The Effect of Problem-Based Learning on Middle School Students’ Problem-Solving Skills: The Content Area of Probability
Article Sidebar
Main Article Content
Abstract
This study investigated the effect of the problem-based learning (PBL) approach on the problem-solving skills of middle school students as they learned about probability, a content area of eighth-grade curriculum. The research was carried out in the 2018–2019 academic year. The study group consisted of 39 eighth-grade students (14 female and 25 male students) studying at a middle school located in a province in the northern part of the Black Sea Region of Türkiye. Data collection tools included the equivalence test (ET), the problem-solving test (PST), the Semi-Structured Interview Form (SSIF), and scenarios and activities prepared for the experimental group (EG). Statistical Package for the Social Sciences (SPSS) 22.0 statistical software was used for data analysis. Analyses were performed using the Wilcoxon signed-rank test for paired samples and the Mann-Whitney U Test. The results showed that the problem-solving skills of the EG students, who were taught using the PBL approach, were better than those of the control group (CG) students, who were taught using traditional expository teaching. Therefore, in mathematics teaching, PBL is the recommended approach to support students’ problem-solving process in the mathematics curriculum.
Article Details
Neslihan Usta, Bartın University
Neslihan Usta is currently Associate Professor in the Faculty of Education, Department of Mathematics and Science Science Education, Mathematics Education, Bartin University, Bartın, Turkey. Her research interests include mathematics education, teaching mathematics, teaching mathematics with games, problem solving, problem posing, problem-based learning, computational thinking, algebra.
Ali Özkaya, Akdeniz University
Ali Özkaya is a faculty member in the Department of Mathematics Education at Akdeniz University. His research primarily focuses on STEM education, ethnomathematics, and mathematical modeling. He specializes in inclusive mathematics education, with a particular emphasis on developing instructional materials and intervention strategies for visually impaired students and learners with dyscalculia. His academic work also explores preservice teachers' engineering design competencies and the integration of cultural elements into mathematics instruction.
Nihal Düzalan, Kastamonu University
Nihal Düzalan is pursuing her doctorate in Mathematics Education at Kastamonu University. Her research focuses on computational thinking, problem solving, and dyscalculia.

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
1. Publication and Promotion: In consideration of the Publisher’s agreement to publish the Work, Author hereby grants and assigns to Publisher the non-exclusive right to print, publish, reproduce, or distribute the Work throughout the world in all means of expression by any method now known or hereafter developed, including electronic format, and to market or sell the Work orany part of it as Publisher sees fit. Author further grants Publisher the right to use Author’s name in association with the Work inpublished form and in advertising and promotional materials
2. Copyright: Copyright of the Work remains in Author’s name.
3. Prior Publication and Attribution: Author agrees not to publish the Work in print form prior to publication of the Work by the Publisher. Author agrees to cite, by author, title, and publisher, the original Interdisciplinary Journal of Problem-based Learning publication when publishing the Work elsewhere
4. Author Representations: The Author represents and warrants that the Work:
(a) is the Author’s original Work and that Author has full power to enter into this Agreement;
(b) does not infringe the copyright or property of another;
(c) contains no material which is obscene, libelous, defamatory or previously published, in whole or in part.
Author shall indemnify and hold Publisher harmless against loss of expenses arising from breach of any such warranties.
5. Licensing and Reuse: Reuse of the published Work will be governed by a Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0; http://creativecommons.org/licenses/ by-nc/4.0/). This license lets others remix, tweak, and build upon the Work non-commercially; although new works must acknowledge the original Interdisciplinary Journal of Problem-based Learning publication and be non-commercial, they do not have to be licensed on the same terms.
