Mohamed Arselene Ayari1
Abdellatif Sellami2*
Malavika E. Santhosh2
Khalid Kamal Naji1
Abdulla Al-Ali1Saleh Mohammad Ali Al-Hazbi1- 1Educational Research Center, College of Education, Qatar University, Doha, Qatar
- 2College of Engineering, Qatar University, Doha, Qatar
Introduction: This systematic review investigates the implementation of Problem-Based Learning (PBL) in K-12 mathematics education, offering a recent synthesis of current interventions.
Methods: In line with PRISMA guidelines and predefined inclusion and exclusion criteria, the review shortlisted 40 relevant studies. The analysis focused on four key questions: the types of PBL models and intervention strategies employed, the mathematics topics most frequently addressed, the type of PBL frameworks implemented, and the student outcomes assessed.
Results: Findings reveal that integrated PBL approaches are more common (n = 26) than exclusive PBL models (n = 16), incorporating game-based, ethnomathematics-based, digital-based, STEM-oriented, and project-based interventions. Within PBL interventions, Geometry (n = 15) and Algebra (n = 14) emerged as the most addressed domains, followed by Arithmetic (n = 7) and Applied Mathematics (n = 5). The five-step PBL framework, involving the steps: (1) Orient/Identify, (2) Investigate/Plan, (3) Implement/Solve, (4) Evaluate/Reflect, and (5) Extend/Share, was the most frequently applied model (n = 22). Analysis of investigated student outcomes indicates that PBL interventions support a broad range of cognitive, affective, social, and meta-cognitive outcomes. Problem-solving skills (n = 13) and mathematics achievement (n = 12) were the most assessed, followed by self-efficacy/self-confidence (n = 5) and emotional outcomes (n = 4).
Discussion: For policymakers and educational stakeholders, these findings emphasize the importance of contextually relevant integrated-PBL strategies to enhance student learning outcomes, support student development, and promote active engagement across diverse mathematics topics.
1 Introduction
Problem-Based Learning (PBL) has become a very important pedagogical approach in mathematics education, particularly in K-12 settings (Nurin et al., 2024). Rooted in constructivist learning theory, PBL emphasizes inquiry, collaboration, and real-world problem contexts as vehicles for developing both content knowledge and higher-order thinking skills (Shongwe, 2024). Unlike traditional instruction that relies on rote memorization and teacher-led demonstrations, PBL situates students as active participants in the learning process. This pedagogical shift is particularly significant for mathematics, a subject frequently perceived by students as abstract, difficult, and disconnected from daily life (Slimane, 2024). By incorporating mathematical concepts in authentic settings, PBL aims to foster deeper conceptual understanding, critical thinking, and motivation for learning.
Over the past decade, the integration of PBL into mathematics curricula has gained momentum worldwide. Policymakers, curriculum developers, and practitioners have recognized its potential to address pressing challenges in mathematics education, including low achievement levels, limited problem-solving capacity, and declining student engagement. A significant body of empirical studies illustrates the range of PBL applications, ranging from technology-assisted models, such as digital and mobile-based interventions (Al-Qora’n et al., 2023; Vaithianathan et al., 2024), to culturally contextualized approaches such as ethnomathematics (Barak and Yuan, 2021; Garim et al., 2023). These innovations reflect the adaptability of PBL to diverse contexts and its alignment with global educational models that emphasize 21st-century skills, including collaboration, creativity, and lifelong learning (Almazroui, 2022; Fachrin, 2025). However, despite its promise, the existing body of research is inconsistent, with variations in PBL models, mathematics domains addressed, frameworks adopted, and student outcomes measured.
Therefore, systematic reviews are very useful in synthesizing existing knowledge and providing a clearer understanding of how PBL is implemented in K-12 mathematics education. As this review aims at understanding how PBL is implemented during foundational stages of mathematics education, the focus was limited to the K-12 setting (primary, middle, and high school), typically covering students from approximately ages 5 to 18. Concentrating on this span is justified because pedagogical innovations adopted during these years shape learners’ conceptual development, study habits, and long-term attitudes toward mathematics. Previous reviews have largely focused on general STEM disciplines or higher education contexts, leaving a gap in the systematic integration of PBL applications specific to K-12 mathematics. This study aims to address that gap by offering an updated review of empirical research published between 2014 and June 2025. By systematically analyzing 40 shortlisted studies, the review seeks to identify patterns and trends in intervention design, curricular focus, and outcome measurement. In doing so, it provides evidence-based insights for researchers, educators, and policymakers.
The remainder of this paper is structured as follows. The Methods section details the search strategy, inclusion and exclusion criteria, and data extraction processes used in line with PRISMA guidelines. The Results and Discussion section presents findings on PBL models, mathematics domains, frameworks, and student outcomes, complemented by descriptive trends across geography, study design, and educational levels. The Limitations and Future Scope section highlights methodological constraints and areas requiring further inquiry, while the Conclusion synthesizes the review’s key contributions and implications for policy and practice in mathematics education.
