Teacher Professional Development and Student Mathematics Achievement: A Meta-Analysis of the Effects and Moderators

Abstract

An essential element for increasing student mathematics achievement is providing teachers with professional development (PD) aimed at the design and delivery of high-quality mathematics instruction. To date, however, there is a lack of consistent data on the efficacy of PD on student outcomes; moreover, there is a need to explore PD characteristics as moderators of student outcomes. The purpose of this meta-analysis was to synthesize the effects of teacher PD on mathematics outcomes for students in PreK through 12th grade. Additionally, this study explored whether specific characteristics (i.e., grade level, format, PD focus, PD days, and inclusion of students with or at risk of disabilities) served as potential moderators of the effect of PD programs. The 20 studies included in the review investigated PD intended for in-service teachers who work with a full range of learners, including students with or at risk of disabilities. The results showed that there was a positive average effect of PD on student mathematics outcomes (g = 0.34, 95% PI = [−0.47, 1.15]), with wide heterogeneity of most effects ranging from −0.20 to 5.83. In addition, the five moderators examined in this meta-analysis were not significantly correlated with the relation between PD efficacy and student mathematics outcomes. Recommendations for improving the features of PD programs as well as exploring mechanisms of change hypothesized to improve student mathematics outcomes are discussed.

1. Introduction

With national efforts to improve mathematics achievement for students, professional development (PD) for teachers has been put forth as a central focus for mathematics education reform (National Governors Association Center for Best Practices & Council of Chief State School Officers, 2010; National Research Council, 2011). In this study, we operationalized PD as deliberate training, coaching, or professional learning communities (PLCs) to support in-service teachers’ content knowledge or pedagogical practices for teaching mathematics to the full range of learners in PreK–12 classrooms. PD can play a key role in improving teacher quality and effective delivery of instruction (Darling-Hammond et al., 2017; Koellner et al., 2024; Sims & Fletcher-Wood, 2021), which in turn may increase student mathematics achievement (Dash et al., 2012; Department for Education, 2016; K. K. Hill et al., 2017; Prast et al., 2018).

Despite the acknowledged importance of PD in teacher learning, a consensus is lacking in the literature about the overall effects of PD on student outcomes, as well as potential moderators of those effects (Garrett et al., 2019; Lynch et al., 2025; Kraft et al., 2018). Empirical evidence from studies focused on PD programs for mathematics teachers has returned mixed results regarding the effects of PD on student outcomes (e.g., for positive results see Brendefur et al., 2016, 2022; Copur-Gencturk et al., 2024; Jacobs et al., 2007; Roschelle et al., 2010; for null results see Garet et al., 2010; Jacob et al., 2017; Randel et al., 2016; Santagata et al., 2010). Thus, the purpose of this meta-analysis is to quantify the efficacy of PD on student mathematics achievement outcomes and examine features of PD programs and student-level characteristics as moderators of those outcomes.

1.1. Previous Reviews of Studies of PD on Student Mathematics Outcomes

To date, we identified only five systematic reviews or meta-analyses that summarized the effects of PD on student mathematics outcomes. Kennedy (1998) conducted a systematic review of 12 studies published between 1979 and 1996 that focused on examining the content of PD and its subsequent effects on student outcomes in mathematics and science. Eight of the 12 studies focused specifically on mathematics outcomes. Of the mathematics studies, Kennedy found the studies focusing on subject matter knowledge and on student learning of particular subject matter (e.g., number facts, computation) yielded a larger average effect (effect sizes range from 0.42 to 0.70) compared to studies focusing on teachers’ behaviors (e.g., teaching practices, changes in teacher knowledge; effect sizes range from −0.41 to 0.29).

Clewell et al. (2005) extended Kennedy (1998) by conducting a systematic review of 18 studies published between 1979 and 2004. They also focused on the effects of PD on student outcomes in mathematics and science. Clewell et al. looked at the types of content focus based on Kennedy’s classification, and reviewed the key PD characteristics (e.g., subject matter, grade span, participants, total contact hours, study duration, and effect sizes). They concluded that effective PD included content tied to curriculum. The authors also reported that effective PD included a minimum of 80 contact hours to observe a change in teachers’ instructional practices and a minimum of 160 contact hours to observe a change in the classroom environment.

Overall, the studies by Kennedy (1998) and Clewell et al. (2005) represented an important shift toward focusing on student learning outcomes in in-service teacher PD. Consequently, Blank and de las Alas (2009) conducted a meta-analysis of 16 studies, published between 1989 and 2007, synthesizing the effects of PD on student mathematics outcomes. Blank and de las Alas also investigated to what extent the characteristics of PD (e.g., content focus, duration, coherence, active learning, and collective participation of teachers) contributed to PD effectiveness. Their results suggested mathematics-focused PD yielded a significant and positive mean effect (pre-post design mean ES = 0.21; post-only design mean ES = 0.13) on student mathematics achievement. The authors reported larger average effects on student mathematics achievement for studies conducted at the elementary level, compared to middle and high school.

Yoon et al. (2007) and Gersten et al. (2014) investigated the effect of PD on student mathematics outcomes by applying the What Works Clearinghouse (WWC) research design standards. In a review of more than 1300 studies of PD (including science, mathematics, reading, and English/language arts) conducted between 1986 and 2006, Yoon et al. found that only nine studies demonstrated the methodological rigor necessary to meet the WWC standards. Of these nine studies, all focused on elementary grades and only two focused on mathematics. The sole negative effect across these nine studies was from a mathematics study (fraction computation). Gersten et al. extended the work of Yoon et al. by focusing specifically on PD in the area of mathematics in a review of 32 studies published between 2006 and 2012. Of five studies that met WWC design standards, Gersten et al. found two studies that demonstrated positive effects (ES range = 0.09–0.84) on student mathematics achievement (i.e., Perry & Lewis, 2011; Sample McMeeking et al., 2012). While Yoon et al. and Gersten et al. focused on investigating the quality of PD studies, the current study aims to fill a gap in the literature by using meta-analysis to determine the average effect of teacher PD on student mathematics achievement and the extent to which specific features of PD affect student outcomes. In short, previous studies have tended to focus on mathematics, science, and reading together, or have focused on study quality; the literature about mathematics specifically needs to be brought up to date.

