to identify themes within Fellows’ responses. Each independently coded two years of data (e.g., rater 1 coded years 1–2 and rater 2 coded years 3–4), identifying lines of transcript (direct phrases and quotes from Fellows) first for the main themes of mathematics, mathematics teaching, and leadership, and then for any themes that arose organically in the data. The evaluator and GRA met to confirm phrases/quotes included in the main themes for consistency across all 4 years, to form consensus and consistency on the organic themes each had identified in their independent coding, and to identify specific subthemes that appeared within each theme. A complete analysis of Fellows’ focus group data is provided in Boston et al. (2024). Herein, we include themes and quotes to describe the Fellows’ development and their perspectives on their development, as teacher leaders (RQ2), as well as to triangulate the quantitative data on changes in Fellows’ mathematics knowledge and practice (RQ1). Focus groups from project leaders and school administrators were used to triangulate data provided by Fellows and to explore connections between project components or factors that appeared to support leadership development. For example, different types of leadership roles were described by Fellows, and we examined the level of support (and enthusiasm) for the project communicated by Fellows’ school administrators to look for patterns. Project artifacts were used to identify leadership activities required by the project (e.g., course assignments) and self-initiated by Fellows (e.g., leadership activities log). The data analysis also includes intentional examination across data sources.

4. Results

First, we present results related to RQ1, “In what ways have teachers’ mathematical knowledge for teaching and instructional practices changed throughout their participation in the project?” based on findings from the LMT content assessment and the IQA classroom observation data.

4.1. Research Question 1: Changes in Mathematical Knowledge and Instructional Practices: Mathematical Knowledge for Teaching

4.1.1. Mathematical Knowledge

Table 1. Comparison of pre-post1 and pre-post2 LMT scores.

	Mean IRT Scores			Pre-Post1 (n = 14)				Pre-Post2 (n = 13)
Elementary	Pre	Post1	Post2	Change	t	p	Effect Size	Change	t	p	Effect Size
NCOP	0.62	1.01	1.22	0.38	0.8	0.44	0.17	0.60	3.01	0.01 *	0.44
PFA	0.64	0.86	0.84	0.22	1.55	0.15	0.29	0.20	0.73	0.48	0.16
GEOM	0.51	0.38	0.57	−0.13	−0.56	0.58	−0.1	0.06	−0.05	0.96	0.01
Middle Level
NCOP	−0.54	0.24	0.22	0.78	2.95	0.01 *	0.66	0.76	3.49	0.005 *	0.7
PFA	−0.74	−0.32	−0.26	0.42	2.37	0.04 *	0.39	0.48	3.12	0.01 *	0.44
GEOM 4–8	−0.56	0.06	0.04	0.62	4.45	<0.001 *	1.07	0.59	3.92	0.002 *	0.77
PDS 4–8	−0.50	−0.30	−0.07	0.20	2.09	0.06 **	0.6	0.43	2.29	0.04 *	0.73

* Statistically significant at p < 0.05. ** Marginally significant at p < 0.05.

provides LMT data on the pre-post (pre-post1) and post-post (pre-post2) comparisons in IRT scores. LMT assessments for the elementary modules were collected before (pre; April 2021) and after (post; December 2021) Fellows’ engagement in the first mathematics content knowledge for teaching course. Results for pre-post1 indicate small positive non-significant gains in 2 of the 3 modules. LMT assessments for the middle-level modules were collected before (pre; August 2021) and after (post; December 2022) Fellows’ engagement in the second mathematics content knowledge for teaching course. After the second course, Fellows’ pre-post scores on the four LMT middle-level modules all indicated significant positive growth, with effect sizes ranging from 0.39 to 1.07.

The post2 assessments (to assess maintenance/sustainability) for the LMT elementary and middle-level modules were administered at the completion of Fellow’s University coursework and doctoral dissertation research (May 2024). Across the three years of the program, significant growth occurred in Fellows’ mathematics knowledge for teaching as measured using the LMT Elementary Number Concepts and Operations module and all four middle-level modules. When comparing significant growth from pre-post1 to pre-post2, Fellows maintained the significant growth in content knowledge exhibited in Year 2 across the four LMT middle-level modules and enhanced their growth to the level of significant change in the Elementary Number Concepts and Operations module.