Therefore, systematic reviews play a key role in synthesizing existing research and illuminating how PBL is implemented in K-12 mathematics education. Previous reviews have largely focused on general STEM disciplines or higher education contexts, leaving a gap in the understanding of PBL applications specific to K-12 mathematics, especially in non-Western contexts. This study aims to address that gap by offering an updated review of empirical research published between 2014 and June 2025. By systematically analyzing 40 shortlisted studies, the review seeks to identify patterns and trends in intervention design, curricular focus, and outcome measurement. In doing so, it provides evidence-based insights for researchers, educators, and policymakers.
2 Review objectives and research questions
Based on the preceding rationale, this review aims to synthesize and evaluate empirical research on PBL in K-12 mathematics education. Specifically, it seeks to:
• Map the range of PBL models and intervention strategies applied in K-12 mathematics contexts.
• Identify the mathematics domains most frequently targeted by these interventions.
• Examine the frameworks, phases, or procedural steps that structure PBL implementation; and
• Assess the student outcomes reported in relation to PBL-based instruction across cognitive, affective, social, and meta-cognitive domains.
These objectives collectively provide a structured foundation for understanding how PBL is operationalized in mathematics classrooms and the extent to which it influences diverse learning outcomes. To achieve these objectives, the review is guided by the following research questions:
1) What types of PBL models and intervention strategies have been implemented in K-12 mathematics education?
2) Which mathematical domains or topics are most frequently addressed through PBL interventions?
3) What instructional frameworks, steps, or procedural phases characterize PBL implementation in K-12 mathematics?
4) What categories of student learning outcomes are examined following PBL interventions in K-12 mathematics, and how are these outcomes measured?
These questions operationalize the review’s aims and serve as an analytical framework for synthesizing evidence across the shortlisted studies.
3 Methods
The databases Web of Science, Scopus, and the Education Resources Information Center (ERIC) were systematically searched to identify peer-reviewed studies relevant to this review. The search and selection process adhered to the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) 2020 framework (Page et al., 2021). To ensure both breadth and precision, combinations of carefully selected keywords and Boolean operators were used, including: (“PBL” OR “problem-based learning” OR “problem based learning”) AND (“Math*” OR “mathematics”) AND (“students” OR “youth” OR “adolescent” OR “children” OR “school” OR “elementary” OR “primary” OR “middle school” OR “secondary” OR “high school”).
The search covered publications from January 2014 to June 2025. All retrieved records were imported into the Rayyan software for screening and management, enabling duplicate removal, independent review, and structured coding of inclusion and exclusion decisions. The overall procedure ensured transparency, replicability, and methodological rigor consistent with PRISMA standards.
3.1 Inclusion/ exclusion criteria
Studies were included in this review if they met specific criteria designed to ensure relevance, methodological rigor, and alignment with the review’s objectives. Eligible studies were those that reported empirical research investigating the implementation or impact of PBL within K-12 mathematics education. The participant population was required to consist of students enrolled in elementary, middle, or secondary school settings, corresponding to the K-12 educational range. Only peer-reviewed journal articles published between January 2014 and June 2025 were considered, and studies had to be written in English and available in their final publication form at the time of screening. These parameters were established to ensure both the quality and comparability of the studies analyzed, as well as to capture the most recent decade of research on PBL in mathematics education.
In contrast, studies were excluded if they did not meet the aforementioned inclusion criteria. Specifically, exclusions applied to publications that (a) did not involve a PBL-based intervention or failed to focus on mathematics instruction; (b) targeted populations outside the K-12 range, such as early childhood, vocational, or higher education students, as well as teachers, parents, or school administrators; or (c) lacked an empirical research design, including theoretical papers, literature reviews, conceptual discussions, book chapters, opinion pieces, or editorials. Furthermore, non-English publications, in-press articles, and conference papers or proceedings that had not undergone full peer review were also excluded. These exclusion parameters were essential for maintaining methodological consistency and for ensuring that the synthesis reflected high-quality empirical evidence directly relevant to K-12 mathematics contexts. Collectively, these criteria provided a robust framework for selecting studies that contribute to understanding how PBL is applied and evaluated in school-level mathematics education.
3.2 Data extraction
Following the application of the predefined search strategy, a total of 5,714 records were retrieved across three databases: Scopus (n = 1,367), Web of Science (n = 1,055), and the Education Resources Information Center (ERIC) (n = 3,292). All records were imported into Rayyan software for systematic management and screening. The software facilitated the removal of duplicate entries (n = 2,326), after which 3,388 unique studies remained for title and abstract screening. Based on the inclusion and exclusion criteria, 40 studies were ultimately deemed eligible for inclusion in this review. This multi-stage process adhered to the PRISMA 2020 protocol (Page et al., 2021), ensuring methodological transparency and replicability.
Data from the included studies were extracted using a structured extraction template specifically developed by the research team to maintain consistency and accuracy. The template captured both descriptive and analytic information across several dimensions, including (a) bibliographic details such as author(s), year of publication, and country; (b) participant characteristics (educational level, sample size, and demographic information, where available); (c) study design and methodological approach (quantitative, qualitative, or mixed methods); (d) intervention characteristics, detailing the type, intensity, and duration of the implemented PBL model; (e) framework or theoretical orientation guiding the intervention; and (f) learning outcomes assessed, categorized into cognitive, affective, social, and meta-cognitive domains.
