The Application of Design Thinking in Differential Learning to Develop Students' Critical Thinking Ability

Authors

  • Ayu Endah Pratiwi Departement of Mathematics Education, IKIP PGRI Semarang University, Indonesia
  • Muhtarom Departement of Mathematics Education, IKIP PGRI Semarang University, Indonesia
  • Aryo Andri Nugroho Departement of Mathematics Education, IKIP PGRI Semarang University, Indonesia

DOI:

https://doi.org/10.21009/jtp.v27i3.61183

Keywords:

Design Thinking, Differential Learning, Critical Thinking Ability, Mathematics Education, Innovative Learning

Abstract

This study examines the effectiveness of implementing a design thinking approach in differential learning to enhance students’ critical thinking skills. A quasi-experimental method with a pretest–posttest control group design was employed. The participants consisted of 60 undergraduate students enrolled in a Differential Calculus course, who were assigned to an experimental group (n = 30) receiving design thinking-based instruction and a control group (n = 30) receiving conventional instruction. The research instrument was an essay-based critical thinking test developed according to five indicators: interpretation, analysis, evaluation, inference, and explanation. Data were analyzed using descriptive statistics and an independent samples t-test. The findings revealed a statistically significant difference in critical thinking skills between the experimental group (M = 83.67) and the control group (M = 68.43), with p < 0.001. The experimental group achieved an N-Gain score of 0.64, categorized as moderate to high and substantially higher than the control group’s N-Gain of 0.32. Furthermore, Cohen’s effect size was 2.41, indicating a very large effect. Improvements were observed across all critical thinking indicators, with the analysis indicator demonstrating the greatest gain (a mean difference of 16.67 points). In conclusion, design thinking-based learning is effective in enhancing students’ critical thinking skills in differential calculus and represents a promising alternative instructional approach for university-level mathematics education.

References

Afriani, I. S., Zawawi, I., & Huda, S. (2024). Implementation of Differentiated Learning on Mathematical Critical Thinking Ability. Prisma Sains: Jurnal Pengkajian Ilmu dan Pembelajaran Matematika dan IPA IKIP Mataram, 12(1), 61-70. https://doi.org/10.33394/j-ps.v12i1.9600

Al Abri, M. H., Al Aamri, A. Y., & Elhaj, A. M. A. (2024). Enhancing student learning experiences through integrated constructivist pedagogical models. European Journal of Contemporary Education and E-Learning, 2(1), 130-149. https://doi.org/10.59324/ejceel.2024.2(1).11

Amalia, L., Makmuri, M., & El Hakim, L. (2024). Learning design: To improve mathematical problem-solving skills using a contextual approach. JIIP-Jurnal Ilmiah Ilmu Pendidikan, 7(3), 2353-2366. https://doi.org/10.54371/jiip.v7i3.3455

Azevedo, B. F., de Souza, R. M., Pacheco, M. F., Fernandes, F. P., & Pereira, A. I. (2023, September). Application of pattern recognition techniques for mathe questions difficulty level definition. In International Conference on Optimization, Learning Algorithms and Applications (pp. 300-315). Cham: Springer Nature Switzerland. https://doi.org/10.1007/978-3-031-53025-8_21

Berthold, K., & Renkl, A. (2009). Instructional aids to support a conceptual understanding of multiple representations. Journal of educational psychology, 101(1), 70. https://doi.org/10.1037/a0013247

Bigotte de Almeida, M. E., Queiruga-Dios, A., & Cáceres, M. J. (2020). Differential and integral calculus in first-year engineering students: a diagnosis to understand the failure. Mathematics, 9(1), 61. https://doi.org/10.3390/math9010061

Carlgren, L., Elmquist, M., & Rauth, I. (2014). Design thinking: Exploring values and effects from an innovation capability perspective. The Design Journal, 17(3), 403-423. https://doi.org/10.2752/175630614X13982745783000

Cobbinah, G. I. D. E. O. N. (2023). The effect of incorporating geogebra in cycle model of teaching calculus at university of education, Sekondi study centre (Doctoral dissertation, University of Education Winneba). http://41.74.91.244:8080/handle/123456789/3419

Corrales-Estrada, M. (2020). Design thinkers’ profiles and design thinking solutions. Academia Revista Latinoamericana de Administracion, 33(1), 9-24. https://doi.org/10.1108/ARLA-01-2018-0028

Duru, D. C., & Obasi, C. V. (2023). Critical thinking ability as a correlate of students’ mathematics achievement: A focus on ability level. Journal of Instructional Mathematics, 4(1), 41-51. https://doi.org/10.37640/jim.v4i1.1753

Ely, R. (2021). Teaching calculus with infinitesimals and differentials. ZDM–Mathematics Education, 53(3), 591-604. https://doi.org/10.1007/s11858-020-01194-2

Erdogan, F. (2019). Effect of cooperative learning supported by reflective thinking activities on students’ critical thinking skills. Eurasian journal of educational research, 19(80), 89-112.