Figure 2 and Figure 3 provide an illustration of the changes in IRT scores for LMT elementary and middle-level modules. IRT scores are similar to z-scores, indicating how the performance compares (in standard deviations) to the overall mean performance (score of 0) of the population. Hence, positive IRT scores indicate that the mean score for the group of Fellows in this project was greater than the overall mean score of all teachers in the LMT national database for that module, and negative IRT scores indicate lower performance on the module than the national average in the LMT database. For the set of elementary LMT modules, Fellows’ mean scores at the beginning of the project were approximately half (0.51–0.64) a standard deviation above the national average. As indicated by the statistical tests, only Number Concepts and Operations increased significantly, with a change of 0.38 points, to end at 1.22 standard deviations above the national mean. The middle-level modules all began below the national average by at least a half standard deviation (−0.50 to −0.74), indicating that Fellows (the majority of whom taught elementary mathematics) began the project with less mathematical knowledge for teaching middle-level mathematics than the LMT national database. Fellows’ scores on each module exhibited a significant increase at post1, directly following the course focused on middle-level mathematics content knowledge for teaching, with two modules (Number Concepts and Operations and Geometry 4–8) exceeding the national average. At post2, only Number Concepts and Operations remained above the national average (0.22), though the increase of 0.43–0.76 points still indicated significant changes in Fellows’ content knowledge for teaching in all four modules.

To triangulate the LMT data, in Year 1 focus group data (prior to seeing the Year 1 LMT results), the project leader, who served as the instructor of the mathematics content for teaching courses, noted a slower-than-expected pace to the course. The instructor stated that Fellows entered the project through different pathways, having different prerequisite courses, and hence having different levels of prior knowledge related to mathematics content knowledge for teaching. The instructor adapted the pacing to move more slowly and felt the course ended with unfinished learning and less of a change in Fellows’ mathematics abilities. In Year 2 focus group data, the instructor expressed that Fellows were “displaying their vulnerability and asking questions, seeking support and being more successful with the mathematics of the course this semester” (Year 2 transcript). The instructor attributed this to Fellows coming together as a cohort, feeling more comfortable with themselves and the instructor, and in large part to Fellows’ experiences with another project leader in the Mathematics as Gateway experiences, where they engaged in conversations about the importance of exploration and curiosity in mathematics and vulnerability as mathematics learners. The instructor also expressed that Fellows who taught in middle-level classrooms were sharing more explicit connections to their teaching and their own understanding of middle-level mathematics topics than in the previous year, when the focus was on elementary mathematics.

In Years 2–4 focus groups, Fellows identify changes to their mathematics content knowledge. In many of these sample quotes (each from a different Fellow), Fellows indicate how enhanced content knowledge contributed to changes in instructional practice:

• “I’m reflecting back on how I was teaching before the …program, and how we never truly went over the “why” because again, I didn’t understand why things worked one hundred percent… We are conceptually understanding every aspect within the mathematics, which I did not have full background of, except for …whatever my teacher taught me when I was in first grade.” (Year 2)
• “…for me, one of the biggest (changes) I do now is, I now understand when kids solve it with a different strategy. I can make connections and make sense of their math. Because I can see what they’re doing, because a lot of it has been previewed with [the course instructor], and because I now can make the connections, I see my own students making connections” (Year 2)
• “So this semester specifically we’re going over middle school math, and I teach middle school math. I have literally taken segments of what she’s done with us in class and brought it into my classes. There was one lesson where we modeled equations using algebra tiles, and I immediately did that with my class that same week.” (Year 2)
• “I really feel like I’m becoming more of an expert in mathematics.” (Year 3)
• “I feel like now I could understand the student’s perspective a little bit more. And it helps me to make the math more accessible to my students.” (Year 4)

4.1.2. Instructional Practices

Fellows submitted videos of themselves teaching mathematics lessons in their own classrooms in Year 1 (September 2021), Year 3 (January–March 2023), and Year 4 (January–March 2024). In the scope of this report, we provide pre-post comparisons between lesson observation scores in Year 1 (pre; Fellows’ first semester in the program) and Year 4 (post; following Fellows’ completion of coursework in May 2023 and as they engaged in completing their dissertations in the spring semester 2024).

In the [observation tool], scores of 3 or 4 indicate high forms of cognitive demand and/or instructional practices within each rubric. Figure 4 illustrates the percentages of lessons scoring highly in each rubric across Years 1, 3, and 4. In most rubrics, there is a positive trend in the percentage of high-level scores over time, with the exception of Teacher Linking and Student Linking peaking in Year 3.

