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Cited by 0Problem and Project Based LearningMathematics Education and PedagogySTEM Education

Can project-based learning improve students’ mathematics learning outcomes: a three-level meta-analysis

Open access
Wang, Chunting, Zhang, Wenlan, Cheng, Jiaxin·2026·Frontiers in Psychology
DOI 10.3389/fpsyg.2026.1868415PMC PMC13586001
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Abstract

Against the backdrop of the worldwide shift toward competency-driven basic education reform, project-based learning (PBL) is widely recognized for its student-centered design and authentic problem-solving approach. Empirical evidence on the effectiveness of Mathematics PBL is highly varied; traditional meta-analysis often fails to properly address nested data structures. This study conducted a three-level meta-analysis spanning the past 20 years, a total of 35 eligible studies were included. In the primary meta-analytic model, two statistically outlying studies were identified and excluded based on Cook’s distance. Ultimately, 33 studies with 84 effect sizes were incorporated into the main effect analysis.to comprehensively quantify PBL’s impact on students’ mathematical achievement. The results indicated a significant overall effect size for PBL (Cohen’s d = 0.529, 95% CI [0.38, 0.68]), but publication bias analyses suggested potential overestimation (trim-and-fill corrected estimate = 0.275); therefore, findings should be interpreted cautiously. Moderator analyses revealed that cultural background and intervention duration significantly influenced outcomes. Notably, PBL demonstrated strong effectiveness within a 1-to-8-week timeframe. Non-cognitive abilities showed a numerically larger effect than cognitive abilities, but the difference was not statistically significant ( p = 0.083). No significant moderators were found for educational level, class size, group size, mathematics knowledge domain, publication type, or the number of technology types used, suggesting that PBL is broadly generalizable across various mathematics teaching contexts. Given the presence of publication bias, these results provide moderate rather than robust support for the localized application of mathematics PBL. Systematic review registration: https://www.crd.york.ac.uk/PROSPERO/view/CRD420251105265 , identifier CRD420251105265.

AI snapshot

Written from the paper’s full text.

TL;DR

This three-level meta-analysis of 33 studies (84 effect sizes) finds a medium-to-large positive overall effect of project-based learning on mathematics learning outcomes (Cohen’s d = 0.529), but publication-bias correction reduces the estimate to 0.275. Intervention duration and cultural background significantly moderate effects, while most other instructional moderators do not.

Key findings

  • PBL had a significant overall positive effect on mathematics learning outcomes: Cohen’s d = 0.529, 95% CI [0.38, 0.68], t = 7.14, p < 0.001. Trim-and-fill correction estimated 23 missing studies and reduced the effect to d = 0.275, 95% CI [0.157, 0.394], suggesting possible overestimation.
  • Intervention duration significantly moderated effects (F(2, 81) = 5.33, p < 0.01): 1–8 weeks produced the strongest effect (d = 0.666), 9–18 weeks d = 0.528, and >18 weeks the weakest (d = 0.110).
  • Cultural background significantly moderated effects: the individualism–collectivism index was a negative predictor (β = −0.022, F(1, 82) = 29.56, p < 0.01), meaning lower scores (stronger collectivism) predicted greater PBL effects.
  • Non-cognitive outcomes showed a numerically larger effect (d = 0.605) than cognitive outcomes (d = 0.581), but the difference was not statistically significant (p = 0.083). Educational level, class size, group size, mathematics knowledge domain, publication type, and number of technology types were not significant moderators.

Methods

  • Three-level meta-analysis following PRISMA 2020 and prospectively registered in PROSPERO (CRD420251105265). Searches in Chinese and English databases on July 15, 2025, updated December 1, 2025–January 10, 2026, yielded 4,715 initial records; 35 studies were included, and after removing two Cook’s-distance outliers, 33 studies with 84 effect sizes entered the main analysis.
  • Inclusion required empirical studies of PBL effects on mathematics learning outcomes with sufficient effect-size data, participants from elementary through tertiary education, and exclusion of problem-based learning, integrated STEM unless mathematics effects were isolated, and special-needs samples. Two researchers coded studies with 100% agreement; quality was assessed with a seven-item checklist and Cochrane ROB1.
  • Analyses used R 4.5.2 with metafor: random-effects models fitted by REML, Cohen’s d as effect size, three-level variance decomposition, Q and I² heterogeneity tests, log-likelihood model comparisons, subgroup and meta-regression moderator analyses, and publication-bias checks including funnel plots, multilevel Egger’s regression, trim-and-fill, fail-safe N, leave-one-out, and Cook’s distance sensitivity analyses.

Limitations

  • The paper states that publication bias suggests the true effect may be smaller than the original estimate; despite including grey literature and unrestricted language criteria, the sample was dominated by Chinese and English published studies, so unpublished non-significant findings and other-language studies may be missing.
  • The paper states that primary studies varied in reported contextual and instructional information, with partial missing data for group size and insufficient reporting for school resources, teacher training, implementation quality, and task complexity; evidence was also uneven across educational stages, with limited university mathematics data.
  • The paper states that most included studies used quasi-experimental designs, which may be subject to unmeasured confounding and novelty effects, and that excluding two outlier studies may narrow contextual applicability. The text also makes evident that no included study was rated as a true RCT or matched design in the quality table, and the cultural moderator was measured at the national level, which may not capture classroom- or school-level cultural variation.

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.3389/fpsyg.2026.1868415

Cites

45 of 47 references verified2 citation errors · 0 not checkable

Statistics

Claims the paper makes

20 of 44 cited sources checked · 11 supported · 1 flagged · accuracy not yet measured

  • Premisecitation

    Some studies report non-significant effects of PBL on mathematics achievement.

