In many Western countries, students' proficiency in subjects like mathematics has declined (12). The need to assess the situation has been recognized.

Teaching yields positive impacts on learning, holding a pivotal role in the success of educational interventions (3;6;18;19). In-service teachers' professional development (TPD) refers to structured, targeted, and continuous efforts to elevate quality of teaching in the classrooms (3;7;8;10;11;19). TPD fosters the continuum of teachers' professional learning, growth, and adaptation to evolving educational settings through improved competences(3;5;19;14).

The effectiveness of TPD has been assessed through student and teacher-level outcomes (8;20;19). Quality TPD has been found to yield improvements in teachers' knowledge, skills, practices, work confidence, increase well-being, professional growth, and reflection (2;3;4;5;8;9;14). Studies also indicate that effective TPD programs targeting relevant and specific instructional practices can improve student achievement in core subjects like mathematics (10;13;15).

However, teachers' professional learning and how it translates into behavioral change is not yet a well-understood (9). Research literature indicates that identifying the optimal program characteristics for effective in-service TPD has proven difficult, especially in subject-specific contexts (9;13;15;18). This lack of understanding reduces the ability to plan and implement quality TPD that produces positive outcomes that  sustain and cause behavioral changes that preceed student learning (9;11;13;16;17).

Common TPD program components include coaching, mentoring, instruction, feedback, resource sharing, workshops, and learning communities, with varying features such as duration, focus, and form (1;3;5;9;13). Yet these alone may not hold the keys to success. Emphasis can be on qualitative factors or on characteristics that align with varying needs. Specific program components can also be more effective when combined rather than implemented alone. (9;15). In addition, the effectiveness data of many TPD components like "professional learning communities" vary between studies (9).

This variability emerges as an overarching theme across TPD research, where frameworks, terminology, research methods, and reported effect sizes differ (9;13;15;16;19) . Yet, most researchers seem to agree that TPD needs to be sustained, practically align with real classroom settings and incorporate active learning, reflection and collaboration.

That said, the research quality in the field has constantly improved, and the focus has shifted towards experimental designs with validated measures (13;14). This development raises hopes for understanding what works and how it works in TPD.

Despite the progress made, there are still significant research gaps. One is the ongoing need to identify and evaluate effective subject-specific TPD characteristics that contribute to optimal teacher learning, since TPD programs often fail to produce expected outcomes (9;13). Mathematics, with its abstract nature and the wide individual variability in skill levels, deserves our attention for TPD characteristics that can produce strong and sustainable learning outcomes (5;8;15;18).

Although prior research supports the notion that combining multiple TPD elements results in more positive teacher learning (1;3;9;11), this study will delve deeper into evaluating program characteristics, aiming to improve the evidence base for research, policymaking, planning and implementation for mathematics focused TPD.

The present study systematically examines studies focusing on in-service mathematics teachers' professional development and learning. It identifies and classifies key program characteristics (e.g duration, intensity, content focus, and implementation methods) and analyzes how their effectiveness can be linked to teacher learning outcomes. We aim to identify the TPD characteristics that yield positive changes in teachers' knowledge, skills, attitudes, and practices and explore the magnitude and durability of these effects.

Research questions:
RQ1. What characteristics of professional development programs can be identified for in-service mathematics teachers?
RQ2. Can the reported effectiveness outcomes at the teacher-level be linked to these program characteristics?
RQ3. What teacher-level effectiveness outcomes have TPD programs produced in terms of effect sizes and sustainability of these effects?

To address the research gap, a systematic review and meta-analysis is conducted. The aim is to identify Mathematics focused TPD characteristics that effectively promote in-service teachers' professional learning. We will identify, evaluate, and synthesize the characteristics of TPD programs and their effectiveness on teacher-level outcomes. This research synthesizes data from multiple peer-reviewed studies published between 2008 and 2025, focusing on Mathematics education for grades 1–10. It uses a structured approach to search and identification processes, utilizing quality assessment, to determine how TPD characteristics relate to effect sizes and sustainability. Systematic review and quantitative data meta-Synthesis is conducted following Siddaway (2019) guide for systematic reviews, PRISMA guidelines and Booth et al. (2022) systematic literature review guide. The systematic review will also be pre-registered in the Open Science Framework (OSF) in spring 2025. PEO framework is used (Population, Exposure, and Outcome) to focus the Boolean search phrase (Moola et al., 2015). Searches from ERIC, Scopus, EBSCO, PsycINFO, and Web of Science Databases are then conducted and identified records are downloaded to RIS files and gathered to Zotero, where duplicates are removed. Identified records are screened following the PRISMA protocol and evaluated against inclusion criteria. Search processes are documented in the PRISMA chart. The screening process will utilize Rayya's platform. Inter-rater reliability (Kw) will then be calculated (Belur et al., 2021). Independent reviewers' kappa rate should reach (≥ 0.6) for medium or (≥ 0.8) for strong agreement (McHugh, 2012). After screening 50% of the abstracts, the first author will complete the screening independently. Selected studies will then undergo a quality assessment process (EPHPP) by two independent reviewers (McMaster, 2022). Studies with a strong or medium overall quality rating will be included in the final synthesis. All discrepancies will be resolved in the reviewers' Consensus meeting. Focus information is tabulated, including participant demographics (age, N, country), program characteristics (e.g., duration, intensity, content focus, and pedagogical methods), and reported effectiveness data. In the meta-analysis, effect sizes are synthesized, and coded characteristics serve as potential moderators to investigate which aspects of TPD programs correlate with larger or smaller effect sizes. This approach will help clarify how specific program characteristics may contribute to teacher-level outcome improvements.

We hypothesized that the most used components of TPD programs are also prevalent in mathematics related TPD and that the relationship between mathematics content knowledge and pedagogical content knowledge will be emphasized in most of the TPD programs. Preliminary results, after screening 400 records and identifying 9 studies for preliminary synthesis, indicate that most programs focused on teacher knowledge. Mathematical Knowledge for Teaching, Content knowledge and Pedagogical Content Knowledge were the most common focuses, followed by teaching practices and teacher beliefs. Studies favored longer duration aligning with contemporary TPD recommendations. Results also indicate that in shorter programs, effects fade faster. Most reported TPD components were learning communities, workshops, instruction, resource provision and feedback. Randomized controlled trial (RCT) designs were rarer than quasi-experimental designs, and sustainment was not often measured (N=3). Results also confirm previous observations for large variability in impact reporting, complicating comparison between program characteristics. Discussion: The theoretical and educational significance, after identifying and analyzing 9 in-service TPD studies for mathematics’ our results indicate that elements generally associated with effective TPD are also prevalent in the context of mathematics education. Elements like longer duration, combining knowledge with practical context and communal active learning seem to help build effective framework for mathematics TPD where teachers’ professional learning serves as a primary interactive mediator expected to yield student outcomes.

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