For the scope of this report, we provide additional insight into the increases from Year 1 to Year 4. In Year 1, 0–29% of lessons scored highly (score of 3 or 4) on each rubric, with medians at or below 2, indicating that instruction primarily focused on procedures and computations, without connection to the underlying mathematical meaning and understanding. All but one Implementation featured instruction primarily focused on procedures and computations, without connection to deep mathematical understanding. While all teachers held some form of whole group discussion following students’ work on the task, these discussions mainly featured presentations of procedural steps (e.g., Discussion mean and median of 2), even if more than one strategy was used, and were not characterized by rich mathematical explanations or discoveries (e.g., Student Providing mean and median ≤ 2). Twelve (12) of 14 lessons scored 2 or lower on each rubric except Tasks and Questioning, indicating a focus on computational or procedural aspects of the mathematics rather than connections, meaning, and sense-making. In many of these lessons, raters noted that teachers asked questions such as “How did you get that?” or “How do you know?” However, in many of these instances, the question pertained to a mathematical procedure rather than a mathematical concept (the “how” rather than the “why”) or resulted in the explanation being provided by the teacher rather than the students. Teachers appeared to have the “form” of ambitious instruction (e.g., ask for more than one strategy, ask students how they know, hold a discussion where students’ strategies are discussed), but not the “function” of using these moves to elicit thinking and reasoning. The teaching moves or questions were applied to tasks that did not have the potential for rich thinking, reasoning, or discussion (e.g., only 29% of lessons featured high-level tasks) or applied to procedural aspects of an idea or strategy rather than conceptual aspects. Raters noted that teachers were asking questions, but often about procedures students already knew, and were using “story problems” where the context did not support students’ reasoning and sense-making. Overall, lesson observation data from Year 1 indicate that the majority of mathematical work and thinking was provided by the teacher.

In Year 4, Tasks and Teacher Questioning continued to exhibit the highest scores across all rubrics, but now with Implementation, Teacher Press, and Student Providing posting means above 2.5 as well. At least half of the lessons (50–79%; a range of 7–11 lessons) scored highly on all rubrics except Teacher Linking and Student Linking (during whole group discussions). Raters noted the occurrence of Teacher Linking during small group discussions; however, the rubric is only rated during whole-group discussions. Student Linking was generally lacking in both small and whole group discussions. From Year 1 to Year 4, all rubrics (except Teacher Linking) show an increase in the number of lessons with high scores. Tasks, Implementation, Questioning, Teacher Press, and Student Providing show a shift of at least 7 lessons (≥50%) from Year 1 scores of 1 or 2 to Year 4 scores of 3 or 4.

To determine if the observed changes are statistically significant,

Table 2. Comparison of Year 1 (2021) and Year 4 (2024) lesson observations (n = 14; df = 13).

	Mean (Median) Year 1	Mean (Median) Year 4	Mean Difference	W(ns/r) **	z	p (One-Tailed)
Task	2.29 (2)	3.00 (3)	0.71	W(8) = 31	none given	<0.025 *
Implementation	2.07 (2)	2.71 (3)	0.64	W(7) = 28	none given	<0.01 *
Discussion	2.07 (2)	2.36 (2.5)	0.29	W(11) = 16	0.69	0.25
Questioning	2.00 (2)	3.14 (3.5)	1.14	W(12) = 70	2.73	0.003 *
Teacher Linking	1.64 (2)	1.86 (2)	0.22	W(8) = 12	none given	none given
Student Linking	1.29 (1)	1.21 (1)	−0.08	W(7) = 3	none given	none given
Teacher Press	1.93 (2)	2.79 (3)	0.86	W(13) = 57	1.97	0.02 *
Student Providing	1.79 (2)	2.50 (3)	0.71	W(11) = 40	1.76	0.04 *
Overall Score (paired t-test)	15.07	19.57	4.50		t = 2.43	0.015 *

* Significant at p (one-tailed) < 0.05. ** Wilcoxon Signed Rank Test.

provides a comparison of Year 1 and Year 4 lesson observation scores by rubric. Five individual rubrics and overall lesson scores exhibited statistically significant growth, which aligns with important changes in Fellows’ teaching practices and students’ opportunities to learn mathematics. In Year 4, statistically significant changes are evidenced in lessons featuring cognitively challenging tasks (Task) and implemented in ways that maintained students’ opportunities for thinking and sense-making (Implementation); teachers asking mathematically rich questions (Questioning) and following up on students’ responses with extended press for explanations and reasoning (Teacher Press); and students frequently providing thorough explanations (Student Providing). Areas of further enhancement include (1) the mathematical quality of students’ contributions to the whole group discussion (Discussion) (e.g., opportunities for students to share and discuss their mathematical work and thinking, including use of multiple strategies and representations), (2) teachers asking students to build on the ideas of their peers in whole group discussions (Teacher Linking), and (3) students building on the ideas of their peers during whole group discussions (Student Linking).