    “However, some studies report non-significant effects of PBL on mathematics achievement (Rijken and Fraser, 2023; Tabuk and Özdemir, 2009).”
    Quote in the paperNot a substantial claim1 of 2 sources checked
    • cites Rijken and Fraser, 2023 source

      The paper’s ‘Instructional method and gender as determinants of learning environment and outcomes’ section reports that project students had significantly lower mathematics achievement than non-project students. Appendix A, Table 2 marks the achievement difference as significant (F = 11.15, p < 0.01). Its statement that most differences were nonsignificant concerns other measured scales, not achievement. (LLM, conf=0.90)

      Checked by a reasoning model — may be wrong.

      Experimental — accuracy not yet measured
    • cites Tabuk and Özdemir, 2009

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • Premisecitation

    Some research reports non-significant effects on non-cognitive outcomes.

    “However, some research reports non-significant effects on non-cognitive outcomes (Zhang and Ma, 2023; Chen and Yang, 2019).”
    Quote in the paperNot a substantial claim1 of 2 sources checked
    • cites Zhang and Ma, 2023 source
    • cites Chen and Yang, 2019 source
  • Premisecitation

    Several meta-analyses and systematic reviews have demonstrated positive impacts of PBL on academic achievement.

    “Several meta-analyses and systematic reviews have synthesized the effects of PBL in education, demonstrating positive impacts on academic achievement (Chen and Yang, 2019; Zhang and Hu, 2019; Zhang and Ma, 2023).”
    Quote in the paperNot a substantial claim1 of 3 sources checked
    • cites Chen and Yang, 2019 source
    • cites Zhang and Hu, 2019 source
    • cites Zhang and Ma, 2023 source
  • Interpretationcitation

    The finding that PBL enhances mathematics learning is consistent with prior empirical and review studies.

    “consistent with prior empirical and review studies (Juandi et al., 2025)”
    Quote in the paperNot a substantial claim1 of 1 sources checked
    • cites Juandi et al., 2025 source
  • Findingown data

    Educational level was not a significant moderator of PBL effects.

    “No significant moderators were found for educational level, class size, group size, mathematics knowledge domain, publication type, or the number of technology types used”
    Quote in the paperSubstantial claim
  • Classified as probably not a substantial claim. 43
  • May combine two claims. 46

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    Zhang and Ma (2023) report stronger effects of PBL in Asia, especially Southeast Asia, than in Western Europe and North America.

    “Conversely, Zhang and Ma (2023) report stronger effects of PBL in Asia, especially Southeast Asia, than in Western Europe and North America.”
    Quote in the paperNot a substantial claim1 of 1 sources checked
    • cites Zhang and Ma, 2023 source

  • Classified as probably not a substantial claim.

    Study design and conductcitation

    The study adhered to PRISMA 2020 guidelines.

    “To ensure systematicity and replicability, this study adhered to the PRISMA 2020 guidelines (Page et al., 2021).”
    Quote in the paperSubstantial claim1 of 1 sources checked
    • cites Page et al., 2021 source

  • May combine two claims.

    Premisecitation

    Studies indicate that PBL significantly enhances learning interest, motivation, classroom engagement, and self-efficacy, while reducing mathematics anxiety.

    “At the non-cognitive level, studies indicate that PBL significantly enhances learning interest, motivation, classroom engagement, and self-efficacy, while effectively reducing mathematics anxiety (Alenezi, 2023; Holmes and Hwang, 2016).”
    Quote in the paperNot a substantial claim1 of 2 sources checked
    • cites Alenezi, 2023 source

      The Analysis of Students’ Motivation, Engagement, and Interest section reports a significant increase in those three measures after the PBL intervention, and the Discussion of Students’ Attitudes section describes the same positive impact. The cited paper does not report a separate self-efficacy result or a reduction in mathematics anxiety. (LLM, conf=0.88)

      Experimental — accuracy not yet measured
    • cites Holmes and Hwang, 2016 source

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    In mathematics education, PBL effectively bridges abstract mathematical concepts and real-world applications.

    “In mathematics education, PBL effectively bridges abstract mathematical concepts and real-world applications, enabling learners to deepen their understanding and apply mathematical knowledge while solving authentic problems, thereby avoiding rote memorization and formalistic learning (Rijken and Fraser, 2023).”
    Quote in the paperNot a substantial claim1 of 1 sources checked
    • cites Rijken and Fraser, 2023 source

      The Project-based learning section describes students applying mathematical concepts to a practical suburb-planning project, supporting the claim that PBL connects mathematics with real-world problems. But the Conclusion and significance section reports lower achievement for project-based students than for traditional-class students and notes that some found mathematical connections difficult. The unqualified claim that PBL does this effectively is therefore stronger than this study supports. (LLM, conf=0.86)

      Experimental — accuracy not yet measured

  • May combine two claims.

    Premisecitation

    Research confirms that PBL significantly enhances students' problem-solving skills, knowledge transfer, and mathematical application abilities.

    “At the cognitive level, research confirms that PBL significantly enhances students’ problem-solving skills, knowledge transfer, and mathematical application abilities (Saparbayeva et al., 2025; Rehman et al., 2023; Alenezi, 2023).”
    Quote in the paperSubstantial claim3 of 3 sources checked
    • cites Saparbayeva et al., 2025 source

      The Research background section distinguishes problem-based learning (PBL) from project-based learning (PjBL) and reports stronger analytical skills and retention among PBL students. Sections 2.1–2.2 and the Conclusion attribute improved mathematical problem-solving and practical application to PjBL, not PBL. The cited paper therefore does not establish the claimed PBL effects on knowledge transfer or mathematical application abilities. (LLM, conf=0.86)

      Experimental — accuracy not yet measured
    • cites Rehman et al., 2023 source

      The Results report a statistically significant post-intervention difference in math problem-solving scores favoring the PBL group. The Methodology says test questions assessed students’ ability to apply mathematical concepts to real-world scenarios, but the paper does not report a separate significant improvement in mathematical application abilities or demonstrate improved knowledge transfer. The study concerns primary-school math students, rather than students generally. (LLM, conf=0.87)

      Experimental — accuracy not yet measured
    • cites Alenezi, 2023 source

      The Discussion of the Impact of PBL on Students’ Problem-Solving Skills in Mathematics reports significantly better problem-solving scores and real-world mathematical solutions for the Madrasati PBL group. The Literature Review says PBL can promote knowledge transfer, but the paper does not report a significant measured improvement in knowledge transfer. Its findings are also limited to secondary-school mathematics taught through Madrasati. (LLM, conf=0.87)

      Experimental — accuracy not yet measured

  • May combine two claims.

