The effectiveness of training teachers in problem-based learning implementation on students’ outcomes: a mixed-method study

The paper investigates whether training teachers to implement problem-based learning (PBL) improves third-grade students’ outcomes in mathematics, specifically knowledge application and attitudes toward mathematics. PBL positions students as active problem-solvers working in small groups on authentic, ill-structured problems, with the facilitator guiding learning processes. In mathematics, PBL contextualizes knowledge in real-life situations to help students understand when and how to apply mathematics, potentially improving both application and attitudes. However, students often require support to shift from passive learning habits to self-regulated learning (SRL), and teachers need facilitation skills to scaffold metacognitive processes. The study addresses: (1) How do trained and untrained teachers implement PBL? (2) What are the effects of teacher training in implementing PBL on students’ mathematical applications? (3) What are the effects of teacher training in implementing PBL on students’ attitudes towards mathematics?

Prior K–12 research generally finds PBL enhances knowledge application and promotes positive attitudes compared with traditional, teacher-centered methods. Examples include improved application and attitudes in mathematics under PBL (e.g., Tong et al., 2021; Wirkala & Kuhn, 2011; Wong & Day, 2009), though most PBL research has been in higher education and medicine, with limited work in primary schools. Regarding teacher training, theory and reviews stress the importance of facilitator skills for effective PBL (Barrows, 1996; Hmelo-Silver & Barrows, 2006; Leary et al., 2009). A meta-analysis (Leary et al., 2013) reported a significant positive relationship between tutor training and student achievement, suggesting untrained facilitators may yield outcomes similar to traditional teaching. Yet, few primary studies have experimentally isolated teacher training effects on student outcomes. This study contributes by experimentally examining how training in PBL implementation affects primary students’ mathematics application and attitudes.

Design: Mixed-methods with a quasi-experimental quantitative core and qualitative observations/interviews for triangulation. A within-subjects factor of time (pre, post) and a between-subjects factor of group were analyzed via mixed-factor ANOVA. Participants and setting: One randomly selected private primary school in Hail, Saudi Arabia. Seven third-grade classes (ages 8–9) randomly selected; 127 pupils total, middle socioeconomic status, predominantly Saudi; no special education students. Three experienced male mathematics teachers (all Egyptian, ~10 years experience, first degrees in mathematics), similar beliefs about active learning and math problem-solving; none previously trained in PBL. Groups: A (trained teacher using PBL; 3 classes; N=52), B (untrained teacher using traditional teaching methods, TTM; 2 classes; N=39), C (untrained teacher using PBL; 2 classes; N=36). Topic: Data display. Duration: 10 sessions of 45 minutes over 2.5 weeks (7.5 hours), equivalent time across groups. Teacher training (professional development): One-week (8–10 hours) program developed by the author focused on PBL facilitation: scaffolding and feedback, prompting independent thinking, facilitating collaborative knowledge construction, monitoring learning processes, modeling behaviors, focusing on critical thinking, and intervention strategies (what/when/how to intervene). Included three 45-minute practice PBL sessions with non-sample students and extensive feedback (>1 hour each session). Ongoing daily feedback during implementation. Students also received two sessions on working within PBL. PBL implementation: Small groups of 4–6; problems presented, group discussion to understand the problem, class-wide discussion, group solution, and whole-class solution discussion. Adopted Barrows’ PBL characteristics (student-centered, small groups, authentic problems, problem-solving skills development, self-directed learning). Problems were real-life, ill-structured, age-appropriate, clear/concise, and of appropriate difficulty; students acted as stakeholders. Instruments: Mathematics application test using age-appropriate TIMSS (2003/2007/2011) items (MCQ, short answer, fill-in tables, drawing); dichotomous scoring. Attitudes toward mathematics scale: TIMSS 2007 four-item, 4-point Likert (with reverse coding for “mathematics is boring”), total score range 4–16. Validity: face validity by 8 arbitrators; Reliability: test–retest r=0.86 (math), 0.88 (attitudes); Cronbach’s alpha 0.747 (math), 0.808 (attitudes); item-total correlations >0.3. Qualitative data: Field observation notes (10 lessons per teacher) capturing teacher interventions, student practices/responses, group interaction, and PBL processes; reflective notes maintained. Post-implementation semi-structured interviews (13–23 minutes, Arabic; recorded, transcribed, translated) with PBL-implementing teachers (trained and untrained). Deductive content analysis using a predefined matrix with two categories: (1) understanding the problem and (2) use of metacognitive strategies. Statistical analysis: Mixed-factor ANOVA (time within; group between), Tukey post hoc tests where appropriate. Partial eta squared reported with Cohen’s benchmarks (0.01 small, 0.06 medium, 0.14 large). Analyses in SPSS v22, alpha=0.05.