To triangulate the observation data, we draw on Fellows’ own descriptions of changes in their classroom practice in Years 2–4. In addition to quotes in the previous section where Fellows connect changes in their content knowledge to changes in their instructional practices, additional quotes from focus group transcripts describe instructional changes Fellows attribute to the project (each quote is from a different Fellow):

• “I’ve started actually evaluating the tasks that I present to my students. So I look at the potential of the task …and then my implementation of the task. I look at the students’ evidence and teachers’ questions to make sure that the quality of the tasks that I’m doing is more level four tasks where there’s that justification.” (Year 2)
• “now that we’ve been talking about the [observation tool] I’ve been noticing as I’m giving problems, ‘Boy, there’s a lot of procedural problems here.’ I need to change up what I’m asking the students. That’s fairly new, because we’ve recently started doing that, but it’s almost automatic. Now, when I’m looking at a lesson, I start rethinking what I need to start asking kids because I’m not asking the right questions.” (Year 2)
• “I did a lot of the talking prior to this, and now I’ve become more comfortable, like letting the student voice dominate the conversation, even if what they say isn’t correct. I give them some time to explain their thought process.” (Year 4)
• “before, I was so focused on, ‘Hey, what’s the answer?’ But now going through that process …something that used to scare them, is something that they look forward to… They enjoy engaging in math, because I have learned how to make math accessible and not scary.” (Year 4)
• “So I think just being able to take a little bit more time exploring the math at a deeper level is something that I wasn’t doing before this program.” (Year 4)
• “the students’ voice guides the conversation, and that’s something that’s really stuck with me…. Now, it’s like mistakes are springboards in my classroom. So when we go through a math problem, we look for evidence of where students made mistakes to understand why, and then we use that as a point of learning. So that’s something that I’ve definitely learned from [project leader] that I can utilize mistakes to help progress students’ learning.” (Year 4)

Fellows’ self-assessment of changes in their instructional practices aligns with significant changes observed in the Tasks, Implementation, Questioning, Teacher Press, and Student Providing rubrics.

As a summary of results for RQ1, the LMT and IQA observation data provide evidence of important and statistically significant growth in Fellows’ mathematics content knowledge for teaching and ambitious instructional practices throughout their participation in Years 1–4 of the project. Focus group data from a project leader (the course instructor) provides a possible explanation for why significant changes in mathematics content knowledge occurred in Year 2, and focus group data from Fellows in Years 2–4 indicate that the Fellows themselves attribute changes in mathematics content knowledge and instructional practices to their experiences in the project.

4.2. Research Question 2: Change in Fellows’ Leadership Activities

To investigate RQ2, “In what ways have teachers’ roles as mathematics instructional leaders changed throughout their participation in the project?” we consider prong 2 of our theory of action and how the project created space for Fellows to develop as teacher leaders. Data on Fellows’ leadership activities consist of (1) descriptions of course assignments and other program components intended to position Fellows as instructional leaders, supported by focus group data; (2) a log of Fellows’ self-reported leadership activities from Years 1–4; and (3) analysis of the type of leadership activities in which Fellows’ engaged, based on focus group interviews with project leadership, Fellows, and school administrators.

4.2.1. Project Components That Position Fellows as Teacher Leaders

Project leaders intentionally designed project components and course assignments to provide Fellows with opportunities to interact with their school principals in the role of teacher leaders.

Table 3. Project components to position Fellows as Mathematics Teacher Leaders.

	Year 1	Year 2	Year 3	Year 4
Teacher Leader Academy	x	x	x	x
Mentoring of school-based interns from a non-profit	x	x	x	x
Catalyzing Change Needs Assessment	x
Milestone 1 Gap Assessment		x
Affirming Learning Walks		x	x	x
Dissertation Research			x
Intentional Recognition within the District	x	x	x	x
Opportunities to Participate in the Mathematics Education Professional Community		x	x	x

identifies project components intended to position Fellows as mathematics teacher leaders throughout the project, and this section provides additional details about these opportunities.

TLA and Coursework

During the four years of the program, Fellows participated in a Teacher Leader Academy (TLA). Throughout the TLA and other project components, Fellows read practitioner-based articles and research articles on ambitious mathematics instruction and were introduced to a research-based classroom observation tool. In the first semester, within a course on school structure and systemic change, Fellows conducted a “Catalyzing Change Needs Assessment” and were required to share the results with their school principal. In the Catalyzing Change Needs Assessment, Fellows conducted an analysis of their setting, identified changes needed, suggested action steps, met with building administrators to share their findings, and wrote a thoughtful reflection related to the assignment and meeting with their administrator. The course instructor (a project leader) described the purpose of the Catalyzing Change Needs Assessment as providing “experience in initiating conversations as education leaders” (Year 1 Project Leader focus groups), resonating with the notion of “rehearsals” of leadership practice for beginning teacher leaders’ (e.g., analogous to Grossman’s (2021) use of rehearsals for beginning teachers).