References
Alesandrini, K. & Larson, L. (2002) Teachers bridge to constructivism. The Clearing House, 75(3), 118–121. https://doi.org/10.1080/00098650209599249
Allen, D. E., Donham, R. S., & Bernhardt, S. A. (2011). Problem-based learning: evidence-based teaching. New Directions For Teaching and Learning, 128, 21–29. https://doi.org/10.1002/tl.465
Aryan, P. H., & Shettar, A. (2023). Effectiveness of computational thinking in problem based learning, Journal of Engineering Education Transformations, 36(2), 179–185. https://dx.doi.org/10.16920/jeet/2023/v36is2/23025
Ata, A. (2013). Investigation of procpective teachers’ conceptual and procedural knowledge levels in probability [Unpublished master’s thesis]. Osmangazi University. https://tez.yok.gov.tr/UlusalTezMerkezi/
Ausubel, D. P. (1962). A subsumption theory of meaningful verbal learning and retention. The Journal of General Psychology, 66(2), 213–224. https://doi.org/10.1080/00221309. 1962.9711837
Ausubel, D. P. (1963). The psychology of meaningful verbal learning. Grune & Stratton.
Ausubel, D. P. (2000). The acquisition and retention of knowledge: a cognitive view. Kluwer Academic Publishers.
Ausubel, D. P., & Robinson, F. G. (1969). School learning: An introduction to educational psychology. Holt, Rinehart Winston.
Baki, A. (2014). Mathematics education from theory to practice. Harf.
Baki, A. (2018). The knowledge of teaching maths. Pegem Academy.
Barrows, H. (2002). Is it truly possible to have such a thing as dPBL? Distance Education, 23(1), 119–122. https://doi.org/10.1080/01587910220124026
Barrows, H. S. (1984). A specific problem-based, self-directed learning method designed to teach medical problem-solving skills, and enhance knowledge retention and recall. Tutorials in problem-based learning, 16–32.
Barrows, H. S. (1986). A taxonomy of problem‐based learning methods. Medical Education, 20(6), 481–486. https://doi.org/10.1111/j.1365-2923.1986.tb01386.x
Barrows, H. S. (1996). Problem‐based learning in medicine and beyond: A brief overview. New Directions for Teaching and Learning, 1996(68), 3–12. https://doi.org/10.1002/tl.37219 966804
Barrows, H. S., & Tamblyn, R. M. (1980). Problem-based learning: An approach to medical education. Springer Publishing Company.
Baykul, Y. (2014). Teaching mathematics in secondary school (Grades 5-8). Pegem Academy
Biesta, G. (2004). Mind the gap! Communication and the educational relation. Counterpoints, 259, 11–22. https://www.jstor.org/stable/42978490
Boaler, J. (2008). Promoting ‘relational equity’and high mathematics achievement through an innovative mixed‐ability approach. British Educational Research Journal, 34(2), 167–194. https://doi.org/10.1080/01411920701532145
Bosica, J., Pyper, J. S., & Mac Gregor, S. (2021). Incorporating problem-based learning in a secondary school mathematics preservice teacher education course. Teaching and Teacher Education, 102, https://doi.org/10.1016/j.tate.2021. 103335
Brock, S. (2003). Creating scenarios using a reflective cycle and “PIA PRISM.” In E. Errington (Ed.), Developing scenario-based learning: Practical insights for tertiary educators (pp. 19-30). Palmerston North, New Zealand: Dunmore Press.
Brooks, J. G., & Brooks, M. G. (1993). In search of understanding: The case for constructivist classrooms. Association for Supervision and Curriculum Development, Alexandria: VA.
Bulut, S. (1994). The effects of different teaching methods gender on probability achievement and attitudes toward probability [Unpublished doctoral dissertation], Middle East Technical University. https://tez.yok.gov.tr/UlusalTezMerkezi/
Çakmak, Z. T., & Durmuş, S. (2015). Determining the concepts and in the area of learning statistics and probability that 6–8th grade math students have difficulties. Abant İzzet Baysal Üniversitesi Eğitim Fakültesi Dergisi, 15(2), 27–58. https://dergipark.org.tr/tr/ pub/aibuefd/issue/1516/18631
Carpenter, T. P., Ansell, E., Franke, M. L., Fennema, E., & Weisbeck, L. (1993). Models of problem solving: A study of kindergarten children's problem-solving processes. Journal for Research in Mathematics Education, 24(5), 428–41. https://doi.org/10.2307/749152
Carter, T. A. (2005). Knowledge and understanding of probability and statistics topics by preservice pk-8 teachers [Unpublished doctoral dissertation], Texas A&M University.