To enhance the credibility of the extracted data, two independent reviewers conducted parallel data extraction and cross-verification. Any discrepancies between reviewers were discussed and resolved through consensus to minimize potential bias. The use of Rayyan further supported transparent record management, enabling annotation, coding, and efficient retrieval of extracted content throughout the review process. Consistent with PRISMA recommendations, all extracted data were subsequently coded and synthesized using descriptive statistics and qualitative content analysis to identify emerging trends, patterns, and thematic categories. This rigorous approach ensured that the resulting synthesis accurately reflected both the breadth and depth of empirical research on PBL in K-12 mathematics education.
3.3 Summary of included studies
Supplementary Table S1 presents an overview of the forty empirical studies included in this systematic review. Each study was analyzed in terms of its bibliographic information (author(s), year, and country), participant characteristics (sample size and educational level), research design, PBL intervention type, and outcomes assessed. The studies reflect various geographical contexts, methodological approaches, and curricular emphases, and also demonstrate the widespread adoption of PBL in K-12 mathematics education across continents.
Most studies were conducted in Asian countries, especially Indonesia (n = 20), followed by Africa (e.g., Nigeria), Europe, and the Middle East, and hence highlight regional variations in contextualized pedagogical innovation. Research designs ranged from quasi-experimental and mixed-method studies to purely qualitative classroom-based inquiries. The majority focused on upper-primary and secondary education levels, although a growing number of interventions were reported in early and middle schooling contexts.
The types of PBL interventions employed were broadly categorized in this review as exclusive PBL (where PBL constituted the sole instructional model) and integrated PBL (where PBL was embedded within broader pedagogical frameworks such as STEM-based, digital-assisted, project-based, or ethnomathematics-informed models). Outcomes measured across these studies encompassed cognitive (e.g., problem-solving, reasoning, achievement), affective (e.g., motivation, self-efficacy), social (e.g., collaboration, teamwork), and meta-cognitive (e.g., self-regulation, habits of mind) dimensions. A concise subset of representative studies is presented in Supplementary Table S1 to illustrate the diversity of designs and findings.
3.4 Quality assessment (inter-rater reliability)
To ensure the reliability and rigor of the study selection process, an inter-rater reliability assessment was conducted. Two independent reviewers participated in the screening and eligibility phases, evaluating each study against the predefined inclusion and exclusion criteria. The level of agreement between reviewers was quantified using Cohen’s Kappa (κ) coefficient, calculated through SPSS statistical software. This measure provides an index of agreement that accounts for chance, thereby offering a more robust indicator of consistency than simple percentage agreement. The resulting Kappa value of κ = 0.792 indicated a substantial level of agreement between reviewers following the interpretive benchmarks proposed by Landis and Koch (1977), where coefficients between 0.61 and 0.80 represent substantial concordance. The result was also statistically significant (p = 0.001), confirming that the reviewers’ judgments were highly consistent and that the selection process was both systematic and dependable.
Any discrepancies identified during the screening or eligibility stages were discussed and resolved through consensus meetings, with reference to the inclusion criteria to ensure objectivity and transparency. For example, one discrepancy arose when a study was excluded by one reviewer because it described an inquiry-based activity, while the other reviewer included it as PBL. After revisiting the operational definition of PBL used in this review, both reviewers agreed that the study met the criteria and it was therefore included. This approach to quality assurance enhanced the credibility of the dataset and reinforced the methodological soundness of the review; it also helped ensure that the final pool of 40 studies accurately reflected the most relevant empirical research on PBL in K-12 mathematics education.
Following the establishment of methodological rigor through inter-rater reliability testing, the next phase of analysis focused on synthesizing the extracted data to identify overarching trends and thematic insights. The analytical process combined descriptive and qualitative techniques to ensure both systematic quantification of study characteristics and interpretive depth in understanding the varied implementations of PBL across K-12 mathematics contexts. The procedures adopted for this stage are outlined below.
3.5 Data analysis and synthesis
The extracted data were analyzed through an integrated descriptive–qualitative synthesis approach designed to capture both the breadth and depth of the evidence base. Descriptive statistics, including frequency counts and cross-tabulations, were first employed to map patterns across key study characteristics—such as the type of PBL model implemented, mathematical domain addressed, educational level targeted, research design, and categories of learning outcomes assessed. This quantitative mapping provided an overview of how PBL has been operationalized across diverse contexts.
A narrative synthesis was conducted to interpret and consolidate the findings beyond numerical trends. Studies were thematically grouped according to the nature of the PBL intervention, framework structure, and outcome focus (cognitive, affective, social, and meta-cognitive). Through iterative comparison, the synthesis identified areas of convergence (shared trends and outcomes) and divergence (context-specific or methodologically distinct findings) (see Figure 1).
Figure 1. PRISMA flow diagram showcasing the identification, screening, and selection of the articles (Page et al., 2021).
To strengthen analytic rigor, two independent reviewers systematically examined emerging themes and discussed interpretive differences until consensus was reached. This collaborative validation process ensured the reliability, transparency, and interpretive coherence of the final synthesis, aligning with best practices in systematic review methodology.