In the Year 1 focus group interviews, Fellows noted the value of reading articles and books directly applicable to their teaching and leadership role, including policies and procedures in education and examples of educational research. Fellows described readings and class discussions as presenting strategies and best practices they could immediately apply in their classroom or as a leader in their school, specifically identifying Catalyzing Change (NCTM, 2020a, 2020b) as impacting their thinking and practice. The majority of fellows (n = 11; 79%) identified the Catalyzing Change Needs Assessment as positioning them as leaders in their schools and in the eyes of their principals in new ways, as described in the following sample of quotes (Year 1 focus groups):

• “we have to have a one on one with our principal about things that we’ve noticed in data we’ve collected, and for me that was really outside of my comfort zone.”
• “to step really out of my comfort zone and have those types of conversations with my principal and the curriculum resource teacher about changes that we may need to start making in math in our school, has really pushed me to be more outspoken.”
• “This is really pushing me and building me to have better leadership skills… I think the Catalyzing Change assignment really built my confidence, my ability for leadership.”

In the second year, the TLA course instructor (a project leader) introduced “Affirming Learning Walks” (ALW; Ross et al., 2023), a framework for instructional observations or walk-throughs where only positive feedback is provided to the observed teachers. In the role of instructional leaders, Fellows conducted the ALWs with their school administrators and other teachers in their schools. Fellows worked together to coordinate schedules, forming small groups of three to four members to visit each other’s schools. The district supported this initiative by providing substitute teachers for each Fellow. Throughout the first three years, the TLA course instructor actively participated in these visits; however, in the fourth year, the Fellows fully assumed leadership of the ALWs.

In Year 2 focus groups with project leaders, the TLA course instructor expressed how the ALWs were “reframing a classroom walkthrough” and had provided Fellows with “a platform to lift up their colleagues” and be seen in the role of instructional leaders in their schools. The instructor also attributed ALWs with engaging Fellows in identifying the teaching practices discussed in the course “in action,” such as ideas from the IQA, Catalyzing Change (NCTM, 2020a, 2020b), and Teaching Practices from America’s Best Urban Schools: A Guide for School and Classroom Leaders (Johnson et al., 2019).

In Year 2 focus groups, with Fellows, every Fellow (n = 14) individually identified the ALWs as valuable and positive experiences, enabling them to provide exactly the type of feedback teachers in their schools needed at the moment to lift morale. Fellows stated that it helped legitimize their role as teacher leaders within their schools and set the tone for the type of leader they wanted to be. Several fellows stated that typical classroom observations in their schools were negative experiences for teachers; however, with the ALWs, teachers expressed gratitude for positive feedback and invited the Fellows back for additional observations.

Recognition as Teacher Leaders

In supporting Fellows’ emerging roles as teacher leaders, the project also included opportunities for district administrators to recognize the Fellows as leaders, in addition to the course assignments and ALWs. For example, Fellows were recognized at a school board meeting in Year 1, where they shared their biographies and engaged in discussion with school board members. In Year 2, project leaders arranged a meeting between district leadership and Fellows to provide guidance on new state legislation on mathematics curriculum and instruction, as well as to support Fellows’ work in their own classrooms and in their role supporting other teachers in their schools. In Year 3, a project leader connected a group of Fellows with district-level administrators to plan mathematics professional learning experiences across multiple schools.

Mentoring School-Based Interns

Within the TLA, Fellows were assigned as mentors to volunteers conducting school-based internships with a city-wide non-profit organization. In Year 1, after initial meetings, Fellows were tasked with determining the direction and focus of their mentoring work with the interns and what contribution this work would make to the overarching goals of the project around ambitious mathematics teaching and learning in K-8 classrooms. Project leaders described this activity as a turning point in Fellows’ perceptions of themselves as teacher leaders and having ownership in the project, and Fellows described this aspect of the project as “positioning them as teacher leaders” (Year 1 Project Leader focus groups). Mentoring of the school-based interns continued across all four years of the project. By Years 3 and 4, Fellows were creating professional learning opportunities specifically for the interns and engaging interns in community outreach projects.

Milestones and Dissertation Research

The nature of research required by the project also served to position Fellows as instructional leaders within their schools. As part of their doctoral work, Fellows completed three required Milestones as precursors to their dissertation research. The first Milestone was the completion of a gap analysis paper. The Fellows analyzed a complex problem of practice within their school setting from both a psychological and an organizational perspective. They collected both quantitative and qualitative data and then recommended research-based, theoretically driven solutions to address the identified gap. For many Fellows, the gap analysis paper served as a sort of pilot project for the dissertation. Similar to the Catalyzing Change Needs Assessment, the Milestone 1 gap analysis was intended to provide an opportunity for Fellows to interact with their school principals in the role of an instructional leader. The second and third Milestones were directly related to the dissertation (e.g., developing a prospectus, completing an annotated bibliography, securing a dissertation committee, and writing the dissertation proposal). The dissertation served as the culmination of their doctoral degree and was conducted as a Dissertation in Practice. Fellows identified a need in their setting aligned to the Catalyzing Change Framework, with 12 Fellows using a school-level setting (either whole school, grade level, or grade band) and two Fellows using the district-level setting. To maintain focus and consistency on project goals, three of the project leaders chaired the Fellows’ dissertations, and all four project leaders served as committee members on any dissertations they were not chairing. Notably, two Fellows applied to the district for permission to continue their research beyond the completion of their dissertations.