1.2. Potential Moderators of PD Efficacy on Student Outcomes

Despite growing research on PD and its efficacy, there is a lack of consensus about which moderators affect the relationship between PD and student outcomes. Previous studies claimed that inconsistency among PD characteristics made it difficult for researchers to investigate the extent to which those characteristics determine PD effectiveness and in turn influence student outcomes (Darling-Hammond et al., 2017). Because of this variation, we limited our investigation to the following five moderating variables: (a) grade level, (b) format, (c) PD focus, (d) PD days, and (e) inclusion of students with or at risk of disabilities. Moderators (a) through (d) are malleable characteristics that appeared frequently as PD characteristics in our review of the literature. By focusing on these malleable characteristics, the results of the current meta-analysis will provide school administrators with targeted recommendations as they identify PD needs for teachers of mathematics. Although not a malleable characteristic, moderator (e) was selected to investigate if the effects of PD on student outcomes were different for students who have different learning needs. A discussion of the literature on these chosen variables and a rationale for exploring each one follows.

1.2.1. Grade Level

According to previous studies, PD may have different effect sizes on student outcomes depending on grade levels. Blank and de las Alas (2009) found that studies conducted in elementary grades had larger effects than those conducted in secondary grades. However, the results varied depending on when separate effect sizes were computed across grade levels (e.g., positive results for Grade 6, negative results for Grade 7, and null effects on Grade 8; META Associates, 2006). This finding has been replicated in more recent studies. For example, Taylor et al.’s (2018) analysis reported inconsistent associations between student outcomes and grade level. Similarly, Lynch et al. (2019) found no significant relation between these variables.

1.2.2. Format

Teacher PD can be delivered in various ways, in person or virtually, including training, workshops, coaching, PLCs, or a combination of these formats. As PD has evolved over time, it has moved beyond traditional classroom settings, leveraging online platforms and hybrid models to train in-service teachers (Darling-Hammond et al., 2017; Stevenson et al., 2015). The number of online PD options has grown due to its perceived benefits, including flexibility, access, networking, and cost effectiveness (Lay et al., 2020). PD can focus on a single component, such as in-person training, or it can be combined with other formats like integrating virtual training with coaching support (Piper et al., 2018). However, rigorous evidence to support effective PD design and delivery remains scarce (Sims & Fletcher-Wood, 2021; Yoon et al., 2007). Further, previous studies have concluded that the variety of formats used in PD makes it difficult to determine the extent to which format affects the relationship between PD and student outcomes (Didion et al., 2020).

1.2.3. PD Focus

The focus of PD can be subject-specific content, pedagogy, or a mixture of the two. In recent years, there has been a growing interest in how content-focused PD in mathematics deepens teachers’ content knowledge (Ball et al., 2008; Garet et al., 2016). Some studies indicated that content-focused PD had a positive impact on student achievement, although most of those results were not statistically significant (e.g., Jacobs et al., 2007; Jacob et al., 2017). Other researchers reported that PD highlighting a combination of content knowledge and pedagogical strategy was effective in improving student outcomes (Clewell et al., 2005; Ingvarson et al., 2005). This notion stems from the belief that teachers should have a solid foundation in both content knowledge and pedagogical strategies that can be adapted in their classrooms.

1.3. PD Days

PD days is defined as the number of hours spent on PD (Kennedy, 2016). Several researchers have focused on identifying the optimal number of days that teachers should attend PD to maximize student outcomes (Darling-Hammond et al., 2009; Desimone, 2009; Garet et al., 2010, 2016; Guskey & Yoon, 2009; Yoon et al., 2007). For example, Yoon et al. (2007) reported that PD duration should consist of more than 14 h because less than that demonstrated little to no effect on student achievement outcomes. Other scholars, however, have reported the need for greater intensities, including 20 h (Desimone, 2009), 30 h (Guskey & Yoon, 2009), 49 h (Darling-Hammond et al., 2009), and 68 h (Garet et al., 2010).

Inclusion of Students with or at Risk of Disabilities

There has been an increasing concern regarding a lack of studies demonstrating teachers’ abilities to support diverse student populations in their classrooms (Prast et al., 2018; Valiandes & Neophytou, 2018). Approximately 65% of students with disabilities spend more than 80% of their school day in general education classrooms (National Center for Education Statistics, 2019). Thus, it is vital to identify if PD effects vary when classrooms include students with disabilities. The provision of instructional support to students with a history of low achievement may be especially critical for them to benefit from rigorous mathematics instruction to minimize the observed widening of achievement gaps over time (Fuchs et al., 2021). The literature suggests that teachers are rarely supported with PD that focuses on students with disabilities (Darling-Hammond et al., 2009), creating difficulty when it comes to supporting these students and other struggling learners (e.g., students with or at risk for mathematics learning disabilities, students who are bilingual) in their classrooms (Allsopp & Haley, 2015). In conclusion, the five moderators that are the target of the current analysis have mixed findings across studies, indicating a need for further investigation with meta-analytic techniques.

1.4. Purpose of the Current Study

The present study fills a gap in the literature in the following ways. First, compared to the previous literature on PD (e.g., a combination of reading, mathematics, and science), the current study focuses exclusively on mathematics PD, as a potential method of remedying the decrease in mathematics achievement in the nation (National Center for Education Statistics, 2022). Second, the current study includes student-level characteristics as moderators, allowing us to investigate how these characteristics affect the relation between PD and student outcomes. Third, the current study adapts up-to-date meta-analytic procedures (i.e., meta-analysis with robust variance estimation using a correlated and hierarchical effects working model; Pustejovsky & Tipton, 2022) for better estimation of effect sizes and moderator effects. Fourth, research on PD has grown, leading to the need to summarize recent research findings by synthesizing the past 25 years of studies, between 2000 and 2024, to understand current practices. Taken together, a key aim of the current study is to add to the evidence that PD can enhance students’ mathematics achievement. The following research questions were addressed:

• What are the main effects of PD on mathematics achievement for students in PreK–12?
• To what extent do features of PD (i.e., grade level, format, PD focus, PD days, grade level, and inclusion of students with or at risk of disabilities) moderate its effects on student mathematics achievement?