Ericson, J. D. (2022). Mapping the relationship between critical thinking and design thinking. Journal of the Knowledge Economy, 13(1), 406-429. https://doi.org/10.1007/s13132-021-00733-w

Ericson, J. D. (2022). Mapping the relationship between critical thinking and design thinking. Journal of the Knowledge Economy, 13(1), 406-429. https://doi.org/10.1007/s13132-021-00733-w

Foster, M. K. (2021). Design thinking: A creative approach to problem solving. Management Teaching Review, 6(2), 123-140. https://doi.org/10.1177/2379298119871468

Fung, D. C. L., To, H., & Leung, K. (2016). The influence of collaborative group work on students’ development of critical thinking: The teacher’s role in facilitating group discussions. Pedagogies: An International Journal, 11(2), 146-166. https://doi.org/10.1080/1554480X.2016.1159965

Gholami, H., Ayub, A. F. M., & Yunus, A. S. M. (2021). Analysis of the Mathematics Function Chapter in a Malaysian Foundation Level Textbook Adopted by a Public University. Mathematics Teaching Research Journal, 13(3), 81-98.

Guaman-Quintanilla, S., Everaert, P., Chiluiza, K., & Valcke, M. (2023). Impact of design thinking in higher education: a multi-actor perspective on problem solving and creativity. International Journal of Technology and Design Education, 33(1), 217-240. https://doi.org/10.1007/s10798-021-09724-z

Habre, S., & Abboud, M. (2006). Students’ conceptual understanding of a function and its derivative in an experimental calculus course. The Journal of Mathematical Behavior, 25(1), 57-72. https://doi.org/10.1016/j.jmathb.2005.11.004

Henriksen, D., Cain, W., & Mishra, P. (2018). Everyone designs: Learner autonomy through creative, reflective, and iterative practice mindsets. Journal of Formative Design in Learning, 2(2), 69-81. https://doi.org/10.1007/s41686-018-0024-6

Henriksen, D., Richardson, C., & Mehta, R. (2017). Design thinking: A creative approach to educational problems of practice. Thinking skills and Creativity, 26, 140-153. https://doi.org/10.1016/j.tsc.2017.10.001

Henriksen, D., Richardson, C., & Mehta, R. (2017). Design thinking: A creative approach to educational problems of practice. Thinking skills and Creativity, 26, 140-153. https://doi.org/10.1016/j.tsc.2017.10.001

Hitchcock, D. (2017). Critical thinking as an educational ideal. In On reasoning and argument: Essays in informal logic and on critical thinking (pp. 477-497). Cham: Springer International Publishing. https://doi.org/10.1007/978-3-319-53562-3_30

Karakoc, G., Alacaci, C., & Ayas, A. (2025). A strategy to engage students in inquiry-based learning of mathematics: predict, observe and explain. Instructional Science, 53(5), 1195-1222. https://doi.org/10.1007/s11251-025-09733-8

Kim, H. J., Yi, P., & Ko, B. W. (2023). Deepening students' experiences with problem identification and definition in an empathetic approach: lessons from a university design-thinking program. Journal of Applied Research in Higher Education, 15(3), 852-865. https://doi.org/10.1108/JARHE-03-2022-0083

Kitsantas, A., Baylor, A. L., & Hiller, S. E. (2019). Intelligent technologies to optimize performance: Augmenting cognitive capacity and supporting self-regulation of critical thinking skills in decision-making. Cognitive Systems Research, 58, 387-397. https://doi.org/10.1016/j.cogsys.2019.09.003

Kitsantas, A., Baylor, A. L., & Hiller, S. E. (2019). Intelligent technologies to optimize performance: Augmenting cognitive capacity and supporting self-regulation of critical thinking skills in decision-making. Cognitive Systems Research, 58, 387-397. https://doi.org/10.1016/j.cogsys.2019.09.003