In Year 3 and 4 focus groups, Fellows identified how their engagement with and in research has supported them to act as teacher leaders (each quote is from a different Fellow):

• “So I feel like I’ve gotten a lot more brave, and … I think that the brave part comes from knowing that what I’m advocating for is grounded in research, right? It is not just based on my feelings… But I think now that I am more confident in what I know in the literature, I am a lot more vocal about it.” (Year 3)
• “I think, throughout the program, especially in the last year or so, it’s more of like, no, this isn’t what’s good for kids. And I’m going to tell you what’s good for kids, and I can support why it’s good for kids. And then, do you want me to go have the conversation with other grade levels? … taking on that stance, I think, has changed my outlook in the program. And then, just feeling like, I do have something to say that matters, has been a big change.” (Year 4)
• “at the beginning, …I asked a lot of permission, and now, I know what’s best for our kids, at least, when it comes to this. This is what we went to school for. This is what I’m voicing more. And people are actually listening.” (Year 4)

Professional Community

Beginning in Year 2, project leaders also created pathways for Fellows to participate in the professional mathematics education research community. This support included helping to secure travel funds and/or helping Fellows find their own funding to start attending (and then presenting) at conferences. First, Fellows were encouraged to attend state and national professional conferences, attend presentations, and meet with mathematics education researchers. Fellows were then supported to submit presentations at these conferences, based on their own research as part of the Milestones program and their early dissertation research. Fellows were also encouraged and supported to present sessions for teachers at practitioner-centered conferences. Interestingly, two Fellows who did not have a high level of support from their school principals to engage in school-level leadership activities were the first two Fellows to actively embrace leadership opportunities in the professional community in Year 2 and to begin mentoring other Fellows to pursue these opportunities. For these two Fellows, the opportunity to engage in the professional community appeared to be an important pathway for leadership activities when school-based leadership activities were not readily available. Figure 5 (in the next section) provides quantitative data on Fellows’ leadership activities in the professional community, with all 14 Fellows engaged in the professional community by Year 4.

In summary, the project activities described throughout this section were intentionally planned by project leaders to provide a platform for Fellows to act and be recognized as mathematics teacher leaders in a variety of settings. By embedding intentional leadership activities into the project design, project leaders supported Fellows’ development as teacher leaders. Engaging in these activities over the course of the project provides evidence of changes in Fellows’ roles as teacher leaders.

4.2.2. Fellows’ Self-Reported Leadership Activities

In addition to programmed opportunities to engage as teacher leaders, Fellows also initiated leadership activities at the school, district, or professional community level. Notably, these leadership activities emerged authentically as Fellows gained knowledge and confidence in their ability to effectively engage in these activities. Project leaders encouraged and supported these efforts. Project leaders recognized that, during the first three years of the program, Fellows had limited availability due to their full-time teaching responsibilities while pursuing their EdD. To accommodate this, engagement activities remained optional until year four, at which point Fellows were required to participate in defined leadership activities beyond the standard programmed opportunities, such as ongoing support for our non-profit partner organization. Starting in Year 4, Fellows were given a list of defined leadership activities to choose from, such as submitting a manuscript for publication, giving a presentation, engaging in local/national service, and engaging in a district research project. Leadership activities were self-reported by Fellows, confirmed by project leaders, and compiled into the Leadership Activities Log each year. The Activity Log was initiated in Year 2 as a way to document their engagement as well as a motivational tool for the Fellows to encourage and support one another. Results from the leadership activities log are provided in Figure 5.

Figure 5. Fellows’ leadership activities.

Figure 5. Fellows’ leadership activities.

The number of school-based activities peaked in Year 1, though only half of the Fellows (n = 7) reported engaging in school-based leadership activities that year. The number of school-based activities remains relatively steady through Years 2 and 3, and the number of Fellows reporting such activities increases to 13 (out of 14; 93%) in Year 3. Note the emergence of leadership activities at the district level and professional community in Year 2. District-level leadership activities also peaked in Year 3 in the number of activities and number of Fellows. Professional community leadership activities grew steadily and peaked in Year 4, with all 14 Fellows engaging in some type of leadership activity at the professional level. We posit that the decline in school- and district-level leadership activities self-reported in Year 4 may be partially due to the nature of the activities Fellows chose to report: (1) in Years 2 and 3, Fellows recorded leadership activities requested by the school and self-initiated, whereas in Year 4, they appear to submit only self-initiated activities; and (2) Fellows came to see school-based leadership activities as part of their everyday work in Year 4 and hence did not enter them into the chart. By displaying the number and type of Fellows’ leadership activities over time, Figure 5 provides evidence to answer RQ2 as an indicator of changes in Fellows’ roles as instructional leaders.

