Beyond Mean Comparison: Assessing the Proportional Diostribution of Critical Thinking Mastery in Problem Based Learning on Pressure Concepts Using Chi-Square Analysis
DOI:
https://doi.org/10.37251/isej.v7i3.3068Keywords:
Chi Square Test, Critical Thinking, Pressure Concept, Problem Based Learning, Proportional Mastery DistributionAbstract
Purpose of the study: The study evaluates the effectiveness of Problem-Based Learning (PBL) in improving students’ critical thinking mastery of pressure concepts by analyzing the proportional distribution of mastery rather than relying solely on mean score comparisons.
Methodology: A quasi-experimental pretest-posttest nonequivalent control group design was employed with 60 eighth-grade students selected through purposive sampling from intact classes. Students were assigned to a PBL group (n=30) or a conventional instruction group (n=30). Critical thinking was measured using a validated 10-item multiple-choice test adapted from Ennis’s indicators. Baseline equivalence was tested with the Mann–Whitney U test, within-group mastery shifts with McNemar’s test, and between-group distributional differences with the Chi-square test of independence. Reliability was confirmed (Cronbach’s α = 0.86).
Main Findings: The PBL group achieved a significantly higher mastery rate (83%) compared to the conventional group (60%), χ²(1) = 4.02, p = 0.045, with a moderate effect size (Cramer’s V = 0.26). McNemar’s test confirmed a statistically significant mastery transition within the PBL class (p < 0.05). The strongest gains occurred in analytical explanation and inferential reasoning dimensions.
Novelty/Originality of this study: Analyzing mastery distribution reveals equitable learning outcomes that mean comparisons obscure. The findings demonstrate that PBL systematically shifts categorical achievement toward competency thresholds, particularly in higher-order cognitive dimensions. In practice, this supports the adoption of distributional analysis in classroom assessment. The study’s novelty lies in its methodological shift from continuous mean scoring to categorical mastery distribution, offering a more pedagogically relevant framework for evaluating instructional equity.
References
[1] P. C. Abrami, R. M. Bernard, E. Borokhovski, D. I. Waddington, C. A. Wade, T. Persson, “Strategies for teaching students to think critically: A meta-analysis," Rev. Educ. Res., vol. 85, no. 2, pp. 275–314, 2015. doi: 10.3102/0034654314551063. DOI: https://doi.org/10.3102/0034654314551063
[2] D. F. Halpern, Thought and Knowledge: An Introduction to Critical Thinking, 5th ed. Psychology Press, 2014. doi: 10.4324/9781315881853.
[3] R. Paul & L. Elder, Critical Thinking: Tools for Taking Charge of Your Learning and Your Life, 3rd ed. Pearson, 2014.
[4] R. W. Bybee, The Case for STEM Education: Challenges and Opportunities. NSTA Press, 2013.
[5] J. Osborne, “Teaching critical thinking? New directions in science education,” Sch. Sci. Rev., vol. 95, no. 352, pp. 53–62, 2014.
[6] S. Arslan, “The effect of problem-based learning on students’ critical thinking and achievement,” Think. Skills Creat., vol. 37, pp. 100668, 2020. doi: 10.1016/j.tsc.2020.100668.
[7] OECD, PISA 2018 Results (Volume I): What Students Know and Can Do. OECD Publishing, 2019. doi: 10.1787/5f07c754-en. DOI: https://doi.org/10.1787/5f07c754-en
[8] S. Freeman, S. L. Eddy, M. McDonough, M. K. Smith, N. Okoroafor, H. Jordt, and M. P. Wenderoth, “Active learning increases student performance in science, engineering, and mathematics,” Proc. Natl. Acad. Sci., vol. 111, no. 23, pp. 8410–8415, 2014. doi: 10.1073/pnas.1319030111. DOI: https://doi.org/10.1073/pnas.1319030111
[9] M. Prince, “Does active learning work? A review of the research,” J. Eng. Educ., vol. 93, no. 3, pp. 223–231, 2004. doi: 10.1002/j.2168-9830.2004.tb00809.x. DOI: https://doi.org/10.1002/j.2168-9830.2004.tb00809.x
[10] C. E. Hmelo-Silver, R. G. Duncan, & C. A. Chinn, “Scaffolding and achievement in problem-based learning,” Educ. Psychol., vol. 42, no. 2, pp. 99–107, 2007. doi: 10.1080/00461520701263368. DOI: https://doi.org/10.1080/00461520701263368
[11] A. W. Lazonder & R. Harmsen, “Meta-analysis of inquiry-based learning,” Rev. Educ. Res., vol. 86, no. 3, pp. 681–718, 2016. doi: 10.3102/0034654315627366. DOI: https://doi.org/10.3102/0034654315627366
[12] B. Barron & L. Darling-Hammond, “Teaching for meaningful learning: A review of research on inquiry-based and cooperative learning,” Edutopia Res. Rep., 2008. doi: 10.54300/edutopia.2008.1.