    Interpretationcitation

    Disparities arising from varied educational systems and resource endowments across contexts will constrain the depth of in-class inquiry and compromise implementation fidelity, ultimately restraining the complete realization of PBL's pedagogical merits.

    “Given its sophisticated procedural design and time-intensive operation, disparities arising from varied educational systems and resource endowments across contexts will constrain the depth of in-class inquiry and compromise implementation fidelity, ultimately restraining the complete realization of PBL’s pedagogical merits (Sánchez-García and Angosto, 2026).”
    Quote in the paperNot a substantial claim1 of 1 sources checked
    • cites Sánchez-García and Angosto, 2026 source

      The Procedural dimension section describes PBL implementation as resource-intensive and time-consuming. The Discussion says differences in resources, curricula, and teacher training affect implementation fidelity, and that rigid curricula can limit sustained inquiry. But the claim's unqualified prediction that disparities will have these effects across contexts is stronger than the review's context-dependent findings; its Limitations section cautions that the results cannot be generalized to all PBL implementations. (LLM, conf=0.84)

      Experimental — accuracy not yet measured
    • Rests on an assumption: PBL implementation is contingent on abundant resources such as well-equipped facilities and specialized teacher training.

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Premisecitation

    Zhang and Ma (2023) demonstrated that interventions lasting 9-18 weeks produce the most significant effects, with diminishing returns beyond 18 weeks.

    “Zhang and Ma (2023) demonstrated that interventions lasting 9–18 weeks produce the most significant effects, with diminishing returns beyond 18 weeks.”
    Quote in the paperNot a substantial claim1 of 1 sources checked
    • cites Zhang and Ma, 2023 source

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Study design and conductown data

    Two reviewers independently assessed the quality of the 35 studies using the quality index checklist developed by Montuori et al. (2024) and Nie et al. (2025).

    “Two reviewers independently assessed the quality of the 35 studies using the quality index checklist developed by Montuori et al. (2024) and Nie et al. (2025) (see Table 3).”
    Quote in the paperNot a substantial claim1 of 2 sources checked
    • cites Montuori et al. (2024) source
    • cites Nie et al. (2025) source

  • May combine two claims.

    Premisecitation

    Zhang and Ma (2023) confirmed advantages for small classes, senior high schools, and groups of 4-5 students.

    “Zhang and Ma (2023) confirmed advantages for small classes, senior high schools, and groups of 4–5 students.”
    Quote in the paperNot a substantial claim1 of 1 sources checked
    • cites Zhang and Ma, 2023 source

  • May combine two claims.

    Interpretationcitation

    According to Higgins et al. (2003), within-study heterogeneity was mild, whereas between-study heterogeneity was substantial, indicating a strong influence of study-level characteristics on effect sizes.

    “According to Higgins et al. (2003), within-study heterogeneity was mild, whereas between-study heterogeneity was substantial, indicating a strong influence of study-level characteristics on effect sizes.”
    Quote in the paperNot a substantial claim1 of 1 sources checked
    • cites Higgins et al. (2003) source

      Table 2 and the ‘Clinically important subgroups’ discussion report low heterogeneity within tamoxifen-treatment-duration subgroups (I² = 13%) and high heterogeneity between those subgroups (I² = 96%). That supports a within- versus between-subgroup contrast, but not the claim’s ‘within-study’ contrast or a general conclusion that study-level characteristics strongly influenced effect sizes. Page numbers are unavailable in our copy. (LLM, conf=0.86)

      Experimental — accuracy not yet measured

  • May combine two claims.

    Premisecitation

    Juandi et al. (2025) confirm that content type influences mathematics achievement in PBL environments, with measurement content demonstrating the strongest effects.

    “Juandi et al. (2025) confirm that content type influences mathematics achievement in PBL environments, with measurement content demonstrating the strongest effects.”
    Quote in the paperNot a substantial claim1 of 1 sources checked
    • cites Juandi et al., 2025 source

      The Mathematics Content section reports that mathematics content significantly differentiated achievement and that measurement topics had a significantly higher effect than other topics. The finding is specifically about Indonesian students using computer-assisted mathematics education integrated into PBL; the citing sentence leaves out those limits. (LLM, conf=0.84)

      Experimental — accuracy not yet measured

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    Collaborative teamwork lies at the core of PBL, as students work collectively to tackle authentic real-world mathematical problems.

    “Collaborative teamwork lies at the core of PBL, as students work collectively to tackle authentic real-world mathematical problems (Rehman et al., 2023).”
    Quote in the paperNot a substantial claim1 of 1 sources checked
    • cites Rehman et al., 2023 source

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    Zhang and Ma (2023) identified benefits for small classes and groups of 4-5 individuals.

    “Zhang and Ma (2023) identified benefits for small classes and groups of 4–5 individuals”
    Quote in the paperNot a substantial claim1 of 1 sources checked
    • cites Zhang and Ma (2023) source

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    Achievement Goal Theory (AGT) posits that within achievement-related contexts, including educational environments, individuals' motivation and achievement-relevant behaviors are influenced by their goal orientations, which define how learners perceive success and assess their own competence.

    “Achievement Goal Theory (AGT) posits that within achievement-related contexts, including educational environments, individuals’ motivation and achievement-relevant behaviors are influenced by their goal orientations, which define how learners perceive success and assess their own competence (Jiang and Zhang, 2021).”
    Quote in the paperNot a substantial claim1 of 1 sources checked
    • cites Jiang and Zhang, 2021 source

  • May combine two claims.

