Impact of problem-based learning on the interdisciplinary skills of upper secondary school mathematics students

Daniel Martín-Cudero; Rocío Guede-Cid; Ana Isabel Cid-Cid

doi:10.29333/iejme/17799

Full Text (PDF)

Daniel Martín-Cudero ¹ ^* , Rocío Guede-Cid ¹ , Ana Isabel Cid-Cid ¹

More Detail

¹ Consolidated Research Group in STEM Education (GIESTEM), Area of Mathematics Education, Rey Juan Carlos University, Madrid, SPAIN^* Corresponding Author

Abstract

This study explores the impact of problem-based learning methodology on high school students. To do so, an activity based on the logistic function was designed, connecting learning with real and contextualized problems. The research involved 42 students from the scientific-technological and social sciences (SS) specializations. A mixed questionnaire was used, consisting of 26 closed Likert-type questions, which measured the impact of the problem, the methodology, its practical application, and the students’ awareness, along with 3 open-ended questions that provided a more comprehensive view of the students’ perceptions. Positive results were obtained in both groups, with averages ranging from 3 to 5 in all measurable items, though the effects were more moderate in the SS group. The results suggest that PBL enhances motivation and learning in mathematics and strengthens the value of this discipline, although its implementation should be adapted to the context and specific needs of the students.

Keywords

problem-based learning
teaching and learning of mathematics
interdisciplinary learning
GeoGebra
logistic function

