Fostering twenty-first century skills among primary school students through math project-based learning

The study addresses low mathematics performance and a prevalent teacher-centered pedagogy that limits students’ engagement and development of twenty-first century skills in Pakistan. National policy documents (NEP 2009; National Curriculum 2006) call for a shift from information transmission to facilitating learning environments that deepen mathematical understanding. Reported national assessments highlight poor performance in mathematics and geometry among primary students. To prepare learners for contemporary demands, teachers are urged to adopt innovative, student-centered methods—potentially supported by ICT where feasible—to cultivate collaborative, critical thinking, and problem-solving skills. The study investigates whether project-based learning (PBL) in primary math can improve students’ collaboration, problem-solving, and critical thinking.

The review situates PBL within the 4Cs framework (communication, collaboration, creativity, critical thinking), focusing on collaboration, problem-solving, and critical thinking as especially relevant to math. Collaborative learning (CL) enhances understanding through small-group work, active engagement, and teacher facilitation, moving beyond lecture-centric classrooms. Effective collaboration depends on student involvement and teacher capacity to scaffold and evaluate projects. PBL positions learners to co-construct knowledge, generate products, and apply higher-order thinking. For problem-solving, PBL engages students with real-world tasks requiring planning, communication, and creative solutions; however, implementation can be challenging without adequate scaffolds and student readiness. For critical thinking, PBL supports analysis, evaluation, reasoning, and reflection, aligning with frameworks such as Paul-Elder; math learning inherently interweaves critical thinking with conceptual understanding and argumentation. Prior studies show PBL can improve achievement and attitudes, though effects vary by context, alignment, and implementation quality. Theoretical underpinnings include social constructivism (emphasizing active, collaborative learning), Gardner’s multiple intelligences (supporting varied activities for diverse learners), and Kolb’s experiential learning theory (learning through authentic experiences and reflection), all consistent with PBL’s emphasis on real-world tasks and group work.

Design: Convergent mixed-methods study combining a quantitative quasi-experimental, non-equivalent control group pretest–posttest design with qualitative classroom observations. Random sampling was not possible due to the school’s fixed schedule. Participants: Seventy 5th-grade students divided into two intact sections: experimental group (n=35) received PBL; control group (n=35) received traditional instruction. Homogeneity was checked prior to intervention via pretests on collaboration, critical thinking, and problem-solving. Duration and content: Six-week intervention, 5 hours/week (30 class hours). Math content focused on angles/geometry and decimals, aligned to 5th-grade math core standards (geometry/measurement and algebra/problem-solving reasoning strands). PBL implementation: Students worked in groups (six girls per group; five to seven groups depending on activity) on a math project culminating in a product and presentation. Elements included a driving question (e.g., identifying, naming, and classifying angles; measuring angles with protractors), new knowledge acquisition (e.g., percentages, discounts), student-driven work with teacher as facilitator (ZPD support), realistic goals aligned to standards, and real-world applications (identifying angles in everyday objects). Teachers used worksheets, projects, and Buck Institute operational stages for assessment. Instruments: - Collaboration: 37-item 5-point Likert collaborative scale adapted from Tibi (2015); used pre/post in both groups. Classroom collaborative framework tool (validated prior to use) guided observations. - Problem-solving: Researcher-designed math test (20 items; 10 on angle measurement, 10 on geometry) based on 5th-grade standards. ITEMAN analysis yielded difficulty indices 0.33–0.85 and discrimination indices 0.31–0.82, meeting accepted quality thresholds. - Critical thinking: Ten open-ended problems adapted from Gelerstein et al. (2016), Yoon (2017), and Sumarni & Kadarwati (2020), covering interpretation, analysis, inference, evaluation, explanation, and self-regulation (see description of subskills). Reported reliability (Cronbach’s alpha) 0.76; instrument reported as valid and reliable. Procedures: 1) Pretesting of collaboration, critical thinking, and problem-solving for both groups; verification of group homogeneity. 2) Experimental group received PBL lessons and project work; control group received traditional instruction on the same content. 3) Posttesting on the same measures. 4) Qualitative observations of the experimental group throughout the 6-week intervention focusing on collaboration (individual accountability, social skills, group processing) with inductive/deductive coding cycles. Analysis: - Quantitative: Levene’s tests for homogeneity of variances; one-way ANCOVA comparing posttests controlling for pretests for collaboration and critical thinking; independent-samples t-tests for problem-solving pre/post between groups; paired-samples t-tests within groups; effect size (Cohen’s d) reported for posttest comparisons. - Qualitative: Thematic analysis from observations, generating themes on group work processes, shared responsibilities, decision-making, and interdependence.