    Findingown data

    Non-cognitive abilities showed a numerically larger effect than cognitive abilities, but the difference was not statistically significant (p = 0.083).

    “Non-cognitive abilities showed a numerically larger effect than cognitive abilities, but the difference was not statistically significant (p = 0.083).”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    After removing the two outliers, the final analysis included 33 studies and 84 effect sizes.

    “After removing the two outliers, the final analysis included 33 studies and 84 effect sizes.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    Log-likelihood ratio tests demonstrated a significantly better fit for the three-level model compared to two-level models with either Level 2 (χ2 = 78.609, p < 0.001) or Level 3 (χ2 = 17.895, p < 0.001) variance constrained to zero.

    “Log-likelihood ratio tests demonstrated a significantly better fit for the three-level model compared to two-level models with either Level 2 (χ2 = 78.609, p < 0.001) or Level 3 (χ2 = 17.895, p < 0.001) variance constrained to zero”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    The trim-and-fill method estimated 23 missing studies on the left; the adjusted overall effect size was Cohen's d = 0.275 (95% CI [0.157, 0.394]).

    “The trim-and-fill method estimated 23 missing studies on the left; the adjusted overall effect size was Cohen’s d = 0.275 (95% CI [0.157, 0.394])”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Findingown data

    Model fit statistics were AIC = 104.584, BIC = 111.841.

    “Model fit statistics were as follows: AIC = 104.584, BIC = 111.841.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Findingown data

    Inter-rater reliability was excellent (Cohen's Kappa = 0.977, p < 0.001).

    “Inter-rater reliability was excellent (Cohen’s Kappa = 0.977, p < 0.001).”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    Variance decomposition revealed that 37.19% of the total variance was attributable to within-study variation (σ2 = 0.076, p < 0.001), while 55.53% was due to between-study variation (σ2 = 0.113, p < 0.001).

    “Variance decomposition revealed that 37.19% of the total variance (I2_level2 = 37.19%) was attributable to within-study variation (σ2 = 0.076, p < 0.001), while 55.53% (I2_level3 = 55.53%) was due to between-study variation (σ2 = 0.113, p < 0.001).”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    Other moderators-educational stage, class size, group size, type of mathematical knowledge, and number of technology types-showed no significant effects (p > 0.05).

    “Other moderators—educational stage, class size, group size, type of mathematical knowledge, and number of technology types—showed no significant effects (p > 0.05).”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    A small number of studies had a high risk of bias, with several studies showing high risk in confounding bias, missing data bias, and outcome measurement bias.

    “A small number of studies had a high risk of bias, with several studies showing high risk in confounding bias, missing data bias, and outcome measurement bias.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    Short-term interventions lasting 1-8 weeks produced the strongest effect (Cohen's d = 0.666), whereas interventions exceeding 18 weeks demonstrated the weakest effect (Cohen's d = 0.110).

    “Short-term interventions lasting 1–8 weeks produced the strongest effect (Cohen’s d = 0.666), whereas interventions exceeding 18 weeks demonstrated the weakest effect (Cohen’s d = 0.110).”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    In total, 10 studies were identified as high-risk literature, while the remaining 25 were at moderate overall risk of bias.

    “In total, 10 studies were identified as high-risk literature, while the remaining 25 were at moderate overall risk of bias.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    The overall risk of bias of the included literature was acceptable, and no studies presented severe methodological flaws.

    “Combined with the visualized results after weighted scoring, the overall risk of bias of the included literature was acceptable, and no studies presented severe methodological flaws.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    The subgroup for mathematical literacy contained a limited number of studies with a small sample size and wide confidence intervals, and no formal between-group difference tests were conducted.

    “The subgroup for mathematical literacy contained a limited number of studies with a small sample size and wide confidence intervals, and no formal between-group difference tests were conducted.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Findingown data

    Subgroup descriptive analyses indicated a graded pattern of effect sizes across specific learning indicators, with mathematical literacy yielding the largest effect, followed by learning emotion, attitude, and motivation, and academic performance showing the smallest magnitude.

    “Subgroup descriptive analyses indicated a graded pattern of effect sizes across specific learning indicators, with mathematical literacy yielding the largest effect, followed by learning emotion, attitude, and motivation, and academic performance showing the smallest magnitude.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    PBL yielded comparable improvements in students' cognitive and non-cognitive mathematical outcomes with no significant statistical difference.

    “Further analyses demonstrated that PBL yielded comparable improvements in students’ cognitive and non-cognitive mathematical outcomes with no significant statistical difference”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning

    Traditional two-level models can bias parameter estimation, fail to distinguish within- and between-study variance, and reduce the accuracy of moderator identification and reliability of conclusions.

    “This limitation can bias parameter estimation—such as producing inaccurate standard errors—fail to distinguish within- and between-study variance, and reduce the accuracy of moderator identification and the reliability of conclusions.”
    Quote in the paperSubstantial claim
    • Rests on an assumption: Ignoring within-study data dependence may cause statistical bias and unstable pooled results.

  • Probably not a substantial claim: may not pass S4 (based).

    Premisenone given

    Few studies focus specifically on mathematics.

    “However, few studies focus specifically on mathematics.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Premisecitation

    PBL is grounded in Kolb's experiential learning theory and constructivism.

    “The development of PBL is grounded in robust theoretical foundations: Kolb’s experiential learning theory provides methodological guidance for the inquiry process in PBL, while constructivism (Piaget and Vygotsky) establishes the core logic of student agency and active knowledge construction (Sancar-Tokmak and Dogusoy, 2023).”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Sancar-Tokmak and Dogusoy, 2023 source

  • May combine two claims.

    Premisereasoning

    The three-level meta-analytic model decomposes variance in effect sizes into sampling error, within-study variance, and between-study variance, thereby improving estimation accuracy.