4.2.3. Analysis of Types of Leadership Activities from Focus Group Data

Three types of leadership activities emerged during focus group interviews over the course of the project (Boston et al., 2024), which connects with data shared in Figure 4:

• Classroom-based, informal leadership activities (Rutledge, 2023): Fellows describe being the “math go-to person” at their school or grade-level; colleagues seeking them out and generating organic opportunities to provide support; providing colleagues with resources and instructional materials; sharing their knowledge of mathematics, mathematical strategies, and the development of students’ mathematical knowledge; and offering teaching suggestions to grade-level teams. In Year 4, more Fellows described modeling instructional practices for colleagues or inviting colleagues to observe their classrooms.
• School-wide or district-wide formal leadership activities: Fellows describe mentoring new teachers and pre-service teachers; presenting professional learning sessions; leading PLCs or grade-level teams; conducting Affirming Learning Walks; hosting district-wide observers in their classroom; observing classrooms and providing feedback; and initiating and leading school-wide or district-wide programs or presenting to other administrators. In Year 3, Fellows and administrators described how Fellows were now initiating and leading leadership activities with teachers and developing activities and programs for students (e.g., math or STEM teams or after-school programs).
• Participation in the professional mathematics education community: Fellows describe writing articles; participating in professional organizations; attending professional conferences and/or making presentations, including National Council of Teachers of Mathematics (NCTM) Virtual Conference, Noyce Leadership Summit, their [State] Council of Teachers of Mathematics, NCTM Annual Meeting and Research Conference, and NCSM Leadership in Mathematics Education Annual Conference. In Year 4, two Fellows gave international invited presentations, and four Fellows were selected as members of professional boards, committees, working groups, and/or journal department editors. Fellows also began encouraging their colleagues to attend and/or present at conferences, even assisting in securing funding for colleagues to attend these events.

Hence, data from project components (Table 3), Fellows’ log of leadership activities (Figure 5), and focus groups provide evidence of the changes in Fellows’ roles as mathematics instructional leaders over the course of the project (RQ2). With support from project leaders, Fellows exhibited growth in both the quantity and nature of leadership activities in which they engaged over Years 1–4.

5. Discussion: Factors That Appear to Support the Development of Instructional Leadership

With the goal to empower K-8 mathematics teachers as leaders to initiate and sustain improvements in our education system, we assert the need to provide (1) opportunities for teachers to develop the beliefs, knowledge, and practices necessary to thrive as experts in mathematics teaching and learning and (2) the space for their development as leaders to occur. Together, the two prongs support K-8 teachers to act and to be seen as mathematics instructional leaders in their schools, districts, and professional community. In the research presented herein, Fellows describe connections between different aspects of the project that support the value of the two-pronged approach in our theory of action. Based on these results, we suggest several factors that appear to support the development of instructional leaders.

First, we underscore the importance of enhancing teachers’ mathematics knowledge for teaching (including pedagogical content knowledge) and instructional practices as a worthy goal in itself, and also because growth in knowledge and practices subsequently enhanced teachers’ confidence to act as instructional leaders in this project. The increase in content knowledge evidenced on the Year 2 (post) and Year 4 (post-post) LMT results was a factor Fellows self-identified in the focus groups as supporting their confidence to initiate leadership activities and as minimizing their feelings of imposter syndrome. Fellows describe how enhanced content knowledge equipped them as teacher leaders with the background knowledge necessary to support peers, make suggestions, evaluate curriculum, and create or adapt tasks, resonant with prior research on the importance of content knowledge on leadership activities (e.g., Quebec Fuentes & Jimerson, 2020; Steele et al., 2015). This is exemplified in a Year 4 focus group quote:

“What makes me a leader in my school is the fact that my content knowledge can just fly… this week a first grade teacher came up to me and said, I hate balance equations … and so I immediately am able to pull out, ‘Well, you know, we want them to understand about the equal sign and what that means. That it doesn’t mean that the answer is coming next. And have you tried using a balance scale and helping them to understand what’s happening there?’ And she’s like, I never thought of that. Let me go try it.’ And so that content knowledge is, I think, what makes us leaders”.