Chinnappan, M. (1998). Schemas and mental models in geometry problem solving. Educational Studies in Mathematics, 36(3), 201–217. https://doi.org/10.1023/A:1003134323371
Collins, A. (1994). Goal-based scenarios and the problem of situated learning: A commentary on Andersen Consulting's design of goal-based scenarios. Educational Technology, 34(9), 30–32. https://www.jstor.org/stable/44428239
Dahl, B. (2018). What is the problem in problem-based learning in higher education mathematics, European Journal of Engineering Education, 43(1), 112–125, https://doi.org/10.1080/03043797.2017.1320354
Delisle, R. (1997). How to use problem-based learning in the classroom. Alexandria, VA: Association for Supervision and Curriculum Development (ASCD) Publication.
Dorimana, A., Uworwabayeho, A., & Nizeyimana, G. (2022). Mathematics teachers’ self-efficacy in using problem-based learning for the fourth industrial revolution. In B. Chirinda, K. Luneta, & A. Uworwabayeho (Eds.), Mathematics Education in Africa. Springer, Cham. https://doi.org/10.1007/978-3-031-13927-7_7
Dow, G. T., & Mayer, R. E. (2004). Teaching students to solve ınsight problems: evidence for domain specificity in creativity training. Creativity Research Journal, 16(4), 389–402. https://doi.org/10.1207/s15326934crj1604_2
Drake, K. N., & Long, D. (2009). Rebecca’s in the dark: A comparative study of problem-based learning and direct instruction/experiential learning in two 4th-grade classrooms. Journal of Elementary Science Education, 21(1), 1–16. https://link.springer.com/article/10.1007/ BF03174712
Duruhan, K. (2004). Türkiyede okulda geleneksel anlayış ve yöntemlerle insan yetiştirmenin olumsuz etkileri [The negative effects of raising people with traditional understanding and methods at school in Turkey]. National Educational Sciences Congress, (pp. 1–13). Malatya.
Er Nas, S. (2008). Determining effectiveness of the materials about ?the ways of spread of heat? based on the elaborate stage of the 5E model. [Unpublished master’s thesis], Karadeniz University. https://tez.yok.gov.tr/UlusalTezMerkezi/
Erdem, E. (2011). An investigation of the seventh grade students’ mathematical and probabilistic reasoning skills [Unpublished master’s thesis]. Adıyaman University. https://tez.yok.gov.tr/UlusalTezMerkezi/
Erickson, D. K. (1999). A Problem based approach to mathematics ınstructions. Mathematics Teacher, 92(6), 516–521. https://doi.org/10.5951/MT.92.6.0516
Fischbein, E. (1975). The intuitive sources of probabilistic thinking in children. Reidel.
Fischbein, E., & Schnarch, D. (1997). The evolution with age of probabilistic, intuitively based misconceptions. Journal for Research in Mathematics Education, 28(1), 96–105. https://psycnet.apa.org/doi/10.2307/749665
Franklin, C., Kader, G., Mewborn, D., Moreno, J., Peck, R., Perry, M., & Scheaffer, R. (2005). Guidelines for assessment and instruction in statistics education (GAISE) report. Alexandria, VA: American Statistical Association.
Gallagher, S. A., Stepien, W. J., & Rosenthal, H. (1992). The effects of problem-based learning on problem solving. Gifted Child Quarterly, 36(4), 195–200. https://doi.org/10.1177/001698629203600
Gürbüz, R., Çatlıoğlu, H. Birgin, O., & Erdem, E. (2010). An investigation of fifth grade students’ conceptual development of probability through activity based instruction: a quasi-experimental study. Educational Sciences: Theory & Practice, 10(2), 1021–1069.
Güzel, N. & Ünal, H. (2013). Olmak ya da olmamak: olasılık; işte bütün mesele [To be or not to be: possibility; that is the question]. İ.Ö. Zembat, M. F. Özmantar, E. Bingölbali, H. Şandır, & A. Delice (Eds.), Tanımları ve tarihsel gelişimleriyle matematiksel kavramlar [Mathematical concepts with their definitions and historical developments] (s. 709–720). Pegem Academy.