License

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

INT ELECT J MATH ED, Volume 21, Issue 1, February 2026, Article No: em0865

https://doi.org/10.29333/iejme/17799

Publication date: 26 Jan 2026

Article Views: 40

Article Downloads: 20

Open Access References How to cite this article

References

Alreshidi, N. A. K., & Lally, V. (2024). The effectiveness of training teachers in problem-based learning implementation on students’ outcomes: A mixed-method study. Humanities and Social Sciences Communications, 11, Article 1137. https://doi.org/10.1057/s41599-024-03638-6
Arévalo-Duarte, M. A., García-García, M. Á., & Jaramillo-Benítez, J. E. (2024). Problem-based learning (PBL) as a methodology to strengthen mathematical skills–problem solving–in basic education. Cultura, Educación y Sociedad, 15(1), Article e033884443.
Arroyo, L. E., & Pallasco, M. S. (2025). Habilidades cognitivas en el aprendizaje de la matemática [Cognitive skills in learning mathematics]. Revista Científica de Innovación Educativa y Sociedad Actual “ALCON”, 5(1), 81-93. https://doi.org/10.62305/alcon.v5i1.385
Auzmendi, E. (1992). Las actitudes hacia la matemática-estadística en las enseñanzas media y universitaria. Características y medición [Attitudes towards mathematics and statistics in secondary and university education: Characteristics and measurement]. Mensajero.
Bacaër, N. (2008). Histoires de mathématiques et de populations [Stories of mathematics and populations]. Éditions Cassini.
Barrantes, M. (2003). Caracterización de la enseñanza-aprendizaje de la geometría en primaria y secundaria [Characterization of the teaching and learning of geometry in primary and secondary education]. Campo Abierto Revista, 24, 15-36.
Bosica, J., Pyper, J. S., & MacGregor, S. (2021). Incorporating problem-based learning in a secondary school mathematics preservice teacher education course. Teaching and Teacher Education, 102, Article 103335. https://doi.org/10.1016/j.tate.2021.103335
Boyce, E. S., & Agyei, D. D. (2024). Understanding problem-based learning and its application in learning mathematics concepts among pre-service teachers. European Journal of Mathematics and Science Education, 5(1), 51-65. https://doi.org/10.12973/ejmse.5.1.51
Braun, V., & Clarke, V. (2006). Using thematic analysis in psychology. Qualitative Research in Psychology, 3(2), 77-101. https://doi.org/10.1191/1478088706qp063oa
Cadena-Zambrano, V., & Nuñez-Naranjo, A. (2020). ABP: Estrategia didáctica en las matemáticas [PBL: A teaching strategy in mathematics]. Digital Publisher CEIT, 5(1), 69-77. https://doi.org/10.33386/593dp.2020.1.184
Cruz, R. I., Serrano, C. L., & Rodríguez, B. J. (2021). Modelo de mejoramiento productivo: Una aplicación de la fabricación digital incorporada al aprendizaje basado en proyectos (ABP) en la educación superior [Productive improvement model: An application of digital manufacturing incorporated into project-based learning (PBL) in higher education]. Formación Universitaria, 14(2), 65-74. https://doi.org/10.4067/S0718-50062021000200065
Cuong, L. M., Tien-Trung, N., Ngu, P. N. H., Vangchia, V., Thao, N. P., & Thao, T. T. P. (2025). Mathematics problem-solving research in high school education: Trends and insights from the Scopus database (1983-2023). European Journal of Science and Mathematics Education, 13(2), 77-89. https://doi.org/10.30935/scimath/16038
de Winter, J. C. F., Dodou, D., & Wieringa, P. A. (2009). Exploratory factor analysis with small sample sizes. Multivariate Behavioral Research, 44(2), 147-181. https://doi.org/10.1080/00273170902794206
Deakin, R. E. (2018). The logistic function. Bonbeach VIC.
Dolmans, D., De Grave, W., Wolfhagen, I., & Van Der Vleuten C. (2005). Problem-based learning: Future challenges for educational practice and research. Medical Education, 39(7), 732-741. https://doi.org/10.1111/j.1365-2929.2005.02205.x
Domènech-Casal, J. (2018). Aprendizaje basado en proyectos en el marco STEM. Componentes didácticas para la competencia científica [Project-based learning within the STEM framework. Didactic components for scientific competence]. Ápice. Revista de Educación Científica, 2(2), 29-42. https://doi.org/10.17979/arec.2018.2.2.4524
El Sayary, A. M. A., Forawi, S. A., & Mansour, N. (2015). STEM education and problem-based learning. In R. Wegerif, L. Li, & J. C. Kaufman (Eds.), The Routledge international handbook of research on teaching thinking (pp. 357-368). Routledge.
Field, A. (2018). Discovering statistics using IBM SPSS statistics (5th ed.). SAGE.
Godino, J., Batanero, C., & Font, V. (2019). The onto-semiotic approach: Implications for the prescriptive character of didactics. For the Learning of Mathematics, 39(1), 38-43.
Goos, M., Carreira, S., & Kizito, I. (2023). Mathematics and interdisciplinary STEM education: Recent developments and future directions. ZDM Mathematics Education, 55, 1199-1217. https://doi.org/10.1007/s11858-023-01533-z
Hmelo-Silver, C. E. (2004). Problem-based learning: What and How do students learn? Educational Psychology Review, 16(3), 235-266. https://doi.org/10.1023/B:EDPR.0000034022.16470.f3
Hmelo-Silver, C. E., & DeSimone, C. (2013). Problem-based learning: An instructional model of collaborative learning. In C. E. Hmelo-Silver, C. Chinn, C. Chan., & A. O’Donnell (Eds.), The international handbook of collaborative learning (pp. 370-386). Routledge. https://doi.org/10.4324/9780203837290
Kyurkchiev, N., & Markov, S. (2015). Sigmoid functions: Some approximation, and modelling aspects. LAP LAMBERT Academic Publishing. https://doi.org/10.11145/j.bmc.2015.03.081
Lloyd, P. J. (1967). American, German and British antecedents to Pearl and Reed’s logistic curve. Population Studies, 21, 99-108. https://doi.org/10.1080/00324728.1967.10405468
Martínez-Artero, R., & Checa, A. N. (2020). Actitud hacia las matemáticas en el grado de maestro de primaria [Attitude towards mathematics in the primary school teacher degree]. Revista Electrónica Interuniversitaria de Formación del Profesorado, 23(2), 225-239. https://doi.org/10.6018/reifop.348061
McKendrick, A. G., & Kesava, M. (1911). The rate of multiplication of microorganisms: A mathematical study. Proceedings of the Royal Society of Edinburgh, 31, 649-655. https://doi.org/10.1017/S0370164600025426
Muñiz-Rodríguez, L., Alonso, P., Rodríguez, L. J., & Valcke, M. (2016). Is there a gap in initial secondary mathematics teacher education in Spain compared to other countries? Revista de Educación, 372, 106-132. https://doi.org/10.4438/1988-592X-RE-2015-372-317
Nufus, H., & Mursalin, M. (2020). Improving students’ problem-solving ability and mathematical communication through the application of problem based learning. Electronic Journal of Education, Social Economics and Technology, 1(1), 43-48. https://doi.org/10.33122/ejeset.v1i1.8
OECD. (2023). PISA 2022 assessment and analytical framework. OECD Publishing. https://doi.org/10.1787/dfe0bf9c-en
Ortiz, W., Martínez, R., Tolozano, M. R., & Vazquez, A. (2025). Problem-based learning through digital environments: An experience in graduate mathematics teacher education. Formación Universitaria, 18(1), 143-152. https://doi.org/10.4067/s0718-50062025000100143