[13] S. M. M. Loyens, P. A. Kirschner, & F. Paas, “Problem-based learning,” Educ. Psychol. Rev., vol. 24, no. 3, pp. 403–425, 2012. doi: 10.1007/s10648-012-9198-1. DOI: https://doi.org/10.1037/13275-016
[14] J. R. Savery, “Overview of problem-based learning: Definitions and distinctions,” Interdiscip. J. Problem-Based Learn., vol. 1, no. 1, pp. 9–20, 2006. doi: 10.7771/1541-5015.1002. DOI: https://doi.org/10.7771/1541-5015.1002
[15] H. G. Schmid, J. I. Rotgans, E. H. J. Yew, “The process of problem-based learning,” Med. Educ., vol. 45, no. 8, pp. 792–806, 2011. doi: 10.1111/j.1365-2923.2011.04035.x. DOI: https://doi.org/10.1111/j.1365-2923.2011.04035.x
[16] F. Dochy, M. Segers, P. V. d. Bossche, and D. Gijbels, “Effects of problem-based learning: A meta-analysis,” Learn. Instr., vol. 13, no. 5, pp. 533–568, 2003. doi: 10.1016/S0959-4752(02)00025-7. DOI: https://doi.org/10.1016/S0959-4752(02)00025-7
[17] D. Gijbels, F. Dochy, P. V. d. Bossche, and M. Segers, “Effects of problem-based learning: A meta-analysis from the angle of assessment,” Rev. Educ. Res., vol. 75, no. 1, pp. 27–61, 2005. doi: 10.3102/00346543075001027. DOI: https://doi.org/10.3102/00346543075001027
[18] L. Mason, “Multiplicity in the digital era: Processing and learning from multiple sources and modalities of instructional presentations,” Learning and Instruction, vol. 57, pp. 76-81, 2018, doi: 10.1016/j.learninstruc.2018.03.004. DOI: https://doi.org/10.1016/j.learninstruc.2018.03.004
[19] R. K. Sawyer, “Teaching creativity in art and design studio classes: A systematic literature review,” Educational research review, vol. 22, pp. 99-113, 2017, doi: 10.1016/j.edurev.2017.07.002. DOI: https://doi.org/10.1016/j.edurev.2017.07.002
[20] J. L. Docktor & J. P. Mestre, "Synthesis of discipline-based education research in physics," Phys. Rev. Spec. Top. Phys. Educ. Res., vol. 10, no. 2, p. 020119, 2014. doi: 10.1103/PhysRevSTPER.10.020119. DOI: https://doi.org/10.1103/PhysRevSTPER.10.020119
[21] M. S. Al-Rsa'ı, J. M. Khoshman, and K. A. Tayeh, “Jordanian pre-service physics teacher’s misconceptions about force and motion,” Journal of Turkish Science Education, vol. 17, no. 4, pp. 528-543, 2020, doi: 10.36681/tused.2020.43. DOI: https://doi.org/10.36681/tused.2020.43
[22] C. E. Hmelo-Silver, “Problem-based learning: What and how do students learn?”, Educ. Psychol. Rev., vol. 16, no. 3, pp. 235–266, 2004. doi: 10.1023/B:EDPR.0000034022.16470.f3. DOI: https://doi.org/10.1023/B:EDPR.0000034022.16470.f3
[23] J. W. Creswell & J. D. Creswell, Research Design: Qualitative, Quantitative, and Mixed Methods Approaches, 5th ed. SAGE, 2018.