2. Method

2.1. Search Procedures

We conducted a comprehensive review of the literature. First, we searched through four databases: Academic Search Complete, Education Source, ERIC, PsycINFO. The Boolean search string was: “professional development” OR “career development” OR “professional education” OR “teacher development” OR train* OR coach* OR “communit* of practice” OR PLC OR “professional learning communit*” OR “inservice teacher education” OR AND math* OR algebra OR geometry AND teachers. The search was completed within peer reviewed journals from January 2000 to August 2024. Second, we conducted a manual search of the following journals specializing in teacher education and mathematics: Review of Educational Research, Journal of Research on Educational Effectiveness, Journal of Mathematics Teacher Education, and Teaching and Teacher Education from January 2000 to August 2024. During the manual search, we reviewed the tables of contents of each journal to identify any additional studies that met this study’s inclusion criteria. Further, we conducted a backward and forward search of included studies to identify other relevant studies. Finally, we conducted a first author search of all included studies to investigate the first author’s other published studies.

2.2. Inclusion Criteria and Exclusion Criteria

To be included in this meta-analysis, studies had to meet seven inclusion criteria.

• Topic of PD. Each study included teacher PD. The format of the PD in the studies varied, including training, workshops, coaching, or PLCs. PD learning goals, as defined by the studies, all focused on improving teacher knowledge as a way of increasing student mathematics achievement.
• Population. Each study included in-service teachers. Studies including preservice teachers were excluded.
• Grade. Each study included teachers who taught PreK–12.
• Time. Each study was published in English between January 2000 and August 2024. We selected a start date of 2000, as this date aligned with the release of the National Council of Teachers of Mathematics (NCTM, 2000) Principles and Standards, which was a new impetus for altering the direction of mathematics standards in the United States. The 2000 NCTM Principles and Standards included recommendations for preschool learners not present in the initial 1989 NCTM standards, as well as more details for specific skills to be taught at each grade, which significantly impacted the broader standards movement in U.S. education.
• Study design. Each study used a randomized controlled trial or a quasi-experimental design. Studies that used literature reviews, single-subject designs, qualitative methods, and quantitative methods that used descriptive analyses, correlational designs, or mixed methods were excluded. This choice was made because a meta-analysis requires the selection of certain types of study designs to extract necessary information (e.g., pretest and posttest scores for treatment and control group).
• Type of publication. Each study was published in peer-reviewed educational journals in English. Gray literature (e.g., dissertations, book chapters, conference proposals, and technical reports) was excluded. In this study, our exclusion criterion sought to reduce the complexity and heterogeneity of gray literature, making the processes of search, analysis, and coding more manageable and replicable (Zhang et al., 2020). In addition, we made this decision to ensure that each study was reviewed by experts in the field as part of the peer review process.
• Outcome measure. Each study included at least one student mathematics achievement outcome measure.

2.3. Screening Process and Study Identification

This study used two search methods to identify relevant studies (Figure 1). An electronic search identified a total of 12,768 studies. During this initial screening, 4314 studies were immediately removed because they were duplicates (k = 2302) or not peer-reviewed articles (k = 2012), yielding 8454 articles. The 8454 studies were then screened based on titles of the articles to identify if they were on the topic of PD in mathematics. A number of studies were removed as they were irrelevant to PD (k = 6998), irrelevant to math (k = 633), or identified as additional duplicates (k = 192); this title screening search yielded 631 articles. In the following step, the abstract search was reviewed to determine whether the research met the seven inclusion criteria. During this process, a number of studies were removed because they did not meet one or more of the following inclusion criteria: (a) research study (k = 28), (b) group design (k = 239), (c) preK-12 teachers (k = 33), (d) in-service teachers (k = 93), (e) about PD (k = 35), (f) focused on PD on student mathematics outcomes (k = 11). This electronic abstract screening search yielded 192 articles, qualifying for a full-text screening. In addition, 91 studies from the other search methods, including table of contents hand search (k = 46), forward and backward searches (k = 43), and first author searches (k = 2), qualified for full-text screening. The electronic and other search methods yielded 283 studies, which qualified for a full-text screening. During the full-text screening process, a number of studies were removed for the following reasons: (a) the studies did not use group designs (k = 89), (b) did not focus on preK-12 in-service teachers (k = 23), (c) did not focus on PD in mathematics (k = 54), (d) did not have outcome measures for students (k = 71), and (e) did not provide sufficient information to calculate effect sizes (k = 15), and (f) were duplicates (k = 11). At the end of the full-text screening process, 20 studies satisfied all the inclusion criteria.

The first and second authors led the screening process with two graduate research assistants (one master’s and one doctoral student in school psychology). The first author holds a PhD in special education and the second author holds a PhD in quantitative methods. Both authors have experience with conducting meta-analyses. The first author oriented the two research assistants through a 1 h screening training, an overview of inclusion criteria, instruction on the coding process, and practice opportunities with two articles. Then these two assistants coded two articles independently; the calculated interrater reliability (IRR) for this process was 91%. We calculated the IRR as [agreements/(agreements + disagreements) × 100]. Throughout the entire coding process, the first author held 1 h weekly meetings to address ongoing questions, discuss disagreements about coding, and provide continued support for the purpose of screening process reliability. The first author and the two graduate assistants double-coded 20% of the abstract, and the IRR was 89. The full screening was 20% double-coded, and the IRR was 84.5. All the discrepancies were discussed during these meetings and allowed all coders to reach 100% consensus. The second author double-checked the screening process by counting the number of studies that met eligibility for each stage, using the R program.