Similarly, Fellows expressed how their new expertise in ambitious mathematics pedagogy enabled them to offer advice, insight, and strategies into mathematical content, curriculum, and student thinking; for example: “With the [observation tool], I feel like I am a lot more confident with using things like that to edit what we’re given by the district, and I do it with a lot more confidence now, because I know what needs to change, so that students can get better tasks” (Year 2). Fellows identify how their learning of the research, based on ambitious mathematics teaching and learning (developed from their coursework, milestone projects, and their own dissertation research), equipped them to serve as teacher leaders, particularly to advocate for ambitious mathematics instruction. Hence, Fellows’ self-reports confirm the changes in knowledge and instructional practices identified in the data and suggest that enhanced knowledge of mathematics, ambitious mathematics instruction, and research supported their ability (and confidence) to act as instructional leaders.

Third, embedding leadership activities into program requirements positioned teachers to act and to be seen as instructional leaders in their schools and with opportunities to “practice” being in the role of instructional leaders (e.g., analogous to the value of rehearsals or approximations of practice described by Grossman (2021)). In Bush et al. (2025), we describe how the ALWs were implemented using the cognitive apprenticeship approach of modeling, coaching, and fading (Collins et al., 1987), providing both the space and a developmental pathway for Fellows to grow into their role as teacher leaders. Fellows noted how the assigned leadership activities provided initial opportunities for them to interact with school administrators as instructional leaders. In addition to embedded leadership activities at the school level, project leaders also created opportunities for Fellows to be recognized publicly and to participate as teacher leaders within the district and professional community. Professional conferences provided Fellows with networking opportunities, where they were able to attend sessions by and meet in person several researchers whose work they had read. In giving presentations, not only were Fellows able to act as experts or leaders, but they also realized they had something worthwhile and valuable to contribute to the discussion of ambitious mathematics instruction within the professional community. Findings by Barth et al. (2023) and Berg and Zoellick (2019) point to the strong impact the role of recognition plays on teacher leader identity.

6. Conclusions

In this project, expertise in K-8 mathematics content knowledge and ambitious instructional practices appeared to equip teachers to act as mathematics teacher leaders in their schools, districts, and the professional community. Additionally, expertise in mathematics education research also seemed to support Fellows’ role in advocating for ambitious mathematics instruction. As implications for practice, our results suggest that developing teachers’ expertise in knowledge, instructional practice, and research can provide the foundation for teachers to act and be seen as teacher leaders in the three types of leadership roles identified in our work: (1) informal or classroom-based leader that other teachers go to for ideas, resources, support, feedback, or as a model of ambitious instruction; (2) school or district-level leaders of PLCs, grade-level teams, or professional learning experiences; or (3) in the professional community.

As a second implication for practice, while providing opportunities for teachers to develop expertise is essential, so too is providing teachers with embedded, intentional opportunities to act and be seen in the role of teacher leaders, in each of the three types of leadership roles. We hypothesize that early assignments embedded in a program (e.g., the Catalyzing Change Needs Assessment and the Affirming Learning Walks) can serve to initiate conversations that position teachers as teacher leaders with their principals and colleagues. Over time, embedded assignments and other project components (e.g., the Milestones and dissertation research) can be used to scale up and support teachers’ engagement in leadership activities within the school, district, and professional community.

Future work to support our theory of action would include replication studies that utilize the theory of action and general project components discussed herein to design and study the development of teacher leaders (classroom-based or formal leadership roles), including the development of teacher leaders in other grade bands or content areas.

We acknowledge limitations to our study, beginning with the possible lack of generalizability due to the small sample size. Having a small group of Fellows allowed for more individualized attention and support than what might be possible with a larger cohort and perhaps contributed to overall positive outcomes. Additionally, a relatively small number of Fellows distributed across a very large school district may have provided increased opportunities for leadership activities than what would be experienced by larger cohorts and/or smaller school settings. A second limitation possibly impacting our results is the prior experiences of Fellows. Many Fellows began the project having completed a master’s degree program aligned with the mathematical and pedagogical goals of this project. These prior experiences positioned Fellows to take the next step in their professional growth and leadership development. Finally, the specific focus on K-8 mathematics content and pedagogy may not directly transfer to the development of teacher leaders in other subjects and contexts. Despite these limitations, we contend that our model for developing teacher leaders could transfer to other subject areas and contexts. The first prong would maintain the focus on developing teachers’ content and pedagogical expertise, specific to the desired grade band and content area. Similarly, the second prong would provide opportunities for teachers to be seen and to act as instructional leaders, through intentional assignments such as the needs assessment and ALWs, and intentional experiences such as attending and presenting at professional conferences.

In conclusion, our work indicates that positioning K-8 mathematics teachers as instructional leaders requires providing them with content and pedagogical expertise and the space to enable such expertise as teacher leaders in their schools, districts, and professional community. Our work is in service of the overall goal that well-equipped mathematics teacher leaders can support sustained change in mathematics teaching and learning from within schools themselves, so that all students have access to effective and impactful high-quality mathematics learning experiences.