[24] C. S. Reichardt, “Quasi-experimental design,” in The SAGE handbook of quantitative methods in psychology, pp. 46-71, 2009. DOI: https://doi.org/10.4135/9780857020994.n3
[25] R. H. Ennis, “Ideal critical thinkers are disposed to,” Inquiry Crit. Think. Across Discipl., vol. 26, no. 2, pp. 4, 2011. DOI: https://doi.org/10.5840/inquiryctnews201126214
[26] P. A. Facione, Critical Thinking: What It Is and Why It Counts. Insight Assessment, 2015.
[27] D. H. J. M. Dolmans, S. M. M. Loyens, H. Marcq, D. Gijbels, “Deep and surface learning in problem-based learning: A review of the literature," Adv. Health Sci. Educ., vol. 21, no. 5, pp. 1087–1112, 2016. doi: 10.1007/s10459-015-9645-6. DOI: https://doi.org/10.1007/s10459-015-9645-6
[28] S. K. Carpenter, T. J. Lund, C. R. Coffman, P. I. Armstrong, M. H. Lamm, and R. D. Reason, “A classroom study on the relationship between student achievement and retrieval-enhanced learning,” Educational Psychology Review, vol. 28, no. 2, pp. 353-375, 2016, doi: 10.1007/s10648-015-9311-9. DOI: https://doi.org/10.1007/s10648-015-9311-9
[29] H. E. Vidergor, “Effectiveness of the multidimensional curriculum model in developing higher-order thinking skills in elementary and secondary students,” The curriculum journal, vol. 29, no. 1, pp. 95-115, 2018, doi: 10.1080/09585176.2017.1318771. DOI: https://doi.org/10.1080/09585176.2017.1318771
[30] E. H. J. Yew & K. Goh, “Problem-based learning: An overview of its process and impact,” Health Professions Educ., vol. 2, no. 2, pp. 75–79, 2016. doi: 10.1016/j.hpe.2016.01.004. DOI: https://doi.org/10.1016/j.hpe.2016.01.004
[31] F. M. Mardiana, and N. Y. Ningsih, “Cooperative learning model on atomic structure material and it’s influence on the scientific attitude of class x students at senior high school,” Integr. Sci. Educ. J., vol. 4, no. 1, pp. 23–29, 2023, doi: 10.37251/isej.v4i1.273. DOI: https://doi.org/10.37251/isej.v4i1.273
[32] R. H. Ennis, “The nature of critical thinking: An outline of critical thinking dispositions and abilities,” Univ. of Illinois, 2011.
[33] D. W. S. Rahadiyani, P. A. Rivani, and F. Untari, “Implementation of Problem Based Learning Model as an Effort to Improve Student Activities and Outcomes in Temperature and Heat Materials”, In. Sci. Ed. J, vol. 4, no. 1, pp. 19–22, Jan. 2023, doi: 10.37251/isej.v4i1.292. DOI: https://doi.org/10.37251/isej.v4i1.292
[34] E. Chrisdiyanto and S. Hamdi, “Efektivitas problem based learning dan problem solving terhadap kemampuan berpikir kritis dan kemandirian belajar matematika [Effectiveness PBL dan problem solving on critical thinking and independent learning in mathematics],” J. Ris. Pendidik. Mat., vol. 10, no. 2, pp. 165–174, 2023. doi: 10.21831/jrpm.v10i2.65754. DOI: https://doi.org/10.21831/jrpm.v10i2.65754
[35] T. Sukmono, E. J. Wicaksana, and P. A. Jayanti P, A. “The influence of problem based learning (PBL) model based on STEM approach on critical thinking ability Phase-E in biology learning,” J. Penelit. Pendidik. IPA, vol. 9, no. 9, pp. 7056–7063, 2023, doi: 10.29303/jppipa.v9i9.4568. DOI: https://doi.org/10.29303/jppipa.v9i9.4568
[36] I. D. Sopwan, U. Soetisna, and S. Redjeki, “Implementation of PBL model to enhance critical thinking skills and argumentation skills of students,” Edubiol. J. Penel. Ilmu Dan Pendidikan Biol, vol. 6, no. 2, pp. 94-98, 2018, doi: 10.25134/edubiologica.v6i2.2369. DOI: https://doi.org/10.25134/edubiologica.v6i2.2369