    “The three-level meta-analytic model addresses these issues by decomposing variance in effect sizes into sampling error, within-study variance (Level 2), and between-study variance (Level 3), thereby improving estimation accuracy and fully leveraging the data’s value.”
    Quote in the paperSubstantial claim
    • Rests on an assumption: Ignoring within-study data dependence may cause statistical bias and unstable pooled results.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    Students in societies with a strong long-term orientation demonstrate significantly better mathematics achievement than those in short-term oriented societies.

    “Students in societies with a strong long-term orientation demonstrate significantly better mathematics achievement than those in short-term oriented societies.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Hu et al., 2018

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Study design and conductnone given

    The study was prospectively registered in PROSPERO (Registration No.: CRD420251105265).

    “The study was prospectively registered in PROSPERO (Registration No.: CRD420251105265).”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Study design and conductcitation

    Cultural background was operationalized using Hofstede et al. (2010) individualism-collectivism index.

    “Cultural background was operationalized using Hofstede et al. (2010) Insights individualism–collectivism index (0–100, higher = more individualistic).”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Hofstede et al. (2010)

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Study design and conductnone given

    Two researchers independently coded all studies and reached 100% agreement through discussion.

    “Two researchers independently coded all studies and reached 100% agreement through discussion.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

    Premisecitation

    Cultural background strongly influences mathematics learning.

    “Cultural background strongly influences mathematics learning.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    Chen and Yang (2019) find that school location significantly affects learning outcomes, with stronger effects in Europe, North America, and West Asia compared to East Asia.

    “Chen and Yang (2019) find that school location significantly affects learning outcomes, with stronger effects observed in Europe, North America, and West Asia compared to East Asia.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Chen and Yang, 2019 source

  • Classified as probably not a substantial claim. May combine two claims.

    Study design and conductnone given

    Separate coding was applied to multiple independent samples or multiple effect sizes within a single paper.

    “Separate coding was applied to multiple independent samples (e.g., different grades) or multiple effect sizes (e.g., achievement and interest) within a single paper.”
    Quote in the paperSubstantial claim

  • Classified as probably not a substantial claim.

    Study design and conductnone given

    This study adopted the Cochrane ROB1 tool to assess the quality of all included original studies.

    “This study adopted the Cochrane ROB1 tool to assess the quality of all included original studies.”
    • Also stated in: § Assessment of risk of bias in studies · plain
      “The ROB1 tool was used to assess the risk of bias across seven domains.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    Artificial intelligence tools exert a growing influential effect on students' learning outcomes.

    “Artificial intelligence tools exert a growing influential effect on students’ learning outcomes (Younas et al., 2025d).”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Younas et al., 2025d

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • May combine two claims.

    Interpretationown data

    The pooled effect size from peer-reviewed articles is close to the original estimate (0.529), indicating that the inclusion of gray literature did not substantially bias the results.

    “close to the original estimate (0.529), indicating that the inclusion of gray literature did not substantially bias the results”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationown data

    The three-level specification is validated: effect sizes varied significantly both within and between studies.

    “thereby validating the three-level specification: effect sizes varied significantly both within and between studies”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    Zhang and Hu (2019) concluded that a greater variety of technology types enhances the impact of PBL on academic achievement.

    “Similarly, Zhang and Hu (2019) categorize technology into information access, communication-collaboration, productivity, cognitive/contextual, and assessment/other tools, concluding that a greater variety of technology types enhances the impact of PBL on academic achievement.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Zhang and Hu, 2019 source

  • May combine two claims.

    Interpretationown data

    The low risk ratings for classification of interventions and selection bias indicate rigorous literature screening and standardized definition of intervention variables, with no systematic bias caused by baseline selection or intervention grouping.

    “indicating rigorous literature screening and standardized definition of intervention variables, with no systematic bias caused by baseline selection or intervention grouping.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Premisecitation

    Younas et al. (2025b) found that the adoption of AI technologies facilitates personalized learning and enhances student engagement.

    “Furthermore, Younas et al. (2025b) conducted a comprehensive investigation of peer-reviewed articles published between 2020 and 2023 and found that the adoption of AI technologies facilitates personalized learning and enhances student engagement.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Younas et al., 2025b

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • May combine two claims.

    Interpretationown data

    Leave-one-out analyses confirm minimal influence of individual studies or effect sizes and stable overall conclusions.

    “confirming minimal influence of individual studies or effect sizes and stable overall conclusions”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Premisecitation

    Other studies have shown non-significant effects of group size, with PBL effects remaining consistent across educational stages and group sizes.

    “However, other studies have shown non-significant effects of group size, with PBL effects remaining consistent across educational stages and group sizes (Chen and Yang, 2019).”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Chen and Yang, 2019 source

  • Probably not a substantial claim: may not pass S2 (checkable).

    Interpretationown data

    These findings further support PBL as a reform model for mathematics instruction.

    “These findings further support PBL as a reform model for mathematics instruction.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    Chen and Yang (2019) found that implementing PBL for more than 2 h per week yields stronger effects than less than 2 h.

    “Chen and Yang (2019) found that implementing PBL for more than 2 h per week yields stronger effects than less than 2 h.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Chen and Yang, 2019 source

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Premisecitation

    Zhang and Hu (2019) reported the weakest effects for durations of 0 to 3 months and the strongest effects for interventions lasting over 6 months.

    “Zhang and Hu (2019) reported the weakest effects for durations of 0 to 3 months and the strongest effects for interventions lasting over 6 months, suggesting that longer durations improve achievement.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Zhang and Hu, 2019 source

  • Classified as probably not a substantial claim. May combine two claims.

    Study design and conductnone given

    The empirical evidence synthesized in this study relies entirely on existing published studies, and the credibility of analytic outcomes is contingent upon the methodological design and reporting quality of primary research.

    “The empirical evidence synthesized in this study relies entirely on existing published studies, and the credibility of analytic outcomes is contingent upon the methodological design and reporting quality of primary research.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing), S4 (based). May combine two claims.