4 Results
4.1 Descriptive analysis
Figure 2 presents the descriptive analysis of the shortlisted studies across multiple dimensions. As shown in Figure 2a, the distribution by country of publication indicates that the largest number of studies originated from Indonesia (n = 20), followed by Nigeria (n = 4). These regional patterns may reflect broader systemic and cultural factors influencing the uptake of PBL in mathematics education. For example, the dominance of Asian countries, particularly Indonesia, may be linked to ongoing national reforms emphasizing student-centered pedagogies, strong governmental support for innovative teaching approaches, and an expanding research culture in mathematics education. In contrast, lower representation from other regions may relate to differences in research funding, policy priorities, or access to training in inquiry-based pedagogies. Figure 2b depicts the trend in publications by year, revealing a marked increase in studies after 2017, which suggests a rising global emphasis on integrating PBL into K-12 mathematics curricula.
Figure 2. Number of shortlisted articles by (a) country of study, (b) year of publication, (c) type of study design, (d) education level of students, (e) type of PBL model employed in K-12 mathematics, (f) duration of PBL intervention.
In terms of research design, Figure 2c highlights that the majority of studies employed quantitative methods using student surveys (n = 20). A substantial number also adopted mixed methods approaches (n = 16), combining surveys with interviews or classroom observations. A smaller proportion (n = 4) relied on purely qualitative analyses, often involving student worksheets, assignments, and teacher observations to capture problem-solving outcomes.
When analyzed by educational level (Figure 2d), most interventions targeted high school students (grades 10 to 12; n = 19), with a nearly balanced representation for middle school (grades 7 to 9; n = 11) and primary school (grades 1 to 6; n = 10). This distribution may reflect the assumption that PBL is particularly employed for high school students who possess stronger cognitive and problem-solving skills, although its implementation at earlier stages is also evident. In terms of pedagogical models (Figure 2e), studies were grouped into two categories: exclusive PBL and integrated PBL (where PBL is combined with other approaches such as game-based learning, STEM-based models, or mobile learning). Notably, the majority fell into the integrated category (n = 24), indicating that researchers often experiment with hybrid pedagogies to maximize learning outcomes.
Finally, the analysis of intervention duration reveals extensive variability (Figure 2f). While many studies did not report duration (n = 20), those that did ranged from less than one month (n = 4) to two months (n = 4), with five studies reporting an average duration of 1.5 months. This suggests that short- to medium-term interventions, typically spanning several weeks to two months, are the most common in the literature on PBL implementation in K-12 mathematics. These findings highlight not only where and how PBL research is being conducted but also reveal important methodological and contextual patterns that inform future research and practice.
RQ1: What types of PBL models and corresponding intervention strategies are implemented in K-12 mathematics education?
The PBL interventions implemented in K-12 mathematics education were classified into two broad categories: exclusive PBL (n = 16) and integrated PBL (n = 26) (refer to Table 1). The exclusive PBL category comprised studies that used the PBL model as the sole instructional approach (Figure 3). In contrast, integrated PBL refers to models that combine PBL with other pedagogical strategies, such as game-based, digital-based, project-based, or STEM-oriented approaches.
Table 1. Studies showing types of PBL approach employed in K-12 mathematics education.
Figure 3. Graphical representation of the types of PBL approach employed in K-12 mathematics education.
Among integrated PBL models, digital-based PBL was the most frequently employed strategy (n = 16), utilizing technology to enhance students’ engagement, conceptual understanding, and problem-solving skills (Table 1). For example, GeoGebra-assisted worksheets helped high school students visualize and construct abstract calculus concepts (Yerizon et al., 2022). Flipped PBL models combining online and offline instruction via Google Classroom fostered independent learning and motivation (Ramadhani et al., 2019), while technology-enhanced activities integrating GeoGebra and smartboards supported achievement and positive attitudes toward mathematics (Çetinkaya, 2019).
Game-based PBL approaches were also common for K-12 mathematics education, providing interactive environments for applying mathematical concepts. Educational escape rooms (Charlo, 2020) and augmented reality (AR) applications (Argüelles Cruz et al., 2023), such as the Ramanth 2.0 AR app, engaged students in updated problem scenarios. Similarly, Mobile Math Trails engaged middle school learners in real-world numeracy tasks within their school environment using mobile technology (Nurin et al., 2024). These trails guided students along outdoor routes with stops where they solved problems such as estimating the height of a flagpole, calculating the slope of a ramp, or determining the area of a flowerbed while exploring Quantity, Geometry, Data, Uncertainties, and Algebra (Nurin et al., 2024).
Several studies employed cultural and ethnomathematics-based PBL models, connecting mathematics learning to students’ cultural contexts. Suryawan et al. (2023) employed a digital, multimodal PBL approach using Balinese ethnomathematical contexts, allowing students to analyze, question, collaborate, and justify their solutions. Macun and Isik (2022) implemented STEM-integrated PBL lessons on ratios and percentages through real-life contexts such as gear wheels, bridge models, and nutrition, helping students link mathematical concepts to daily life. Sari et al. (2023) used traditional Malay snacks in PBL activities to teach Systems of Linear Equations in Two Variables, integrating cultural experiences to enhance conceptual understanding and motivation.