Kramer, L., Fuller, E., Watson, C., Castillo, A., Oliva, P. D., & Potvin, G. (2023). Establishing a new standard of care for calculus using trials with randomized student allocation. Science, 381(6661), 995-998. DOI: 10.1126/science.ade9803

Lisnawati, L., & Nirmala, S. D. (2024). The Effectiveness of Differentiated Learning Strategies on Elementary Students' Mathematical Critical Thinking Ability. AL-ISHLAH: Jurnal Pendidikan, 16(3), 3882-3895. https://doi.org/10.35445/alishlah.v16i3.5746

Lo, C. K., & Hew, K. F. (2021). Developing a flipped learning approach to support student engagement: A design‐based research of secondary school mathematics teaching. Journal of Computer Assisted Learning, 37(1), 142-157. https://doi.org/10.1111/jcal.12474

Micheli, P., Wilner, S. J., Bhatti, S. H., Mura, M., & Beverland, M. B. (2019). Doing design thinking: Conceptual review, synthesis, and research agenda. Journal of Product innovation management, 36(2), 124-148. https://doi.org/10.1111/jpim.12466

Oehrtman, M., Soto-Johnson, H., & Hancock, B. (2019). Experts’ construction of mathematical meaning for derivatives and integrals of complex-valued functions. International Journal of Research in Undergraduate Mathematics Education, 5(3), 394-423. https://doi.org/10.1007/s40753-019-00092-7

Richland, L. E., & Begolli, K. N. (2016). Analogy and higher order thinking: Learning mathematics as an example. Policy Insights from the Behavioral and Brain Sciences, 3(2), 160-168. https://doi.org/10.1177/2372732216629795

Şahin, Z., & Akkoç, H. (2021, October). The Role of Technology in Mathematics Teachers’ Approaches to Overcoming a Misconception Related to the Graphical Understanding of Derivatives. In SITE Interactive Conference (pp. 244-249). Association for the Advancement of Computing in Education (AACE).

Santos, P., El Aadmi, K., Calvera-Isabal, M., & Rodríguez, A. (2025). Fostering students’ motivation and self-efficacy in science, technology, engineering, and design through design thinking and making in project-based learning: a gender-perspective study in primary education. International Journal of Technology and Design Education, 1-27. https://doi.org/10.1007/s10798-025-10001-6

Sembiring, R. K., Hadi, S., & Dolk, M. (2008). Reforming mathematics learning in Indonesian classrooms through RME. ZDM, 40(6), 927-939. https://doi.org/10.1007/s11858-008-0125-9

Simeon, M. I., Samsudin, M. A., & Yakob, N. (2022). Effect of design thinking approach on students’ achievement in some selected physics concepts in the context of STEM learning. International Journal of Technology and Design Education, 32(1), 185-212. https://doi.org/10.1007/s10798-020-09601-1

Simeon, M. I., Samsudin, M. A., & Yakob, N. (2022). Effect of design thinking approach on students’ achievement in some selected physics concepts in the context of STEM learning. International Journal of Technology and Design Education, 32(1), 185-212. https://doi.org/10.1007/s10798-020-09601-1

Triyono, A., Nuary, R. H., Permatasari, N., Yuni, Y., & Wibowo, T. (2024). The level of effectiveness of tps and conventional methods judging from students' geometry learning results using the N-Gain Test. AlphaMath: Journal of Mathematics Education, 142-156. DOI: 10.30595/alphamath.v10i1.21530

Vivanco-Galván, O., Castillo-Malla, D., Suconota, E., Quizphe, R., & Jiménez-Gaona, Y. (2024, October). Enhancing mathematical function understanding in university students: A comparative study of design thinking vs. traditional teaching methods. In Frontiers in Education (Vol. 9, p. 1364642). Frontiers Media SA. https://doi.org/10.3389/feduc.2024.1364642

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Published

2025-12-29

How to Cite

Pratiwi, A. E., Muhtarom, & Nugroho, A. A. (2025). The Application of Design Thinking in Differential Learning to Develop Students’ Critical Thinking Ability. JTP - Jurnal Teknologi Pendidikan, 27(3), 992–1008. https://doi.org/10.21009/jtp.v27i3.61183