Hassan Majeed, B., Fouad Jawad, L., & Alrikabi, H. T. S. (2021). Tactical thinking and its relationship with solving mathematical problems among mathematics department students. International Journal of Emerging Technologies in Learning, 16(9), 247–262. https://doi.org/10.3991/ijet.v16i09.22203
Hemker, L., Prescher, C., & Narciss, S. (2017). Design and evaluation of a problem-based learning environment for teacher training. Interdisciplinary Journal of Problem-Based Learning, 11(2), 10. https://doi.org/10.7771/1541-5015.1676
Hmelo-Silver, C. E. (2004). Problem-based learning: What and how do students learn?. Educational Psychology Review, 16, 235–266.
https://doi.org/10.1023/B:EDPR.0000034022.16470.f3
Hung, W., Jonassen, D. H., & Liu, R. (2007). Problem-based learning. In D. Jonassen, M. J. Spector, M. Driscoll, M. D. Merrill, J. van Merrienboer, & M. P. Driscoll (Eds.), Handbook of research on educational comminications and technology (3rd Edition). Routledge.
Jitendra, A. K., Griffin, C. C., Deatline-Buchman, A., & Sczesniak, E. (2007). Mathematical word problem solving in third-grade classrooms. The Journal of Educational Research, 100(5), 283–302.
Karaaslan, K. G. & Ay, Z. S. (2017). Examination of pre-service teachers’ subject matter knowledge of probability within the scope of conceptual-procedural knowledge. Abant İzzet Baysal Üniversitesi Eğitim Fakültesi Dergisi, 17(2), 716–736. https://doi.org/10.17240/aibuefd.2017.17.30227-326594
Karadeniz, Ş., Büyüköztürk, Ş., Akgün, Ö. E., Demirel, F., & Kılıç Çakmak, E. (2020). Scientific research methods. Pegem Academy.
Kazak, S. (2010). Why is probability subject difficult for students? E. Bingölbali & M. F Özmantar (Eds.), Mathematical difficulties and solution suggestions encountered in primary education, (2th edition) in (217–239). Pegem Academy.
Kindley, R. (2002). The power of simulation-based e-learning (SIMBEL). The eLearning Developers’ Journal, 17, 1–8. https://www.learningguild.com/pdf/2/091702des-h.pdf
Kocadağ, Y. (2010). The effects of cased-based learning approach on the elimination of misconceptions about the subject of genetic [Unpublished master’s thesis]. Karadeniz Technical University.
Koh, K., & Chapman, O. (2019). Problem-based learning, assessment literacy, mathematics knowledge, and competencies in teacher education. Papers on Postsecondary Learning and Teaching: Proceedings of the University of Calgary Conference on Postsecondary Learning and Teaching, 3, 74–80.
Koh, K., & Tan, C. (2016). Promoting reflection in pre-service teachers through problem-based learning: An example from Canada. Reflective Practice, 17(3), 347–356. https://doi.org/10.1080/14623943.2016.1164683
Konold, C. (1994). Teaching probablity through modeling real problems. The Mathematics Teacher, 87(4), 232–235. https://doi.org/10.5951/MT.87.4.0232
Koparan, T., & Güven, B. (2014). The effect of project-based learning on students’ statistical literacy levels for inference. Karaelmas Journal of Educational Sciences, 2(1), 33–48. https://dergipark.org.tr/en/pub/kebd/issue/67214/1049094
Korkmaz, A. (2005). The birth of probability theory. Ankara University SBF Journal, 60(2), 171–193.
Lambros, A. (2004). Problem-based learning in K-8 classrooms: A teacher's guide to implementation. Corwin press.
Lavigne, N. C., & Lajoie, S. P. (2007). Statistical reasoning of middle school children engaged in survey inquiry. Contemporary Educational Psychology, 32(4), 630–666. https://doi.org/10.1016/j.cedpsych.2006.09.001
Lee, M., Larkin, C. J. K., & Hoekstra, S. (2023). Impacts of problem-based ınstruction on students’ beliefs about physics and learning physics. Educ. Sci. 13(321), 10–16. https://doi.org/10.3390/educsci13030321
Leuchter, M., Saalbach, H., & Hardy, I. (2014). Designing science learning in the first years of schooling. an intervention study with sequenced learning material on the topic of ‘floating and sinking'. International Journal of Science Education, 36(10), 1751–1771. https://doi.org/10.1080/09500693.2013.878482
Lohman, M. C., & Finkelstein, M. (2000). Designing groups in problem-based learning to promote problem-solving skill and self-directedness. Instructional Science, 28, 291-307.