Project-based and STEM-integrated PBL linked mathematics to hands-on, authentic experiences while integrating it with other STEM disciplines. Rehman et al. (2023) guided students to explore Angles, Geometry, and Decimals through model building and presentations, fostering autonomy and problem-solving skills. Farmer et al. (2019) integrated mathematics with civic engagement by designing environmentally themed products addressing waste management and water conservation. Shongwe (2024) implemented STEM-based PBL in high school mathematics through group projects linking energy, gravity, velocity, friction, and slope to real-world problems, with laboratory tours, hands-on activities, and presentations guided by STEM professionals.
Some other integrated PBL approaches include collaborative PBL (Xie et al., 2025), creative PBL (Hidajat, 2023), ADDIE-based PBL (Purnomo et al., 2024), etc. Collaborative PBL emphasized group-based problem-solving and reflective learning, where Xie et al. (2025) engaged students in real-life contexts aligned with learning objectives, facilitating collaborative analysis and solution development. The Analysis, Design, Development, Implementation, and Evaluation (ADDIE)-based PBL model was applied in elementary mathematics (Purnomo et al., 2024), to structure PBL modules that emphasized problem-solving and real-world applications.
Overall, integrated PBL models dominated K-12 mathematics interventions (compared with exclusive PBL models), with digital-based approaches being the most prevalent. Interventions frequently combined technology, game-based environments, cultural contexts, collaborative learning, and real-world applications to enhance mathematical understanding, engagement, and problem-solving skills.
RQ2: Which branches or topics of mathematics are most frequently addressed using PBL in K-12 education?
In K-12 mathematics education, PBL has been adopted across a range of mathematical domains, though the extent of its application varies considerably (Figure 4).
Figure 4. Number of studies reporting the mathematics branches or topics in which PBL was implemented in K-12 education.
Among these, geometry stands out as the most extensively examined area (n = 15). Studies in this domain have addressed topics such as Pythagoras’ theorem, transformations, solid geometry, quadrilaterals, polygons, angles, circles, and measurement (Table 2). A substantial proportion of research has concentrated on solid geometry, exploring how PBL can support students’ understanding of three-dimensional figures (Amin et al., 2021; Çetinkaya, 2019; Negara et al., 2022; Rehman et al., 2023; Yerizon et al., 2022). Other work has focused on the Pythagorean theorem, employing PBL activities to foster conceptual reasoning and problem-solving skills (Argüelles Cruz et al., 2023; Minarni and Napitupulu, 2017; Putri Apriliana et al., 2019; Ramli et al., 2020). Uygun and Tertemiz (2014) examined the topic of circles and measurement, designing fifteen scenario-based tasks in which students engaged with PBL activities in classrooms, libraries, and computer laboratories using tailored worksheets and learning materials. Similarly, Nasir and Hadijah (2019) demonstrated how animated media could be combined with PBL to teach tetragon concepts, presenting mathematical ideas through dynamic, visually rich representations that enhanced students’ comprehension.
Table 2. Shortlisted studies by core mathematics branches/topics demonstrating the implementation of PBL in K-12 education.
Algebra emerged as the second most frequently investigated branch (n = 14), covering a diverse set of topics such as systems of linear equations in two variables (SLETV), first-degree equations, indices and logarithms, algebraic expressions and equations, as well as series and sequences (Table 2). Several studies illustrated how PBL can make algebraic concepts meaningful by connecting them to students’ experiences. For example, Sari et al. (2023) implemented a PBL model grounded in ethnomathematics, using scenarios of buying and selling traditional Malay snacks to teach the concepts of SLETV. Uyen et al. (2021) guided students through structured PBL activities, including worksheets and assignments, to develop problem-solving strategies for solving first-degree equations. Similarly, Fatade et al. (2013) targeted indices, logarithms, algebraic equations, and series by blending guided reflection with ill-structured homework, where students prepared chalkboard presentations, critiqued peers’ solutions through independent research and class discussions. In a broader application of PBL within mathematics, Alemdar et al. (2018) engaged learners in cross-disciplinary STEM challenges such as Data, Systems, Visualizations, and Designs that integrated science, mathematics, and engineering practices.
PBL interventions are also common, particularly in foundational topics such as ratios, percentages, addition, subtraction, multiplication, division, fractions, and decimals (n = 7). Xie et al. (2025) incorporated collaborative, real-life tasks to teach fractions, multiplication and division, decimals, and word problems, demonstrating how PBL can support multiple foundational skills. Similarly, Zakaria et al. (2025) integrated digital platforms, including Telegram, Google Meet, and Quizizz, where students were introduced to objectives, tasks, and multimedia prompts via Telegram, worked collaboratively to explore potential solutions using various applications, and presented their findings through discussions on Google Meet. Macun and Isik (2022) adopted a STEM-oriented PBL approach through six lessons, involving gear wheels, speed-time-path, elevator construction, bridge modelling, and nutritional value calculations to teach ratios and percentages in applied contexts. Argüelles Cruz et al. (2023) used the game-based augmented reality application, named Ramanth 2.0, enabling students to engage with updated problems involving operations and fractions.
Applied mathematics, focusing on practical problem-solving contexts such as distance, speed, discharge, weight, magnitudes, and word problems, was investigated in a moderate number of studies (Ahdhianto et al., 2020; Chaidam and Poonputta, 2022; Charlo, 2020; Ramadhani et al., 2019; Xie et al., 2025). Trigonometry and data, probability, and statistics were less frequently explored, with trigonometry covering trigonometric ratios, identities, and functions (Hendriana et al., 2018; Mustafa et al., 2019; Prastiti, 2020) and statistics focusing on data, measurements, patterns, central tendency, and probability (Nurin et al., 2024; Xie et al., 2025).