Páez, S. A. (2017). Strengthening of the mathematics competence problem solving in high school education, through learning based on problems (LBP). Eco Matemático, 8(1), 25-33. https://doi.org/10.22463/17948231.1472
Pazos-Yerovi, E. I., & Aguilar-Gordón, F. R. (2024). El aprendizaje basado en problemas como estrategia metodológica para el desarrollo del pensamiento crítico [Problem-based learning as a methodological strategy for the development of critical thinking]. Revista de Estudios y Experiencias en Educación, 23(53), 313-340. https://doi.org/10.21703/rexe.v23i53.2658
Pearl, R. (1922). The biology of death. J. P. Lippincott and Co. https://doi.org/10.1073/pnas.6.6.275
Pearl, R., & Reed, L. J. (1920). On the rate of growth of the population of the United States since 1790 and its mathematical representation. PNAS, 6(6), 275-288.
Rahmatjati, A. M., Ardiansyah, A. S., & Rochmad. (2023). Effectiveness of problem based learning integrated STEAM on students’ mathematical problem solving ability. Unnes Journal of Mathematics Education, 12(3), 270-279. https://doi.org/10.15294/ujme.v12i3.78959
Ramadhani, R., & Narpila, S. D. (2018). Problem based learning method with GeoGebra in mathematical learning. International Journal of Engineering & Technology, 7(3), 774-777. https://doi.org/10.14419/ijet.v7i3.2.18753
Recio, T., Richard, P. R., & Vélez, M. P. (2019). Designing tasks supported by GeoGebra automated reasoning tools for the development of mathematical skills. International Journal of Technology in Mathematics Education, 26(2), 81-89. https://doi.org/10.1564/tme_v26.2.05
Rehmat, A. P., & Hartley, K. (2020). Building engineering awareness: Problem-based learning approach for STEM integration. The Interdisciplinary Journal of Problem-Based Learning, 14(1). https://doi.org/10.14434/ijpbl.v14i1.28636
Reyes, J., Insorio, A. O., Ingreso, M. L. V., Hilario, F. F., & Gutiérrez, C. R. (2019). Conception and application of contextualization in mathematics education. International Journal of Educational Studies in Mathematics, 6(1), 1-18.
Robertson, T. B. (1908). On the normal rate of growth of an individual and its biochemical significance. Archiv für Entwicklungsmechanik der Organismen, 25, 581-614. https://doi.org/10.1007/BF02163864
Rządkowski, G., & Sobczak, L. (2020). A generalized logistic function and its applications. Foundations of Management, 12, 87-92. https://doi.org/10.2478/fman-2020-0007
Saá-Rojo, M. D., Carrillo-Gallego, D., Dólera-Almaida, J., Ibáñez-López, F. J., Maurandi-López, A., & Sánchez-Jiménez, E. (2022). Propuestas constructivistas en didáctica de las matemáticas: Percepción de los futuros maestros [Problem-based learning as a methodological strategy for the development of critical thinking]. Educatio Siglo XXI, 43(1), 121-142. https://doi.org/10.6018/educatio.542351
Santillán-Aguirre, P., Jaramillo-Moyano, E., Hernández-Andrade, L., & Santos-Poveda, R. (2023). ABP and STEAM as active learning methodologies. ESPOCH Congresses: The Ecuadorian Journal of S.T.E.A.M., 3(1), 764-779. https://doi.org/10.18502/espoch.v3i1.14485
Satrústegui, A., & Mateo, E. (2023). Mejora del pensamiento crítico en alumnos de ESO a través del aprendizaje basado en problemas en un entorno STEAM [Improving critical thinking skills in secondary school students through problem-based learning in a STEAM environment]. Revista de Estilos de Aprendizaje, 16(32), 19-32. https://doi.org/10.55777/rea.v16i32.5990
Savin-Baden, M., & Major, C. H. (2004). Foundations of problem-based learning. McGraw-Hill Education.
Septian, A., Inayah, S., Fazrianto, R., & Nugraha, R. (2020). GeoGebra-assisted problem based learning to improve mathematical problem solving ability. In Proceedings of the SEMANTIK Conference of Mathematics Education (pp. 67-71). Atlantis Press. https://doi.org/10.2991/assehr.k.200827.119
Simanjuntak, M. P., Hutahaean, J., Marpaung, N., & Ramadhani, D. (2021). Effectiveness of problem-based learning combined with computer simulation on students’ problem-solving and creative skills. International Journal of Instruction, 14(3), 519-534. https://doi.org/10.29333/iji.2021.14330a
Smith, K., Maynard, N., Berry, A., Stephenson, T., Spiteri, T., Corrigan, D., Mansfield, J., Ellerton, P., & Smith, T. (2022). Principles of problem-based learning (PBL) in STEM education: Using expert wisdom and research to frame educational practice. Education Sciences, 12(10), Article 728. https://doi.org/10.3390/educsci12100728
Stelzer, F., Vernucci, S., Aydmune, Y. S., del Valle, M. V., & Andrés, M. L. (2020). Diseño y validación de una escala de actitudes hacia las matemáticas [Design and validation of an attitude scale towards mathematics]. Revista Evaluar, 20(2), 51-68. https://doi.org/10.35670/1667-4545.v20.n2.30109
Sukayasa, S., Mundiana, I. N., Hasbi, M., & Saiman, S. (2025). Development of problem-based learning model devices to improve junior high school students’ critical thinking skills regarding number patternstopic. AIP Conference Proceedings, 3038(1), Article 020005. https://doi.org/10.1063/5.0254425
Suratno, J., & Waliyanti, I. K. (2023). Integration of GeoGebra in problem-based learning to improve students’ problem-solving skills. International Journal of Research in Mathematics Education, 1(1), 67-80. https://doi.org/10.24090/ijrme.v1i1.8514
Tsybulsky, D., & Oz, A. (2019). From frustration to insights: Experiences, attitudes, and pedagogical practices of preservice science teachers implementing PBL in elementary school. Journal of Science Teacher Education, 30(3), 259-279. https://doi.org/10.1080/1046560X.2018.1559560
Verhulst, P. F. (1838). Notice sur la loi que la population poursuit dans son accroissement [Note on the law that the population pursues in its growth]. Correspondance Mathématique et Physique, 10, 113-121.
Verhulst, P. F. (1845). Recherches mathématiques sur la loi d’accroissement de la population [Mathematical research on the law of population growth]. Mémoires del’Académie Royale des Sciences, 18, 1-45. https://doi.org/10.3406/marb.1845.3438
Wen, R., & Dubé, A. K. (2022). A systematic review of secondary students’ attitudes towards mathematics and its relations with mathematics achievement. Journal of Numerical Cognition, 8(2), 295-325. https://doi.org/10.5964/jnc.7937
Yew, E. H. J., & Goh, K. (2016). Problem-Based Learning: An overview of its process and impact on learning. Health Professions Education, 2(2), 75-79. https://doi.org/10.1016/j.hpe.2016.01.004
Yohannes, A., & Chen, H. L. (2021). GeoGebra in mathematics education: A systematic review of journal articles published from 2010 to 2020. Interactive Learning Environments, 31(9), 5682-5697. https://doi.org/10.1080/10494820.2021.2016861
Zúñiga-Tinizaray, F., & Marín, V. (2024). Estrategias educativas STEM-STEAM en nivel superior: Revisión sistemática de literatura [STEM-STEAM educational strategies at higher education level: A systematic literature review]. Revista Espacios, 45(4), 16-30. https://doi.org/10.48082/espacios-a24v45n04p02