Manikyamba, V. R. V. T. R., & Ramalakshmi, C. (2024). Probability with real life applications and it’s significance. International Journal of Creative Research Thoughts, 12(7), 909–913.
Martin, D., & Jamieson-Proctor, R. (2022). Pre-service teachers’ perceptions of problem-based learning for developing their mathematics teaching pedagogy. The Interdisciplinary Journal of Problem-based Learning, 16(1), https://doi.org/10.14434/ijpbl.v16i1.28739
Merritt, J., Lee, M., Rillero, P., & Kinach, B. M. (2017). Problem-based learning in K–8 mathematics and science education: A literature review. The Interdisciplinary Journal of Problem-based Learning, 11(2). https://doi.org/10.7771/1541-5015.1674
Miles, M. B., & Huberman, A. M. (1994). An expanded source book: Qualitative data analysis. Sage Publications.
Ministry of National Education. (2013). Mathematics curriculum (grades 5, 6, 7 and 8) curriculum and guide. Board of Education.
Ministry of National Education. (2018). Mathematics curriculum (grades 1, 2, 3, 4, 5, 6, 7 and 8). Board of Education.
Nariman, N., & Chrispeels, J. (2016). PBL in the era of reform standards: Challenges and benefits perceived by teachers in one elementary school. Interdisciplinary Journal of Problem-based Learning, 10(1). https://doi.org/10.7771/1541-5015.1521
National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standarts for school mathematics. Reston,VA.
National Council of Teachers of Mathematics. (2000). Principles and standard for school mathematics. Reston, VA.
Nickerson, R. S. (2004). Cognition and chance: The psychology of probabilistic reasoning. Psychology Press.
Norman, G. R., & Schmidt, H. G. (1992). The psychological basis of problem-based learning: A review of the evidence. Academic medicine, 67(9), 557-65.
O’Connell, A. A. (1999). Understanding the nature of errors in probability problem-solving. Educational Research and Evaluation, 5(1), 1–21. https://doi.org/10.1076/edre.5.1.1. 3887
Özçelik, D. A. (2013). Test preparation guide (5th edition). Pegem Academy.
Polya, G. (1962). Mathematical discovery: On understanding, learning, and teaching problem solving. Wiley.
Polya, G. (1973). How to solve it: A new aspect of mathematical method. Princeton University Press.
Popper, K. R. (1998). The logic of scientific discovery. Yapı Kredi Publications.
Rillero, P., Koerner, M., Jimenez-Silva, M., Merritt, J., & Farr, W. J. (2017). Developing teacher competencies for problem-based learning pedagogy and for supporting learning in language-minority students. Interdisciplinary Journal of Problem-Based Learning, 11(2). https://doi.org/10.7771/1541-5015.1675
Roh, K. H. (2003). Problem-based learning in mathematics. ERIC Digest. p. 1–7. ERIC Identifier: ED482725
Ronis, D. (2008). Problem based learning for math and science: integrating inquiry and the internet. Skylight Training and Publishing.
Rybarczyk, B. J., Baines, A. T., McVey, M., Thompson, J. T., & Wilkins, H. (2007). A case‐based approach increases student learning outcomes and comprehension of cellular respiration concepts. Biochemistry and molecular biology education, 35(3), 181–186. https://doi.org/10.1002/bmb.40
Schank, R. C. (1999). Dynamic memory revisited. Cambridge University Press.