    Premisenone given

    According to the reciprocal determinism of social cognitive theory, human behavior is neither determined merely by external incentives and sanctions nor fully governed by internal disposition. Instead, it stems from mutual interactions among personal cognition, behavior, and environment.

    “According to the reciprocal determinism of social cognitive theory, human behavior is neither determined merely by external incentives and sanctions nor fully governed by internal disposition. Instead, it stems from mutual interactions among personal cognition, behavior, and environment.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Study design and conductreasoning

    Unpublished non-significant findings and studies reported in other languages may not be fully captured in the current dataset.

    “Unpublished non-significant findings and studies reported in other languages may not be fully captured in the current dataset.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based). May combine two claims.

    Interpretationreasoning

    When participating in collaborative mathematical PBL activities, these students strive to strengthen their logical thinking skills, attach great importance to group outcomes, and are willing to split complex cognitive tasks and exchange ideas with peers reciprocally.

    “When participating in collaborative mathematical PBL activities, these students strive to strengthen their logical thinking skills, attach great importance to group outcomes, and are willing to split complex cognitive tasks and exchange ideas with peers reciprocally.”
    Quote in the paperNot a substantial claim
    • Rests on an assumption: Learners raised in collectivist cultural contexts generally embrace both mastery goals and group-oriented achievement goals simultaneously.

  • May combine two claims.

    Interpretationreasoning

    These disengaged behaviors hinder environmental improvement, and the suboptimal learning context further undermines sustained active exploration.

    “These disengaged behaviors hinder environmental improvement, and the suboptimal learning context further undermines sustained active exploration.”
    Quote in the paperNot a substantial claim

  • Classified as probably not a substantial claim. May combine two claims.

    Study design and conductreasoning

    The individualism-collectivism index is measured at the national level and may not capture classroom- or school-level cultural variations.

    “The index is measured at the national level and may not capture classroom- or school-level cultural variations.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S2 (checkable).

    Interpretationreasoning

    In mathematics education, the quantity of technology does not equate to the quality of integration.

    “In mathematics education, the quantity of technology does not equate to the quality of integration.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S2 (checkable). May combine two claims.

    Premisereasoning

    Learners are agentic; they adjust their actions via reflection and self-regulation, and their behaviors reciprocally reshape the learning environment.

    “Learners are agentic; they adjust their actions via reflection and self-regulation, and their behaviors reciprocally reshape the learning environment.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    Lin et al. (2025) noted that the duration of experimental interventions may relate to variations in learning outcomes.

    “Lin et al. (2025) also noted that the duration of experimental interventions may relate to variations in learning outcomes.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Lin et al. (2025) source

  • May combine two claims.

    Interpretationcitation

    Extended projects continuously consume learners' finite cognitive resources and increase demands on self-regulation.

    “Extended projects continuously consume learners’ finite cognitive resources and increase demands on self-regulation.”
    Quote in the paperSubstantial claim

  • Classified as probably not a substantial claim. May combine two claims.

    Interpretationown data

    The foregoing outcomes only characterize the empirical sample included in this meta-analysis and solely indicate that robust positive effects of long-cycle project-based interventions could not be reliably identified in the current dataset.

    “the foregoing outcomes only characterize the empirical sample included in this meta-analysis and solely indicate that robust positive effects of long-cycle project-based interventions could not be reliably identified in the current dataset”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing).

    Interpretationreasoning

    These findings do not rule out the possibility that carefully refined long-form PBL curricula with differentiated supports and streamlined task structures may still yield tangible beneficial outcomes for students' mathematical development.

    “These findings do not rule out the possibility that carefully refined long-form PBL curricula with differentiated supports and streamlined task structures may still yield tangible beneficial outcomes for students’ mathematical development.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationcitation

    The resultant vicious cycle triggers chronic cognitive overload and gradually erodes the instructional benefits of project-based learning.

    “The resultant vicious cycle triggers chronic cognitive overload and gradually erodes the instructional benefits of project-based learning (Schunk and DiBenedetto, 2020).”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Schunk and DiBenedetto, 2020 source

  • May combine two claims.

    Study design and conductown data

    Most included studies adopted quasi-experimental approaches, which may be subject to unmeasured confounding factors and novelty effects.

    “Most included studies adopted quasi-experimental approaches, which may be subject to unmeasured confounding factors and novelty effects”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationcitation

    Within a condensed timeline, students gain periodic mastery experiences and sustain active inquiry through self-regulation; proactive behaviors improve environmental conditions, which further reinforce learning engagement and produce robust learning outcomes.

    “Within a condensed timeline, students gain periodic mastery experiences and sustain active inquiry through self-regulation; proactive behaviors improve environmental conditions, which further reinforce learning engagement and produce robust learning outcomes (Schunk, 2012; Schunk and DiBenedetto, 2020).”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites Schunk, 2012 source
    • cites Schunk and DiBenedetto, 2020 source

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

    Interpretationreasoning

    Such motivational differences further shape the overall instructional effectiveness of PBL.

    “Such motivational differences further shape the overall instructional effectiveness of PBL.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Study design and conductnone given

    All included studies adopted quasi-experimental designs, which are susceptible to novelty effects and may overestimate the actual efficacy of the interventions.

    “Notably, all included studies adopted quasi-experimental designs, which are susceptible to novelty effects and may overestimate the actual efficacy of the interventions.”
    Quote in the paperSubstantial claim

  • Classified as probably not a substantial claim.

    Study design and conductreasoning

    Differences in national curricula, teacher training, implementation fidelity, and instructional resources across countries could confound the observed cultural effect.

    “Moreover, differences in national curricula, teacher training, implementation fidelity, and instructional resources across countries could confound the observed cultural effect.”
    Quote in the paperSubstantial claim

  • Classified as probably not a substantial claim.

    Interpretationown data

    Simply adding more types of tools or novel technologies does not guarantee better outcomes.