Overall, the evidence highlights that PBL interventions in K-12 mathematics are most heavily employed in geometry and algebra, followed by arithmetic and applied mathematics, while trigonometry, probability, and cross-disciplinary STEM applications receive comparatively less attention. The prominence of algebra and geometry in PBL studies likely stems from their central position in school curricula and their suitability for problem-based inquiry. These topics naturally lend themselves to real-world modelling, visual reasoning, and multi-step problem solving, making them compelling contexts for examining PBL’s effectiveness. Topics that are more abstract or procedurally oriented may offer fewer opportunities for open-ended problem contexts, which could explain their limited representation in the literature.
RQ3: What PBL frameworks (steps or phases) are commonly implemented in K-12 mathematics education?
Across the reviewed studies, a range of PBL frameworks were employed, with notable variation in their structure (Table 3). The five-step PBL model emerged as the most prevalent approach, adopted by the majority of studies (refer to Table 3). The 5-step PBL framework engages students in meaningful, inquiry-driven learning. In the first step, Orient/Identify, students are introduced to the problem, identify key issues, and clarify the context or setting. The second step, Investigate/Plan/Organize, involves students working collaboratively in groups to explore potential solutions, organize ideas, plan their approach, guide investigations, and analyze the problem in depth. During the Implement/Solve phase, students apply their plans, engage in inquiry, collaborate effectively, and present their solutions. The fourth step, Evaluate/Reflect/Verify, emphasizes reviewing and evaluating solutions, drawing conclusions, self-correcting, and analyzing outcomes to ensure understanding and accuracy. Finally, in Extend/Generalize/Share, students refine their final products, improve solutions, and share their findings with a broader audience, thereby extending learning beyond the classroom.
Table 3. Overview of PBL step frameworks and study frequency.
A smaller cluster of studies utilized a 4-step PBL framework (Ahdhianto et al., 2020; Çetinkaya, 2019; Dorimana et al., 2022). These frameworks streamlined the problem-solving cycle into: (1) understanding or identifying the problem, (2) planning or investigating, (3) implementing solutions, and (4) evaluating or verifying outcomes. Their conciseness made them particularly suited to lessons requiring shorter instructional cycles, such as targeted algebraic procedures or basic geometry (Ahdhianto et al., 2020; Çetinkaya, 2019; Dorimana et al., 2022).
Several studies adopted alternative PBL frameworks. One study applied the ADDIE framework (Analyse, Design, Develop, Implement, and Evaluate) to structure PBL activities in mathematics (Purnomo et al., 2024). By integrating this systematic instructional design, it offers a more formal approach to lesson development that enhances students’ mathematical connections and habits of mind (Purnomo et al., 2024). A few researchers explored engineering and STEM-oriented approaches. Alemdar et al. (2018) implemented the Engineering Design Process, enabling students to define problems, research and generate solutions, select and test designs, and refine their work through iterative evaluation. Students engage in cross-disciplinary STEM activities that integrate science, math, and engineering practices, including data collection, analysis, probability, and modeling (Alemdar et al., 2018). Similarly, Shongwe (2024) designed mathematics instruction through a STEM-based PBL model, emphasizing the definition of real-world problems, assessment of prior knowledge, identification of resources, solution evaluation, and presentation of findings. Students worked on group projects that connected STEM concepts such as potential and kinetic energy, conservation, gravity, velocity, friction, and slope to real-world problems. They participated in hands-on activities, received feedback from STEM professionals, toured laboratories, and submitted final reports (Shongwe, 2024). Farmer et al. (2019) employed project-based PBL in K-12 mathematics with a focus on environmental and civic engagement. Students explored issues such as trash and pollution, designed bird feeders, discussed water crises, interacted with guest speakers, and produced tangible outcomes, including interviews, surveys, and conservation-themed postcards for relevant stakeholders (Farmer et al., 2019).
RQ4: What student outcomes are assessed following PBL interventions in K-12 mathematics?
Analysis of K-12 mathematics PBL interventions demonstrates that these approaches target a broad spectrum of student outcomes across cognitive, affective, social, and meta-cognitive domains (refer to Table 4). Within the cognitive domain, the most frequently assessed outcome was problem-solving skills, including understanding, planning, implementing, verifying solutions, perseverance, and problem-solving beliefs (n = 13). Mathematics achievement, encompassing overall performance, quantitative ability, and mastery of concepts, was also widely examined [n = 12]. Other examined cognitive outcomes were: critical thinking skills (Ahdhianto et al., 2020; Putri Apriliana et al., 2019; Rehman et al., 2023; Suryawan et al., 2023), mathematical reasoning, and thinking abilities (Alpaslan and Yalvac, 2023; Hidajat, 2023; Negara et al., 2022), mathematical representation skills (Ahmad et al., 2023; Lestari et al., 2020; Minarni and Napitupulu, 2017), and literacy skills (Farmer et al., 2019).
Table 4. Student outcomes assessed following PBL interventions in K-12 mathematics.
