The study's rationale stems from the urgent need to equip students with 21st-century skills, particularly in math, to thrive in a competitive global economy. Pakistan's education system, highlighted by poor math scores in reports like Alif Ailaan's 2017 "Powering Pakistan for the 21st Century," underscores this need. The teacher-centered nature of many classrooms hinders active student engagement. The 2009 National Education Policy and the 2006 National Curriculum advocate for adapting teaching methods to student needs, shifting from information transmission to fostering a supportive learning environment. However, various factors, including school settings and resources, impact the effective implementation of the math curriculum. The study explores project-based learning (PBL) as a potential solution to address these challenges and enhance students' 21st-century skills.

The literature review emphasizes the importance of 21st-century skills, particularly critical thinking, collaboration, and problem-solving. The 4Cs (communication, cooperation, creativity, critical thinking) are highlighted, with this study focusing on the latter three within the context of math education. PBL, aligned with constructivist principles, is presented as an effective instructional approach to cultivate these skills. PBL engages students in research-oriented activities, promoting collaboration, critical thinking, and communication. The challenges within Pakistan's education system, including funding issues and traditional teaching methods, are discussed, further emphasizing the need for innovative approaches like PBL in math, a subject crucial for cognitive development. The literature review explores existing research on PBL's effectiveness in enhancing collaborative skills, problem-solving abilities, and critical thinking skills. It also touches on the theoretical frameworks underpinning PBL, such as constructivist theory, multiple intelligences theory, and experiential learning theory, providing a comprehensive background for understanding the chosen pedagogical approach.

Employing a convergent mixed-methods design, this quasi-experimental study with a non-equivalent control group pre-test-post-test design compared a PBL experimental group (n=35, 5th graders) and a traditionally-taught control group (n=35). Random sampling was not feasible due to school scheduling constraints. The six-week PBL intervention focused on angle measurement, geometry, and decimal concepts, aligned with 5th-grade math core standards. Data collection involved pre- and post-tests measuring collaborative skills (Tibi, 2015 scale), problem-solving skills (a 20-item math test), and critical thinking skills (a 10-item test adapted from Gelerstein et al., 2016; Yoon, 2017; Sumarni & Kadarwati, 2020; Ventista, 2018). The instruments' reliability was established through Cronbach's alpha (0.76 for critical thinking). Classroom observations using a collaborative framework provided qualitative data. The PBL project involved a hands-on component, driving questions, introduction of new information, student-driven elements, realistic goals, and real-world applications. Data analysis included ANCOVA for collaborative and critical thinking skills and independent samples t-tests for problem-solving skills, along with qualitative thematic analysis of observational data.

The quantitative findings demonstrate significant improvements in the experimental group compared to the control group. ANCOVA analysis revealed significant differences in collaborative skills (F=253.564, p=0.000) and critical thinking skills (F=23.281, p=0.000) favoring the PBL group. For problem-solving skills, the independent samples t-test showed a significant difference between the post-intervention means of the experimental (25.54) and control (16.94) groups (t=8.284, p=0.000), with a large effect size (Cohen's d = 1.82). Qualitative analysis, based on classroom observations, identified four key themes: student group work, shared responsibilities, collaborative decision-making, and interdependent work. These observations indicated that students effectively collaborated, shared responsibilities, made joint decisions, and understood the interconnectedness of their contributions to the project. The qualitative data supported the quantitative findings, indicating that PBL fostered higher-level collaborative skills among students.

The study's findings strongly support the hypothesis that PBL enhances 21st-century skills in primary school math. The significant improvements in collaboration, critical thinking, and problem-solving observed in the experimental group highlight the effectiveness of PBL as an instructional approach. The qualitative data corroborate these findings, showcasing the development of collaborative skills through shared responsibilities, decision-making, and interdependent work within group projects. These results align with previous research demonstrating the positive impact of PBL on student learning and engagement. The study's context within Pakistan's education system makes it a particularly relevant contribution, offering a viable approach to address the challenges faced by the country's schools and improve math education outcomes. The findings underscore the potential of PBL to cultivate essential skills for success in a rapidly evolving world.

This study provides strong empirical evidence of PBL's effectiveness in fostering 21st-century skills in primary school math. The significant improvements in collaboration, critical thinking, and problem-solving abilities demonstrate the value of a student-centered approach. Future research could explore the long-term effects of PBL, investigate optimal strategies for teacher training and support in implementing PBL, and examine its effectiveness across diverse cultural contexts and grade levels. The study offers valuable insights for educators and policymakers seeking to improve math education and equip students with the essential skills needed for success in the 21st century.

The study's limitations include the non-randomized sample due to school scheduling constraints and the limited duration of the intervention (six weeks). The generalizability of the findings might be restricted to similar school settings and student populations. Future research could address these limitations by employing a larger, randomized sample and conducting a longitudinal study to assess the long-term impact of PBL. Additionally, a more detailed analysis of the specific aspects of PBL that contributed to the observed improvements could provide further insights into the mechanism of action.