2.4. Coding Procedure

We developed a coding sheet and protocol based on the guidelines proposed by Cook et al. (2015) and the Institute of Education Sciences (2014). The coding sheet included the following study features: grade level, format, PD focus, PD days, and inclusion of students with or at risk of disabilities. Grade levels were categorized into a dichotomous variable: preK/kindergarten/elementary school (Grades 1–5) was coded as 0, and middle/high school (Grades 6–12) was coded as 1. Format refers to whether PD was provided via in-person workshop (coded as 0), or a combination of in-person workshop with another PD format such as online workshop, coaching, follow up meetings, and PLCs (coded as 1). PD focus of the content was coded as general pedagogical knowledge (coded as 0) or specific mathematics content knowledge (coded as 1), based on the primary focus. The combination of both pedagogical and content knowledge was coded as 2. PD days was coded as a continuous variable indicating days, such as 1 day or 10 days. A day was assumed to be 8 h long; if the study described the PD in hours, the variable was coded accordingly. For example, if the PD lasted only 4 h, PD days was coded as 0.5 days. Inclusion of students with or at risk of disabilities was coded as 1 if the PD included strategies for integrating these students into the classroom or presented data on this group. If PD did not include information on students with or at risk of disabilities or was focused on teaching strategies without any specific mention of these students, it was coded as 0.

The first author and second author tested the coding sheet using an example study. The IRR for this example study was 89%. After discussion, the two authors reached a 100% consensus, and the coding sheet was revised accordingly. To ensure the coding procedure was followed consistently, the first author independently coded all studies, and 20% of the studies were double-coded by the second author to establish IRR. These two coders held 1 h weekly meetings to resolve any discrepancies and discuss potential coding issues. Overall, the average IRR was 89.27% (range across categories = 81% to 96%). The IRR was 96.45% for grade level, for 90.15% format, 87.21% for PD focus, 81.56% for PD days, and 91% for the inclusion of students with disabilities. The first and second authors discussed any discrepancies and reached a consensus before the analysis stage; the final IRR was 100%.

2.5. Effect Size Calculation

We calculated the standardized mean of effect sizes of the PD for each study using Hedges’s g (Hedges, 1981). The effectiveness of PD reported by each study was based on the experimental or quasi-experimental group design, including independent groups in cross-sectional data (e.g., PD group and non-PD group), matched groups in repeated measures (e.g., pretest and posttest scores for one group), and independent groups of repeated measures (e.g., pretest and posttest scores for PD group and non-PD group). For studies that did not report the correlation between the pretest and posttest scores, we assumed the correlation of 0.6, considering the minimum correlation between repeated measures (Polly et al., 2017; Prast et al., 2018; WWC, 2020). If a study did not report sufficient descriptive statistics, we used other statistics to calculate the standardized mean difference. For example, we used F statistics in Brendefur et al. (2016) and McGatha et al. (2009), and Z statistics in Walker et al. (2012), with sample sizes to calculate the standardized mean difference.

2.6. Analysis

Before conducting meta-analyses, we examined the outliers in the raw effect sizes by using Tukey’s (1977) definition of outliers. If any values were less than the first quartile minus 1.5 × interquartile range (IQR) or greater than the third quartile plus 1.5 × IQR, we detected them as outliers and substituted ±1.5 × IQR. We conducted a sensitivity analysis with unadjusted and adjusted outliers to examine if the results changed significantly.

We employed a random effects meta-analysis with robust variance estimation (RVE) to examine the heterogeneity across the effect sizes. RVE addresses the issue of dependency among multiple effect sizes within a study, which could violate the assumption of the meta-analysis that each effect size should be independent (Hedges et al., 2010). In this case, RVE provides a robust standard error (SE) estimator even with the unknown covariance structure of the effect sizes. We assumed a 0.8 correlation for RVE and conducted a sensitivity analysis to examine if the effect size estimates differed across the correlation size. Additionally, a correlated and hierarchical effects working model (CHE; Pustejovsky & Tipton, 2022) was used while using RVE. This working model takes account of both within-study and between-study heterogeneity in true effect size, as in the hierarchical working model, while also handling correlation between the effect sizes within the study while assuming the constant correlation, as in the correlated working model.

Given the limited number of studies included, we employed small sample correction to adjust for inflated Type I errors in test statistics based on RVE using t tests (Tipton, 2015; Tipton & Pustejovsky, 2015). The meta-analysis was estimated using a restricted maximum likelihood estimation (REML). We reported tau-squared statistics, which assess heterogeneity among effect sizes, and I-squared statistics, the proportion of the observed variance that explains true differences in effect size estimates (Borenstein et al., 2011).

Following the meta-analysis, we conducted a meta-regression to evaluate the moderator effect on the relation between the PD and the student mathematics outcomes. We began by including all moderators in the model. Finally, we applied the Benjamini–Hochberg correction for the adjusted p value to control Type I errors across multiple statistical tests (Benjamini & Hochberg, 1995; Polanin & Pigott, 2015).

Lastly, we evaluated potential publication bias among effect size estimates without outliers. Publication bias may occur for several reasons, such as small-study effects or unpublished studies. To address publication bias, we used a funnel plot and a modified version of Egger’s regression test (Egger et al., 1997; Pustejovsky & Rodgers, 2019).

All the analyses were conducted in R 4.4.2 (R Core Team, 2024). We used the metafor (Viechtbauer, 2010), clubSandwich (Pustejovsky, 2017), and robumeta packages (Fisher & Tipton, 2015) to calculate effect sizes, conduct the meta-analysis, and demonstrate meta-analysis results. Only one value was missing for the intensity moderator, and we employed list-wise deletion to handle this missing datum. We followed the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines for reporting the results (Moher et al., 2009, 2015).

2.7. Examination of Outliers

According to Tukey’s (1977) definition of outliers, we detected seven outliers: two effect sizes from Saxe et al. (2001), three from Bruns et al. (2017), and two from Wang et al. (2013). We adjusted these outliers to the value of ±1.5 × IQR. The weighted averages of the effect of PD with adjusted and unadjusted outliers were both reported in the subsequent meta-analysis.