    “Simply adding more types of tools or novel technologies does not guarantee better outcomes.”
    Quote in the paperSubstantial claim

  • Classified as probably not a substantial claim.

    Study design and conductreasoning

    The conclusion that quality of technology integration matters more than quantity is limited by the fact that many primary studies did not report technology use in sufficient detail.

    “this conclusion is limited by the fact that many primary studies did not report technology use in sufficient detail.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    As Holmes and Hwang (2016) argued, learning within PBL environments demands active student engagement via hands-on projects and collaborative activities.

    “As Holmes and Hwang (2016) argued, learning within PBL environments demands active student engagement via hands-on projects and collaborative activities.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Holmes and Hwang (2016) source

  • Probably not a substantial claim: may not pass S2 (checkable).

    Interpretationreasoning

    The significant moderation by cultural background should be seen as hypothesis-generating rather than definitive causal evidence.

    “Therefore, the significant moderation by cultural background should be seen as hypothesis-generating rather than definitive causal evidence.”
    Quote in the paperNot a substantial claim
    • Rests on an assumption: The instructional potency of project-based learning depends fundamentally on sustained, deep collaborative inquiry.
    • Rests on an assumption: Group-aligned achievement motives facilitate full engagement in co-constructive knowledge building, thereby amplifying the incremental benefits of inquiry pedagogy.
    • Rests on an assumption: Exclusive focus on individual performance may precipitate social loafing and perfunctory task engagement, constraining the cognitive resources allocated to rigorous mathematical reasoning and attenuating the relative advantage of PBL over didactic lecture instruction.

  • May combine two claims.

    Interpretationown data

    The moderating effects of intervention duration and cultural context account for the heterogeneous effectiveness of mathematical PBL and partially explain the inconsistent findings observed in previous studies.

    “which account for the heterogeneous effectiveness of mathematical PBL and partially explain the inconsistent findings observed in previous studies”
    Quote in the paperSubstantial claim
75 of 75

  • The paper relies on this without support.

    Empirical research on mathematical PBL is relatively scarce compared with other disciplines.

    “Compared with other disciplines, empirical research on mathematical PBL is relatively scarce and presents substantial cross-study heterogeneity.”

  • The paper relies on this without support.

    Ignoring within-study data dependence may cause statistical bias and unstable pooled results.

    “Ignoring within-study data dependence may cause statistical bias and unstable pooled results.”

  • The paper relies on this without support.

    Both the U.S. Common Core State Standards and China’s 2022 Compulsory Education Mathematics Curriculum Standards advocate PBL implementation to advance competency-based mathematics education.

    “Given these theoretical and pedagogical strengths, both the U.S. Common Core State Standards and China’s 2022 Compulsory Education Mathematics Curriculum Standards advocate PBL implementation to advance competency-based mathematics education.”

  • The paper relies on this without support.

    PBL implementation is contingent on abundant resources such as well-equipped facilities and specialized teacher training.

    “PBL implementation is contingent on abundant resources such as well-equipped facilities and specialized teacher training.”

  • The paper relies on this without support.

    Learning settings in PBL are positively correlated with students’ intrinsic motivation, which in turn facilitates academic learning outcomes.

    “Such learning settings are positively correlated with students’ intrinsic motivation, which in turn facilitates academic learning outcomes.”

  • The paper relies on this without support.

    Learners raised in collectivist cultural contexts generally embrace both mastery goals and group-oriented achievement goals simultaneously.

    “Learners raised in collectivist cultural contexts generally embrace both mastery goals and group-oriented achievement goals simultaneously.”

  • The paper relies on this without support.

    The instructional potency of project-based learning depends fundamentally on sustained, deep collaborative inquiry.

    “The instructional potency of project-based learning hinges fundamentally on sustained, deep collaborative inquiry.”

  • The paper relies on this without support.

    Group-aligned achievement motives facilitate full engagement in co-constructive knowledge building, thereby amplifying the incremental benefits of inquiry pedagogy.

    “Group-aligned achievement motives facilitate full engagement in co-constructive knowledge building, thereby amplifying the incremental benefits of inquiry pedagogy.”

  • The paper relies on this without support.

    Exclusive focus on individual performance may precipitate social loafing and perfunctory task engagement, constraining the cognitive resources allocated to rigorous mathematical reasoning and attenuating the relative advantage of PBL over didactic lecture instruction.

    “Conversely, exclusive focus on individual performance may precipitate social loafing and perfunctory task engagement, constraining the cognitive resources allocated to rigorous mathematical reasoning and attenuating the relative advantage of PBL over didactic lecture instruction.”
9 of 9

Statistics recomputed

Every reported test result, recomputed from its test statistic and degrees of freedom. A result shows as not adding up only once an independent check has confirmed it.

  • Consistentz = 5.234reported p < .001 · recomputed p < .001

    “z = 5.234, p < .001”

  • ConsistentQ(83) = 659.185reported p < .001 · recomputed p < .001

    “Q(83) = 659.185, p < .001”

  • ConsistentF(2, 81) = 5.33reported p < .01 · recomputed p = .007

    “F(2, 81) = 5.33, p < .01”

3 of 3

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

Each contradiction between two passages listed here was confirmed by an independent check.

  • Outcome comparison is called significant despite a non-significant test

    Major

    The results say the effect on non-cognitive abilities was significantly stronger, but the abstract reports that the difference was not statistically significant (p = 0.083).

  • Different cultural index values are assigned to China

    Major

    The methods say each study received the index value of its sample country, yet Table 2 assigns China a value of 72 in one study and 43 in another. This inconsistency concerns the variable reported as a significant moderator.

  • One study's quality score is one point too high

    Minor

    Del Valle-Ramón et al. have five indicators scored 1, not the reported quality score of 6. The reported 85.71% also corresponds to six of seven indicators rather than five.

    Reported 6 · recomputed 5

  • Outcome-specific effect-size counts exceed the total

    Minor

    Table 4 lists 60 cognitive and 26 non-cognitive effect sizes, totaling 86, although its overall row reports 84.