[37] M. L. McHugh, “The Chi-square test of independence,” Biochem. Med., vol. 23, no. 2, pp. 143–149, 2013. doi: 10.11613/BM.2013.018. DOI: https://doi.org/10.11613/BM.2013.018
[38] A. R. Saavedra & V. D. Opfer, “Learning 21st-century skills requires 21st-century teaching,” Phi Delta Kappan, vol. 94, no. 2, pp. 8–13, 2012. doi: 10.1177/003172171209400203. DOI: https://doi.org/10.1177/003172171209400203
[39] D. A. Putri & Z. Zulfadewina, “Effectiveness of PBL in science learning on critical thinking skills of fifth graders,” J. Cakrawala Pendas, vol. 9, no. 4, pp. 642–654, 2023. doi: 10.31949/jcp.v9i4.5927. DOI: https://doi.org/10.31949/jcp.v9i4.5927
[40] M. Lineberry, Y. S. Park, D. A. Cook, and R. Yudkowsky, “Making the case for mastery learning assessments: key issues in validation and justification,” Academic medicine, vol. 90, no. 11, pp. 1445-1450, 2015, doi: 10.1097/ACM.0000000000000860. DOI: https://doi.org/10.1097/ACM.0000000000000860
[41] F. Setiawan, S. Masitoh, and A. Mariono, “PBL-STS model for achieving critical thinking in elementary students,” Int. J. Soc. Learn., vol. 3, no. 3, 2022. doi: 10.47134/ijsl.v3i3.193. DOI: https://doi.org/10.47134/ijsl.v3i3.193
[42] S. M. Loyens, S. H. Jones, J. Mikkers, and T. van Gog, “Problem-based learning as a facilitator of conceptual change,” Learning and Instruction, vol. 38, pp. 34-42, 2015, doi: 10.1016/j.learninstruc.2015.03.002. DOI: https://doi.org/10.1016/j.learninstruc.2015.03.002
[43] D. Kuhn, “Thinking together and alone,” Educ. Res., vol. 44, no. 1, pp. 46–53, 2015. doi: 10.3102/0013189x15569530. DOI: https://doi.org/10.3102/0013189X15569530
[44] L. Fleet and T. Dobson, “Growing and fixing: Comparing the creative mindsets of teachers and artist practitioners,” Thinking Skills and Creativity, vol. 48, pp. 101312, 2023, doi: 10.1016/j.tsc.2023.101312. DOI: https://doi.org/10.1016/j.tsc.2023.101312
[45] C. Jackson, M. J. Mohr-Schroeder, S. B. Bush, C. Maiorca, T. Roberts, C. Yost, and A. Fowler, “Equity-oriented conceptual framework for K-12 STEM literacy,” International Journal of STEM Education, vol. 8, no. 1, pp. 38, 2021, doi: 10.1186/s40594-021-00294-z. DOI: https://doi.org/10.1186/s40594-021-00294-z
[46] R. Agni, A. Febriawan, and S. Zainal, “Uncovering the veil: Overcoming challenges in science teaching standards,” In. Sci. Ed. J, vol. 5, no. 3, pp. 181–186, 2024, doi: 10.37251/isej.v5i3.1272. DOI: https://doi.org/10.37251/isej.v5i3.1272
[47] R. L. Ebel & D. A. Frisbie, Essentials of Educational Measurement, 5th ed. Prentice Hall, 1991.
[48] J. R. Fraenkel et al., How to Design and Evaluate Research in Education, 8th ed. McGraw-Hill, 2012.
[49] A. C. Cheung, and R. E. Slavin, “How methodological features affect effect sizes in education,” Educational Researcher, vol. 45, no. 5, pp. 283-292, 2016, doi: 10.3102/0013189X16656615. DOI: https://doi.org/10.3102/0013189X16656615
[50] Q. Zhou, “Using chi-square categorical testing to analyse the survey data and find people’s attitude towards inequalities,” Journal of Education, Humanities and Social Sciences, vol. 24, pp. 330-339, 2023, doi: 10.54097/5rjf5w02. DOI: https://doi.org/10.54097/5rjf5w02
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