- Collaborative skills: Levene’s test indicated homogeneity (F=0.806, p=0.373). One-way ANCOVA showed a significant treatment effect favoring PBL (F=253.564, p<0.001), indicating improved collaboration in the experimental group. - Critical thinking: Levene’s test indicated no significant variance difference (F=3.711, p=0.58). ANCOVA showed a significant effect favoring PBL (F=23.281, p<0.001). The abstract also reports a significant ANCOVA for critical thinking (F=104.833, p<0.001). - Problem-solving: Pretest means were similar (Experimental 12.46, Control 11.80; independent t=0.809, p>0.05; table text reports p=0.421 at pretest). Posttest means favored the experimental group (Experimental 25.54, Control 16.94); independent t=8.284, p<0.001; large effect size Cohen’s d=1.82. Paired t-tests showed significant gains within both groups, with much larger gains for the experimental group (Experimental mean change −16.780, t=−25.252, p<0.001; Control mean change −5.941, t=−12.251, p<0.01). - Qualitative observations: PBL promoted effective group work from planning through presentation; students shared responsibilities with deadlines, made collective decisions (often via discussion and voting), and demonstrated interdependence (delays in individual tasks affected group outputs). Students extended collaboration beyond class (e.g., WhatsApp groups), reported increased confidence in voicing opinions, and produced artifacts displayed in school, evidencing application of angle concepts to real contexts.

Findings across quantitative and qualitative strands consistently indicate that PBL enhanced fifth graders’ twenty-first century skills in mathematics. Significant gains in collaborative skills and critical thinking, along with large improvements in problem-solving performance, directly answer the research questions by showing PBL’s superiority over traditional instruction in this context. Observational data illuminate mechanisms: structured group processes (shared duties, decision-making, interdependence) and authentic tasks fostered engagement, communication, and joint problem-solving. These outcomes align with social constructivist and experiential learning theories and with prior literature reporting PBL’s positive effects on engagement, collaboration, and higher-order thinking. The study underscores PBL’s relevance for under-resourced settings by leveraging low-tech, hands-on activities to cultivate essential skills, while highlighting the importance of teacher facilitation and alignment with curriculum standards.

The study provides empirical evidence that project-based learning in primary mathematics can significantly improve students’ collaboration, critical thinking, and problem-solving—key twenty-first century skills. Results support student-centered, inquiry-based, and authentic learning experiences as effective means to prepare learners for complex contemporary challenges. The work contributes uniquely within the Pakistani context by detailing local implementation and demonstrating feasibility and benefits in technology-limited public schools using low-tech resources (manipulatives, posters, group activities). The findings can inform teachers and policymakers aiming to enhance math outcomes and essential skills through PBL. The authors note that PBL effectiveness depends on factors such as teacher training/support, curriculum alignment, assessments, and student readiness, and that implementation may require substantial time and resources. Further research is recommended across subjects, grade levels, and cultural contexts to identify optimal implementation conditions.

- Design and sampling: Quasi-experimental, non-equivalent control group design; random sampling was not possible due to the school’s fixed schedule, which may limit causal inference and generalizability. - Implementation dependencies: The effectiveness of PBL may depend on teacher training/support, curriculum alignment, assessment quality, and student readiness; implementing PBL may require significant time, resources, and training, posing challenges in certain contexts. - Context specificity: Conducted within a specific educational context (Pakistani public school setting with limited technology), which may affect transferability to other settings. - Data sharing: Some data are restricted due to anonymity requests and future publications, potentially limiting external reanalysis (though de-identified data are available upon request).