2.8. Publication Bias

Figure 2 illustrates the funnel plot that demonstrates the effect sizes included in the meta-analysis. The x axis of the graph indicates the effect sizes, and the y axis shows the SE. The smaller SE demonstrates the effect sizes with greater weights. This funnel plot shows the symmetry of the effect sizes, indicating no publication bias in the included studies. The result of Egger’s regression also showed that the included studies have no publication bias (t = −0.49, df = 85, p = 0.63). Thus, we concluded that the included studies provided representative overall effect sizes for the PD effect. The overall effect size was not adjusted to address potential publication bias.

3. Results

Within the 20 studies that examined the effect of PD, 87 effect sizes representing student achievement outcomes were identified. The number of effect sizes per study varied between one and 18 (M = 4.35 effect sizes per study). The total number of participating teachers across the studies was 21,271 (range: 14 to 5030 per study). The total number of participating students across the studies was 25,010 (range: 245 to 5658 per study). A list of study characteristics is shown in

Table 1. PD Characteristics of the Included Studies.

Study Authors (Year)	Title of PD	Topics of PD	Format	Grade Level	No. of Participants	No. of Included Students with Disabilities	Number of Days (h)	Measure of Student Mathematics Outcomes
Antoniou and Kyriakides (2013)	The Dynamic Integrated Approach	Critical reflection and focus on teaching skills of the dynamic model which correspond to teacher developmental stage and needs	In-person	Elementary	130 teachers 2356 students	—	12 days	Student achievement in mathematics (criterion-reference tests)
Brendefur et al. (2013)	Professional Development and Activities	Content knowledge, active learning, coherence	In-person	PreK	16 teachers 111 students	—	1 day	Prekindergarten – Primary Screener for Mathematics
Brendefur et al. (2016)	Developing Mathematical Thinking	Mathematics, student thinking, and pedagogy	In-person Summer workshop Ongoing follow-up PD	K-5	993 teachers (T = 424, C = 569) 3045 students (T = 1457, C = 1588)	242	18 days	Idaho State Achievement Test
Brendefur et al. (2022)	Developing Mathematical Thinking	Mathematics, student thinking, and pedagogy	In-person	Elementary	184 teachers (T = 98, C = 86) 4618 students (T = 2470, C = 2148)	—	22 days	Measures of Academic Progress
Bruns et al. (2017)	Continuous Professional Development Course: EmMa	Competence-orientation, participant-orientation, case-relatedness, various instruction formats, stimulation cooperation and fostering (self-)reflection	In-person	Early childhood	99 teachers (T = 51, C = 48)	—	100 h	Mathematical content knowledge test
Campbell and Malkus (2011)	Coaching	Mathematical content, pedagogy, and curriculum	In-person	Elementary	1593 teachers 24759 students	—	15 days	Statewide standardized achievement test
Dash et al. (2012)	Online professional development program	Using models to understand fractions, algebraic thinking, and the complexities of measurement	Online	Elementary	79 teachers 1438 students	—	9 days (70 h)	Researcher-developed assessment that measures fractions, algebraic thinking, and measurement
Fisher et al. (2010)	A Computerized Professional Development Program	A lesson plan, a blank Concept Diagram, students with whom to practice, and a coach to prompt their application	Hybrid	Elementary	59 teachers (T = 30, C = 29)	—	2 days	Student concept acquisition test
Hilton et al. (2016)	An ongoing professional development program	Proportional reasoning	In-person	Middle	130 teachers	—	4 days	Diagnostic instrument
Jacob et al. (2017)	Math Solutions Professional Development	Mathematics content knowledge, insight into individual learners through formative assessment, understanding of how children learn math, effective instructional strategies	In-person	Elementary	105 teachers (T = 51, C = 54) 1523 students (T = 780, C = 743)	—	13 days	State standardized assessment Researcher-developed assessment
Jacobs et al. (2007)	A professional development project	Algebraic reasoning	In-person	Grade 1–5	180 teachers (T = 89, C = 14) 3735 students (T = 1827, C = 373)	—	8 days (16.5 h)	Written Mathematics Tests
Lindvall (2017)	Swedish PD programs	Five mathematical competencies	In-person	Elementary	90 teachers 5000 students	—	9 days	Mathematical tests (McIntosh, 2008)
McGatha et al. (2009)	A year-long professional development program	Rational number	In-person	Middle	40 teachers (T = 20, C = 20)	—	5 days in addition to 30 h	National Assessment of Educational Progress
Piasta et al. (2015)	The professional development adapted from Core Knowledge Preschool Sequence	Identifying similarities and differences, classifying and sorting using one characteristic, classifying and sorting using more than one characteristic, identifying a pattern using only one alternating characteristic, and identifying and creating complex patterns involving at least two characteristics	In-person	Early childhood	65 teachers (T = 31, C = 34) 385 students (T = 191, C = 194)	—	10.5 days (64 h)	Applied Problems subtest (Woodcock–Johnson Tests of Achievement III) Tools for Early Assessment in Math
Polly et al. (2017)	Curriculum-Based Professional Development Program	Exploring mathematical tasks, examining lessons in their curriculum, and modifying curriculum-based lessons	In-person	Kindergarten	15 teachers 245 students	—	80 h	Student achievement measure
Prast et al. (2018)	A Teacher Professional Development Program	Differentiated instruction in primary mathematics	In-person	Elementary	76 teachers 5658 students	—	30 h	Cito Mathematics Tests
Roschelle et al. (2010)	The SimCalc Approach	Rate and proportionality, linear function	In-person	Middle	218 teachers 539 students	—	6 days	Researcher-developed assessment that measures rate, proportionality, and linear function
Sample McMeeking et al. (2012)	A Teacher Professional Development Program	A sequence of content-oriented and pedagogy-oriented structured courses	In-person	Middle	2319 students (T = 1002, C = 1317)	233	4 days	Colorado Student Assessment Program
Santagata et al. (2010)	A Teacher Professional Development Program	Fractions, ratio and proportion, and expressions and equations	Hybrid	Middle	59 teachers 3900 students	—	1 day	District-wide Quarterly Assessments and the California Standards Test
Saxe et al. (2001)	The Educational Leaders in Mathematics Project	Skills with fractions procedures and understandings of fractions concepts	In-person	Elementary	23 teachers (T = 17, C = 6)	—	5 days	Researcher developed test that contained both computation and more conceptually oriented items
Wang et al. (2013)	Mathematics Science Partnership professional development project	Teachers’ knowledge of mathematics content and pedagogy	In-person	Elementary	185 teachers 5070 students	—	9 days	End-of-unit assessments

Note. Dash indicates data were not reported. T = treatment group, C = control group.