Qualitative implementation differences: - Understanding the problem: The trained teacher required students to articulate problem understanding (e.g., explain in own words), waited longer, and encouraged reflection before moving to solution; the untrained teacher advanced after brief checks (e.g., accepting a shouted “yes”). - Metacognitive facilitation: The trained teacher monitored groups and coached thinking with metacognitive questions (what done so far, what next, considering alternatives), used think-alouds and modeling, and avoided giving solutions, fostering student independence. The untrained teacher tended to provide similar examples to lead students toward solutions; students frequently relied on the teacher for examples. Quantitative outcomes: - Mathematics application (Applying Achievement): Pre→Post means (SD): • Group A (Trained+PBL): 1.10 (0.96) → 2.65 (1.36) • Group B (Traditional): 0.90 (0.97) → 1.74 (1.43) • Group C (Untrained+PBL): 0.97 (1.10) → 2.03 (1.67) Mixed-measures ANOVA: Main effect of time significant, F(1,121)=76.795, p<0.001, partial η²=0.388 (large). Time×Group interaction significant, F(2,121)=4.333, p=0.015, partial η²≈0.067 (medium). Tukey post hoc: Trained+PBL vs Traditional p=0.009 (significant); Untrained+PBL vs Traditional p=0.202 (ns); Trained+PBL vs Untrained+PBL p=0.121 (ns). Interpretation: Training in PBL led to significantly greater gains in application than traditional instruction; untrained PBL did not differ significantly from traditional on application. - Attitudes toward mathematics: Pre→Post means (SD): • Group A (Trained+PBL): 10.54 (1.75) → 11.35 (1.57) • Group B (Traditional): 10.15 (1.93) → 8.74 (3.04) • Group C (Untrained+PBL): 10.28 (2.07) → 11.11 (2.53) Mixed-measures ANOVA: Main effect of time not significant, F(1,121)=0.480, p=0.490, partial η²=0.004. Time×Group interaction significant, F(2,121)=12.486, p<0.001, partial η²=0.171 (large). Tukey post hoc: Trained+PBL vs Traditional p<0.001; Untrained+PBL vs Traditional p=0.008; Trained+PBL vs Untrained+PBL p=0.794 (ns). Interpretation: PBL significantly improved attitudes relative to traditional methods, regardless of teacher training. Overall: Training primarily enhanced students’ application outcomes (via metacognitive facilitation), while PBL pedagogy/content improved attitudes irrespective of teacher training.

The findings address three questions. First, implementation quality differed: trained teachers provided structured time and prompts to ensure problem understanding and used metacognitive coaching, modeling, and timely interventions; untrained teachers offered example-led guidance, promoting dependence. Second, teacher training significantly enhanced students’ mathematics application compared to traditional teaching, indicating that facilitation skills—particularly metacognitive scaffolding—are critical to activate students’ self-regulated learning within PBL. Untrained PBL did not outperform traditional instruction on application, aligning with meta-analytic evidence that tutor training is linked to student achievement and that untrained facilitation may yield traditional-like outcomes. Third, PBL significantly improved attitudes toward mathematics relative to traditional teaching irrespective of teacher training, likely due to engaging, real-life problems, small-group collaboration, and active learning features that foster interest and intrinsic motivation. These results reinforce the dual nature of PBL’s impact: content and environment primarily drive affective gains, while facilitator expertise is pivotal for cognitive application gains.

PBL is effective for fostering positive attitudes toward learning mathematics among third-grade students, irrespective of teacher training. However, to improve students’ application of mathematical knowledge, teacher training in PBL—especially in metacognitive facilitation strategies—is necessary. The study underscores the importance of professional development that equips teachers to scaffold, model, and strategically intervene in students’ learning processes. Future work should test these effects across different grade levels, subjects, school contexts, and with more diverse and randomly selected samples to strengthen generalizability and to refine which training components most enhance student outcomes.

- Population and subject specificity: Findings pertain to young (third-grade) students and mathematics only. - Sampling: School/classes and teacher selection within one private school; sample not fully random, limiting generalizability. - Context: All participants were male due to Saudi Arabia’s gender-segregated schooling; cultural-context factors may limit external validity. - Quasi-experimental design: Potential for unmeasured confounds despite efforts to equate groups; single-school setting may limit broader applicability.