In the affective domain, outcomes related to students’ motivation, enthusiasm, and interest (Alemdar et al., 2018; Ramadhani et al., 2019; Zakaria et al., 2025), as well as their self-efficacy and self-confidence, were investigated (Ahmad et al., 2023; Alemdar et al., 2018; Hendriana et al., 2018; Hidajat, 2023; Macun and Isik, 2022). Additionally, emotional factors, such as anxiety, stress, fear, and burnout, were also assessed (Alemdar et al., 2018; Amin et al., 2021; Charlo, 2020; Macun and Isik, 2022). These outcomes highlight the role of PBL in supporting students’ attitudes, beliefs, and emotional engagement with mathematics.
Within the social domain, PBL interventions promoted teamwork and collaboration, including communication, conflict resolution, and collective problem-solving abilities, emphasizing cooperative learning and peer engagement (Ramli et al., 2020; Rehman et al., 2023; Xie et al., 2025). Finally, in the meta-cognitive domain, studies examined mathematical values and habits of mind, such as accuracy, conjecturing, creativity, consistency, systematic working, and flexibility (Purnomo et al., 2024), as well as self-regulation skills, including goal-setting, time management, and self-evaluation (Hidajat, 2023).
These findings illustrate that K-12 mathematics PBL interventions targeted cognitive mastery as well as affective, social, and meta-cognitive development, and therefore support holistic student growth in mathematical competence and broader learning skills. The findings further highlight where and how PBL research is being conducted, and reveal important methodological and contextual patterns that inform future research and practice.
5 Discussion
The preceding analysis provides a descriptive overview of how PBL is implemented across K-12 mathematics contexts, noting dominant intervention types, subject domains, frameworks, and learning outcomes. The following discussion interprets these findings in relation to previous systematic reviews and broader educational debates. It examines how the emerging evidence aligns with or departs from prior research on PBL in STEM and higher-education settings, explores disciplinary and regional trends shaping implementation patterns, and reflects on the pedagogical implications of adopting integrated versus exclusive PBL models in diverse schooling environments.
The findings of this review extend the results of earlier systematic reviews that examined PBL across broader STEM or higher-education contexts (e.g., Barak and Yuan, 2021; Vaithianathan et al., 2024). Whereas prior analyses emphasized the cognitive and affective benefits of PBL in developing critical thinking, self-direction, and collaborative learning, this review reveals that K-12 mathematics applications have diversified in both scope and design. In contrast to studies in higher education that typically adopt discipline-specific or professional-training orientations, K-12 interventions frequently integrate technology-mediated, game-based, and ethnomathematical components that adapt PBL to younger learners’ developmental and motivational needs. This shift reflects a broader pedagogical evolution—from using PBL as an inquiry-based framework for advanced learners to positioning it as a foundational strategy for cultivating mathematical reasoning and engagement from early schooling onward.
The predominance of Geometry and Algebra in the reviewed studies can be attributed to both curricular emphasis and conceptual suitability for problem-based approaches. Geometry, by nature, lends itself to visualization, modeling, and manipulation of real-world objects, making it especially conducive to the exploratory and collaborative elements of PBL. Tasks involving measurement, transformation, and spatial reasoning enable students to apply mathematics to tangible phenomena, thereby enhancing conceptual understanding. Similarly, Algebra provides fertile ground for problem formulation, hypothesis testing, and generalization—core processes aligned with the PBL cycle of identifying, investigating, and solving problems. The relative scarcity of PBL studies in topics such as trigonometry and probability suggests that these areas are still taught through procedural or lecture-based methods, underscoring the need for further curricular innovation to extend PBL’s reach across all mathematical domains.
The geographical concentration of studies in Indonesia and, to a lesser extent, Nigeria, highlights the influence of national education reforms that promote student-centred learning as a means to raise mathematics achievement. In Indonesia, sustained government initiatives since the 2013 Curriculum Reform have encouraged the incorporation of inquiry- and project-based learning models, explaining the high volume of empirical work in this area. Nigerian studies similarly reflect an increasing policy focus on learner autonomy and problem-solving competence. Beyond regional context, the dominance of integrated PBL models—those that combine digital, game-based, or cultural elements with core PBL principles—suggests a pragmatic response to classroom realities in resource-variable settings. These hybrid designs appear to enhance engagement and contextual relevance while mitigating some of the implementation challenges associated with purely exclusive PBL models. The evidence therefore, supports the view that integrated frameworks offer greater pedagogical flexibility and adaptability across diverse educational systems.
While this review offers an all-inclusive synthesis of PBL implementation in K-12 mathematics education, several limitations must be acknowledged. This review did not assess potential publication bias or language bias, as only peer-reviewed studies published in English were included. Grey literature was also excluded. This may have excluded valuable research conducted in other languages or regional contexts. Nonetheless, this restriction was necessary to ensure consistency in systematic screening and the manageable handling of a large volume of articles. Second, considerable heterogeneity across the included studies (in terms of research designs, sample sizes, intervention durations, and assessment tools), makes direct comparison difficult and reduces the generalizability of the findings. Finally, most studies placed greater emphasis on short-term student outcomes such as problem-solving skills and mathematics achievement, while long-term impacts remain underexplored.