    Reported 84 · recomputed 86

  • Non-significant class-size coefficient carries significance stars

    Minor

    Table 5 marks the large-class coefficient's t value with two stars, denoting p < 0.01, although its confidence interval includes zero and the paper states that class size was not a significant moderator.

5 of 5

Cites

Flagged first, then by citations

Research works printed but not linked: 26

  1. Carter, 2016, Traditional vs. project-based Learning: The Effects on Student Performance and Motivation in Honors level Mathematics Courses
  2. Cervantes, 2015, The impact of project-based learning on minority student achievement: implications for school redesign, NCPEA Educ. Leader. Rev. Doctor. Res., 2, 50, 10.15320/ELRDR.2015.2.2.50 · DOI
  3. Chen, 2024, An Empirical Study on project-based Learning Promoting the Development of Eighth-grade Students' Mathematical Modeling Ability
  4. Condori Condori, 2024, Aprendizaje basado en proyectos en el desarrollo de competencias de matemática en estudiantes del CEBA José Antonio Encinas de Azángaro-2022 (Project-based learning in the development of mathematical competencies in students of CEBA José Antonio Encinas de Azángaro-2022) (Publication No. 32008137) [Tesis de segunda especialidad en Educación Básica Alternativa (Second Specialization in Alternative Basic Education), Universidad Nacional del Altiplano]
  5. Feng, 2024, Research on the design and Application of process-Oriented Evaluation in project-based Learning of senior high school Mathematics
  6. Garner, 2020, The Impact of Project-Based Learning on Reading and Mathematics Scores of Eighth Grade Students
  7. Hofstede, 2010, Cultures and Organizations: Software of the mind
  8. Holmes, 2022, Active Engagement: A Study of project-based Learning in the math Classroom
  9. Lang-Raad, 2025, Mathematics Teaching Reimagined: Seven Competencies to foster robust Student Learning and Engagement using the CMC Framework for Deeper Mathematical Thinking
  10. Li, 2022, Research on the design and Practice of project-based Learning in junior high school Mathematics Curriculum
  11. Lyu, 2023, Research on the Teaching design and Experiment of Comprehensive and Practical Activities in Primary school Mathematics based on project-based Learning
  12. Ma, 2024, Research on the Construction and Practice of project-based Learning Teaching model in junior high school Mathematics: A Case Study of the Tugui Method
  13. Peker Ünal, 2018, Effect of the web project-based presentation of a mathematics unit on student success and students' opinions on the project process, Int. J. Eur. Soc. Sci., 9, 34, 10.33463/ijess.93120183455 · DOI
  14. Qiu, 2023, Research and Practice of Project-based Learning in Ninth-grade Mathematics Teaching of Junior High School
  15. Quigley, 2010, Project-based Learning and Student Achievement
  16. Sahli, 2017, An Examination of the Effectiveness of Project-Based Learning on Student Academic Achievement and Teacher Perceptions of Project-Based Learning
  17. Shchetynska, 2020, The Effectiveness of project-based Learning on Student Geometry Achievement and Creativity within the Requirements of 21st-Century Learning
  18. Tabuk, 2009, The effects of multiple intelligence approach in project based learning on mathematics achievement, Int. Online J. Educ. Sci., 1, 177, 10.13092/iojes.v1i1.244 · DOI
  19. Wang, 2022, A Practical Research on project-based Teaching of Mathematics in junior high school
  20. Wang, 2023, Proceedings of IConSES 2023:International Conference on Social and Education Sciences, 1
  21. Xu, 2025, A Practical Study on Improving junior high school Students' Higher-order Thinking Skills in Mathematics through project-based Learning
  22. Zhang, 2016, Research on the design and Practical effect of project-based Learning in Primary school Mathematics based on the Network Environment
  23. Zhang, 2024, Research on the Practice of junior high school Mathematics project-based Teaching based on GeoGebra Software and ARCS Motivation model
  24. Zhang, 2024, Research on the Application of project-based Learning in senior high school Mathematics Oriented to deep Learning
  25. Zhang, 2019, Has the learning effect of project-based learning occurred? A meta-analysis based on 46 experimental and quasi-experimental studies, J. Educ. Technol. Res., 40, 95, 10.13811/j.cnki.eer.2019.02.012 · DOI
  26. Zhao, 2023, Research on the design and Practice of project-based Learning in junior high school Mathematics under the Information Environment

Cited by

Still being checked.

Authors
Wang, C., Zhang, W., & Cheng, J.
Affiliations
Shaanxi Normal University (CN)
Corresponding author
Zhang, Wenlan
ORCID
Venue
Frontiers in Psychology
Publisher
Frontiers Media SA
Published
2026-09-04
Volume
17
Pages
1868415-1868415
ISSN
1664-1078 (ISSN-L)
DOI
10.3389/fpsyg.2026.1868415
PMC
PMC13586001
OpenAlex
W7208763957
Semantic Scholar
b557261bbe84a03b249ed01fe957ed6f958f3a23
Cited by
0
References
47
FWCI
0.00
Type
journal article
Language
en
Open access
Licence
Locations
  • Frontiers in Psychology (publishedVersion, cc-by)
  • PubMed (publishedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion)
  • PubMed Central (submittedVersion, cc-by)
Topics
  • Social Sciences › Education › Problem and Project Based Learning
  • Physical Sciences › Mathematics › Applied Mathematics › Mathematics Education and Pedagogy
  • Social Sciences › Education › STEM Education
Keywords
project-based learning, mathematics achievement, nested data structures, publication bias, cultural background, intervention duration, non-cognitive skills, cognitive ability, mathematics education, student-centered learning

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Claims read by deepseek-v4.1-flash under definition version 3 (extract-v3) on 2026-10-25.

Classified by jev-1.13-20260917 (gold-guideline-v0.2) on 2026-10-25.

Cited sources are checked by gpt-6-sol.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

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