. The characteristics include title of PD, topics of PD, format, grade level, number of participants, number of included students with or at risk of disabilities, number of days, and measure of student mathematics outcomes.

3.1. Overall PD Effects on Student Mathematics Achievement

Figure 3 illustrates the distribution of the effect sizes in included studies using a forest plot. The size of the square symbols reflects the weight of each effect size, with larger squares representing effect sizes with greater weight. The variance of the effect sizes is shown as bars around the effect sizes, and the overall effect size is drawn with a diamond figure at the bottom of the forest plot. The details of the overall effect size values are also provided.

Table 2. Overall Professional Development Effects on Student Mathematics Outcome.

Effect	m	k	${\mathit{I}}^2$	${\mathit{\tau }}_{\mathit{b}\mathit{e}\mathit{t}\mathit{w}\mathit{e}\mathit{e}\mathit{n}}^2$	${\mathit{\tau }}_{\mathit{w}\mathit{i}\mathit{t}\mathit{h}\mathit{i}\mathit{n}}^2$	g	SE	95% CI	95% PI	df	p
Unadjusted PD	20	87	97.32	0.13	0.14	0.39	0.11	[0.16, 0.61]	[−0.63, 1.40]	86	0.001
Adjusted PD	20	87	95.82	0.09	0.08	0.34	0.10	[0.15, 0.53]	[−0.47, 1.15]	86	<0.001

Note. m indicates the number of studies and k indicates the number of effect sizes.

shows the weighted average effect sizes of PD effects on student mathematics achievement. The average effect size with unadjusted outliers was 0.39 (SE = 0.11, 95% CI = [0.16, 0.61], 95% PI = [−0.63, 1.40], p = 0.001), and with adjusted outliers was 0.34 (SE = 0.10, 95% CI = [0.15, 0.53], 95% PI = [−0.47, 1.15], p < 0.001). The difference between the average effect size estimates from the two models was negligible. Both average effect sizes were large (Kraft, 2020) and statistically significant, indicating the positive weighted average of PD effects was statistically different from zero, regardless of the outlier adjustment. However, both prediction intervals contain zero, indicating that the true effect in future studies might not be different from zero. The sensitivity analysis showed negligible difference in the average effect size across different correlation values for RVE, ranging from 0 to 1. The estimated $I^2$ was 97.32 with ${\tau }^2$ = 0.14 for within-study and 0.13 for between-study for the meta-analysis with unadjusted outliers. Also, the estimated $I^2$ was 95.82 with ${\tau }^2$ of 0.09 for within-study and 0.08 for between-study for the same model with adjusted outliers, indicating a similar amount of heterogeneity across the studies between the two models. Therefore, we used the effect sizes that adjusted outliers throughout the analyses. To further determine the source of the heterogeneity, we conducted moderator analyses.

3.2. Moderator Analyses for PD Characteristics

We examined the moderating effects of five PD characteristics on the impact of teacher PD on student mathematics outcomes. The PD characteristics included (a) grade level, (b) format, (c) PD focus, (d) PD days, and (e) inclusion of students with or at risk of disabilities. Among the five moderators, none showed a significant effect (see

Table 3. Moderator Analyses of PD on Student Mathematics Outcome.

Variable	Est.	SE	95% CI	df	p
Secondary grade level (vs. Primary)	−0.79	0.57	[−1.93, 0.34]	80	0.17
Combination format (vs. In-person)	0.10	0.33	[−0.55, 0.75]	80	0.76
PD focus					0.17
Specific (vs. General)	1.30	0.63	[0.05, 2.56]	80	0.04
Combination (vs. General)	−0.29	0.39	[−1.07, 0.48]	80	0.45
PD days	−0.01	0.01	[−0.03, 0.02]	80	0.54
Inclusion of students with or at risk of disabilities (vs. without these students)	0.55	0.40	[−0.25, 1.36]	80	0.17

Note. The number of studies (m) = 20; the number of effect sizes (k) = 86; $I^2$ = 96.07; ${\tau }^2$ = 0.14 for within-study and 0.14 for between-study; p-values were adjusted for multiple comparison using the Benjamini–Hochberg Correction.

). Specifically, the coefficient estimate for the PD focus was 1.30 larger for studies in which the PD focus was specific to math content compared to general instructional strategies (b = 1.30, SE = 0.63, 95% CI = [0.05, 2.56], p < 0.05). However, the Wald test indicated that the focus type was not a significant moderator overall. In addition, a combined focus compared to a general focus of PD did not significantly moderate the effect size (b = −0.29, SE = 0.39, 95% CI = [−1.07, 0.48], p = 0.45). The moderating effect of grade level (b = −0.79, SE = 0.57, 95% CI = [−1.93, 0.34], p = 0.17) did not significantly moderate the effect size. The moderating effect of format (combination vs. in-person workshop; b = 0.10, SE = 0.33, 95% CI = [−0.55, 0.75], p = 0.76) did not significantly moderate the effect size. The moderating effect of PD days (b = −0.01, SE = 0.01, 95% CI = [−0.03, 0.02], p = 0.54) did not significantly moderate the effect size. The moderating effect of inclusion of students with or at risk of disabilities (b = 0.55, SE = 0.40, 95% CI = [−0.25, 1.36], p = 0.17) did not significantly moderate the effect size.