Future research should work toward bridging these gaps. Greater inclusion of cross-cultural perspectives would help capture how PBL operates across diverse educational contexts, involving varied theoretical frameworks. Longitudinal studies are needed to examine the sustained effects of PBL interventions beyond immediate learning gains. Where sufficient comparable studies exist, meta-analysis could help identify the most effective PBL-based teaching models, while moderator analyses could clarify how factors such as student group size, educational level, and type of PBL framework influence outcomes. Such directions would provide educators, curriculum developers, and policymakers with evidence-based insights, enabling more context-sensitive, scalable, and sustainable applications of PBL in mathematics education.
6 Conclusion
This systematic review provides a comprehensive synthesis of how PBL has been implemented across K-12 mathematics education between 2014 and 2025. The evidence reveals that PBL has evolved from a specialized instructional innovation to a mainstream pedagogical framework that supports different cognitive, affective, social, and meta-cognitive outcomes. Across the forty studies analyzed, integrated models, which combine digital tools, game-based learning, ethnomathematical contexts, or STEM-oriented frameworks, were more prevalent than exclusive PBL designs. Geometry and Algebra emerged as the most frequently targeted domains, reflecting their conceptual compatibility with learning based on inquiry and their curricular prominence in mathematics education. The five-step PBL framework was also found to be the most widely employed structure, highlighting its adaptability across grade levels and learning contexts.
The findings carry important implications for educational practice and policy. The predominance of integrated PBL models points to the need for curriculum frameworks that encourage cross-disciplinary and contextually relevant learning rather than compartmentalized subject teaching. Ministries of Education and curriculum developers should consider embedding PBL-based competencies, such as collaboration, inquiry, creativity, and reflective thinking, into mathematics standards and teacher evaluation systems. Furthermore, teacher professional development should be prioritized to strengthen educators’ capacity in designing, facilitating, and assessing PBL lessons, especially in resource-limited settings. The review also highlights the potential of culturally grounded and technology-enhanced approaches to make mathematics more engaging and meaningful to diverse learners.
Nevertheless, several limitations should be acknowledged. The review was restricted to English-language, peer-reviewed publications, which may have excluded relevant studies published in other languages or regional outlets. Considerable methodological heterogeneity was observed across the included studies, particularly regarding sample sizes, intervention durations, and assessment tools, limiting the comparability and generalizability of results. In addition, most interventions focused on short-term learning outcomes such as problem-solving ability and mathematics achievement, with few exploring long-term impacts on metacognition, persistence, or transfer of skills. Addressing these limitations would require longitudinal and cross-context investigations that move beyond immediate achievement effects.
Future research should expand the existing research by examining underrepresented mathematical domains, such as trigonometry, probability, and statistics, and by exploring PBL implementation in understudied regions. Comparative and longitudinal designs could illuminate how national policies, teacher training systems, and classroom resources influence PBL effectiveness. Mixed-methods studies that combine classroom observations, learner analytics, and qualitative reflections can further capture the processes of inquiry, collaboration, and problem-solving in authentic mathematics learning environments. By advancing context-sensitive, evidence-based, and replicable models of PBL, future research can contribute to the transformation of mathematics education into a more participatory, equitable, and inquiry-oriented enterprise for 21st-century learners.
Data availability statement
The original contributions presented in the study are included in the article/Supplementary material, further inquiries can be directed to the corresponding author.
Author contributions
MA: Conceptualization, Writing – review & editing, Project administration, Supervision, Funding acquisition, Writing – original draft. AS: Writing – original draft, Funding acquisition, Project administration, Conceptualization, Supervision, Writing – review & editing, Formal analysis, Investigation, Methodology. MS: Software, Investigation, Writing – review & editing, Methodology, Formal analysis, Writing – original draft, Conceptualization. KN: Supervision, Writing – original draft, Conceptualization, Writing – review & editing, Project administration. AA-A: Supervision, Conceptualization, Project administration, Writing – original draft, Writing – review & editing. SA-H: Writing – review & editing, Supervision, Conceptualization, Writing – original draft, Project administration.
Funding
The author(s) declared that financial support was received for this work and/or its publication. This research was funded by the National Priorities Research Program (NPRP) by Qatar National Research Fund (QNRF) (grant number: NPRP12C-0828-190023).
Conflict of interest
The author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
Generative AI statement
The author(s) declared that Generative AI was not used in the creation of this manuscript.
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Supplementary material
The Supplementary material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/feduc.2025.1731307/full#supplementary-material
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Keywords: K-12, mathematics, PBL, problem-based learning, systematic review
Citation: Ayari MA, Sellami A, Santhosh ME, Naji KK, Al-Ali A and Al-Hazbi SMA (2025) From problems to performance: a systematic review of problem-based learning in K-12 mathematics. Front. Educ. 10:1731307. doi: 10.3389/feduc.2025.1731307
Edited by:
Patrick Johnson, University of Limerick, IrelandReviewed by:
Mark Prendergast, University College Cork, IrelandKhusnul Khotimah, Surabaya State University, Indonesia
Copyright © 2025 Ayari, Sellami, Santhosh, Naji, Al-Ali and Al-Hazbi. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: Abdellatif Sellami, YXNlbGxhbWlAcXUuZWR1LnFh