Schank, R. C., Berman, T. R., & Macpherson, K. A. (1999). Learning by doing. In C. M. Reigeluth (Ed.), Instructional-design theories and models: Vol. 2. A new paradigm of instructional theory, 161–181. Erlbaum. https://doi.org/10.4324/9781410603784
Schettino, C. (2016). A framework for problem-based learning: Teaching mathematics with a relational problem-based pedagogy. Interdisciplinary Journal of Problem-Based Learning, 10(2). https://doi.org/10.7771/1541-5015.1602
Schlottmann, A. (2001). Children’s probability intuitions: understanding the expected value of complex gambles. Child Development, 72(1), 103–122.
Schmidt, H. G. (1983). Problem-based learning: rationale and description. Medical Education, 17(1), 11–16. https://doi.org/10.1111/j.1365-2923.1983.tb01086.x
Schoenfeld, A. H. (1983). Problem solving in the mathematics curriculum: A report, recommendations and an annotated bibliography. Mathematical Association of America.
Schoenfeld, A. H. (1985). Mathematical problem solving. Academic Press.
Sorin, R. (2013). Exploring partnerships in early childhood teacher education through scenario-based learning. World Journal of Education, 3(1), 39–45. http://dx.doi.org/10.5430/wje.v3n1p39
Süğümlü, Ü. (2009). The effectiveness of scenario based-learning approaches on grammar ınstruction: types of words, sample [Unpublished master’s thesis], Sakarya University.
Şimşek, A. (2011). Instructional Design. Nobel Publications.
Thayer-Bacon, B. J. (2004). Personal and social relations in education. Counterpoints, 259, 165–179. https://www.jstor.org/stable/42978500
Tan, O.S. (2003). Problem-based learning innovation: Using problems to power learning in the twenty-first century. Gale Cengage Learning.
Torp, L., & Sage, S. (2002). Problems as possibilities: Problem-based learning for K–16 education (2nd ed.). Association for Supervision and Curriculum Development.
Tunç, E. (2006). Evaluation of acquasition levels of grade 8 students in private and public schools about knowledge and skills in the subject of probability [Unpublished master’s thesis], Balıkesir University.
Uygun, N, & Tertemiz, N. I. (2014). Effects of problem-based learning on student attitudes, achievement and retention of learning in math course. Education ve Science, 39(174), 75–90. https://doi.org/10.15390/EB.2014.1975
Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2014). Elementary and middle school mathematics. Teaching Developmentally (7th edit.) Pearson, (Trans. Edt. S. Durmuş). Nobel Publication.
von Glasersfeld, E. (1995). Radical Constructivism: A Way of Knowing and Learning. Studies in Mathematics Education Series: 6. ISBN-0-7507-0387-3, Falmer Press, Taylor & Francis Inc.
Wan Hassan, W.A.S, Ariffin, A, Ahmad, F, Hamzah, N, Rubani, S.N.K, & Zakaria, N. (2020). The use of problem based learning (PBL) in the solve me web towards student achievement in technical and vocational education, Journal of University of Shanghai for Science and Technology, 22(11), 623–627. https://jusst.org/the-use-of-pbm-in-the-solve-me-web-towards-student-achievement-in-technical-and-vocational-education/
Westwood, P. (2011) The problem with problems: Potential difficulties in implementing problem-based learning as the core method in primary school mathematics. Australian Journal of Learning Difficulties, 16(1), 5–18, https://doi.org/10.1080/19404158.2011.563475
Wong, K. K. H., & Day, J. R. (2009). A comparative study of problem-based and lecture-based learning in junior secondary school science. Research in Science Education, 39(5), 625–642. http://doi.org/10.1007/s11165-008-9096-7
Wood, T., Cobb, P., & Yackel, E. (1991). Change in teaching mathematics: A case study. American Educational Research Journal, 28(3), 587–616.
Yahya, F. H., & Zaman, H. H. B. (2008). Development of interactive multimedia courseware using problem based learning for mathematics form 4 (PBL MathS-Set), IEEE, 4, 4–9.
Yıldırım, A., & Şimşek H. (2018). Qualitative research methods in the social sciences (11th ed). Ankara: Seçkin Publication.
Zamir, S., Yang, Z., Wenwu, H., & Sarwar, U. (2022) Assessing the attitude and problem-based learning in mathematics through. PLS-SEM modeling. PLoS ONE 17(5), e0266363. https://doi.org/10.1371/journal.pone.0266363