4. Discussion

Many educational stakeholders would agree that high-quality PD is necessary for teachers to implement evidence-based practices and, in turn, positively impact student achievement in mathematics (Darling-Hammond et al., 2017). However, there is insufficient evidence for what constitutes effective PD. Therefore, we undertook a meta-analysis that explored features of teacher PD and student-level characteristics in mathematics and the impact they have on student achievement. We asked two research questions: (a) What are the main effects of PD on mathematics achievement for students in PreK–12? (b) To what extent do features of PD (i.e., grade level, format, PD focus, PD days, and inclusion of students with or at risk of disabilities) moderate its effects on student mathematics achievement? We concluded that teachers who received PD yielded a more positive impact on student mathematics outcomes when compared to teachers who did not receive PD. In addition, we found the five moderators did not significantly moderate the relation between PD efficacy and student mathematics outcomes.

4.1. Effect of PD on Student Mathematics Outcomes

Our primary research aim was to explore the effects of teacher PD on student mathematics outcomes. We included 20 studies in the meta-analysis; 98% of participants in PD were teachers of typically developing students from PreK to Grade 12. The results showed that there was a positive average effect of PD on student mathematics outcomes (g = 0.34), large enough to be of interest to policy makers in the field of education (Hedges & Hedberg, 2007). These findings add to the growing body of evidence suggesting that effective teacher PD has the potential to elevate student outcomes (e.g., Blank & de las Alas, 2009; Jacobs et al., 2007; Kraft et al., 2018; Roschelle et al., 2010). Despite the potential of training, prior research has indicated that evidence for the impact on student outcomes is still in the process of being established. For example, previous studies found the effect sizes for PD’s impact on student-level outcomes are relatively small, ranging from 0.14 to 0.37 (e.g., 0.14 for Egert et al., 2018; 0.21 for Markussen-Brown et al., 2017; 0.37 for Jung et al., 2018) compared to those reported in other meta-analyses that synthesized findings at the teacher level (e.g., 0.67 for Filderman et al., 2022; 0.57 for Gesel et al., 2021) and the classroom level (e.g., 0.45 for Egert et al., 2018). The current conversation regarding PD’s effect on student outcomes can be centered around either inconsistent findings of the effect of PD on student outcomes or a weak link between teacher impact on student outcomes compared to teacher outcomes. Although there is a strong belief that PD has a positive impact on student outcomes (Darling-Hammond et al., 2017), the consensus among researchers is that more research is needed to gather evidence of its impacts, particularly in mathematics. The number of PD programs focused on mathematics is relatively small compared to other content areas, such as language and literacy (Kraft et al., 2018; Piper et al., 2018). For instance, Brunsek et al. (2020), in their meta-analysis and systematic review in early childhood education, found the majority of PD focused on school readiness, social and emotional functioning, and language and literacy outcomes. The research investigating PD in mathematics is limited, and teachers receive insufficient PD to specifically enhance their mathematics content knowledge and pedagogical skills.

Our findings add value to the literature supporting the impact of PD on student outcomes and emphasizing the importance of PD. Approaches such as lesson study (Lewis & Perry, 2014, 2017) and teacher noticing (van Es & Sherin, 2002, 2021) are examples of long-standing PD programs in mathematics for K-12 teachers. However, continued investments in a range of instructional approaches have improved teachers’ competence and performance and students’ learning while also allowing for iterative adaptation. Thus, more PD opportunities for teachers are needed to explore effective ways of addressing instructional needs, particularly for students with low achievement or those with, or at risk of, disabilities. Given the low achievement trends in mathematics education (National Center for Education Statistics, 2022) and our study’s findings on the positive average effect of PD, providing teachers with more mathematics-specific PD could be a missing link. Thus, continued research on PD could investigate factors contributing to low achievement trends, supporting teachers to improve the trajectory of student mathematics achievement.

4.2. Moderator Analyses

With our second research question, we concluded that grade level did not significantly impact the overall efficacy of teacher PD on student mathematics outcomes. In other words, PD effects did not vary in studies examining teachers in early childhood or elementary schools compared to the studies with teachers in middle or high schools. This aligns with previous literature (e.g., Kennedy, 1998; Lynch et al., 2019; Taylor et al., 2018), which found no differences in intervention effects across grade levels. Although some studies (e.g., Blank & de las Alas, 2009) reported that grade level in elementary grades had larger effects than for secondary schools, our results did not find different effects across grades.

PD days was not found to moderate the effects of PD on student outcomes. These findings could be due to the variability of characteristics among the PD studied. Many researchers reported on the optimal number of days or contact hours of PD that teachers should receive to make significant differences in their practice to change student outcomes, at ranges including 20 h (Desimone, 2009), 30 h (Guskey & Yoon, 2009), 49 h (Darling-Hammond et al., 2009), and as much as 68 h (Garet et al., 2010). Although these studies claim that specific levels of intensity moderate PD effectiveness for student outcomes, our study aligns with the many meta-analyses showing that intensity does not moderate PD effectiveness (e.g., Blank & de las Alas, 2009; Kennedy, 2016; Kraft et al., 2018).

Likewise, our study found that format had no moderating effects on student mathematics outcomes. This may be partially due to the variety of PD types (e.g., coaching, PLC, online) found within the studies we examined. But, as with PD days, our finding aligns with previous studies that have attributed the lack of a moderating effect to the heterogeneity of PD formats (e.g., Blank & de las Alas, 2009; Didion et al., 2020; Yoon et al., 2007). For both PD days and format, more research needs to be conducted to more reliably explain the moderating effects of specific PD days and specific types of PD format. Until then, it is not possible to make definitive claims about which PD characteristics have the greatest moderating effects on student outcomes.