How to cite this article

APA

Martín-Cudero, D., Guede-Cid, R., & Cid-Cid, A. I. (2026). Impact of problem-based learning on the interdisciplinary skills of upper secondary school mathematics students. International Electronic Journal of Mathematics Education, 21(1), em0865. https://doi.org/10.29333/iejme/17799

Vancouver

Martín-Cudero D, Guede-Cid R, Cid-Cid AI. Impact of problem-based learning on the interdisciplinary skills of upper secondary school mathematics students. INT ELECT J MATH ED. 2026;21(1):em0865. https://doi.org/10.29333/iejme/17799

AMA

Martín-Cudero D, Guede-Cid R, Cid-Cid AI. Impact of problem-based learning on the interdisciplinary skills of upper secondary school mathematics students. INT ELECT J MATH ED. 2026;21(1), em0865. https://doi.org/10.29333/iejme/17799

Chicago

Martín-Cudero, Daniel, Rocío Guede-Cid, and Ana Isabel Cid-Cid. "Impact of problem-based learning on the interdisciplinary skills of upper secondary school mathematics students". International Electronic Journal of Mathematics Education 2026 21 no. 1 (2026): em0865. https://doi.org/10.29333/iejme/17799

Harvard

Martín-Cudero, D., Guede-Cid, R., and Cid-Cid, A. I. (2026). Impact of problem-based learning on the interdisciplinary skills of upper secondary school mathematics students. International Electronic Journal of Mathematics Education, 21(1), em0865. https://doi.org/10.29333/iejme/17799

MLA

Martín-Cudero, Daniel et al. "Impact of problem-based learning on the interdisciplinary skills of upper secondary school mathematics students". International Electronic Journal of Mathematics Education, vol. 21, no. 1, 2026, em0865. https://doi.org/10.29333/iejme/17799