We also found no moderator effect for PD focus, which researchers have consistently found to include both specific subject content and pedagogical content (Blank & de las Alas, 2009; Markussen-Brown et al., 2017). This is somewhat unsurprising because, based on previous literature (Markussen-Brown et al., 2017), PD combining both subject and pedagogical content may be more beneficial for meeting the complexity of teachers’ needs than PD that only focuses on one or the other. This supports the assertions of Diamond and Powell (2011), who held that PD needs to offer sustained opportunities to understand specific content, recognize the challenges teachers encounter daily, and promote active learning. However, determining the specific effects of PD focus poses unique challenges for researchers, as the presence of both types of content makes it difficult to determine which component moderates the relation between PD and student outcomes (Didion et al., 2020). Another factor that makes this challenging is the ongoing debate about whether to use subject-specific observation instruments versus pedagogical content observation instruments for analyzing instructional quality (H. C. Hill & Grossman, 2013; Schoenfeld, 2018). Thus, it is likely that due to the complexity of PD and the varied research findings on its content focus, there is a paucity of solid evidence about effective PD design and implementation (Sims & Fletcher-Wood, 2021; Yoon et al., 2007).

Finally, the results of this meta-analysis indicate that the inclusion of students with or at risk of disabilities did not moderate effects. These findings align with Didion et al. (2020), who found no moderating effect of student characteristics related to disability status on the impact of PD on student reading outcomes. However, a null effect does not imply an absence of differences in the effectiveness of PD targeting specific student populations. This finding might be due to challenges in isolating the student population from the total sample, considering that many students with disabilities receive their education in inclusive settings. In fall 2021, according to the National Center for Education Statistics (2023), 95% of school-age children served under the Individuals with Disabilities Education Act were enrolled in regular schools. Despite this high enrollment in regular schools, teachers rarely receive PD tailored for supporting students with disabilities (Darling-Hammond et al., 2009). Because students with mathematics disabilities often have unique and persistent learning challenges and need individualized instruction, teachers in inclusive settings may require specific instructional strategies or intensified instruction to effectively support these students (Fuchs et al., 2021; Park et al., 2024). Further investigation is needed to determine if the effects of PD on student outcomes differ between students with disabilities and typically developing students.

4.3. Limitations and Implications for Research

There are several limitations to this study, and related key implications for research emerged from it. In this section, we provide suggestions for future research that may address these limitations. First, our meta-analysis only considered student mathematics outcomes, rather than teacher-level outcomes, as a way to measure the short-term effectiveness of PD in PreK–12. Our inclusion criteria focused only on studies that followed a randomized controlled trial or quasi-experimental design; other types of research design, such as qualitative studies, might have offered more contextualized information about the effectiveness of PD, information that could not be captured with student achievement outcomes only. While we considered student-level outcomes, researchers may also consider investigating the impact of teacher PD on teacher-level outcomes—for example, teachers’ knowledge, teaching efficacy, or self-esteem (Allsopp & Haley, 2015). The impact of PD on both teacher- and student-level outcomes, such as the improvement of content knowledge or the quality of delivering instruction, might bring different perspectives when designing effective PD. For example, prioritizing teachers’ knowledge, inquiry, and instructional resources might achieve sustained PD effects (e.g., Desimone, 2009; Lewis & Perry, 2017; Schoenfeld, 2018). Additionally, we only considered the short-term effects of teacher PD on student outcomes; researchers should further investigate the long-term effects. Given our specific focus on student-level outcomes and the short-term effects of PD on those outcomes, readers should be cautious about generalizing our results to teacher-level outcomes, non-school setting, and other content areas. Researchers may be able to refine the effectiveness of PD by examining how teacher- and student-level variables interact, investigating the effects of this interaction on teacher PD, and then applying the results when developing new PD.

Second, our analysis included mainly studies focusing on teachers of typically developing students, resulting in a limited view of PD effectiveness for students who receive special education services. Previous literature has indicated a lack of studies that show how PD can improve teachers’ abilities to support students with special needs, academic difficulties, or a mixed population of general and special education students in an inclusive setting (Darling-Hammond et al., 2009; Didion et al., 2020). There needs to be greater inclusion of students with disabilities in studies on teacher PD to create a more well-rounded view of student outcomes in PD studies (Clements et al., 2011; Griffin et al., 2018). To enhance student mathematics outcomes through PD, researchers should emphasize PD characteristics that best serve specific student populations, particularly those in inclusive settings. Thus, conducting more studies of PD specifically geared toward teachers who are instructing specific student populations may provide insights into important questions related to PD design; for instance, identifying characteristics of PD that are more effective for teachers instructing students with disabilities and designing the PD to emphasize those features may enhance student outcomes.

Third, it is important to note that the presence of the null effect of moderators does not mean that we can underestimate their implications for PD characteristics, because studies often describe PD in vague or incomplete terms. Because PD is complex and heterogeneous (Zhang et al., 2020), as noted above, researchers can learn more from PD with clearly defined components, allowing them to examine PD delivery in greater detail. However, in many of the studies in our meta-analysis, we found that PD design was often underdescribed, making it difficult to measure its effectiveness. An important implication was that due to the complexity of PD, it is crucial for researchers to provide detailed information on how the PD is conducted—for instance, implementation, content covered, and other relevant factors—to ensure quality, replicability, and applicability of findings on the impact of PD on student outcomes (Appelbaum et al., 2018; Desimone, 2009; Page et al., 2021). To provide more detailed information, future researchers who conduct PD meta-analyses may consider examining the type of information provided by authors such as quality of PD, research design, type of measures, and so on, to provide targeted recommendations for researchers who conduct and design PD studies.

5. Conclusions

This meta-analysis explored how effective teacher PD is for improving mathematics outcomes for students from PreK to Grade 12. The results of this study showed that PD had a positive average effect on student mathematics outcomes. In addition, we found that the five moderators explored in this meta-analysis had no significant impact on the relation between PD efficacy and student mathematics outcomes. It is important to note that while this meta-analysis found that the moderators were not statistically significant, features of PD recommended by the existing literature should not be ignored; researchers need to investigate the mechanism of effective PD characteristics on student outcomes. Thus, more studies on effective PD are needed to further articulate the relation between PD characteristics and student mathematics outcomes.